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113 List of Appendices Appendix A Survey Electronic media Appendix B Survey Results Electronic media Appendix C CANDE Tool Box User Manual Electronic media Appendix D 2D Analysis Backup Electronic media Appendix E 3D Modeling backup Electronic media Appendix F Field Testing Plans Electronic media Appendix G Specification Backup Electronic media Appendix H Proposed Agenda Items Electronic media Appendix I Live Load Improvements Electronic media Appendix J Regression Data Mined Electronic media Appendix K 3D Model Calibrations Electronic media Appendix L Caltrans Models Electronic media Appendix M 3D Culvert Approach Electronic media
Aâ1 Appendix A â Survey Questions  Appendix A â Survey Questions / Followâup Questions The following pages are is a list of questions provided in the survey. The survey was developed using the SurveyMonkey® web site and was distributed to a list of emails for AASHTO SCOBS and for the AASHTOWare BrDR User group. At the end of this Appendix is a list of questions asked to those participants requesting a followâup phone calls.
Appendix A â Survey Questions  Aâ2 Onâline Survey QuestionsÂ
Appendix A â Survey Questions    Aâ3  Â
Appendix A â Survey Questions  Aâ4Â
Appendix A â Survey Questions    Aâ5  Â
Appendix A â Survey Questions  Aâ6Â
Appendix A â Survey Questions    Aâ7     Â
Appendix A â Survey Questions  Aâ8 Followâup Interview Questions The following is a list of questions asked during the followâup phone interviews: Q: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts?  If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. Q: Is the currently available software adequate for performing required load ratings? Q: Have you used refined methods to rate culverts (such as CANDE) when issues arise?  Q: Are you aware of any culvertârelated research performed by your agency that would be helpful in our investigation?   Q: Do you have any other concerns related to load rating of culverts? Q: If you have any culvert input data (for AASHTO BrR or CANDE), particularly for problem culverts, we would be interested in making use of this for our research so please indicate whether you would be able to contribute any input files.Â
Bâ1 Appendix Bâ Complete Survey Results Appendix B â Complete Survey Results The following pages provide the complete survey results with state and email information removed. This appendix also includes survey questions asked during the followâup phone interviews.Â
Appendix Bâ Complete Survey Results Bâ2 Onâline survey questions/responses Q1:  For which state or U.S. territory DOT/Organization do you work?Â Â ï· Answered: 41 ï· Skipped: 1 Also included:Â ï· Army Corp of Engineers ï· District of Columbia
Appendix Bâ Complete Survey Results  Bâ3  Q2: Are you currently using LRFR to load rate existing Culverts?  If the answer to the question above is âYesâ, what types of culverts are you rating using LRFR and what types using alternate methods?  Only culverts that were designed per LRFD. We have only rated concrete box culverts using LRFR but for all culverts qualifying as "bridges" we intend to rate all types of culverts based on LRFR if LRFR specifications exist. Existing culverts would use the same specification used in the design of the culvert to load rate the culvert whether it be ASD, LFD or LRFD.  Just to clarify, New York State only load rates "bridge size" culverts and threeâsided frames, implying a clear span in excess of 20 feet when measured horizontally along the center line of roadway. I exclusively use the MBE LRFR procedures for precast and castâinâplace arch and box culverts. I have used ASTM C 76 for RCP and ASTM A 796 for CMP. Only new culverts designed by LRFD for the HLâ93 loading are rated by LRFR. All older culverts are rated by LFR. Metal and Concrete Box. concrete box culverts, CMPs, structural steel box culverts using LRFR. We are planning to start using LRFR to load rate NBI length reinforced concrete box culverts and metal pipe culverts. We will begin this task this fall/winter.  We use BrR to rate threeâsided culverts an box culverts. We use Smartculvert to rate conspan type structures. Our initial load rating of RC Box culverts using AASHTOWare BrR software yielded zero rating factor.  As a result, we have initiated an investigate study to find out the reason for zero rating factor.  Initial findings are (1) software were misâcoded whenever axial and moment interaction occurs (2) rating factor equations are not coded properly (3) load factors and earth pressure given within MBE seems to be too high. Concrete box/frame culverts using BRASSâLRFR. Culverts designed after October 1, 2010 are load rated using LRFR.  All culverts designed previous to Oct. 1, 2010 are load rated using LFR.  There are a few instances where design plans for culverts are not available, in which case, the culvert is rated using an engineering judgment procedure. RC Box Culverts â LFR & LRFR RC 3âsided frames â LFR & LRFR CMP â LFR & LRFR. Reinforced Concrete Box culverts. LRFR is used for those culverts designed by LRFD.  We use LFR and ASR for those designed as such. we rate all culverts with LRFR first. if the LRFR results lead to load posting or load restriction, the results will be compared with LFR results and favorable ratings are used. According to Iowa DOT design manual, LFR has two different earth load definitions. One is the same as AASHTO specification and called AASHTO load; the other one is called office load, with which, the lateral earth pressure applied on the exterior walls is taken as an equivalent fluid pressure of 36 psf foer foot. Existing culverts designed LRFD are rated LRFR. All other culverts are LFD rated.Â
Appendix Bâ Complete Survey Results Bâ4 Q3: What types of culverts (material) does your state currently rate? (In the comment box, please provide the name of any software packages used for rating for each culvert type.) Other (please list). Also list any software used to rate a specific culvert type. AASHTOWare BrR used to rate concrete boxes BRASS Concrete ThreeâSided Frames New York State currently uses ETCulvert by Eriksson Technologies Inc. I do all of my ratings by hands and typically use STAAD or other frame programs for box and arch culverts BRASS Culvert, AASHTOWare Bridge Rating Inâhouse program in combination with an older PennDOT box culvert program has been used for the past 15+ years. We are now using AASHTOWare BrR for LRFR culverts. BRASS Culvert and AASHTOWare BrR for concrete culverts We used to rate concrete culverts, but none of the available programs, or the analytical methods, resulted in realistic, consistent results.  Therefore we have stopped rating these structures until reliable methods (AASHTO guidelines) or programs have been developed.  We are considering the use of BRASS Culvert for reinforced concrete box culverts. We may end up using Midas Civil in conjunction with Excel or Mathcad to rate structures that require soilâstructure interaction. We are also considering using the Ohio DOT Excel tools for rating metal pipe culverts in LRFR.  We use CANDE with LFR to rate culverts that cannot be rated using BrR. Purdue University is working on a research for us to rate bridges with no plans that includes culverts. Purdue uses ABACUS for FE and pre and post processing. Arch type structures may be analyzed using MIDAS BRASS Culvert We have attempted to load rate Steel/Metal corrugated culverts.  However, these culverts provide many challenges such as establishing curvature, actual thickness when rust exist and etc. We have used the OHIO DOT's guidance material to load rate the steel corrugated arches. We are using AASHTOWare BrR for Concrete Box culverts. Load ratings for bridgeâlength culverts have been determined primarily using the method of field evaluation and documented engineering judgment.Â
Appendix Bâ Complete Survey Results Bâ5 AASHTOWARE Software BrR BRASS AASHTO BRDR Ohio DOT CMPâExcel AASHTOWare Bridge Rating for Concrete Box Require the fabricator to provide ratings for Concrete Pipe and Metal Corrugated Culv5, CulvLR â both developed for TxDOT through research projects.  Steel/Metal corrugated culverts are load rated using the Ohio DOT cmp spreadsheets, which were modified for the Idaho legal trucks. Concrete boxes are load rated using AASHTOWare BrR software.  The BrR Culvert module is used for most new box culvert ratings, but occasionally only the top slab of the box is rated using a line girder method. Steel/Metal Corrugated â Internally developed spreadsheets RC Box â BRASS Culvert and AASHTO BrR AASHTOWare BrR BRASS/BrR/CANDE BRASS and LARS Bridge for concrete.  We have a study with KTC at the University of Kentucky to do these ratings. Inâhouse developed software (CulvertCalc) is used for concrete box rating For Steel/Metal corrugated structures, in most cases, ratings are provided by manufactures. If not a spreadsheet twisted from Ohio spreadsheet is used Metal Corrugated: Inâhouse templates Concrete Box: BoxCar Concrete Pipes and Thermoplastic Pipes: Assigned ratings based on design loads or based on field evaluation and engineering judgment. spreadsheets for metal and AASHTOWare Bridge Rating (BrR) AASHTOWare Br|R for concrete boxes. Other finiteâelement software for pipes and corrugated as the need arises. We use BrR to rate Concrete Boxes.  Steel â Mathcad/Excel worksheets  Concrete Box â primarily FDOT Mathcad worksheets, also BRASS Culvert, ETCulvert by Eriksson, and CANDE Culvert Concrete Pipe â Mathcad worksheets Virtis/Lars Supplemented with SpreadsheetsÂ
Appendix Bâ Complete Survey Results Bâ6 Q4: Does your state have issues with rating culverts (e.g., culverts that do not rate, but do not appear to be in distress)? Q5: If your answer to Question 3 above is "Yes", provide a brief description next to any specific type of culvert for which you experience an issue, i.e. project failure mode and location. Also note which of the following culvert types are most prone to failing load rating. Steel/ Metal Corrugated Concrete Box Concrete Pipe Thermoplastic Other (please list) We have a spreadsheet adapted from ODOT's spreadsheet.  It is helpful, but often fails well performing culverts, especially under shallow fills. Older culvers lack the proper reinforcement in the bottom slab and corners. Does not rate / shear and code changes â we use inspection to determine rating needs. No issues. Exterior walls can control from horizontal earth loading. Under higher fills, they can fail (RF < 0). Slabs will rate low and can result in posting due to live loads under smaller fill heights.  Culverts with insufficient cover due per NCSPA Design Data Sheet No. 19 Some older box culverts will not rate well for shear. Do not rate, but it's not always for the same reason.  Most often is excessive fill and the culvert will fail under dead load. Most issues are selfâinflicted. Original installed shape was not recorded The analysis show failures however no corresponding distress can be found with the concrete box. Exterior walls are failing in flexure at wall midâheight.Â
Appendix Bâ Complete Survey Results  Bâ7  Steel/ Metal Corrugated Concrete Box Concrete Pipe Thermoplastic Other (please list)  the analysis often shows that these fail in any one of the four walls, oftentimes the sidewalls or bottom slab.    when the AASHTO minimum cover requirements do not meet, the rating factors are very low, but most of the times culverts are in good conditions      Sidewalls typically fail rating, but show no signs of distress.     (refer to "Other" below for fill).   R/C Slab & Frame Culverts under fill and R/C Frame/Box Culverts with insufficient rebar around the corners RF seems too high for cases where arch is already buckled AxialâMoment interaction region; Shear in walls though they are in good condition.    Metal with perforations have limited or no capacity in the steel, but most of the load is carried through soilâstructure interaction and pavement above is not distressed Shear failure in slabs per calculations, but no signs of distress. failure mode older box with only one layer of rebars.    Unknown original culvert shapes â large deformation calculated reduced the load carrying capacity of the culverts that actually performed quite well Legacy designs do not rate.  Yet they have been placed for several decades.     Old Concrete Box Structures.     negative bending in top slab over interior supports, axial capacity of interior walls, positive bending in bottom slabs â the culverts most prone to this are the direct traffic culverts.    CMP's not meeting minimum fill depths High fill depths create high dead loads which reduces the numerator of the rating equation.    Culvert under shallow fill fail in calculations but perform well in the field as long as the retaining material is there  Some of the RC boxes culverts designed by ASTM design tables fail in calculations but perform well in the field. We also had problems with RC culverts failing in shear calculations, N/A N/A   We have load rating "failures" at the 1.3â1.4 mark in the negative moment region for multi barrel culverts that were designed using AS.  However, these culverts do not show distress in the field.   Â
Appendix Bâ Complete Survey Results Bâ8 Steel/ Metal Corrugated Concrete Box Concrete Pipe Thermoplastic Other (please list) DESIGNED AS PINNED STRUCTURES, RATE AS FRAME. Flexural/axial interaction at midâ height of exterior wall; slab shear. Heavy section losses result in zero calculated capacity, but the culverts are often retaining their shape and stability. Often knee and leg moment capacities for boxes or 3âsided frame culverts do not rate well, but appear to be performing adequately. n/a n/a Metal pipes are most prone to failing load ratings. Shallow fill depths. Tall exterior walls. The quality of analysis is uneven. They typically rate lower than design load because of the differences between the rating analysis and the design process.Â
Appendix Bâ Complete Survey Results  Bâ9  Q6: With respect to the previous question above, please describe any workaround procedures your agency has used to modify load ratings for culverts that show deficient load ratings but are performing well in service (to avoid posting or closure).  Answered: 29 Skipped: 13 Response Text Judgment ratings are often used for deeper cover culverts as permitted by AASHTO. Most of our culverts have not been load rated.  If they appear to be performing well through routine inspections, we assume they can support legal loads to avoid posting. We will not post culverts â use inspection results and monitor on state wide bases. We have done 3D modeling and get some benefit, but typically I will ignore exterior wall loads if results are restrictive.  None. If the box culvert has been in service for many years and does not show any signs of shear damage, we will ignore the shear values and rate for moment only. We will sometimes try a different method from ASD to LFD.  We will use the old spec on older culverts that allows the fill weight to be reduced to 70%.  Refine analysis and various assumptions to enhance the capacity.  We resort to engineering judgment.  AASHTO MBE allows engineering judgment for concrete structures with no available structural details.  We apply this practice to concrete culverts even if we do have plans.  Field measurements including fill heights, load testing per MBE. Rate only top and bottom slabs â ignore sidewalls. The majority of ratings for culverts/buried structures are considered unrated or rated based on engineering judgment.  Having a software that would rate different types of culverts/buried structures (metal, concrete boxes, frames, etc.) in all rating methods (ASR, LFR, LRFR) would be beneficial.   N/A; Postponing load posting bridges until research has been completed â refer to questions below. We increase the shear capacity equation to 3Sqrt(f'c) instead of 2Sqrt(f'c) on wall considering the fact that the wall is under compression at all time. We use documented engineering judgment and field evaluations, including consideration of where deterioration has occurred, amount of overburden, progression of deterioration through past inspections, and history of live loads regularly travelling over them. N/A we use original design load for the ratings and with inspection condition to adjust the rating values.  Assigned rating on concrete culverts that have condition rating of 5 or better with at least 2 feet of fill. Review the inspection reports and pictures, if no distress is present we assign the rating for the truck it was designed with. Our policy is still being developed for these cases.  In some cases where the rating results are deficient using analysis methods, the culvert is rating using the engineering judgment procedure, which bases the rating results on bridge condition. We have modified our spreadsheets to incorporate alternate methods to load rate CMP culverts under shallow fill. Invoke MBE clause provided it does not show any signs of distress. Using the caveat in the MBE that says if a concrete structure shows no sign of distress, then we don't have to worry about load rating.  Two different load rating runs in BrR. Rate culvert with design specifications; allow assigned load ratings for culverts performing well for sufficient service time. For the 3âsided frame legs and knees that fail load ratings, we often assign the capacity to meet legal loads since they have been in service for decades carrying legal loads without distress. Neglect existing exterior walls (1) in good condition, and (2) not part of a widening/extension project. We don't rate anything that has more than 6 feet of fill on it.  For ones less than 6 feet of fill, we go thru a process to modify the live load distribution factors.  This process is based on researched that was completed at the university.  Â
Appendix Bâ Complete Survey Results Bâ10 Q7: Has your state performed any studies or research related to the rating of culverts that you would be willing to share with the research team? If âYesâ please describe below and if possible, please provide contact information for the lead researcher. Maybe. Our Engineering and Research Development Center conducted load testing on several culverts but never finished the report. I will see if I can get the draft. Yes, TDOT funded an extensive research project with TN Technology University to investigate methods to load rate concrete box culverts. The vast majority of TN culverts are of concrete box design. The lead researcher was Dr. Sharon Huo (xhuo@tntech.edu). This research project produced load rating software tools and an extensive final report. I can email you the report upon request. For a selected group of culverts slated to be closed or severely load posted, LADOTD tasked M&M to evaluate the  culverts using any reasonable analysis method in hoping it would produce results showing a more favorable load capacity.   Ohio DOT developed Excel files to load rate existing short span CMPs with low covers, the AASHTO required minimum covers are modified in the spreadsheets based on ODOT research. Currently in progress. Completed research through the University of Delaware on frame culverts/slab bridges that had insufficient rebar around the corner.  Research has showed that these bridges can have the load ratings improved significantly. Currently working on research through the University of Delaware that is looking at the dynamic impact versus fill for our buried frame/box culverts and slab bridges. Ping Jiang, PhD. DelDOT Load Rating Engineer 302â760â2297 ping.jiang@state.de.us Our investigative work towards improving the rating factor revolves around BrR software.  We are trying to find work around that provides a rating factor that matches the field observation.  Please note that our field inspectors are finding that the culverts (even those built in 1930s) are functioning without distress.   As a result, we are trying to find the earth pressure that provides a RF of 1.0 and use that pressure as 'operating pressure' for rating bridges. Â
Appendix Bâ Complete Survey Results  Bâ11   murugesu.vinayagamoorthy@dot.ca.gov We have surveyed policies from other states and also considered the recent MBE modification for culvert load ratings with unknown construction details. For new design culverts by LRFR, we did comparison between HL 93 and MN overweight permit vehicles and develop the standard concrete culvert plan sheets meeting both HL 93 and MN overweight permit load requirements. The research report is available on the Center for Transportation Research library. Project No. 0â5849: "Evaluating Existing Culverts for Load Capacity Allowing for Soil Structure Interaction".  There are some older research reports, which we are aware of but we do not have a complete report. We had load tested several CMPs under 2 meter or more fill. We also tested a few CMPs under very shallow fill (less than 2 feet). Their research reports are available on our research website. Dr. Issam Harik and Dr. Abheeta Peiris at the University of Kentucky. we did some culvert load testing. Results show that the live load effect is very limited even with minimum top soil. The pavement can distribute live load a lot and this is ignored in analysis.  It's a little dated, and too simple, but   http://www.dot.state.fl.us/structures/structuresresearchcenter/Final%20Reports/BC354_47_pt2.pdf We did some live load testing to show that the live load effects on culverts are minimal as the fill depth increases.  The AASHTO codes are ridiculous when it comes to the live load effects on culverts for load rating purposes.  FHWA required us to load rate all of our culverts regardless of the amount of fill just because of how things are stated in the manuals.  They wouldn't listen to common sense on the issue.  We did the research project with MU to justify using different live load distribution methods on culverts, when needed for ones that had low load ratings using normal procedures.  Send me an email request at David.Koenig@modot.mo.gov and I will send you a copy of the research report.   Â
Appendix Bâ Complete Survey Results Bâ12 Q8: What software do you use for analysis/rating? (Check any that apply.) Other (provide description) For the design of a new culvert, one consultant used cande to make sure it supported the traffic load. DDOT has not rated any existing culverts.  spreadsheets and MathCAD CANDE has been used for nonâprismatic 3âsided frames. ETCulvert by Eriksson Technologies Inc. is used primarily for 4âsided box culverts and prismatic 3âsided frames. Internal program MathCad Excel sheet from MDOT and check via hand computations. RISA 3D with supplemental Excel sheet for concrete box culverts. We've used BOX5, a PennDOT program.  BRASS has also been used, with the same unreliable results.  It's not so much the programs, perhaps, that have the problem.  It's more so the AASHTO code, at least that's the prevailing theory in our office.   Ohio DOT inâhouse Excel files STAAD (as needed) Wisconsin's inâhouse program. Similar to AASHTOWare BrR. These are for concrete box culverts only. ETCulvert CulvLR â uses Culv5 as an engine for lower level analyses, then Risaâ3D for higher level Culv5 Inâhouse developed spreadsheets LARS Bridge CulvertCalc developed by Iowa DOT and Consultant company Inâhouse Spreadsheets and Mathcad Templates. ET culvert LARS Mathcad worksheetsÂ
Appendix Bâ Complete Survey Results  Bâ13  Q9: Would you be willing to provide input files for culverts rated by your state agency?  If âYesâ which software program(s)? How many input files would you be able to provide? BrR models, unsure of exactly how many we have available. We suggest Eriksson Technologies be contacted for ETCulvert input files.  Eriksson Technologies Inc. Software Company Address: 9385 N 56th St #201, Temple Terrace, FL 33617 Phone:(813) 989â3317 Would for a few in BrR if team would like them. Several Excel sheets we have on file (around 70). 3 We have the models for 2,493 of our standard culvert drawings (1920's to 1990's). Each drawing generates a number of variations depending upon cell depth, skew, fill depth, etc. In all, we have about 45,000 models. These models are all done in BRASS Culvert so there are about 45,000 BRASS Culvert data files. AASHTOWare or BRASS.  Dozens in BRASS, several in AASHTOWare We do not have any as of yet.  BrR, CANDEâ a few bridges BRASS â However many you would like to obtain. BrR software.  We have shared 104 RC Box culvert models.  We will share any models we create from hereafter, if requested. Most of our files are in our inâhouse program, which would be of little use to others without the program. CulvLR â we would be willing to provide 10 input files.  AASHTOWare BrR software, using both the AASHTO and BRASS engines.  Up to 100 input files could be provided. >10 BRASS when we get the files (see research project comment) and LARS bridge. The input files are developed for our inâhouse software Culvertcalc We would rate culverts in BrR as the need arose. However, we do not have any input files at present. We could provide some Virtis files.  I am not sure how many, or if they include the live load modifications that we do with a spreadsheet.  We should be able to provide several hundred without much of a problem. Â
Appendix Bâ Complete Survey Results Bâ14 Q10: Do you wish to discuss over the phone your state's practices and issues related to culvert rating? Q11: Do you have any other concerns related to culvert rating that you think would be beneficial to this research (i.e. shortcomings of the culvert load rating specifications that need to be addressed)? Answered: 31 Skipped: 11 Response Text A potential issue with ASTM designed precast culvert was recently brought up by our design unit. ASTM supposedly uses the circumferential reinforcement equations in box culverts.  We haven't looked into this further.  No See commentary above in Question #10. Will Interim Reports be made available for viewing? We need to use risk based approach â we cannot resource or prioritize rating culverts. Expanded guidelines on horizontal loads (ES, EH, LS), distribution of vertical loads, it has to be better than we are assuming. How to address culverts with no bottom but no load induced damage,  section loss other than NCSPA, include thrust beam effects, local/global pipe reversals due to rail posts, adequately field measure culverts, soil densities to use other than 120pcf, missing bolts in seams, and interaction between closely spaces culverts (2â10ft pipes 3ft apart). Need more accurate load to be applied Concrete culverts with pinned connection evaluation method. The current analysis method is too focused on simplicity such as used on 2d analysis  and also does not take advantage of soilâmember interaction.  No We are highly concerned about this issue, but we have just gotten started looking at it. This is the reason I answered no to questions 9 and 10. I don't really have enough information to speak intelligently about the issue. However, I have ran a few of our Interstate box culverts through BrR, and the results show they should be posted. This is not correct, as these bridge have been in service for 40+ years and show no signs of distress from overloading.  If new rating specifications are put out, an effort should be made to make the equations/methods as brief, simple and quickly executable as possible.  The new LRFR bridge rating specifications are a little out of hand, and without a computer program to run all the sets and subsets of equations, are not that easy to deal with.   Most of the guidance for culvert rating in the MBE is for reinforced concrete culverts. There is not much for metal pipe culverts. I would like a tabular result sheet with help tabs for making the right assumptions and linking the effect of live loads with fill heights for various spans and span combinations for AASHTO live loads and Certain SHV's.Â
Appendix Bâ Complete Survey Results  Bâ15  âSimplified methods for rating steel and concrete pipes/arches/etc.  âMore accurate soil interaction models with no special soil/backfill parameters.    The lack of information, i.e. asâbuilt plans and specifications, materials, thicknesses, depth and type of fill, etc. can be an issue. Not at this time. 1. Whenever DL/LL ratio exceeds a threshold (say 5 or 10), RF approach makes no sense.  C/D ratio would be a better approach.   2. In many situation, amount of compaction, fill material used are not available and therefore, rating engineer need to use approximate values for EH and EV.  Use of operating and inventory load factor/pressure should be made available  3. Shear capacity expressions are very sensitive (especially MCFT). Through research, empirical load ratings may be able to be developed based on construction type, year of construction, overburden, and condition. Culverts which have successfully carried legal loads without any signs of distress do not warrant strenuous finiteâelement soilâstructure interaction analysis to determine load ratings. No. The method shall be simple and clear, not involve a lot of modeling or time consuming analysis because the numbers of culverts in our state are large and majority are on local agencies which have limited resources. One big factor in rating culvert is the assumption of soil pressures.  The pressure distribution is much more complicated than just using active, passive and at rest pressures in the current methodology.  For concrete culverts with little or no fill, the top slab provides the bracing effect that will change the soil pressure distribution.  For culverts with large amount of fill, the arching effect can be significant. The bottom slab design using one subgrade modulus is flawed.  The culvert walls are much stiffer than the bottom slab, the soils beneath the slab would respond accordingly.  The soil reaction will be concentrated under the culvert walls making the bottom slab design and rating unreasonable by overâestimating the soil pressure under the bottom slab.  One possible solution is to change the load factor for buried structures based on structural type and embedment ratios. A study on this effect will greatly benefit the evaluation of the true behavior of the culverts.  Another study will be very beneficial is to study of the structural reliability of the currently installed culverts.  It is my personal belief that most culverts failed because of hydraulic inadequacy, not structural deficiency. Culvert ratings should take advantage of the redistribution of LL due to type of pavement. Based on our experience with these analyses, the guidance for lateral distribution for live load is nowhere near the actual live load distribution for direct traffic culverts or through fill.  Corrugated steel 5x1 seam strength is not listed in specifications.   current MBE only include LRFR method. LFR approach should be included because LFR is still valid. EH, EV, live load distribution through earth fill, live load surcharge, and dynamic load impact factor should be studied and more realistic/representative analysis model shall be provided. none that haven't already been discussed. Culvert ratings appear to be more of an exercise in academia than providing meaningful data. N/A The failure mode of "culverts" is totally different than for "Bridgesâ the load rating requirement is just an exercise in futility as the probably of posting a culvert for load is highly remote.  we'd use engineering judgment based on the condition, height of fill and culvert spans to determine if posting would be warranted rather than the theoretical results. (1) At 1.99ftâtoâ2.01ft D.fill, shear capacity increases stepwise.  (2) The MBE ought to include an easyâtoâfollow example, with classic hingedâends.  (3) For lateral distribution, LRFD's "interaction depth" hides meaning; an E vs D.fill plot would better explain distribution width "E." (3) Include provisions for routine permits, by considering adjacent trucks and multiple presence factors.  (4) AASHTO longitudinal axle overlapping can distribute a light axle to a heavy axle; say whether Boussinesq is better, and easier to program. (5) A slick culvert analysis tool would be nice. There should be an emphasis placed on communicating the effects of the 2.0 live load factor for culverts when used to try to manipulate software to rate structures that are similar in nature to culverts but are not designed as culverts. This larger number in the denominator of the general rating equation has a significant effect on the final answer from the equation. There needs to be some common sense put back into the specifications.  We don't need some load rating method or process that takes a PHD to understand.  Once you get above 6' or so on culverts, the live load effects are very negligible.  I am not saying that we shouldn't design for live load above that fill depth, but we should not have to load rate them once you get above that point. Â
Appendix Bâ Complete Survey Results Bâ16 Followâup interview questions/responses The following questions were asked in the 14 followâup interviews. The table below shows the states/organizations that were interviewed and the date of the interview.  Organization Date Interviewed Army Corp  9/4/15 California 8/26/15 Delaware  * Florida  9/10/15 Indiana * Iowa  8/26/15 Kentucky * Louisiana  9/4/15 Michigan 9/28/15  Minnesota  8/27/15 Missouri * Ohio  9/3/15 Oregon  9/3/15 South Dakota  9/10/15 Tennessee  ** Texas  9/8/15 Virginia  9/11/15 Wisconsin 8/25/15 * Note: Interview requests were mad for these states, they were contacted via email to set up the interview, but as of this writing of this report, a date had not been set up to conduct the interview. ** No phone interview was held, but postâsurvey emails were exchanged to obtain additional information. Q1: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts? If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. Alaska rates 77 culverts of which 8 are concrete box culverts. The remainder are metal corrugated culverts. The steel types of culverts are CMP(circular), pipe arch, low profile arches, horizontal ellipses, and inverted pairs An inverted pair is a subset of long-span culverts and can be found in Figure 12.8.1-1 of the LRFD. This shape is used mainly for railroad to road conflicts as the railroad has specific requirements for clearances. They are currently rating the steel culverts utilizing a spreadsheet from Michigan DOT (which is a modification of a spreadsheet developed by Ohio DOT). For the concrete culverts, they have used RISA 3D with some spreadsheets for post processing. For the concrete culverts, the models have springs in the bottom slabs but the sides do not take into account soil pressure. They are not seeing distress in their concrete culverts. One was constructed in 1904 and is not reinforcement, but is still in good operating condition. The LRFR spec is telling us to use a density of 120, but the specs we are getting are 130-140. The 120 is helping the rating because it is lighter-less dead load.
Appendix Bâ Complete Survey Results  Bâ17  Q1: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts? If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. We have rated culverts that are failing the rating, sometimes a less than zero rating (i.e. failing under earth loads) and the physical inspection of the culvert is good- no distress. The Army has rated culverts with a span length as low as 6', but typically shorter span culverts are reviewed for physical condition. The Air Force on rates culverts over 20' (NBI length). : Almost all of Floridaâs culverts are reinforced concrete. For concrete culverts, some of the problems they are seeing are often with exterior walls; particularly where the wall heights are 8-10â or more. They typically fail and it is mainly due to factored DL. Some of the problem he believes are related to the specification. Culverts that appear in good shape physically, are failing in rating. They are using both LFR and LRFR to rate their culverts. When rating analyses are is performed more rigorously (closer adherence to the spec): â Take shear at dv away from face, and consider provisions for haunches â Use the appropriate shear capacity equations (5.14.5.3-1 for deep fills, or 5.8.3.3 for shallow fills), rather than the simplified 2ââf.c â Use truly coincident loading for shear assessment â Use area-distributed loading, rather than point-distributed load, or point emulations (BRASS) â Consider lateral live load distribution to the bottom slab (Std.Spec. 17th Ed. 16.6.4.3) â Include axial effects Results improve. Commercial culvert programs include many of these considerations. However bespoke MathCAD/Excel worksheets, which frequently perform assessments for older culverts, are necessarily more crude, per time limitations on worksheet development. Other issues related to the specs: â Culvert specs jump around from section-to-section; itâs confusing. â For shallow fills, the shear strength reduction/resistance factor is 0.90 (5.5.4.2.1), or 0.85 (12.5.5-1)? â When longitudinal axle distributions through soil overlap, (1) ââ¦the total load shall be uniformly distributed over the areaâ (Std.Spec. and LRFD 6th Ed.), (2) the distribution triangles overlap, per BRASS method, or (3) the loads are confined to the length of the footprint at the depth of first overlap, per MBE A10.7.4-1. Which method does LRFD endorse? Is a better method available? â For lateral distribution in shallow fills, LRFD 6th Ed 2012 at 3.6.1.2.6 called for 4.6.2.10 (Std.Spec. slab distribution with mpf =1.20), MBE 2013 Interims at C6A.5.12.10.3a says likewise, but LRFD 7th Ed. 2014 at 3.6.1.2.6a calls for 4.6.2.1, which is actually deck distribution. Was the later a typo? â MBE 6A.5.12.5-1 applies a single-lane multiple presence factor of 1.20 to the HL93 lateral distribution; however mpf = 1.00 for the legal loads. This appears inconsistent with other areas of the MBE, which applies mpf=1.20 to both design and legal loads. â It would be helpful to clarify that the longitudinal distribution takes no multiple presence factor. â Some E vs D.fill charts would be useful. â Does E.lateral consider two trucks? Itâs a pretty big difference, one trucks vs two trucks, especially where single-lane mpf=1.00.
Appendix Bâ Complete Survey Results Bâ18 Q1: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts? If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. LADOT is having a lot of issues with cast-in-place reinforced concrete culverts failing in rating for LRFR. Many of the culverts are older. The oldest culverts have one layer of design steel and pretty much everything is failing in LRFR. The culverts are not showing any signs of distress under physical inspection. Louisiana uses the NBI span length and only rates culverts that are greater than 20â in span length. Modjeski & Masters is currently working with LA DOT on load rating of their culverts. Michigan has had issues with RC Box culverts appear to be good upon physical inspection but are not rating well. In some cases, culverts are failing under dead load; this is particularly the case for culverts with deep fill heights. In one case, Michigan reduced the soil density to 70% of its actual weight of 120pcf per the AASHTO edition 6th. This allowed the culvert to rate well, otherwise Michigan wouldâve posted the bridge or closed it due to deep fill height ~ 16.5 ft. Without the reduction, presumably the culvert can NOT support fill and its weight giving a RF of 0.0. Again this a culvert that does not show any physical signs of distress. Michiganâs rating policy for culverts is to rate structures that were built 2010 and prior using LFR. Structures built beyond 2010 and designed with LRFD, are rated using LRFR. The 12â minimum fill criteria effects both sides of the rating equation. From the AASHTO code, the LL impact factor goes up when the fill is below 12â thus effecting the load portion of the rating. The NCSPA (National Corrugate Steel Pipe Association) spec has criteria that effects the capacity side when the fill is below 12â. MnDOT asked if the project involved both precast and CIP box culverts noting that most of their new R/C box culverts are precast although they have both CIP and precast in their inventory. Mr. Clancy responded that a
Appendix Bâ Complete Survey Results  Bâ19  Q1: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts? If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. number of different types of culvert construction are being considered but the types of culverts that are to be part of the field testing program are yet to be determined and this is somewhat dependent upon what the participating DOTs offer up to be tested. Furthermore we are looking to include one or more culverts under construction to allow for more flexibility in instrumentation. From MnDOTâs perspective, there are three primary ways to perform culvert analysis: 1) FEA, 2) Beam on Elastic Foundation and 3) âBrute Forceâ i.e., using a method such as BRASS Culvert or BOXCAR Each of these methods provides different answers and differences can also be attributed to the specifics of the modeling such as the treatment of the haunch with respect to stiffness, location of critical sections, etc. MnDOT would like to see more unification of the methods used to load rate culverts such that it is being done on a more consistent basis. This might also include some guidance on rating based on what is required for various fill-height ranges. ODOT has had issues with rating CMP (Metal culverts) in the past and the AASHTO Specs are lacking for metal culverts which prompted ODOT about 6 years ago to create a spreadsheet for rating CMP culverts. Ohio law requires them to rate culverts that are 10â in span length and above. The creation of the spreadsheet, which can be used for really low covers (as low as 3â), prompted research to be performed by the Ohio State University. This research looked at 3D FEM models of several culverts, and Ms. Wang believes that at least one of those models took into account pavement. The research has gone on for the past year and was used to help validate assumptions that were made in the spreadsheet calculations. Ms. Wang was the manager for ODOT for that research. The spreadsheet will take into account deterioration by entering a percentage loss of the CMP. If deflection is more than 5% a more refined analysis is used (e.g. CANDE). As a follow-up, ODOT said that Michigan has performed some research that has tagged on to the work that ODOT has performed. In the past, Oregon did not rate culverts. Currently, Oregon has 300 NBI culverts (>20â) in their inventory. About half are reinforced concrete and half are steel corrugated. The culverts are currently not rated, but Oregon is looking into the best way to provide load rating for these structures. They have had a consultant do some limited work on 1 or 2 rigid frames (with fill) using BRASS Culvert. They are looking at the new ballot item (which was approved/passed during the last SCOBS), which will be included within the next interim revision of the MBE for RC culverts that are in good condition that perhaps do not need rated. Jon forwarded a copy of the ballot item to me. The ballot items allows for assigning inventory ratings of 1.0 and operating ratings of 1.3 for HL-93 design loads for culverts that have been carrying normal traffic for an appreciable period of time and shows no distress as determined by a physical inspection of the culvert by a qualified inspector and documented in the inspection report. Oregon DOT is currently Working with a consultant to rate the RC and metal culverts in LRFR. South Dakota really hasnât had any large issues with the rating of their culverts. Most of their culverts are reinforced concrete box culverts and about 98% were designed using ASD. This method was used until October, 2010 when the culvert design method was switched to LRFD. South Dakota has approximately 550 NBI records (state-owned) that are culverts out of a total of about 1800 NBI records. South Dakota follows the NBI criteria for span length for NBI records. For culverts designed from 2010 on, ETCulvert (Eriksson) was used for design. These culverts have some minor rating issues in BrR where the inventory rating of the bottom slab can be around 0.95 in some cases. Current design procedures for culverts include designing the culverts in ETCulvert and then checking them in BrR. Prior to the 1970âs culverts were designed using standard culvert detailing drawings. These drawings are available in hard copy format (they have not yet been scanned in). Asked for how many of the culverts in the current inventory were designed using the 1930âs & 1950âs standards, South Dakota estimated that number to be about 40-50% of the culvert inventory. Some of the culverts in the inventory are up to 80+ years old. They agreed to scan and send sample pages of the culvert standards for our review. Texas DOT is rating using LFR. They feel that the distribution of the loads (even on direct traffic culverts) does not provide a true representation of actual loading conditions. They are OK with capacity side of the equation, but think that the demand side may be too conservative. They have some reinforced concrete culverts that are not showing signs of distress but do not pass for rating.
Appendix Bâ Complete Survey Results Bâ20 Q1: Do you have any issues with the current MBE/FHWA requirements for load rating of culverts? If so, please also note the type(s) of culverts that are having issues, describe what is controlling (low) ratings, design method used, age of culverts with issues, etc. They donât have many metal culverts in their system and currently donât have an easy way to rate them. I told him of the spreadsheet that Ohio DOT is using for metal culverts. Virginia hasnât really had any issues with rating culverts. The procedure they use for older culverts is described in the response to the following question. A new ballot item has been approved related to the load rating of reinforced concrete culverts in cases where no plans are available. However, there is nothing similar for other culvert types. ***** Are you having problems rating other culvert types or are they not rating them yet? We have load rated all types of bridge-length culverts using approximate methods which include a combination of calculations, field evaluation and documented engineering judgment. The new AASHTO ballot item provides explicit guidance for using approximate load ratings for concrete culverts, but does not apply this same criteria to flexible buried culverts. The only explicit guidance via national publication on load rating flexible culverts I am aware of is NCSPA Design Data Sheet No. 19, which requires knowledge of seam construction, corrugation pattern, gage thickness, % pipe crown deflection, steel strength, and assumed soil-structure interaction. Many of these parameters are unknown for old buried flexible culverts. These structures are at relatively low risk of immediate failure, so it would make sense to extend the same economical methods of assigning load ratings for these types of culverts as has been defined for reinforced concrete box culverts. Q2: Is the currently available software adequate for performing required load ratings? Alaska is using and Excel spreadsheet from Michigan DOT (that is a modification from and Ohio DOT spreadsheet) along with hand calculations to aid in the load rating of the steel corrugated culverts. They are using RISA 3D with supplemental Excel spreadsheets for concrete box culverts. They mostly use STAAD for analysis and MathCADD spreadsheet to perform the rating. I told Phil about CANDE and will send him the URL to download. Florida is using a combination of both in-house and external software for Culvert rating as shown below: â PSBeam (by Erikson). â BRASS (use most frequently). â AASHTOWare BrDR (have played around with this a bit). â MathCAD (developed in-house). The primary worksheet, for frames, was developed by Design in the 90âs, and most recently updated in 2015. A newer worksheet, for older hinged-end culverts, is under development in Maintenance. Both sheets generate forces internally (stiffness matrix, and area-moment influence matrices). Louisiana uses AASHTOWare BrDR for rating precast reinforced concrete culverts. Many of these are not rating well. He is willing to share input files from BrDR with the research team. (Note that that most precast culverts (ASTM D1433) easily pass LRFR ratings.) LA DOT also uses Midas (2D) for arch type reinforced concrete structures. Midas supports simple soil models. They have not used CANDE in-house, but he used it many years ago. I told him I would send him the link to the latest CANDE software on the NCHRP web site. For metal corrugated culverts, Louisiana is using the Ohio DOT spreadsheet for rating. Michigan currently uses AASHTOWare BrDR and BRASS. When culverts have failed using BrDR they have on occasion been rated with BRASS and provide comparable results. So it appears that the rating issues may be related to the specification. MnDOT is just starting to use AASHTO BrR so they are not able to give any detailed feedback on that software. CANDE is good but it would be better if it had better functionality with respect to load rating. The available software does not have the capability to perform ratings after lining type rehabilitations. Shotcrete and lined/grouted repairs are done by vendors and they have their own way of determining the as-repaired
Appendix Bâ Complete Survey Results  Bâ21  Q2: Is the currently available software adequate for performing required load ratings? strength of the system but MnDOT does not have any means of independently verifying the vendorâs claims. A means to quantitatively determine the strength of a rehabbed culvert is needed. The spreadsheet helps to address rating issues related to CMPs. Long span CMP might use CANDE for more complicated cases. For RCBox culverts, ODOT doesnât really have any load rating issues but ODOT does make exceptions to the LRFR specifications for concrete box culverts. They will send a list of the ODOT specs where exceptions are made. Oregon DOT is just starting to rate culverts. Of the 300 NBI culverts (>20â span length) in Oregonâs inventory, about half are metal corrugated and half are reinforced concrete. Oregon will try to use the Ohio DOT spreadsheet for rating the metal culverts and have not yet selected the RC rating method. They are looking at BRASS and perhaps AASHTOWare (they are not currently an AASHTOWare licensee). ETCulvert â Eriksson software â used for design and BrDR is used to do a rating check for each new design. BrDR is used for rating of the culvert inventory. Culv5 was a program developed in the 1970âs in FORTRAN and is for the analysis of reinforced concrete box culverts. The CulvLR software was developed more recently (2009) and utilizes the Culv5 engine to perform the analysis. If the culvert fails using the Culv5 engine, CulvLR generates a Risa model (2D) which uses plates to model the soil. Both programs were developed for TxDOT through research projects. I asked if this software was available to the research team along with input files that could be utilized by the research team. I also said it would be preferable to have input for culverts that appear to be performing well physically but do not rate well. TxDOT will check to see if the programs are available for use by the research team. For Virginia DOT, newer culverts 2014-15 on are rated with BrR. Culverts designed prior to that use a design table and an accompanying tonnage chart. The designs are for specific size culverts. The ratings are obtained by using the tonnage information in those charts. VDOT agreed to send me the URL information for those design procedures/charts. Yes, in general. However, WisDOT has experienced shear failures in concrete boxes using BrR software in cases where the culvert is performing well in service. In such cases, these failures are neglected (based on condition and performance). **** Where is the software predicting failures (top slab, sidewalls, etc.), What sizes of culverts are they having problems with? What is the age and design method for culverts having this problem. Can they send us an input file? We have only rated a few in BrR but we did see shear ratings coming out lower than the original design for both top and bottom slab, however the sample size is small. BrR has actually added options to âignore shearâ and âexclude bottom slabâ in ratings for box culverts. Their tech support informed us this came at the request of three other agencies. For the most part we have preferred to use our in-house software for concrete box culvert ratings, and have only tested out BrR with a few trial culverts.   Q3: Have you used refined methods to rate culverts (such as CANDE) when issues arise? They have not used CANDE. I will send them a link to the software. They have performed some 3D modeling for some benefit, but it was used mostly to compare the 2D results with and 3D results. Have used CANDE but it is a bit too complicated for their needs. From previous response: LA DOT uses Midas (2D). Have not used CANDE. Have access to BOXCAR but havenât used it. Michigan has not used CANDE. Some special culverts like arch culverts which cannot be analyzed using BrDR or BRASS have been analyzed/rated by consultants using FEM software.
Appendix Bâ Complete Survey Results Bâ22 MnDOT uses CANDE for metal culverts. It was noted that even with CANDE various levels of analysis are available. It was also noted that CANDE is not very user friendly when used as a tool for load rating. Mr. Clancy noted that with Mike Katona on the team it is anticipated that some enhancements to the CANDE software will be implemented to make the software more useful in the research effort and that some of these enhancements will likely make their way into the released product. These enhancements will benefit those who are using the software for load rating. Yes. Long span CMP might use CANDE for complicated cases. Oregon DOT hasnât started using refined methods yet. If needed will most likely use Midas Civil with post processing in Excel. No. Not typically. They have not used CANDE, but CulvLR generates a Risa model (2D) where plates are used to model soil elements. They looked into CANDE but would be too cumbersome to use for the number of culverts that Texas has in its inventory. He (VDOT) thinks that CANDE has been used for cons pan-type arches. Some other non-NBI culverts have used BRASS. No. Q4: Are you aware of any culvert-related research performed by your agency that would be helpful in our investigation? No. Up to 2011 Alaska was not in compliance for rating culverts. Load rating for culverts began in 2013-2014. They now have rated all of the culverts that are owned by the state (77 total culverts). Phil was aware of some culvert field testing that was performed out of the Vicksburg office and will try to locate the research paper. The work was performed around 2006-2007 and involved the instrumentation of culverts for live loading. The paper was not formally published and he asked that keep it within our research team. Since it is unpublished work, if we include it as part of the research, we should let the Army Corps know. Some older research (http://www.dot.state.fl.us/structures/structuresresearchcenter/Final%20Reports/BC354_47_pt2.pdf and http://www.dot.state.fl.us/structures/structuresresearchcenter/CompletedResearch.shtm#evaluations), but not nearly as good as Texas in 2010 http://texashistory.unt.edu/ark:/67531/metapth326775/ Louisiana is preparing to do some field testing (possibly as early as next year). Ching is willing to share that information with the research team. When we are preparing the field testing document, he is interested in talking to our research team regarding our methods for instrumentation. He may be willing to adjust his instrumentation to benefit our research. I told him we would contact him when are preparing our field testing plan and he agreed that we could contact him directly. For metal corrugated culverts, Michigan modified the ODOT spreadsheet to include Michiganâs 28 legal vehicles. Michigan has recently updated the spreadsheet and is willing to provide the research team a copy once they have been reviewed. Primarily changed the way that the live load was distributed through the soil. For Ohio DOTâs version, the assumption was made that the maximum axle for the HL-93 was controlling. Michigan has a lot of different vehicles to rate (28) and developed a spreadsheet to calculate the effect of each of those vehicles on varying fill heights. Vehicles with closer axle spacing begin to have overlapping loads at around 5â-6â of fill. The spreadsheet took this into account and determined the critical vehicle at different fill heights (every 6â). The values were then ported back into the ODOT spreadsheet. They provided the URL for the Michigan version of spreadsheet (along with the spreadsheet to calculate the LL distribution through fill). http://www.michigan.gov/mdot/0,4616,7-151-9625_24768_24773-201633--,00.html
Appendix Bâ Complete Survey Results  Bâ23  Q4: Are you aware of any culvert-related research performed by your agency that would be helpful in our investigation? Michigan is currently working on version 2.0 of the CMP spreadsheet and they will provide that to the research team when it is available. The spreadsheet works for both LFD and LRFD MnDOT has some internal research on PE Pipes and just started some research on looking at various methods of repairing pipes and the structural evaluation of such. MnDOT provided the following links: http://www.dot.state.mn.us/research/TS/2012/2012-27.pdf http://www.dot.state.mn.us/research/TS/2005/200522.pdf http://www.dot.state.mn.us/research/pdf/1992-02.pdf other reports can be found at: http://www.dot.state.mn.us/research/reports-2014.html Yes. ODOT forwarded their most recent research with Ohio University and the Ohio State University. The Michigan report which utilizes the Ohio DOT CMP spreadsheet. Oregon forwarded the URL address. http://www.michigan.gov/mdot/0,4616,7-151-9622_11045_24249_24251-322991--,00.html No. Tennessee DOT provided the following: The only thing that I would add is that TN Tech developed a couple of spreadsheets that act to look up the LFR ratings that they developed for our standard culverts. So, we have all the files that supplement this report. These files included: 1) Two spreadsheets. One for concrete box designs (with a bottom slab) and one for concrete slab designs (without a bottom slab â with footings keyed into rock). 2) Approximately 45,000 BRASS Culvert data files with resulting output files. 3) The standard drawings for the culverts and slabs that were analyzed (over 1,000 standard drawings). Would you be interested any of this other information? It is too much data to send by email but I could probably upload it to you if you have a public folder for such things. Or I could just save it on a thumb drive and mail it to you. All the files total about 5.2 GB on disk. They are mailing the information The research report is available on the Center for Transportation Research library. Project No. 0-5849: "Evaluating Existing Culverts for Load Capacity Allowing for Soil Structure Interaction". Just the VDOT design tables described for the previous question. Links are below: Our load rating page is here: http://www.virginiadot.org/business/bridge_load_rating.asp The tables mentioned are in the back portion of the I&IM 86 linked here: http://www.virginiadot.org/business/resources/Load_Rating_Data/IIM-SB-86.pdf No.   Q5: Do you have any other concerns related to load rating of culverts? Some of the DOTâs concern for culvert rating were expressed in their survey responses and include: How to address culverts with no bottom but no load induced damage, section loss other than NCSPA, include thrust beam effects, local/global pipe reversals due to rail posts, adequately field measure culverts, soil densities to use other than 120pcf, missing bolts in seams, and interaction between closely spaces culverts (2-10ft pipes 3ft apart). Alaska DOT is very interested in this research and wanted to know if they could know of the culvert areas that are being reviewed as the project proceeds. The procedures seem to be conservative on loads. Both the earth loads and live loads, especially on distribution of live loads and earth loads. He believes that for culverts with eight or more feet of fill the horizontal loads on the walls are too conservative.
Appendix Bâ Complete Survey Results Bâ24 Q5: Do you have any other concerns related to load rating of culverts? Concerned with the way the spec interprets the triangular distribution. Perhaps too conservative. For unbraced walls, the wall is rotating about an axis near the bottom, the triangular load distribution assumption used by BrDR is reasonable. However, since the culverts are braced both at the top and bottom of the walls (even more lateral supports for multilevel culverts), the lateral earth pressure distribution become either rectangular or trapezoidal depending upon the soil conditions (see Peck 1967). I copied the above presentation slides from a web site. There are many other studies on the distribution of lateral earth pressure for braced or anchored walls. Even though the above presentation is about braced excavation, the concept is the same â the earth pressure distributions are not triangular. If we cannot model the loads correctly, any effort in improving structural model is futile. There are two issues that Michigan is concerned about: 1. The issue with large fill height causing 0.0 ratings for culverts that donât appear under distressed. This is described in a previous answer. 2. For CMPâs (metal culverts), the issue of the minimum height requirement (12â minimum). Under 12â minimum fill height, the code takes a different path which causes the ratings to fail. Using the equation/criteria for fills less than 12â causes a failure, whereas fills just greater than 12â pass with room to spare. MnDOT would like to see an evaluation of AASHTO BrR in terms of its usability MnDOT has seen differences in the load combinations used to rate culverts in various software tools so further guidance on the correct LCs to consider should be given. The different load factors for vertical and horizontal earth pressure can be difficult to apply when performing a refined analysis such as FEA. No. Metal culvert specification is not as defined as the concrete culvert specification. Mentioned that there seems to be a big change in LRFR at around the 2â fill line. Fills that are 1.9â provide very different results that fills that are 2.1â. They are interested to see if our research would investigate this. He said that this was also an issue in ASD but appears to be more pronounced in LRFR. Being under 2â of fill seems to come with a severe penalty. Current SD procedure is to design at different fill depths (e.g. 1â-5â) and use the critical design. Didnât want the project to be so broad that loses site of improving the specification while keeping it simple. The lateral distribution seems to be way off. The demand side (loads) donât seem to correlate well with the capacities. No. Based on talking to other state DOTs about what they are doing, there seem to be mixed messages from FHWA as to what is required as different agencies are taking different approaches to meet the FHWA requirements. Also, given the number of culverts in the DOT inventories, there does not seem to be a significant benefit to load rating all of these structures given the amount of effort and cost to do so for little benefit given the low risk of failure of these structures.
Appendix Bâ Complete Survey Results  Bâ25    Q6: If you have any culvert input data (for AASHTO BrR or CANDE), particularly for problem culverts, we would be interested in making use of this for our research so please indicate whether you would be able to contribute any input files. The spreadsheet they use is just a copy from MDOT. Has mostly MathCADD spreadsheets. No (from survey). Very little CANDE and BrR. Wouldnât likely be useful. LADOT is willing to share AASHTOWare BrDR input files. Michigan provided 4 AASHTOWare culvert files with rating issues with the following descriptions. ï· 70170025000C020 / M-6/WILDLIFE CROSSING : gives 0.0 RF due to depth fill height, extremely deep culvert ~ 29 ft buried ï· 77177011000C030 / M-19/COWHY DRAIN : it fails for overload class A but we scale down the axle weights for those routine permit trucks presumably will have gage width more 6 ft ï· 77177023000C030 / I-69 WB/ BURT DRAIN : we reduced the soil density and taken it as 70% of its actual weight 120pcf per AASHTO edition 6th otherwise we wouldâve posted the bridge or closing it due to deep fill height ~ 16.5ft (presumably the culvert can NOT support fill and its weight, RF=0.0) ï· 46146041000C010 / M-34 Over BEAR CREEK : this is similar to C03 of 77011 Most of our problems with culvert not rating is /was due to mainly fill heights, extremely deep buried culvert that according to BrR canâ stand fill weight. Also weâd few problems with overload class A vehicles mainly to 60 kips truck. I couldnât find any structure that was done in-house that we ignored shear, there are couple instances that we only analyzed the top slab and ignored the walls. ODOT provided their spreadsheet they developed for CMPs. Just starting to rate culverts. Yes, South Dakota will share a few BrDR input files. TxDOT will check to see if we can use CulvLR/Culv5. I asked VDOT to elaborate on the following comment provided in his survey: âThere should be an emphasis placed on communicating the effects of the 2.0 live load factor for culverts when used to try to manipulate software to rate structures that are similar in nature to culverts but are not designed as culverts. This larger number in the denominator of the general rating equation has a significant effect on the final answer from the equation.â In some cases, BrR is used for culverts that donât quite fit the mold for BrR culverts. For example a three-sided culvert with an elliptical or oval shape (BrR only works with rectangular shaped culverts). VDOT will try to use Bridgeware (BrR) to approximate the loading. This is correct Conceptually, if you use the general equation (6A.4.2.1-1) from the MBE, when 2.0 is substituted for the live load factors given in Table 6A.4.2.2-1, the mathematical effect is to lower the rating factor. Â
Appendix C â CANDE Tool Box Manual C-1 CANDE Tool Box Manual  For Load Rating  1 EXECUTIVE SUMMARY The CANDE Tool Box greatly enhances the user friendliness of the CANDE finite element program to compute load rating factors (RF) for existing culvert-soil systems for any truck or live load configuration. The CANDE Tool Box is a standalone computer program that offers the user several options to ease the pain of developing CANDE input files and computing rating factors. Currently there are five options, which are briefly described below and explained in much greater detail within this manual. 1. Convert any Level-2 input file with half-mesh symmetry into an equivalent Level-3 file with full mesh topology. Useful for applying non-symmetric loading, alternate layering, and void zones. 2. Modify any Level-3 input file to include a pavement layer over the soil surface and/or convert top soil layer to an elastic wearing course. Useful for Load Rating existing culverts to include the load-spreading benefits inherent in pavements and prevent failure of nonlinear soil models. 3. Extend any Level-3 input file to include boundary conditions to simulate live loads moving over the mesh surface. Choose HL93 design or tandem truck or define any truck up to 10 axles. Useful for load rating existing culverts as well as designing new culverts. 4. Permanently revise the node numbering of any Level-3 input file to minimize the bandwidth of mesh topology. Useful for circumventing the time-consuming need to employ CANDEâs built- in bandwidth minimizer that must be activated every time the input file is executed. 5. Compute load-ratings factors RF from CANDE output files including the controlling RF values for each design criteria along with all supporting information printed out at end of the CANDE Output Report. This manual is organized in three major parts called Overview, Getting Started and Option Details. It is not necessary to read the entire manual before using CANDE Tool Box Program because the screen instructions and dialogue lead the user through executing each option and sub option. The user is encouraged to experiment with CANDE Tool Box by clicking on the executable icon contained in the same folder as this user manual.
Appendix C â CANDE Tool Box Manual C-2 CANDE Tool Box Manual  For Load Rating  Table of Contents 1 EXECUTIVE SUMMARY................................................................................................................... 1 2 OVERVIEW ......................................................................................................................................... 3 2.1 Tool Box Purpose. ....................................................................................................................... 3 2.2 Tool Box Options (user choices). ................................................................................................. 3 2.3 Input File Requirements. ............................................................................................................ 3 2.4 File Names and Manipulations. ................................................................................................. 3 3 GETTING STARTED .......................................................................................................................... 5 3.1 Initial Screen Views. ................................................................................................................... 5 3.2 Intermediate Screen Views. ........................................................................................................ 8 3.3 Final Screen View. ...................................................................................................................... 8 4 OPTION DETAILS .............................................................................................................................. 9 4.1 OPTION 1: Level-2 half mesh to Level 3 full mesh. ................................................................ 9 4.2 OPTION 2: Add pavement and/or elastic wearing course. ................................................... 10 4.3 OPTION 3: Add live loads on upper surface. ......................................................................... 11 4.4 OPTION 4: Minimize Bandwidth. .......................................................................................... 17 4.5 OPTION 5: Calculate Load Rating Factor RF. ..................................................................... 18Â
Appendix C â CANDE Tool Box Manual C-3 2 OVERVIEW 2.1 Tool Box Purpose.  CANDE Tool Box (CTB) is a stand-alone computer program that operates on existing CANDE input and output files to generate new executable CANDE input files with enhanced capabilities or to compute load rating factors from previous CANDE solutions with live loads. All generated files and calculations are saved in the originating folder for easy access. Currently there are five options, which are briefly described below and subsequently explained in greater detail. 2.2 Tool Box Options (user choices). 1. Convert any Level-2 input file with half-mesh symmetry into an equivalent Level-3 file with full mesh topology. Useful for applying non-symmetric loading, alternate layering, and void zones. 2. Modify any Level-3 input file to include a pavement layer over the soil surface and/or convert top soil layer to an elastic wearing course. Useful for Load Rating existing culverts to include the load-spreading benefits inherent in pavements and prevent failure of nonlinear soil models. 3. Extend any Level-3 input file to include boundary conditions to simulate live loads moving over the mesh surface. Choose HL93 design or tandem truck or define any truck up to 10 axles. Useful for load rating existing culverts as well as designing new culverts. 4. Permanently revise the node numbering of any Level-3 input file to minimize the bandwidth of mesh topology. Useful for circumventing the time-consuming need to activate CANDEâs built- in bandwidth minimizer that must be activated every time the input file is executed. 5. Compute load-ratings factors RF from CANDE output files that represent LRFR analysis and printout the final RF values with supporting information at the end of the CANDE output report. 2.3 Input File Requirements.  To exercise any of the options, the existing input file (CID) must have been successfully executed by the CANDE program, and the associated CANDE Output file (OUT) is resident in the same folder as the input file, which is the normal case unless the user rearranged the file locations. Taken together, the original input file and output files supply the basic information for creating new CID files with Options 1 to 4. For Option 5, the output file provides the data source to compute load-rating RF values as well as the permanent file to record the results. 2.4 File Names and Manipulations.  For purposes of discussion, assume that the originating CANDE input file is named âMyCulvert.cidâ, and as always, the associated CANDE output file is automatically named âMyCulvert.outâ. The table below shows the final result of applying any Tool Box option on an existing file, MyCulvert.cid. The last column shows the new file name generated by the Tool Box and stored in the original folder. The four- letter prefixes (Full-, Pave-, Live- and Bmin-) remind the user how this file has been modified from the
Appendix C â CANDE Tool Box Manual C-4 originating file. For example, Full-MyCulvert.cid implies a full mesh input file has been created from the Level-2 half mesh file called MyCulvert.cid. Table 1. Overview of Tool Box options and file creation and modifications. Tool Box User Options Originating file identified by user via a browser Additional data Supplied by user via screen prompts New file generated by Tool Box (1) Create Level-3 Full mesh from Level-2 Half mesh MyCulvert.cid (Any Level-2 File) None Full-MyCulvert.cid (Level-3 file) (2) Add Pavement layer or elastic wearing course to surface of soil MyCulvert.cid (Any Level-3 File) Pavement and/or wearing course data: Elastic properties. Pave-MyCulvert.cid (Level-3 file) (3) Add live loads over mesh surface MyCulvert.cid (Any Level-3 File) Vehicle data: Axles, loads, footprints, locations, adjustments, etc. Live-MyCulvert.cid (Level-3 file) (4) Minimize bandwidth by permanently renumbering nodes MyCulvert.cid (Any Level-3 File) None Bmin-MyCulvert.cid (Level-3 file) (5) Compute load-rating values and add to Output Report. MyCulvert.cid (Any Level-3 File) (Or Level-2 File) Load-step data: End of Construction, Start of Live load, End of Live load. MyCulvert.out (Same file as original output file with additional RF data)
Appendix C â CANDE Tool Box Manual C-5 If desired, the Tool Box options may be applied in succession, i.e., one option after another. For example, to add a Pavement overlay to the newly generated full mesh file, select Option 2 and identify the originating file as Full-MyCulvert.cid. The final output from the Tool Box is called Pave-Full- MyCulvert.cid. If all four options are selected in succession, then the final file is named, Bmin-Live- Pave-Full-MyCulvert.cid. Option 1 works on any Level 2 input file including all modifications with Level-2 Extended. For Options 2, 3 and 4 the originating file may be any valid Level 3 cid file, perhaps developed manually or generated by third-party software packages such as NASTRAN or Cande-Cad-Pro. It is not necessary that the originating input file have line tags like those created by the CANDE GUI. If line tags do not exist on the originating file, they will not be inserted on the generated file. Conversely, if line tags are used in the originating file, they will also be inserted in the generated file. Option 5 works on any output file. It does not create a new file, but rather, reads and processes the originating output file to compute the load rating factor RF and then prints the results at the end of the originating output file. Detailed explanations about option 5 as well as the other options are presented in the last section of this document. 3 GETTING STARTED 3.1 Initial Screen Views.  After the CANDE Tool Box (CTB) executable program is downloaded and stored in the computer, the user need only double click the application icon to open the welcoming screen shown below. As shown, the first query requests the user to select the desired option by entering the number 1, 2, 3, 4, or 5. Entering a blank value is the signal to exit the program. The welcoming screen reappears after each option is completed so multiple options can be executed in one session.
Appendix C â CANDE Tool Box Manual C-6 After any option number is entered, the screen shows the number and description of the selected option along with a request for the user to identify the associated CANDE CID file. The example shown below is the view screen when Option 1 is selected. Remember, the selected originating file must have been executed with CANDE before selecting it.
Appendix C â CANDE Tool Box Manual C-7 As indicated by the last sentence in the above screen, the user is required to press âEnterâ on the key board to open a browser to the computer directory in order to select the desired CID file by double clicking. An example browser screen is shown below wherein âTutorial-7.cidâ is the chosen CID file.
Appendix C â CANDE Tool Box Manual C-8 3.2 Intermediate Screen Views.  The above three screen views are similar for all options; however, the subsequent screen views are dependent on the selected option number. Options 1 and 4 require no additional user input, whereas Options 2, 3, and 5 require additional user input as directed by individual queries appearing on the screen. The third column in Table 2 indicates the type of data that is requested from the user; and the last section of this document provides greater detail on the data requested for each option along with default values. The screen views offer reasonable default options that the user may select to answer the queries. 3.3 Final Screen View.  The last screen view is similar for all options. First, a message to the user states that the option was successfully completed. If it had not been successful, the user would have been previously notified of the cause of the problem such as the Output file could not be found in the specified directory. Second, the user is informed of the name of the new CID file generated by options 1, 2, 3 or 4; or for option 5, the user is provided with a summary of the load rating calculations. An example of the final screen view is shown below for option 1. As shown, the new CID file is named âFull-Tutorial-7â, and as indicated by the 2nd to last line, a description of the new CID file is written at the bottom of the input file for future reference. Indeed, all five options provide a written record of user selections and key calculations for future reference.
Appendix C â CANDE Tool Box Manual C-9 4 OPTION DETAILS 4.1 OPTION 1: Levelâ2 half mesh to Level 3 full mesh.  This option is applicable to any existing Level-2 input file including all Level-2-Extended modifications. To develop the new Level-3 input file with full mesh topology, information is taken from the originating Level-2 input file and also from the Level-2 output file. The output file contains generated data from the CANDE pre-processing subroutines including the complete set of nodal coordinates, element properties and boundary conditions that define the right half of the full Level-3 input file. The Option-1 algorithm generates the left-half side of the full mesh as a mirror image of the right-side mesh so that original number of nodes (Nhalf), elements (Mhalf), and boundary conditions (BChalf) become approximately doubled for the full mesh; i.e., Nfull â 2 Nhalf, Mfull â 2 Mhalf, and BCfull â 2 BChalf. Note the relationships are âapproximatelyâ doubled due to the vertical centerline (x = 0) wherein nodes, interface elements and boundary conditions are not counted twice because the centerline does not have a separate mirror image. Specifically, the left-side mesh topology is generated from the right side by assigning each left-side node number nL equal to the corresponding right-side node nR plus the total number of half-mesh nodes, and then expressing the x and y coordinates as the mirror image as shown below. ï· nL = nR + Nhalf for nR = 1, 2, 3 ⦠Nhalf ï· x(nL) = - x(nR) ï· y(nL) = y(nR) In a similar manner, the left side elements mL and boundary conditions bcL are generated from the corresponding right side numbering as shown below. ï· mL = mR + Mhalf for mR = 1, 2, 3 ⦠Mhalf ï· bcL = bcR + BChalf for bcR = 1, 2, 3 ⦠BChalf As already indicated, the above assignments are not performed whenever a node, interface element, or boundary condition is on the centerline (x=0). Special modifications are required for the original boundary conditions on the centerline, i.e., all lateral displacement constraints are removed and the magnitude of vertical forces are doubled to correctly represent the original half- symmetric conditions. Other special treatments include revising the beam element numbering for arch meshes so that the beam elements are in ascending order in traveling from the left footing to the right footing. The new Full-mesh input file as created by Option 1 is theoretically equivalent to the original Level-2 input file so, without further changes, both solutions give essentially the same results. Slight differences in solutions are observed due to truncation of coordinate values recorded in the output report, round-off error in equation solving, and extrapolation approximations for beam-element nodes at the start and end of a pipe group. Of course, the whole purpose of creating the Full-mesh input file is to modify it in order to apply non- symmetric loads and/or material zones to the new mesh. To this end, it is recommended to first execute
Appendix C â CANDE Tool Box Manual C-10 the Full-mesh input file and utilize the GUI Mesh Plot to visualize the nodes, elements and boundary conditions you wish to add or change. 4.2 OPTION 2: Add pavement and/or elastic wearing course.  This option is applicable to any existing Level-3 input file that has a continuous horizontal soil surface. Three sub-options are available: (1) Add pavement layer, (2) Change top layer to and elastic wearing course, and (3) Perform both operations. Each sub-option is explained below. 1. Pavement. Add a pavement layer to the soil surface to take advantage of the real beneficial effects on load-rating analysis. Pavement is modeled with elastic beam elements whose properties are defined by the user in response to screen prompts. Default values represent modest asphalt. ï· Pavement uniform thickness (default = 8.0 inches) ï· Youngâs modulus (default = 200,000 psi) ï· Poisson ratio (default = 0.2) ï· Weight density (default = 140 lbs./ft3) The beam elements are placed over the highest layer of soil elements. Each beam element coincides with the top face of a surface soil element so that the beam-element length matches the soil elementâs surface length. Since beam elements share the same nodes as the soil elements, no new nodes are added to the system, only beam elements. The pavement extends over the entire surface except for the soil elements at the extreme left and extreme right so that pavement does not receive any boundary support from the sides of the mesh. The pavement is formed with BASIC beam elements, which are assigned a group number one digit higher than the highest existing beam group number in the originating input file. 2. Elastic Wearing Course. Change the top row of soil elements from a nonlinear model such as Duncan/Selig or Mohr/Coulomb to an elastic wearing course in order to avoid local failure due to concentrated live loads. Elastic wearing course properties are input by the user in response to screen prompts wherein the default values represent properties of an average soil. ï· Youngâs modulus (default = 1,800 psi) ï· Poisson ratio (default = 0.33) If pavement is not included in the CANDE model, then sub-option 2 is generally required in order to avoid surface failure of nonlinear soil models from concentrated live loads. Engineers do not usually include pavements when designing new installations because construction vehicles operate over soil surface prior to being paved. In such cases, the elastic wearing course is recommended. 3. Pavement plus Wearing Course. Add a pavement layer and change top soil layer to an elastic wearing course. This sub-option is useful when nonconvergence occurs due to sub-pavement soil failure that may occur if the pavement is too flexible. For any of the three sub-options, the new input file is uniquely named by adding the prefix âPave-â to the name of the originating file, and a permanent record of the pavement details and/or wearing course is printed at the end of input file for future reference.
Appendix C â CANDE Tool Box Manual C-11 4.3 OPTION 3: Add live loads on upper surface.  This option is applicable to any existing Level-3 input file that has a continuous horizontal soil surface above the culvert wherein the soil surface may be paved or unpaved. Live loads are simulated by point- like strip forces applied as boundary conditions at specific nodes and load steps. Moving loads are simulated by applying the strip force to a particular node at load-step k and then applying the force to the neighboring node at step k+1 while at the same time removing the strip force from the previous node. This process may be repeated to generate long travel paths and can be generalized for multiple axle loads to simulate truck travel. To make this option as general as possible, the user is required to input a variety of data; however, the default values provided by the program make this task relative easy. The series of data entries and default values are presented below. 1. Identify the pipe-group number of structure subject to live loading . (Default = 1) Often there is only 1 pipe group defined in the input file so that default value often applies. However if multiple pipe groups are defined in the input file, then user selects the group number of the current target structure (Option 3 can repeated for other target group numbers). Once the target structure is identified, the program determines the soil cover height and key node information relative to the target structure and prints the information on the screen for reference. 2. Specify desired truck type â Enter 1, 2 or 3: (Default = 1) ï· Enter 1 for HL93 3-axle Design Truck (as defined by AASHTO) ï· Enter 2 for HL93 2-axle Tandem Truck (as defined by AASHTO) ï· Enter 3 for User-defined truck (N-axles specified by user) If the user enters 1 or 2 no additional truck data is required, and the AASHTO defined truck properties are printed on the screen. If the user enters 3, the following additional data must be supplied: ï· Number of axles (from 1 to 10) ï· Weight of each axle in kips ï· Spacing between axles in feet ï· Wheel footprint dimensions L x W in inches. (Default 10â x 20â for all wheels) ï· Centerline spacing between wheels in feet. (Default 6â for all axles) 3. Answer yes or no to a series of questions on live-load modifications. If the answer is yes, then additional information must be provided, or accept the default value. a) Do you wish to remove previous live loads the input file? If yes, enter the beginning load step numbers of the old live loads. Or accept default. Default = load-step number following the last soil-construction load step. This is a quick way of clearing all previous live-loads in the originating CID file; otherwise, the old live loads will be applied in addition to the new live loads.
Appendix C â CANDE Tool Box Manual C-12 b) Do you wish to add a lane-loading pressure on top surface? If yes, enter the lane pressure in psi units. Or accept default value. Default = 0.444 psi per AASHTO. c) Do you wish to apply a dynamic impact factor to vehicle loads? If yes, enter the impact factor as a fraction of total load. Or accept default calculation. Default = 0.33(1 â H/8), where H is cover height in feet per AASHTO. d) Do you wish to invoke a multi-lane presence factor to increase loads? If yes, enter multi-lane presence factor as a fraction of total load. Or accept default value. Default = 0.2 per AASHTO. Comment on load modifications. The load modifications described in items c and d produce the AASHTO service load value that increases static truck weight. Modifications for longitudinal effects and LRFD load factors are discussed in items 4 and 5, respectively. 4. Do you wish to account for longitudinal load-spreading and 3D stiffness effects? If yes, select the desired method of accounting for longitudinal load spreading and 3D stiffness effects. Whereas longitudianal load spreading is inherent in all culvert installations, the phenomenon of 3D stiffness effects (3DSE) is currently only documented for reinforced concrete boxes and arches under shallow fill, AASHTO Article 4.6.2.10. (For full discussion, see latest vesion of CANDE Solution Methods and Formulations Manual, Chap. 8.1). (1) Enter 1 for the AASHTO Reduced Surface Load (RSL) procedure using AASHTO load- spreading Euations 3.6.1.2.6, (i.e., W(H) = W0 + 1.15H + 0.06*Span/12, where all variables are expressed in inches). RSL reduces the surface load to account for longitudinal load spreading through the soil for 1-wheel or 2-wheel axle loads depending on culvert depth. If requested, 3D stiffnes effects (3DSE) re-adjust the distribution width as required. Note that the term â0.06*Span/12â is realtively new in the AASHTO specifications, and it implies the the reference depth for correcting the surface load is deeper than just the cover depth H, which was the old reference depth used in legacy AASHTO specifications. (2) Enter 2 for the new Continuous Load Spreading (CLS) procedure, which automtically spreads 1- and 2-wheel axle loads by increasing element thicknes as a continuous function of soil depth using the Elasticity-Based-Method for load-spreading. If requested, 3D stiffness effects are also applied to the culvert in a contiuous and mehanistically consistant manner. CLS is considered the most accurate procedure to account for longitudial load-spreading and 3DSE. See latest vesion of CANDE Solution Methods and Formulations Manual, Chap. 8.1.3 for a complete understanding of this revolutionary new procedure.
Appendix C â CANDE Tool Box Manual C-13 (3) Enter -1 for the legacy AASHTO Reduced Surface Load (RSL) procedure using the old AASHTO load-spreading Equation W(H) = W0 + 1.15H (without the âSpanâ term). Otherwise, this choice is identical to (1). AASHTOâs legacy specification is more conservative than AASHTOâs current specification. See latest vesion of CANDE Solution Methods and Formulations Manual, Chap. 8.1.2 for a complete understanding of the currentt AASHTO specifications. If RSL is selected by either 1 or -1, choose a sub-option . Two RSL sub-options are avaiable: (a) constant reduction factor based on minimum soil cover over entire structure, or (b) variable reduction factor based on soil cover between each live-load surface node and the vertical distance to the structureâs periphery. (a) Enter 1 for RSL constant reduction factor for all live-load locations. This is considered the traditional conservative approach (b) Enter 2 for RSL variable reduction factor dependendent on live-load location. This is considered a more realistic approach. For either RSL sub-option, the user has the choice to include 3D stiffness effects (3DSE) to further reduce the surface load in accordaance AASHTO LRFD Specifications 4.6.2.10 for r/c boxes and arches. This choice is activated by entering a non-zero value for the culvert length in response to the following screen request: ï· Enter lay length of precast r/c culvert (feet) â 3DSE is on. ï· Or, enter full length of cast-in-place culvert (feet) â 3DSE is on. ï· Or, enter blank to ignore special 3D effects. â 3DSE is off. The CANDE Tool Box (CTB) computes the RSL reduction factor(s) in two-steps, first load spreading through the soil and then consideration for 3DSE if requested. For load spreading through the soil, the AASHTO Ad Hoc Method (AAM) is employed, which assumes a 30-degree spread beneath the wheel length (W0) as a function of soil depth H. Thus, depending on the userâs choice of the RSL sub-option, H is defined in one of two ways. ï For RSL-suboption (a), H = cover height over crown, a constant value for all live-load locations. ï For RSL-suboption (b), H = variable cover height, i.e., vertical distance between load location on surface and the culvert periphery directly below the loaded node. With the above understanding, CTB caluculates the load-spreading reduction factor for each live- load location in accordance with AASHTO 1-wheel and 2-wheel interaction rules, which are dependent on H and the 2-wheel interaction depth Hint, i.e.; Hint = (S â W0 - D6)/1.15 Where, S = spacing between wheels on axle (inches) W0 = wheel width, typically 20 inches
Appendix C â CANDE Tool Box Manual C-14 6 0.06*Span/12, additional span term for current AASHTO D 0.0, no span term for legacy AASHTO approach ï¬ ï¼ ï½ ï ï½ ï® ï¾ ï¨ ï© ï¨ ï© 0 0 6 int 0 0 6 int W / W + 1.15H + D for H < H Spreading reduction factor = 2W / W + S + 1.15H + D for H H ï¬ ï¼ï¯ ï¯ ï ï½ ï³ï¯ ï¯ï® ï¾ If 3D stiffness effects are activated (3DSE on), enter the culvert 3DSE parameters, Wmin and Wcritical, which are the minimum and critical 3DSE distribution widths, respectively. Or, accept the AASHTO 4.6.2.10 values for r/c box and arch culverts, dependent on the culvertâs span and length. Currently, AASHTO assumes a constant 3DSE distribution width so that Wmin = Wcritical as shown below (all units are inches). ï¨ ï©min critical min criticalW = W = ½ 96.0 + 0.12* , but W & W Culvert lenSpan gth.ï£ Thus, the reduction factor as controlled by 3DSE is given by; n0 min critical min trans H 3DSE reduction factor = W /(W + (W -W )) H Htrans is the transition soil depth wherein the load spreading width is equal to Wcritical, and Hn is the minimum cover for sub-option (a) or the vertical cover beneath the loaded surface node for sub- option (b). Finally, the controlling RSL reduction factor applied to a particular surface load location is given by the minimum value from load spreading and 3DSE calculations. That is, Controlling reduction factor = Minimum of: (load spreading, 3DSE) Comment on RSL methods. RSL sub-option (a) with constant H (soil cover over crown) is the older traditional RSL method that some investigators still prefer. RSL sub-option (b) with variable H (dependent on location of live load) is a newer approach preferred by various practitioners. Clearly for a single live load located directly over the crown both sub-options produce the same results. For multiple axle trucks, sub-option (a) tends to be slightly more conservative, but this is not always the case. If CLS is selected. The CLS method does not require any additional input from the user to simulate load spreading through soil and structure. This is become the CANDE program automatically amplifies the stiffness of each element as a continuous function of soil depth based on the EBM theory of longitudinal load spreading denoted as W(y)..
Appendix C â CANDE Tool Box Manual C-15 If it is also desired to consider 3D stiffness effects (3DSE) for rienforced concrete boxes and arches (AASHTO LRFD Section 4.6.2.10.), then enter a non-zero value to the following screen prompt: ï· Enter lay length of precast r/c culvert (feet) â 3DSE is on. ï· Or, enter full length of cast-in-place culvert (feet) â 3DSE is on. ï· Or, enter blank to ignore special 3D effects. â 3DSE is off. If 3DSE is on , enter the culvert 3DSE parameters, Wmin and Wcritical, which are the minimum and critical 3DSE distribution widths, respectively. Or, accept the AASHTO 4.6.2.10 values for r/c box and arch culverts, dependent on the culvertâs span and length where all units are inches. ï¨ ï©min critical min criticalW = W = ½ Span upper lim96.0 + 0.12* , but W , W Culvert lenit is gth. With the above information, the CLS algorithm in the CANDE program applies the controlling amplification factor to each soil and structure element to simultaneously account for load spreading and 3DSE. For a detailed discussion see latest version of CANDE Solution Methods and Formulations Manual, Chapter 8.1.5. Comment on CLS Method. The CLS method is more accurate than the RSL methods and is easier to use because the CLS method automatically applies the appropriate amplification to each element as a function the element depth beneath the travel surface. No reduction factors are calculated or used; rather, the truckâs service line-load is applied directly to the surface nodes. Thus, the soil beneath the wheel experiences the actual transmitted state of stress, not a reduced stress state like RSL. Although the current AASHTO specifications imply Wmin = Wcritical (one effective parameter), the two parameter methodogy is in anticipation of future changes to the AASHTO LRFD Specifications. 5. Do you wish to apply an LRFD or LRFR load factor to all live-loading steps? If yes, enter load factor applied to all live loads. Or accept default value. Default = 1.75 for ASSHTO LRFD analysis. LRFD (or LRFR) load factors are stored separately at the end of the CANDE input file (E-lines) as a function of load step. Load factors are applied to the service loads generated above prior to each incremental solution obtained at each load step. The beauty of this arrangement is that the user may execute solutions with new load factors without having to regenerate the service loads. 6. Identify load-step number to initiate the first vehicle loading. Enter load-step number to begin vehicle loading. Or accept default load step Default = first load step after construction is complete & lane load is applied. 7. Identify key axle numder for positioning vehicle relative to structure. Enter key axle number of vehicle for positioning. Or accept default axle number. Default = axle number of heaviest axle (first axle number for same weight axles)
Appendix C â CANDE Tool Box Manual C-16 For example, the key axle number for HL93 Design trucks = 2 (2nd axle) 8. Identify the surface node number for the initial key-axle position. Enter surface node number for starting position of key axle. Or accept default node number. Default = the surface node located directly above the left periphery of the structure. 9. Identify the surface node number for the final key-axle position. Enter surface node number for final position of key axle. Or accept default node number. Default = the surface node located directly above the right periphery of the structure. 10. Select node-loading method for axles other than the key axle. Non-key axles are invariably positioned between two adjacent surface nodes, rather than positioned on a single node like the key axle. ï· Enter 1 to apply non-key axle loads at only one node, i.e., the node closest to key- axle position (conseravtive approach). Default method ï· Enter 2 to apply load to both nodes in propotion to the nodeâs promity to the non- key axle load. Thus if the axle is located midway between the nodes, each node would receive 50% of the non-key axle load (reasonable approach). Comment on vehicle travel path. Vehicle travel is from left to right wherein the key-axle is placed at the starting node for the initial live-load step and then advances to the next adjacent node on the next load and so on until the key axle is advanced to the final node position. Thus the number of load-steps associated with vehicle travel is equal to the number of nodes along the key-axle path. All other axles (if any) track in lock-step fashion as dictated by their fixed distances from the key axle. These non-key axle loads are applied to either one node (worst case) or distributed to two nodes (reasonable case) per userâs selection in item 10. The one-node method uses that node of the node pair that is closest to the key-axle load and thereby localizing load contributions, a conservative method. Alternatively, the two-node method may be selected if the one-node appears too conservative. All of the above input data and selections made by the user are permenantly recorded at the end of the new input file. For example, the result of applying Option 3 to a full mesh version of CANDE Tutorial-7 for passage of a tanden truck is copied below.
Appendix C â CANDE Tool Box Manual C-17 4.4 OPTION 4: Minimize Bandwidth.  This option is applicable to any existing Level-3 input file wherein node numbering is not optimum and is alternative to using CANDEâs internal bandwidth minimizer. The downside of CANDEâs internal bandwidth minimizer is that it is time consuming and must be repeated every time the input file is executed. In contrast, the Tool Box bandwidth minimizer creates a permanent change in the nodal numbering scheme within the new input file so that input file may be executed multiple times without the need of any further bandwidth minimization. No additional data is required for Option 4. Bandwidth is proportional to the maximum difference in the nodal numbers assigned to any element. A prime cause of large bandwidths comes from adding nodes and elements into an existing finite model such as introducing an interface or link element between existing elements thereby causing a large mismatch in the elementâs nodal numbers. Another example is a result of Tool Box Option 1 wherein the first row of elements on the mirror side of the centerline contains a fusion of low-numbered and high- numbered node numbers. Thus, applying Option 4 to full Level-3 meshes created from Option 1 is generally a good idea to reduce the time for each CANDE solution. The procedure to minimize bandwidth is to permenantly redefine the nodal numbering, not the coordinate values, but just the node number assigned to the coordinates. This is achieved by starting with node "1"  USERâSELECTED LIVE LOAD PARAMETERS: * Initially applied lane pressure (psi) =  0.4444 * Number of axles on vehicle =  2 * Key axle number for tracking =  1 * Starting node for key axle =  262 * Ending node for key axle =  128 * Beginning vehicle load step # =   8 * Ending vehicle load step # =  16 * Number of nodes loaded for Nonâkey axles =   2  VEHICLE CHARACTERISTICS PER AXLE:   Axle  Axle   Distance to     Wheel LxW    Wheel tire    Wheel line   number     load, lbs  keyâaxle, ft     print, in   spacing, ft  load, lbs/in   1   25000.00    0.00    10 x 20    6.00     625.00   2   25000.00      â4.00    10 x 20    6.00     625.00  MULTIPLIERS ON WHEEL LINEâLOAD DEFINING SERVICE LOAD.  CANDE BOUNDARY CONDITIONS SHOW THE FINAL SERVICE LOAD. * Multilane presence factor (multiplier) =   1.200 * Dynamic impact factor (multiplier) =   1.248  LONGITUDINAL LOAD SPREADING AND 3D STIFFNESS EFFECTS * User selected RSLâconstantâreduction factor procedure. * Wcitical =  55.80, therefore, 3DSE is considered. * Default AASHTO reduction factor is controlled by  Special 3DSE width controls * Value of the default AASHTO reduction factor =   0.358 * User chosen value for constant reduction factor =  0.358  LIVEâLOAD FACTORS FOR LRFD or LRFR ANALYSIS ARE SHOWN  IN THE LAST SEGMENT OF THE ABOVE CANDE INPUT FILE AND ARE  AUTOMATICALLY APPLIED TO THE SERVICE LOADS SHOWN IN THE BCs
Appendix C â CANDE Tool Box Manual C-18 in lower left corner of element located in the lower left corner of the mesh. Node numbers are sequentially increased for the next upward element and so on up to the top surface. Next shiftng to the bottom of the mesh, the process is repeated again and again until the entire mesh has been processed. During the process an â is/wasâ vector is developed that correlates the old node number to the new node number. The is/was vector is used to assign the new node numbers to the element connectivity array and to update the boundary conidtions with the new node numbers. The originating CID file and the new CID file should produce the same results except for round-off error which is less for the new file with the Bmin prefix because there are less calaluations in solving the global system of equations. 4.5 OPTION 5: Calculate Load Rating Factor RF.  This option is applicable to any existing Level-2 or Level-3 output file that contains live loads. Ideally the CANDE analysis should use LRFD methodology, which is directly related to LRFR load rating analysis. Working Stress methodology may be used; however, the user must adjust the applied loads and capacities to represent factored values. The basic assumption is that the associated CANDE input file is developed especially for the particular culvert installation and vehicle being load rated. That is, the load factors, resistance factors, and system parameters are in accordance with the governing LRFR specifications such as ASSHTO Manual for Bridge Evaluation. As defined below, the AASHTO load rating factor RFn must be greater or equal to 1 for all strength- related design criteria in order for a particular vehicle to safely passover the culvert installation. dead n n n live n C - DRF = 1 D ï³ for n = 1, 2, 3 ⦠Equation 5a where, Cn = factored capacity (resistance) for design criterion n. Dndead = factored dead-load demand for dead and earth loads for design criterion n Dnlive = factored live-load demand for vehicle and lane loads for design criterion n n = index number for design criterion, which is dependent on culvert material. Said another way, if RFn ⥠1.0 for all design criterions n =1, 2, 3 â¦, then the culvert safely passes the load-rating test for the particular live load analyzed. The minimum RFn value (simply referred to as RF) is the controlling value, and its value is a multiple of the live-load safety. For example, if RF = 1.80, the culvert system is capable of safely carrying a live-load approximately 1.8 times greater than the magnitude of live-load analyzed. It is important to understand that Equation 5a is exactly equivalent to the LRFD design requirement that the ratio of the total factored demand to factored capacity is less than 1 for all design criteria. That is, total n n n DRatio = 1 C ï£ for n = 1, 2, 3 ⦠Equation 5b where, Dntotal = Dndead + Dnlive = total factored demand for design criterion n.
Appendix C â CANDE Tool Box Manual C-19 To prove that the inequality in Equation 5b is exactly equivalent to the inequality in Equation 5a, muliply both sides of inequality 5b by the factored capacity Cn , then replace Dntotal with the above component definition and subtract Dndead from both sides, and finally divide by Dnlive to get the same inequality shown in 5a. Since CANDE automatically computes Equation 5b in the âassessment summaryâ at the end of each load step, the equivalence of the inequalities expressed in Equations 5a and 5b has the following useful benefit. If the CANDE solution shows that the assessment summaries satisfy, Ration < 1.0, for all load steps and all design criteria, then it is guaranteed that all RFn > 1, meaning the live-load safely passes the load rating test. The opposite is also true, if Ration > 1.0 at any load step and for any design criterion, then it is guaranteed that RFn < 1, meaning the live-load did not safely pass the load rating test. Thus, if an engineer only wants to know if a particular vehicle passes the load rating test (RF ⥠1), then it is only necessary to scan the CANDE assessment summaries to verify that all Ratios are ⤠1 for all load steps. On the other hand, if an engineer wants to know the controlling RFn values, then a much more extensive search through the CANDE output report is required, not just the assessment summaries. This is because the load step and node where Ration is maximum is not necessarily the same load step and node where RFn is minimum. Only in the case Ration = RFn = 1, can it be guaranteed that controlling demand- to-capacity ratio and the controlling load-rating factor occur at the same node and load step. To initiate load-rating process (Option 5), the user is requested to identify the pipe group number under investigation, the load-step number that completes dead loads, and the live-load step numbers that define the start and end of the vehicle path whether it be 1 step or many. As noted below the CTB program provides reasonable default values that may be accepted in lieu of entering data. 1. Enter pipe-group number of structure to be load rated. Or, accept default value = 1. Often there is only 1 pipe group in the input file so that the default value usually applies. However if multiple pipe groups are defined, then choose the group number of the desired structure to be load rated. Other structures (groups) may be load rated on repeated applications of Option 5. 2. Enter load-step number, Stepdead, demarking the completion of dead loads. Or accept default, Stepdead = highest load-step number found in the element property array. 3. Enter load-step number for start of live loads, StepLL-start. Or accept default, StepLL-start = Stepdead + 1, (i.e., begin live-load steps following last dead load) 4. Enter load-step number for end of live loads, StepLL-end. Or accept default, StepLL-end = Last load step, (i.e., input value NINC). The CANDE Tool Box (CTB) program undertakes a brute force search through the CANDE output file to collect all the relevant data needed to ultimately determine the controlling RF value (minimum), along with the associated load-step number (vehicle location), design criterion (failure mode), and node number (location in structure). The CTB step-by-step search and data collection procedure is described below: a) From the assessment summaries at the end of each load step, the controlling demand and capacity values are collected for each design criterion at the controlling node with highest demand-to- capacity ratio. From this set of data, CTB verifies the demands of the dead-load step (Stepdead) do not exceed the corresponding capacities for all design criteria, i.e., Ration ⤠1. If this is not true,
Appendix C â CANDE Tool Box Manual C-20 then dead-load demand already exceeds the capacity so that any additional live loading is not safe (negative rating factor). If this occurs, the load rating analysis is terminated and a message is printed on the screen and the output report describes the dead-load condition. b) Next, CTB undertakes a much larger data collection process to find and store demand and capacity values in large 3-component arrays, i.e., values for each design criteria, load step and node. The collection process is complicated by the different design criteria and diagnostic formats for each pipe type. In particular, the recovery of factored capacities requires melding information from the assessment summaries and pipe-type diagnostic data. The large 3-compnent array is used to extract three subsets of load-rating data that are printed, called tertiary, secondary and primary data sets. c) CTBâs tertiary information is the most comprehensive set of printed load-rating data and shows the controlling RF-values at each node as a separate list under each design criterion. Each nodeâs controlling rating factor is determined by finding the lowest rating factor observed over all live- load steps (StepLL-star to StepLL-end.), and the controlling load step is also shown on the list. d) CTBâs secondary information identifies the controlling RF-values for each design criterion along with the associated node and load step. The secondary information is a subset of the tertiary set wherein the node with the lowest RF-value is identified as the controlling node for that design criterion. e) Finally, CTBâs primary data is the bottom line information that identifies the overall controlling RF-value along with the controlling design criterion, load step and node. The above process could be accomplished manually by the user, but with a great deal of difficulty. Option 5 provides an automated data retrieval process and error-free calculation of RF-values. Primary, secondary, and tertiary data sets and all supporting information are printed at the end of the CANDE output report so that all information is available in one document. An illustration of the Option 5 printout is shown below for the previous example input/output file illustrated for Option 3, named Live-Pave-Full-Tutorial-7. The load-rating summary is printed immediately following the message, Normal Exit from CANDE, which marks the end of the normal CANDE output report. * * * * NORMAL EXIT FROM CANDE * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * CANDE TOOL BOX -- LOAD RATING REPORT. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * LOAD RATING SUMMARY FOR PIPE-GROUP = 1, PIPE TYPE = CONCRETE CANDE FILE NAME: Live-Pave-Full-Tutorial-7.out
Appendix C â CANDE Tool Box Manual C-21 USER-DEFINED KEY LOAD STEPS FOR LOAD RATING ANALYSIS: * Load step used for dead/earth load RF reference = 6 * Load step beginning live-load search range = 7 * Load step terminating live-load search range = 16 BOTTOM LINE FINDINGS FOR LOAD RATING OF CULVERT * Controlling design criterion = STEEL YIELDING (psi) * Controlling load-rating factor RF = 1.17 * Controlling local-node number = 20 * Controlling live-load step number = 10 * Safety assessment of culvert = SAFE LOWEST RATING FACTORS PER DESIGN CRITERION AT CONTROLLING LOAD STEP AND NODE: DESIGN-CRITERION LOAD LOCAL DEAD-LOAD LIVE-LOAD EFFECTIVE *RATING (Strength) STEP NODE DEMAND DEMAND CAPACITY FACTOR *STEEL YIELDING (psi) 10 20 1972.64 48410.19 58500.00 1.17 *CONCRETE CRUSHING (psi) 10 20 539.34 1427.05 3750.00 2.25 *SHEAR FAILURE (lbs/in) 13 26 175.66 318.76 973.00 2.50 *RADIAL-TENSION FAIL (psi) 16 1 0.00 0.03 61.10 2036.67 DEFINITIONS AND RELATIONS FOR EACH CRITERION "n": * Rating Factor(n) = (Capacity(n) - Dead(n))/Live(n) * Total Demand(n) = Dead(n) + Live(n) at specified node * Dead(n) = Dead load demand for criterion n (factored) * Live(n) = Live load demand for criterion n (factored) * Capacity(n) = Capacity for criterion n (factored) - - - - - - - - - - ADDITIONAL DIAGNOSTICS FOR ALL NODES - - - - - - - - - - DIAGNOSTICS FOR 4 STRENGTH DESIGN CRITERIA FOR CONCRETE RATING FACTORS LISTED FOR ALL NODES AT CONTROLLING STEP DESIGN CRITERION # 1 = STEEL YIELDING (psi) LOCAL LOAD DEAD-LOAD LIVE-LOAD EFFECTIVE RATING NODE# STEP# DEMAND DEMAND CAPACITY FACTOR 1 14 1528.27 24656.69 58500.00 2.31 2 15 1401.07 23155.68 58500.00 2.47 3 16 1016.92 1057.20 58500.00 54.37 4 11 370.16 539.96 58500.00 107.66 5 13 172.30 704.42 58500.00 82.80 6 13 788.82 45162.98 58500.00 1.28 7 13 1067.77 1626.28 58500.00 35.32 8 14 1293.09 757.28 58500.00 75.54 9 15 1589.47 28003.94 58500.00 2.03 10 16 1972.64 45471.52 58500.00 1.24 11 16 786.17 248.49 58500.00 232.26 12 16 416.10 349.57 58500.00 166.16 13 11 1013.71 285.38 58500.00 201.44 14 12 2018.81 38057.50 58500.00 1.48 15 14 40422.08 6462.12 58500.00 2.80 16 15 2018.81 37939.91 58500.00 1.49 17 15 1013.71 287.47 58500.00 199.97 18 9 416.10 481.38 58500.00 120.66
Appendix C â CANDE Tool Box Manual C-22 19 9 786.17 299.37 58500.00 192.78 20 10 1972.64 48410.19 58500.00 1.17 21 12 1589.47 1097.79 58500.00 51.84 22 13 1293.09 705.88 58500.00 81.04 23 14 1067.77 27718.34 58500.00 2.07 24 14 788.82 42166.68 58500.00 1.37 25 14 172.30 717.39 58500.00 81.31 26 9 370.16 827.84 58500.00 70.22 27 10 1016.92 1145.57 58500.00 50.18 28 12 1401.07 23032.95 58500.00 2.48 29 14 1528.27 24677.12 58500.00 2.31 DESIGN CRITERION # 2 = CONCRETE CRUSHING (psi) LOCAL LOAD DEAD-LOAD LIVE-LOAD EFFECTIVE RATING NODE# STEP# DEMAND DEMAND CAPACITY FACTOR 1 14 283.43 1078.51 3750.00 3.21 2 15 257.64 1009.40 3750.00 3.46 3 16 179.61 216.93 3750.00 16.46 4 12 48.46 122.22 3750.00 30.29 5 13 38.62 136.53 3750.00 27.18 6 13 239.03 1506.76 3750.00 2.33 7 14 311.35 334.50 3750.00 10.28 8 14 373.05 213.05 3750.00 15.85 9 15 448.44 1153.06 3750.00 2.86 10 16 539.34 1337.56 3750.00 2.40 11 16 174.28 51.85 3750.00 68.96 12 16 130.99 71.68 3750.00 50.49 13 10 251.49 53.76 3750.00 65.08 14 11 451.31 950.92 3750.00 3.47 15 15 1421.24 204.02 3750.00 11.41 16 15 451.31 950.35 3750.00 3.47 17 16 251.49 53.91 3750.00 64.90 18 8 130.99 105.93 3750.00 34.16 19 9 174.28 61.58 3750.00 58.07 20 10 539.34 1427.05 3750.00 2.25 21 11 448.44 216.18 3750.00 15.27 22 13 373.05 200.43 3750.00 16.85 23 14 311.35 1203.96 3750.00 2.86 24 14 239.03 1392.18 3750.00 2.52 25 14 38.62 137.93 3750.00 26.91 26 9 48.46 165.21 3750.00 22.41 27 10 179.61 234.53 3750.00 15.22 28 12 257.64 1010.24 3750.00 3.46 29 14 283.43 1079.04 3750.00 3.21 DESIGN CRITERION # 3 = SHEAR FAILURE (lbs/in) LOCAL LOAD DEAD-LOAD LIVE-LOAD EFFECTIVE RATING NODE# STEP# DEMAND DEMAND CAPACITY FACTOR 1 16 0.32 113.98 973.00 8.53 2 12 56.39 153.78 973.00 5.96 3 13 113.63 228.34 973.00 3.76 4 14 175.66 311.20 973.00 2.56 5 15 143.20 143.63 2117.71 13.75 6 16 75.04 0.00 973.00 10000.00 7 16 66.56 0.00 973.00 10000.00 8 16 68.33 10.44 973.00 86.65 9 16 85.02 24.20 973.00 36.69 10 16 118.35 34.40 973.00 24.84 11 14 193.57 46.56 2117.71 41.33 12 16 448.40 97.60 973.00 5.37 13 16 290.65 62.28 973.00 10.96
Appendix C â CANDE Tool Box Manual C-23 14 16 142.38 35.47 973.00 23.42 15 9 0.00 17.63 973.00 55.19 16 9 142.38 39.59 973.00 20.98 17 9 290.65 67.63 973.00 10.09 18 10 448.40 103.50 973.00 5.07 19 13 193.57 44.23 2117.71 43.50 20 8 118.35 72.27 973.00 11.83 21 8 85.02 65.20 973.00 13.62 22 8 68.33 58.37 973.00 15.50 23 8 66.56 51.40 973.00 17.64 24 8 75.04 43.08 973.00 20.84 25 12 143.20 147.14 2117.71 13.42 26 13 175.66 318.76 973.00 2.50 27 14 113.63 234.25 973.00 3.67 28 15 56.39 158.74 973.00 5.77 29 10 0.32 117.44 973.00 8.28 DESIGN CRITERION # 4 = RADIAL-TENSION FAIL (psi) LOCAL LOAD DEAD-LOAD LIVE-LOAD EFFECTIVE RATING NODE# STEP# DEMAND DEMAND CAPACITY FACTOR 1 16 0.00 0.03 61.10 2036.67 2 16 0.00 0.03 61.10 2036.67 3 16 0.00 0.00 61.10 10000.00 4 16 0.00 0.00 61.10 10000.00 5 16 0.00 0.00 61.10 10000.00 6 16 0.00 0.00 61.10 10000.00 7 16 0.00 0.00 61.10 10000.00 8 16 0.00 0.00 61.10 10000.00 9 16 0.00 0.00 61.10 10000.00 10 16 0.00 0.00 61.10 10000.00 11 16 0.00 0.00 61.10 10000.00 12 16 0.00 0.00 61.10 10000.00 13 16 0.00 0.00 61.10 10000.00 14 16 0.00 0.02 61.10 3055.00 15 16 0.02 0.01 61.10 6108.00 16 16 0.00 0.02 61.10 3055.00 17 16 0.00 0.00 61.10 10000.00 18 16 0.00 0.00 61.10 10000.00 19 16 0.00 0.00 61.10 10000.00 20 16 0.00 0.00 61.10 10000.00 21 16 0.00 0.00 61.10 10000.00 22 16 0.00 0.00 61.10 10000.00 23 16 0.00 0.00 61.10 10000.00 24 16 0.00 0.00 61.10 10000.00 25 16 0.00 0.00 61.10 10000.00 26 16 0.00 0.00 61.10 10000.00 27 16 0.00 0.00 61.10 10000.00 28 13 0.00 0.03 61.10 2036.67 29 16 0.00 0.03 61.10 2036.67
Appendix D â 2D Analysis Backup Dâ1 Appendix D â 2D Analysis BackupÂ
Appendix D â 2D Analysis Backup Dâ2 Model 1 Analysis Backup Input Information Meshes for Model 1 were generated for fills of 0.97â, 2â, 5â and 10â. Using the CANDE ToolBox, different fill depth meshes can be generated if needed for Phase III. M1C1 â Juniata County SR 3020 PennDOT, 25â 0â span box section â Site/Structure Information Depth of Fill (road centerline): Invert elevation:  491.98 ft Top of pavement: 501.45 ft Top of box to top of pavement: 0.97 ft Bedding depth:   18 in. Precast Box Geometry: Span x Rise x Length: 25 ft x 7.5 ft x 4.458 ft Top/Bottom/Sidewall: 14 in., 14 in., 12 in. Haunches: 12 in. x 12 in. top & bottom Reinforcement (Sections 2 thru 6): in.2/ft in.2/in.  Clear cover  AS1 â outside:  C601@ 4 in.  1.320 0.110  2 in.  AS2 â top inside: #8@ 5 in. 1.896 0.158  2 in. AS3 â bottom inside: #8@ 5 in. 1.896 0.158 2.5 in. (run with 2 in. â CANDE only accepts one value â change in level 3) AS4 â side inside #4@ 10 in. 0.240 0.020  2 in. AS5 â top outside #4@ 12 in. 0.200 0.017  2 in. AS6 â bottom outside #6@ 12 in. 0.440 0.037  2 in. Note: Box is postâtensioned longitudinally Materials: Reinforcement yield stress: 60 ksi  Concrete fâc:  5 ksi CANDE Model notes: Concrete tensile rupture strain: 0.0001 in./in. (typically neglected in design, but used for analysis) ~7 fâc0.5  In situ â linear elastic   E = 5,000 psi, Poisson = 0.3 â both assumedÂ
Appendix D â 2D Analysis Backup   Dâ3  Bedding â 18 in. structure backfill, 6 in. No. 8 stone      Duncan Selig â SW100 (assume well compacted) Backfill â Assumed   Duncan/Selig â SW95  Input for level 3 CANDE model for concrete area clear/ center to bar  Node Number Thickness AS (inner cage) In2/in AS (outer cage) in2/in Clear Cover (inner) (in) Clear Cover (outer) (in) 1 14 0.158 0.0167 2.5 2.25 2 14 0.158 0.0167 2.5 2.25 3 14 0.158 0.0167 2.5 2.25 4 14 0.158 0.11 2.5 2.375 5 25 0.158 0.11 2.5 2.375 6 12 0.02 0.11 2.25 2.375 7 12 0.02 0.11 2.25 2.375 8 12 0.02 0.11 2.25 2.375 9 12 0.02 0.11 2.25 2.375 10 12 0.02 0.11 2.25 2.375 11 25 0.158 0.11 3 2.875 12 14 0.158 0.11 3 2.875 13 14 0.158 0.037 3 2.875 14 14 0.158 0.037 3 2.875 15 14 0.158 0.037 3 2.875 16 14 0.158 0.037 3 2.875 17 14 0.158 0.11 3 2.875 18 14 0.158 0.11 3 2.875 19 25 0.158 0.11 3 2.875 20 12 0.02 0.11 2.25 2.375 21 12 0.02 0.11 2.25 2.375 22 12 0.02 0.11 2.25 2.375 23 12 0.02 0.11 2.25 2.375 24 12 0.02 0.11 2.25 2.375 25 25 0.158 0.11 2.5 2.375 26 14 0.158 0.11 2.5 2.375 27 14 0.158 0.0167 2.5 2.25 28 14 0.158 0.0167 2.5 2.25 29 14 0.158 0.0167 2.5 2.25   Â
Appendix D â 2D Analysis Backup Dâ4 The live load distributions (see Table 1 below) for CANDE are in accordance with AASHTO, and were computed through a spreadsheet from Dr. McGrath.  Briefly:Â ï· Concrete culverts and arches, H<2 ft: Strip width from 4.6.2.10 ï· Concrete culverts and arches, Hâ¥2 ft: Section 3.6.1.2.6 (note that the LLDF for concrete pipe is variable with diameter). ï· Concrete pipe and flexible pipe, H<1 ft: Special analysis ï· Concrete pipe and flexible pipe, Hâ¥1 ft: Section 3.6.1.2.6 Table 1 â Reduction of surface load for varying fills for Model 1 Fill Depth (ft) RSL 0.97 0.303 2 .177 5 0.142 10 0.070 Sample Spreadsheet Calculation for Model 1 for a fil depth of 2â.Â
Appendix D â 2D Analysis Backup   Dâ5  CANDE output results Figure 1 displays a typical CANDE plot of model 1 with the Tandem vehicle near midspan. CANDE models the vehicle by using load steps. Each load step removes the subsequent vehicle and places it at its new locations. Figure 2 displays the dead load moment diagrams for the first 6 load steps (incremental fill levels), while Figure 3 displays the live load envelope for the tandem vehicle for all of the live load steps (7â23). Figure 4 displays the deflection (magnified by 40) and shear stress as the tandem vehicle steps across the culvert.  Figure 1 â M1C1 Vertical strain with Tandem Vehicle near midspan (no pavement)    Figure 2 â M1C1â CANDE Bending Moment  â Dead load envelope â Load steps 1â6Â
Appendix D â 2D Analysis Backup Dâ6 Figure 3 â M2C1 â CANDE bending moment envelope â live load steps â load steps 7â23 (2 axle Tandem ,25 kip/axle) (without pavement)Â
Appendix D â 2D Analysis Backup   Dâ7       Figure 4 â M1C1 showing shear stress as Tandem vehicle moves across culvert (0.97â fill, no pavement) Â
Appendix D â 2D Analysis Backup Dâ8 Figure 5 below provides a sample of the CANDE output load rating report for the no pavement and 0.97â fill. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * CANDE TOOL BOX -- LOAD RATING REPORT. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * LOAD RATING SUMMARY FOR PIPE-GROUP = 1, PIPE TYPE = CONCRETE CANDE FILE NAME: Live-TANDEM-Full-M1C1-1ftFill-ModMeshGen.out User-defined key load steps for Load Rating Analysis: * Load step used for dead/earth load RF reference = 6 * Load step beginning live-load search range = 7 * Load step terminating live-load search range = 23 LOAD-STEP NUMBER CAUSING LARGEST STRUCTURAL DISTRESS = 19 DEMANDS & CAPACITIES FOR EACH STRENGTH CRITERION ARE BELOW. DESIGN-CRITERION GROUP DEAD-LOAD LIVE-LOAD TOTAL *RATING (Strength) NODE # DEMAND DEMAND CAPACITY FACTOR STEEL YIELDING (psi) 6 9370.09 29567.11 54000.00 1.51 CONCRETE CRUSHING (psi) 6 1038.72 1679.48 3750.00 1.61 SHEAR FAILURE (lbs/in) 4 301.22 714.68 1330.70 1.44 RADIAL-TENSION FAIL (psi 2 0.00 0.00 61.10 10000.00 DEFINITIONS AND RELATIONS FOR EACH CRITERION "n": * Rating Factor(n) = (Capacity(n) - Dead(n))/Live(n) * Total Demand(n) = Dead(n) + Live(n) at specified node * Dead(n) = Dead load demand for criterion n (factored) * Live(n) = Live load demand for criterion n (factored) * Capacity(n) = Capacity for criterion n (factored) BOTTOM LINE FINDINGS FOR LOAD RATING OF CULVERT * Controlling design criterion = SHEAR FAILURE (lbs/in) * Controlling load-rating factor RF = 1.44 * Controlling group-node number = 4 * Controlling live-load step number = 19 * Safety assessment of culvert = SAFE Figure 5 â CANDE load rating report Model 1 (Tandem Vehicle, no pavement, 0.97â fill)Â
Appendix D â 2D Analysis Backup   Dâ9  Pavement Rating Results A parametric study was performed on the model by varying the fill height in increments. Models were built for fill heights of 0.97â, 2â, 5â, and 10â. The CANDE model with 5â of fill is shown in Figure 6. Note that while the pavement elements are SHOWN at different thicknesses, they are actually this same thickness. This is a glitch in the CANDE graphics software. For fill models of 2â and over, the CANDE shear option for LRFD for fills over 2â was selected. Each model was also reviewed for no pavement and 3 varying pavements. The rating results produced by the CANDE toolbox are provide in Table 2. The vehicle used for loading is the LRFD Tandem vehicle (2â25kip axles spaced at 4â). The node numbering referenced in the table is shown in Figure 7.  There is a noticeable jump in the shear ratings when moving from 0.97â to 2â of fill. The 2â fill takes advantage of the LRFD increase in capacity over the 2â fill level. This is discussed in more in detail under Task 5. For fill levels of 10â, this culvert fails under dead load.  Figure 6 â CANDE model M1C1 with 5â of backfill and pavement   Â
Appendix D â 2D Analysis Backup Dâ10 Table 2 â Model 1 âCANDE Rating Factors (from CANDE Toolbox) Tandem vehicle, without and with pavement (varying fill depths)  Rating No pavement E = 200,000 psiÂ Â ï® = 0.33 Pavement (6â) E = 400,000 psiÂ Â ï® = 0.33 Pavement (6â) E = 600,000 psiÂ Â ï® = 0.33 Pavement (6â) 0.97 ft fill Steel Yielding   1.41(Node 6) 1.47 (Node 6) 1.48 (Node 6) 1.49 (Node 6) Concrete Crushing   1.52(Node 6) 1.55 (Node 6) 1.56 (Node 6) 1.56 (Node 6) Shear Failure* 1.44 (Node 4) 1.84 (Node 4) 1.84 (Node 4) 1.85 (Node 4) RadialâTension Fail   1222.0(Node 1) 1527.25 (Node 29) 1527.25 (Node 29) 1527.25 (Node 29) *Note Uses the < 2â fill shear option in CANDE 2.0 ft fill Steel Yielding 2.18 (Node 24) 2.42 (Node 6) 2.46 (Node 6) 2.49 (Node 6) Concrete Crushing 2.06 (Node 24) 2.15 (Node 6) 2.17 (Node 6) 2.18 (Node 6) Shear Failure 4.86 (Node 26) 5.33 (Node 4) 5.39 (Node 4) 5.43 (Node 4) RadialâTension Fail 3054 (Node 1) 3054 (Node 29) 3054 (Node 29) 3054 (Node 29) 5.0 ft fill Steel Yielding 2.22  (Node 6) 2.26 (Node 6) 2.32 (Node 6) 2.36 (Node 6) Concrete Crushing 3.81 (Node 6) 3.74 (Node 6) 3.86 (Node 6) 3.91 (Node 6) Shear Failure 7.22 (Node 4) 6.97 (Node 4) 7.86 (Node 4) 7.63 (Node 4) RadialâTension Fail 3055 (Node 27) 6107 (Node 29) 6107 (Node 29) 6107 (Node 29) 10.0 ft fill Steel Yielding â0.74** (Node 6) 0.61** (Node 6) 0.61** (Node 6) 0.61** (Node 6) Concrete Crushing 1.55 (Node 24) 2.14 (Node 6) 2.19 (Node 6) 2.22 (Node 6) Shear Failure 11.67 (Node 26) 14.39 (Node 4) 14.61 (Node 4) 14.75 (Node 4) RadialâTension Fail 1526 (Node 27) 1526 (Node 1) 1526 (Node 1) 1526 (Node 1)  **Fails under dead loadÂ
Appendix D â 2D Analysis Backup   Dâ11  * â Note: These were transcription errors in Interim Report #2 that have been corrected.  Figure 7 â Beam node numbering for M1C1 Generated BrDR Model Model 1 was also input into the AASHTOWare BrDR software and run for varying fill heights (1.99â, 2.00â, 5â, 7â, 8â, and 10â). The reinforcement schematic from BrDR is shown in Figure 8. The LRFR ratings (HL93) are shown in Table 3. The ratings are provided at each fill height. For comparison purposes, the LFR rating was performed with the HS25 vehicle. The ratings for LFR are provided as well.  Figure 8  â BrDR Model M1C1 reinforcement schematic Table 3 â BrDR Model M1C1 ratings â LFR/LRFR Fill LRFR Ratings LFR (Ratings) Culvert M1C1  (1.99' fill) HLâ93 (US) 0.727 0.943 HSâ25 0.675 1.127 Culvert M1C1  (2.00' fill) HLâ93 (US) 1.063 1.378 HSâ25 0.783 1.308 Culvert M1C1  (5.00' fill) HLâ93 (US) 1.025 1.329 HSâ25 0.723 1.207 Culvert M1C1  (7.00' fill) HLâ93 (US) 0.353 0.458 HSâ25 0 0 Culvert M1C1  (8.00' fill) HLâ93 (US) 0 0 HSâ25 0 0 Culvert M1C1  (10.00' fill) HLâ93 (US) 0 0 HSâ25 0 0Â
Appendix D â 2D Analysis Backup Dâ12 For the LRFR ratings, a noticeable step can be seen from a fill of 1.99â to 2.00â. For 1.99â the controlling inventory rating of 0.727 is governed by shear in the top slab near the support at the critical shear distance. For the fill of 2â, the controlling inventory rating of 1.063 is governed by flexure in the center of the top slab. This difference is due primarily to the difference in the calculation of concrete shear capacity at the 2â fill level. For fills under 2â of fill the concrete shear capacity Vc is calculated using equation 5.8.3.3â3 (7th Edition, AASHTO LRFD specification) 5.7.3.3â3 (8th Edition). For fills over 2â, Vc is calculated using equation 5.14.5.3â1 (7th Edition, AASHTO LRFD specification) 5.12.7.3â1 (8th Edition) (see Figure 9).  Figure 9 â LRFD Spec Comparison of concrete shear resistance at 2â fill level For model 1 the calculations of the concrete shear capacity and overall shear resistance are presented in Table 4. This jump in shear capacity is discussed more under Task 5. Table 4  â BrDR Model M1C1 shear capacity comparison at 1.99â fill and 2.00â fill Fill depth Inv Rating Oper Rating Concrete Shear Resistance Vc (kips) Steel Shear Resistance Vs (kips) Shear Resistance Vr (kips) Culvert M1C1  (1.99' fill) HLâ93 (US) 0.727 0.943 14.9* 0 12.7 Culvert M1C1  (2.00' fill) HLâ93 (US) 1.063 1.378 24.7 0 21.0 *Note: This uses the AASHTO LRFD Simplified for shear and not the iterative shear method provided in Appendix B of AASHTO. The Appendix B option is not available for culverts in BrDR.
Appendix D â 2D Analysis Backup   Dâ13  Model 2 Analysis Backup Input Information Meshes for Model 2 were generated for fills of 2âand 5â. Using the CANDE ToolBox, different fill depth meshes can be generated if needed for Phase III. The reduction of surface load factor for Model 2 is shown in Table 5 for each fill height. Table 5 â Reduction of surface load for varying fills for Model 2 Fill Depth (ft) RSL 2 0.177 5 0.142  The live load distributions for CANDE are in accordance with AASHTO, and were computed through a spreadsheet from Dr. McGrath. A sample of the spreadsheet is provided in this appendix under âModel 1 Analysis Backupâ.  Briefly:Â ï· Concrete culverts and arches, H<2 ft: Strip width from 4.6.2.10 ï· Concrete culverts and arches, Hâ¥2 ft: Section 3.6.1.2.6 (note that the LLDF for concrete pipe is variable with diameter). ï· Concrete pipe and flexible pipe, H<1 ft: Special analysis ï· Concrete pipe and flexible pipe, Hâ¥1 ft: Section 3.6.1.2.6 Reinforcement Input for BrDR (Based on labeling in Figure 10) Bar Mark Type Bar Number  Spacing (in) A B C H area area/in A1 Corner 7  24 5.25 6.83     0.6 0.025 A2 C Bar 7  24 8.5 4 4   0.6 0.025 A3 Straight 8  24 13       0.79 0.032917 A4 Hook 8  24   8     0.79 0.032917 A5 Bent 6  24 8.25 6.167 8.25 0.5417 0.44 0.018333 A6 Straight 4  12 8.5       0.2 0.016667 A7 Straight 4  18 8.5       0.2 0.011111 A8 Straight 8  24 22.667       0.79 0.032917 Reinforcement Input for CANDE (based on node numbering in Figure 10) Node Bar 1  Bar 2  Bar 3 Area 1 Area 2 Area 3 CANDE input Node Inner Cage                 1 a8     0.032917 0 0 0.033 1 2 a8     0.032917 0 0 0.033 2 3 a8 a5   0.032917 0.018333 0 0.051 3 4 a8 a5   0.032917 0.018333 0 0.051 4 5 a8 a5   0.032917 0.018333 0 0.051 5Â
Appendix D â 2D Analysis Backup Dâ14 Node Bar 1  Bar 2  Bar 3 Area 1 Area 2 Area 3 CANDE input Node 6 a6 0.016667 0 0 0.017 6 7 a6 0.016667 0 0 0.017 7 8 a6 0.016667 0 0 0.017 8 9 a6 0.016667 0 0 0.017 9 10 a6 0.016667 0 0 0.017 10 11 a6 0.016667 0 0 0.017 11 12 a8 a5 0.032917 0.018333 0 0.051 12 13 a8 a5 0.032917 0.018333 0 0.051 13 14 a8 0.032917 0 0 0.033 14 15 a8 0.032917 0 0 0.033 15 16 a8 0.032917 0 0 0.033 16 17 a8 a5 0.032917 0.018333 0 0.051 17 18 a8 a5 0.032917 0.018333 0 0.051 18 19 a8 a5 0.032917 0.018333 0 0.051 19 20 a6 0.016667 0 0 0.017 20 21 a6 0.016667 0 0 0.017 21 22 a6 0.016667 0 0 0.017 22 23 a6 0.016667 0 0 0.017 23 24 a6 0.016667 0 0 0.017 24 25 a8 a5 0.032917 0.018333 0 0.051 25 26 a8 a5 0.032917 0.018333 0 0.051 26 27 a8 a5 0.032917 0.018333 0 0.051 27 28 a8 0.032917 0 0 0.033 28 29 a8 0.032917 0 0 0.033 29 Outer cage 1 a3 a4 a5 0.032917 0.032917 0.018333 0.084 1 2 a3 a4 a5 0.032917 0.032917 0.018333 0.084 2 3 a3 a1 0.032917 0.025 0 0.058 3 4 a1 a2 0.025 0.025 0 0.050 4 5 a1 a2 0.025 0.025 0 0.050 5 6 a1 a2 0.025 0.025 0 0.050 6 7 a1 a2 0.025 0.025 0 0.050 7 8 a1 a2 0.025 0.025 0 0.050 8 9 a1 a2 0.025 0.025 0 0.050 9 10 a1 a2 0.025 0.025 0 0.050 10 11 a1 a2 0.025 0.025 0 0.050 11 12 a1 a2 0.025 0.025 0 0.050 12 13 a1 a3 0.025 0.032917 0 0.058 13 14 a3 a4 a5 0.032917 0.032917 0.018333 0.084 14 15 a3 a4 a5 0.032917 0.032917 0.018333 0.084 15Â
Appendix D â 2D Analysis Backup   Dâ15  Node Bar 1  Bar 2  Bar 3 Area 1 Area 2 Area 3 CANDE input Node 16 a3 a4 a5 0.032917 0.032917 0.018333 0.084 16 17 a1 a3   0.025 0.032917 0 0.058 17 18 a1 a2   0.025 0.025 0 0.050 18 19 a1 a2   0.025 0.025 0 0.050 19 20 a1 a2   0.025 0.025 0 0.050 20 21 a1 a2   0.025 0.025 0 0.050 21 22 a1 a2   0.025 0.025 0 0.050 22 23 a1 a2   0.025 0.025 0 0.050 23 24 a1 a2   0.025 0.025 0 0.050 24 25 a1 a2   0.025 0.025 0 0.050 25 26 a1 a2   0.025 0.025 0 0.050 26 27 a3 a1   0.032917 0.025 0 0.058 27 28 a3 a4 a5 0.032917 0.032917 0.018333 0.084 28 29 a3 a4 a5 0.032917 0.032917 0.018333 0.084 29  Figure 10 â M2C1 reinforcement labeling CANDE output results Figure 11 displays a typical CANDE plot of model 2 with the Tandem vehicle near midspan. CANDE models the vehicle by using load steps. Each load step removes the subsequent vehicle and places it at its new locations. Figure 12 displays the dead load moment diagrams for the first 6 load steps (incremental fill levels), while Figure 13 displays the live load envelope for the tandem vehicle for all of the live load steps (7â23). Figure 14 displays the deflection (magnified by 30) and shear stress as the tandem vehicle steps across the culvert.Â
Appendix D â 2D Analysis Backup Dâ16 Figure 11 â M2C1 Vertical strain with Tandem Vehicle near midspan (no pavement) Figure 12 â M2C1â CANDE Bending Moment  â Dead load envelope â Load steps 1â6 Figure 13 â M2C1 â CANDE bending moment envelope â live load steps â load steps 7â23 (2 axle Tandem ,25 kip/axle) (without pavement)Â
Appendix D â 2D Analysis Backup   Dâ17        Figure 14 â M2C1 showing shear stress as Tandem vehicle moves across culvert (5â fill, no pavement) Â
Appendix D â 2D Analysis Backup Dâ18 Figure 15 below provides a sample of the CANDE output load rating report for the no pavement and 0.97â fill. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * CANDE TOOL BOX -- LOAD RATING REPORT. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * LOAD RATING SUMMARY FOR PIPE-GROUP = 1, PIPE TYPE = CONCRETE CANDE FILE NAME: Live-Full-M2C1-5ftFill-ModMesh.out User-defined key load steps for Load Rating Analysis: * Load step used for dead/earth load RF reference = 6 * Load step beginning live-load search range = 7 * Load step terminating live-load search range = 23 LOAD-STEP NUMBER CAUSING LARGEST STRUCTURAL DISTRESS = 11 DEMANDS & CAPACITIES FOR EACH STRENGTH CRITERION ARE BELOW. DESIGN-CRITERION GROUP DEAD-LOAD LIVE-LOAD TOTAL *RATING (Strength) NODE # DEMAND DEMAND CAPACITY FACTOR STEEL YIELDING (psi) 29 24071.08 7601.92 36000.00 1.57 CONCRETE CRUSHING (psi) 29 1432.90 197.70 2250.00 4.13 SHEAR FAILURE (lbs/in) 29 511.95 169.85 986.40 2.79 RADIAL-TENSION FAIL (psi 27 0.00 0.00 47.30 10000.00 DEFINITIONS AND RELATIONS FOR EACH CRITERION "n": * Rating Factor(n) = (Capacity(n) - Dead(n))/Live(n) * Total Demand(n) = Dead(n) + Live(n) at specified node * Dead(n) = Dead load demand for criterion n (factored) * Live(n) = Live load demand for criterion n (factored) * Capacity(n) = Capacity for criterion n (factored) BOTTOM LINE FINDINGS FOR LOAD RATING OF CULVERT * Controlling design criterion = STEEL YIELDING (psi) * Controlling load-rating factor RF = 1.57 * Controlling group-node number = 29 * Controlling live-load step number = 11 * Safety assessment of culvert = SAFE Figure 15 â CANDE load rating report Model 2 (Tandem Vehicle, no pavement, 5.0â fill)Â
Appendix D â 2D Analysis Backup   Dâ19  Pavement Rating Results The CANDE mesh for this model was generated using the tools in the CANDE Toolbox and the information provided on the design drawings. The general process for generating the model is described in the main body of this report. The CANDE Toolbox will not automatically generate the interior vertical wall. The outside of the box was generated first using the toolbox and the interior vertical was added manually. The rating factors produced by the CANDE Toolbox are summarized in Table 6. The CANDE model local beam node configuration referenced in the table is shown in Figure 16.   Table 6 â Model 2 âCANDE Rating Factors (from CANDE Toolbox) Tandem vehicle, without and with pavement (varying fill depths) Rating No pavement E = 200,000 psi  ï®Â = 0.33 Pavement (6â) E = 400,000 psi  ï®Â = 0.33 Pavement (6â) E = 600,000 psi  ï®Â = 0.33 Pavement (6â) 2.0 ft fill     Steel Yielding 1.47 (Node 27) 1.46 (Node 26) 1.57 (Node 29) 1.61 (Node 27) Concrete Crushing 1.98 (Node 27) 1.97 (Node 27) 2.14 (Node 27) 2.16 (Node 29) Shear Failure 2.87 (Node 29) 1.99 (Node 29) 2.63 (Node 29) 2.62 (Node 29) RadialâTension Fail 2365 (Node 27) 2365 (Node 27) 4730 (Node 27) 4730 (Node 27) 5.0 ft fill     Steel Yielding 1.57 (Node 29) 1.62 (Node 29) 1.65 (Node 29) 1.67 (Node 29) Concrete Crushing 2.52 (Node 27) 2.60 (Node 27) 2.64 (Node 27) 2.66 (Node 27) Shear Failure 2.79 (Node 29) 2.80 (Node 29) 2.81 (Node 29) 2.84 (Node 29) RadialâTension Fail 4730 (Node 17) 4730 (Node 17) 4730 (Node 17) 4730 (Node 17) Â
Appendix D â 2D Analysis Backup Dâ20 Figure 16 â Beam node numbering for M2C1 The rating factors for the 5â fill for the CANDE model do not appreciably increase as is seen in the BrDR model (see next section). Â
Appendix D â 2D Analysis Backup   Dâ21  Generated BrDR Model Model 2 was also input into the AASHTOWare BrDR software and run for varying fill heights (1.99â, 2.00â, 5â, 7â, 8â, and 10â). The reinforcement schematic from BrDR is shown in Figure 17. The LRFR ratings (HL93) are shown in Table 7. The ratings are provided at each fill height. For comparison purposes, the LFR rating was performed with the HS25 vehicle. The ratings for LFR are provided as well.  Figure 17 â BrDR Model M2C1 reinforcement schematic* *Note: There is currently a bug in the BrDR software that prevents hooked and bent bars from displaying properly. The reinforcement was checked to match the drawings. Table 7 â BrDR Model M2C1 ratings â LFR/LRFR Fill LRFR Ratings LFR (Ratings) Culvert M2C1  (1.99' fill) HLâ93 (US) 0.799 1.036 HSâ25 0.665 1.111 Culvert M2C1  (2.00' fill) HLâ93 (US) 1.322 1.714 HSâ25 1.201 2.005 Culvert M2C1  (5.00' fill) HLâ93 (US) 2.615 3.39 HSâ25 3.343 5.582 Culvert M2C1  (7.00' fill) HLâ93 (US) 3.149 4.082 HSâ25 4.357 7.289 Culvert M2C1  (8.00' fill) HLâ93 (US) 3.154 4.089 HSâ25 5.492 9.037 Culvert M2C1  (10.00' fill) HLâ93 (US) 2.651 3.437 HSâ25 5.804 9.656  Similar to Model 1, for the LRFR ratings, a noticeable step can be seen from a fill of 1.99â to 2.00â. For 1.99â the controlling inventory rating of 0.799 is governed by shear in the top slab near the support at the critical shear distance. For the fill of 2â, the controlling inventory rating of 1.322 is governed by flexure in the center of the top slab. This difference is due primarily to the difference in the calculation of concrete shear capacity at the 2â fill level. See the discussion under Model 1. Â
Appendix D â 2D Analysis Backup Dâ22 For model 2 the calculations of the concrete shear capacity and overall shear resistance are presented in Table 8. This jump in shear capacity is discussed more under Task 5. Table 8  â BrDR Model M2C1 shear capacity comparison at 1.99â fill and 2.00â fill Fill depth Inv Rating Oper Rating Concrete Shear Resistance Vc (kips) Steel Shear Resistance Vs (kips) Shear Resistance Vr (kips) Culvert M1C1  (1.99' fill) HLâ93 (US) 0.799 1.036 9.93* 0 8.44 Culvert M1C1  (2.00' fill) HLâ93 (US) 1.322 1.714 16.83 0 14.3 *Note: This uses the AASHTO LRFD Simplified for shear and not the iterative shear method provided in Appendix B of AASHTO. The Appendix B option is not available for culverts in BrDR.
Appendix D â 2D Analysis Backup   Dâ23  Model 3 Analysis Backup Input Information Meshes for Model 2 were generated for a fill of 1.5â. Using the CANDE ToolBox, different fill depth meshes can be generated if needed for Phase III. The reduction of surface load factor for Model 3 is shown in Table 9 for each fill height.  Table 9 â Reduction of surface load for varying fills for Model 3 Fill Depth (ft) RSL 1.5 0.353  Depth of Fill (max â road centerline): Top of box to top of pavement: 16 in. (5 in. reinf. concrete slab, variable depth (2% slope) base course, 2.5 in. binder course, 1.5 in. wearing course) Bedding depth:   12 in. No. 8 coarse aggregate  .  Precast Box Geometry: Span x Rise x Length: 12 ft x 6 ft x 6.46 ft Top/Bottom/Sidewall: 13.5 in./12.5 in./12 in. Haunches:  6 in. x 6 in. top & bottom  Reinforcement CANDE (Sections 2 thru 6):  in.2/ft in.2/in.  Clear cover AS1 â outside:  #5@ 6 in.  0.620 0.052  2.5 in. to top, 1.5 in.  AS2 â top inside: #5@ 6 in.  0.620 0.052  1.5 in. AS3 â bottom inside: #5@ 6 in. 0.620 0.052 2.0 in.  AS4 â side inside #5@ 6 in.  0.620 0.052  1.5 in. AS5 â top outside #4@ 6 in.  0.400 0.033  2.5 in. AS6 â bottom outside #4@ 6 in.  0.400 0.033  1.5 in.  Note: Top slab has inserts for anchors to 5 in. slab.    Materials: Reinforcement yield stress: 60 ksi â epoxy coated Concrete fâc:   6 ksi   CANDE Model notes: Concrete tensile rupture strain: 0.0001 in./in. (typically neglected in design, but used for analysis)      ~7 fâc0.5  In situ â linear elastic   E = 5,000 psi, Poisson = 0.3 â both assumed Bedding â 18 in. structure backfill, 6 in. No. 8 stone      Duncan Selig â SW100 (assume well compacted) Backfill â Assumed   Duncan/Selig â SW95Â
Appendix D â 2D Analysis Backup Dâ24 Reinforcement for BrDR Bar Mark Type Bar Number Spacing (in) A B C A1 Straight 4 6 9.25  A2 Straight 5 6 13.75  A3 Bent 5 6 7.833333 4.416667 4.416667 A4 Straight 5 6 7.833333  CANDE output results Figure 18 displays a typical CANDE plot of vertical strain of model 3 with the Tandem vehicle near midspan. Figure 25 displays the dead load moment diagrams for the first 6 load steps (incremental fill levels), while Figure 20 displays the live load envelope for the tandem vehicle for all of the live load steps (7â23). Figure 21 displays the deflection (magnified by 30) and shear stress as the tandem vehicle steps across the culvert. Figure 18 â M3C1 Vertical strain with Tandem Vehicle near midspan (with pavement) Figure 19 â M3C1â CANDE Bending Moment  â Dead load envelope â Load steps 1â6Â
Appendix D â 2D Analysis Backup   Dâ25   Figure 20 â M3C1 â CANDE bending moment envelope â live load steps â load steps 7â23 (2 axle Tandem ,25 kip/axle) (with pavement)  Â
Appendix D â 2D Analysis Backup Dâ26 Figure 21 â M3C1 showing shear stress as Tandem vehicle moves across culvert (5â fill, no pavement)Â
Appendix D â 2D Analysis Backup   Dâ27  Pavement Rating Results An analysis of the CANDE model 3 was performed using the following options:Â ï· Solution for tandemâtruck load traveling over surface no pavement.Â ï· Solution with pavement with modulus of Elasticity = 200,000 psiÂ ï· Solution with pavement with modulus of Elasticity = 400,000 psiÂ ï· Solution with pavement with modulus of Elasticity = 600,000 psi Base Model 3 differs from the original Contech model in the following ways:Â ï· The top row of SW95 soil elements changed to elastic wearing course using default Tool Box values. This is necessary to avoid failure of the shear failure of one element.Â Â ï· Changed load factor for earth load steps 2 thru 6 to 1.37 (= 1,3 * 1.05).Â ï· Soil Material #3 (Duncan/Selig SW95) upgraded to include Katona Modification for unloading.   LiveâBase Model 3 simulates a tandem truck moving over the soil surface (no pavement): The live loading includes the followingÂ ï· Lane loadingÂ ï· Dynamic impact factor.Â ï· Multilane presence factor.Â ï· Standard liveâload factor (1.75) specified in Eâlines.Â ï· RSL longitudinal modification including 3DSE assuming layâlength = 6 feet.Â ï· Details of the liveâload assumptions are at bottom of the CANDE input file (CID extension) as printed by the tool box. The three pavement models with E = 200,000, 400,000 and 600,000 psi were created by the Tool Box wherein pavement thickness = 6â, Poisson ratio = 0.33 and the pavement density = 0 pcf in each case. Density was set to zero to offset not reducing the dynamic impact factor and RSL from the added 6â.  Table 10 â Model 3 âCANDE Rating Factors (from CANDE Toolbox) Tandem vehicle, without and with pavement (varying fill depths) Rating Factors per Design Criterion No pavement E = 200,000 psi  ï®Â = 0.33 Pavement (6â) E = 400,000 psi  ï®Â = 0.33 Pavement (6â) E = 600,000 psi  ï®Â = 0.33 Pavement (6â) 1.33 ft fill     Steel yielding 1.61 (Node 29) 1.62 (Node 29) 1.64 (Node 29) 1.65 (Node 29) Concrete crushing 3.72 (Node 6) 3.74 (Node 6) 3.75 (Node 6) 3.79 (Node 6) Shear failure 1.98 (Node 4) 2.12 (Node 26) 2.15 (Node 26) 2.18 (Node 26) Radial tension  531.00  (Node 5) 1858.00 (Node 1) 1858.00  (Node 1) 1858.00 (Node 1)  The new results show an improvement in rating as the pavement is added and the elasticity modulus increased.Â
Appendix D â 2D Analysis Backup Dâ28 Figure 22 â Beam node numbering for M3C1 Generated BrDR Model Model 3 was also input into the AASHTOWare BrDR software and run for varying fill heights (1.99â, 2.00â, 5â, 7â, 8â, and 10â). The reinforcement schematic from BrDR is shown in Figure 23. The LRFR ratings (HL93) are shown in Table 11. The ratings are provided at each fill height. For comparison purposes, the LFR rating was performed with the HS25 vehicle. The ratings for LFR are provided as well.Â
Appendix D â 2D Analysis Backup   Dâ29  Figure 23 â BrDR Model M3C1 reinforcement schematic  Table 11 â BrDR Model M3C1 ratings â LFR/LRFR Fill LRFR Ratings LFR (Ratings) Culvert M3C1  (1.99' fill) HLâ93 (US) 1.401 1.816 HSâ25 1.111 1.855 Culvert M3C1  (2.00' fill) HLâ93 (US) 1.177 1.525 HSâ25 1.176 1.965 Culvert M3C1  (5.00' fill) HLâ93 (US) 1.688 2.188 HSâ25 2.677 4.47 Culvert M3C1  (7.00' fill) HLâ93 (US) 1.528 1.981 HSâ25 3.267 5.455 Culvert M3C1  (8.00' fill) HLâ93 (US) 1.441 1.869 HSâ25 3.476 5.805 Culvert M3C1  (10.00' fill) HLâ93 (US) 0.799 1.036 HSâ25 2.636 4.403  Similar to Model 1, for the LRFR ratings, a noticeable step can be seen from a fill of 1.99â to 2.00â. In this case the step is downward and the governing rating is flexure. The culvert, built in 2013, was designed with the LRFD shear specifications accounting for the change at the 2â fill. For model 3 the difference in live load moment is shown in Table 12. The difference in the live loads is likely due to the distribution of live load from LRFD articles 3.6.1.2.6  (greater or equal to 2â) and 4.6.2.10.  Table 12  â BrDR Model M3C1 live load moment at 1.99â fill and 2.00â fill Fill depth  Inv Rating Oper Rating Live Load at critical rating MLL (kipâft) Culvert M3C1  (1.99' fill) HLâ93 (US) 1.401 1.816 11.28 Culvert M3C1  (2.00' fill) HLâ93 (US) 1.177 1.525 13.42  *Note: Even thought this table is for moment, a panel member asked which shear procedure was used. This model uses the AASHTO LRFD Simplified for shear and not the iterative shear method provided in Appendix B of AASHTO. The Appendix B option is not available for culverts in BrDR.  Â
Appendix D â 2D Analysis Backup Dâ30 Model 4 Analysis Backup Input Information Below (Figure 24 and Figure 25) are partial CANDE mesh images provided by CONTECH. The RT had requested the original CANDE input file and it was received by around the time that this report was being prepared. This file will be used for testing in Phase III of this project. Note: The backup for the CANDE analysis of Model is provided for Interim Report #3. Figure 24 â Model 4 Element numberingÂ
Appendix D â 2D Analysis Backup   Dâ31  Figure 25 â Model 4 area of steel for CANDE model  Figure 26 â M4C1â CANDE Bending Moment  â Dead load envelope â Load steps 1â6    Figure 27 â M4C1 â CANDE bending moment envelope â live load steps â load steps 7â47 (2 axle Tandem ,25 kip/axle + Lane loading) (with pavement)  Â
Appendix D â 2D Analysis Backup Dâ32 Figure 28 â M4C1 showing vertical stress as Tandem vehicle moves across culvert (1â fill, no pavement)Â
Appendix D â 2D Analysis Backup   Dâ33  Pavement Rating Results An analysis of the CANDE model 4 (see Figure 29) was performed using the following options:Â ï· Solution for tandemâtruck load traveling over surface no pavement.Â ï· Solution with pavement with modulus of Elasticity = 200,000 psiÂ ï· Solution with pavement with modulus of Elasticity = 400,000 psiÂ ï· Solution with pavement with modulus of Elasticity = 600,000 psi  Figure 29 â CANDE Model 4 (M4C1) Base Model 4 differs from the original Contech model in the following ways:Â ï· Contechâs deep burial elements that enter into the system at load step 9, were reset to come into the system at system at step 99 (i.e., never appear).Â ï· Contechâs working stress methodology (LRFD=0) was changed to LRFD = 1. Dead and earth load factors were set accordingly and soil densities changed to realistic values. (See CANDE User Manual)Â ï· The soil fill above the crown was changed from Duncan SM90 to Duncan/Selig SW90 as the latter is more realistic and less prone to nonconvergence. (See CANDE User Manual)Â ï· A wearing course (linear elastic soil with E = 1800 psi) was inserted on the top row elements.   LiveâBase Model 4 simulates a tandem truck moving over the surface. Included with live load are:Â ï· HL93 lane loading.Â ï· dynamic impact factor.Â ï· Multilane presence factor.Â ï· And the standard liveâload factor (1.75) specified in Eâlines.Â ï· Details of the liveâload assumptions may be observed at the bottom of the CANDE input file as printed out by the CANDE tool box. The three pavement models with E = 200,000, 400,000 and 600,000 psi were created by the CANDE Tool Box wherein the pavement thickness = 6 inches, Poisson ratio = 0.2 and the pavement density = 140 pcf in each case. The CANDE solutions for all live load cases were processed by Option 5 in the CANDE tool box and the bottom line loadârating factors are shown in the Table 13 below.  Â
Appendix D â 2D Analysis Backup Dâ34 Table 13 â Model 4 (M4C1) load ratings for a Tandem Vehicle with lane load  Rating Factors per Design Criterion No pavement E = 200,000 psiÂ Â ï® = 0.20 Pavement (6â) E = 400,000 psiÂ Â ï® = 0.20 Pavement (6â) E = 600,000 psiÂ Â ï® = 0.20 Pavement (6â) 1.0 ft fill Steel yielding 1.00 (Node 29) 1.07 (Node 52) 1.07 (Node 52) 1.08 (Node 52) Concrete crushing 1.15 (Node 29) 1.27 (Node 29) 1.27 (Node 29) 1.29 (Node 29) Shear failure 1.27 (Node 43) 1.35 (Node 43) 1.37 (Node 43) 1.38 (Node 43) Radial tension  5.14  (Node 32) 5.82 (Node 32) 5.90  (Node 29) 5.99 (Node 29)Â
Appendix D â 2D Analysis Backup   Dâ35  Model 5 Analysis Backup Input Information A request has been made of CONTECH for the CANDE input file for this culvert. If we are not able to obtain the file, the CANDE model will be created from the shop drawings provided. Note: The backup for the CANDE analysis of Model is provided for Interim Report #3.     Figure 30 â M5C1 showing vertical stress as Tandem vehicle moves across culvert (no pavement)  Â
Appendix D â 2D Analysis Backup Dâ36 Pavement Rating Results An analysis of the CANDE model 5 (see Figure 31) was performed using the following options:Â ï· Solution for tandemâtruck load traveling over surface no pavement. ï· Solution with pavement with modulus of Elasticity = 200,000 psi ï· Solution with pavement with modulus of Elasticity = 400,000 psi ï· Solution with pavement with modulus of Elasticity = 600,000 psi Figure 31 â CANDE Model 5 (M5C1) Base Model 5, which is a corrugated steel arch under 3 feet of soil cover, remains essentially the same as originally constructed. The only change is replacing the top row of MohrâCoulomb soil elements over the arch with an elastic wearing course whose elastic properties match the MohrâCoulomb model. This is necessary to avoid failure of the Mohr Coulomb elements from the excessive shear forces caused by point loads representing the traveling tandem truck.  (see CANDE User Manual). LiveâBase Model 5 simulates a tandem truck moving over the surface. Included with live load are:Â ï· HL93 lane loading. ï· dynamic impact factor. ï· Multilane presence factor. ï· And the standard liveâload factor (1.75) specified in Eâlines. ï· RSL reduction for longitudinal load spreading is used based on variable cover height. ï· Details of the liveâload assumptions may be observed at the bottom of the cid file as printed out by the CANDE tool box. The three pavement models with E = 200,000, 400,000 and 600,000 psi were created by the CANDE Tool Box wherein the pavement thickness = 6 inches, Poisson ratio = 0.2 and the pavement density = 140 pcf in each case. The CANDE solutions for all live load cases were processed by Option 5 in the CANDE tool box and the bottom line loadârating factors are shown in the Table 14 below. Table 14 â Model 5 (M5C1) load ratings for a Tandem Vehicle with lane load  Rating Factors per Design Criterion No pavement E = 200,000 psiÂ Â ï® = 0.20 Pavement (6â) E = 400,000 psiÂ Â ï® = 0.20 Pavement (6â) E = 600,000 psiÂ Â ï® = 0.20 Pavement (6â) 3.0 ft fill Material thrust yield 3.69 (Node 7) 4.20 (Node 33) 4.27 (Node 33) 4.21 (Node 18) Buckling thrust failure 3.77 4.30 4.37 4.29Â
Appendix D â 2D Analysis Backup   Dâ37  (Node 7) (Node 33) (Node 33) (Node 18) Seam thrust failure 3.39 (Node 7) 3.87 (Node 33) 3.93 (Node 33) 3.90 (Node 18) Plastic penetration 3.14  (Node 3) 3.82 (Node 37) 3.91  (Node 37) 3.90 (Node 37)  Figure 32 provides a copy of the loadârating summaries from CANDE Tool Box that are summarized in Table 14.   (1) No Pavement DESIGN-CRITERION LOAD LOCAL DEAD-LOAD LIVE-LOAD EFFECTIVE *RATING (Strength) STEP NODE DEMAND DEMAND CAPACITY FACTOR *MATERIAL THRUST (psi) 20 7 7480.00 6920.00 33000.00 3.69 *BUCKLING THRUST (psi) 20 7 7480.00 6920.00 33575.00 3.77 *SEAM THRUST (psi) 20 7 7480.00 6920.00 30957.00 3.39 *PLASTIC-PENETRATE (%) 16 3 0.00 28.68 90.00 3.14 (2) Pavement E = 200,000 psi DESIGN-CRITERION LOAD LOCAL DEAD-LOAD LIVE-LOAD EFFECTIVE *RATING (Strength) STEP NODE DEMAND DEMAND CAPACITY FACTOR *MATERIAL THRUST (psi) 24 33 7280.00 6120.00 33000.00 4.20 *BUCKLING THRUST (psi) 24 33 7280.00 6120.00 33575.00 4.30 *SEAM THRUST (psi) 24 33 7280.00 6120.00 30957.00 3.87 *PLASTIC-PENETRATE (%) 26 37 0.00 23.55 90.00 3.82 (3) Pavement E = 400,000 psi DESIGN-CRITERION LOAD LOCAL DEAD-LOAD LIVE-LOAD EFFECTIVE *RATING (Strength) STEP NODE DEMAND DEMAND CAPACITY FACTOR *MATERIAL THRUST (psi) 24 33 7280.00 6020.00 33000.00 4.27 *BUCKLING THRUST (psi) 24 33 7280.00 6020.00 33575.00 4.37 *SEAM THRUST (psi) 24 33 7280.00 6020.00 30957.00 3.93 *PLASTIC-PENETRATE (%) 26 37 0.00 23.04 90.00 3.91 (4)Pavement E = 600,000 psi DESIGN-CRITERION LOAD LOCAL DEAD-LOAD LIVE-LOAD EFFECTIVE *RATING (Strength) STEP NODE DEMAND DEMAND CAPACITY FACTOR *MATERIAL THRUST (psi) 27 18 4930.00 6670.00 33000.00 4.21 *BUCKLING THRUST (psi) 27 18 4930.00 6670.00 33575.00 4.29 *SEAM THRUST (psi) 27 18 4930.00 6670.00 30957.00 3.90 *PLASTIC-PENETRATE (%) 26 37 0.00 23.09 90.00 3.90 Figure 32 â Model 5 (M5C1) â CANDE Toolbox rating output  Â
Appendix D â 2D Analysis Backup Dâ38 Model 6 Analysis Backup Input Information Meshes for Model 6 were created for CANDE for 1.5â and 2â of fill. The reduction for surface load for the fills used in the CANDE models is shown in Table 15. Table 15 â Reduction of surface load for varying fills for Model 6 Fill Depth (ft) RSL 1.5 0.324 2 0.177 The following was provided by Lane Enterprises.Â
Appendix D â 2D Analysis Backup   Dâ39  Â
Appendix D â 2D Analysis Backup Dâ40Â
Appendix D â 2D Analysis Backup   Dâ41   The following figures are output from the CANDE software. Figure 33 represents the bending moment for dead load and the soil load. Figure 34 provides and envelope of the tandem load that is provided in load steps 9â27. Figure 35 provides the deflection and the shear stress as the TANDEM vehicle moves across the structure (with pavement).  Figure 33 â M6C2â CANDE Bending Moment  â Dead load envelope â Load steps 1â8   Figure 34 â M6C2 â CANDE bending moment envelope â live load steps â load steps 9â27 (2 axle Tandem ,25 kip/axle) (with pavement) Â
Appendix D â 2D Analysis Backup Dâ42 Figure 35 â M6C2 â CANDE Shear stress and deflection as Tandem vehicle moves across the structure (with pavement, E=600,000 psi)Â
Appendix D â 2D Analysis Backup   Dâ43  Model 7 Analysis Backup Input Information Meshes for Model 7 were created for CANDE for 2â of fill and were generated with pavement and without pavement. The original model was provided by CONTECH. The reduction for surface load for the fills used in the CANDE models is shown in Table 16. Table 16 â Reduction of surface load for varying fills for Model 7 Fill Depth (ft) RSL 2 0.177  The following figures are output from the CANDE software. Figure 36represents the bending moment for dead load and the soil load. Figure 37 provides and envelope of the tandem load that is provided in load steps 9â27. Figure 38 provides the deflection and the shear stress as the TANDEM vehicle moves across the structure (with pavement).  Figure 36 â M7C1â CANDE Bending Moment  â Dead load envelope â Load steps 1â16 Â
Appendix D â 2D Analysis Backup Dâ44 Figure 37 â M7C1 â CANDE bending moment envelope â live load steps â load steps 17â65 (2 axle Tandem ,25 kip/axle) (with pavement)
Appendix D â 2D Analysis Backup   Dâ45       Figure 38 â M7C1 â CANDE Shear stress and deflection as Tandem vehicle moves across the structure (with pavement, E=200,000 psi) (20X magnified)Â
MEMORANDUM To: Chad Clancy & Tom Murphy, Modjeski and Masters, Mechanicsburg, PA From: Reza Baie, Summit Engineering Group, Littleton, CO RE: Project: NHCRP 15-54 Update on Lusas Modeling Progress Progress on numerical modeling of culverts using LUSAS software is reported herein. This progress report includes a general description of each culvert, geometry, and material properties. Assumptions are listed and analysis method is described. Finally, results of nonlinear analysis under live load is presented. MODEL 1- CANDIDATE 1 (M1C1) Model 1 represents a prototype of reinforced concrete box single-cell culverts. Of three proposed candidates for Model 1 (per Quarterly Progress Report submitted on April 1, 2016), Candidate 1 is selected for this category. Geometry Geometry and layout of Model 1 Candidate 1 (M1C1) is presented in the Quarterly Progress Report and is presented here as Appendix A. Figure 1 (a) presents the section of the culvert and the equivalent geometry that is modeled in Lusas. The thickness of the top flange and side wall elements is set to the actual thickness of the members. Figure 1 (b) depicts the assigned thickness of the corner elements at the chamfered sections of the concrete box culvert. The Lusas model includes the entire length of the culvert. As shown in Figure 1 (a), the depth of model extends to 28â-11â. Laterally, the geometry extends to 45â on each side. Therefore, the cross section of model is 90âx28â-11â and the length is 31â. Material Properties The linear material properties of the culvert are generated based on AASHTO LRFD Bridge Design Specifications for compressive strength of fâc = 5 ksi: modulus of elasticity (E) = 4074 ksi, Poissonâs ratio (ν) = 0.2, unit weight = 150 pcf, and coefficient of thermal expansion (α) = 10.8 e-6 1/C. Overlay and pavement is defined as a linear material with modulus of elasticity (E) = 4000 ksi, Poissonâs ratio (ν) = 0.35, and unit weight = 140 pcf. Table 1 presents the material properties of in-situ soil and backfill. The in-situ soil is defined as an elastic material, while the nonlinear material properties are considered for backfill, varying with depth. The values in Table 1 are adopted from previous study by McGrath et al. (2005). Mesh Quadrilateral quadratic thick shell elements are used to model the culvert. The thick shell elements are used for the culvert to incorporate the shear and bending of the culvert. Hexahedral quadratic solid elements are used to model the pavement (overlay), in-situ soil, and backfill. The mesh size around the culverts and in backfill is 1â-6â and expands to 6â at the boundaries. The mesh size along the length of culvert varies between 6â at the edges to 1â-6â at the center. Appendix E - 3D Modeling Backup E-1
Boundary Condition At the end of the in-situ soil medium, perpendicular restraints are used for each boundary surface, i.e. lateral restraints at vertical faces and vertical restraints at the bottom of the in-situ soil. âTied Mesh Constraintsâ are assigned between the culvert and soil as well as the culvert and overlay to assure deformation compatibility. This option assures compatible deformation of adjacent shell elements and solid elements. No contact element or interaction properties are assigned. Load Cases Gravity is applied as a body force. Soil pressure is considered using vertical and lateral pressure (to provide in-situ conditions with close to zero deflections under soil self-weight). Live Load: âWheel loadâ is modeled as a discrete patch load over a 10âx20â area. A load case with single axle load, and a load case with standard HL-93 truck moving load is applied to model. The truck load is moved across the culvert to capture the critical loading condition. The live load will be updated when the wheel load of the actual truck that is used in the experiment is determined. Results Figures 2 to 18 present the behavior of M1C1 in terms of displacement, strains and stresses under axle load at center of the culvert. Because for nonlinear analysis, all loads must be applied sequentially, gravity and dead loads are applied first, then live load is applied and the final results are under both dead load and live load. Given that for experimental study, only the effect of live load is measured, a load combination is defined in Lusas that removes the effect of dead load by subtracting the results of âdead load analysisâ from the results after application of live load. It should be noted that maximum and minimum envelopes of results under moving loads are available, however, given that Lusas develops two separate envelopes for maximum and minimum, contour presentation may become misleading, unless both envelopes are compared side by side. This is especially important when the dead load effects (constant) are being deduced from the total âdead + live loadâ results. Results of envelop results of moving loads will be presented later where a specific entity or stage of loading is determined. Table 1. M1C1- Material Properties of Backfill and In-Situ Soil Properties Backfill: 0-1 ft Backfill: 1-6 ft Backfill: 6-11 ft In-Situ Soil Modulus of Elasticity, E (ksf) 230.4 576.0 864.0 864.0 Poissonâs Ratio (v) 0.4 0.29 0.24 0.25 Unit Weight (pcf) 121 121 121 127 Initial Cohesion (psf) 0.000144 0.000144 0.000144 - Initial Friction Angle 40 40 40 - Final Friction Angle 40 40 40 - Dilation Angle 10 10 10 - Cohesion Hardening (psf) 0 0 0 - Limiting Plastic Strain 0.001 0.001 0.001 - Appendix E - 3D Modeling Backup E-2
Figure 1. M1C1- Geometry and Culvert Thickness Assignment Appendix E - 3D Modeling Backup E-3
Figure 2. M1C1- Resultant Displacement of Solid Elements â 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-4
Figure 3. M1C1- Vertical Displacement of Solid Elements - 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-5
Figure 4. M1C1- Von Mises Strain of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-6
Figure 5. M1C1- Vertical Strain (EV) of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-7
Figure 6. M1C1- Horizontal Strain (EX) of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-8
Figure 7. M1C1- Von Mises Stress of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-9
Figure 8. M1C1- Vertical Stress (SY) of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-10
Figure 9. M1C1- Horizontal Stress (SX) of Solid Elements- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-11
Figure 10. M1C1- Vertical Displacement of Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-12
Figure 11. M1C1- Von Mises Strain at Top Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-13
Figure 12. M1C1- Von Mises Strain at Bottom Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-14
Figure 13. M1C1- Bending Strain at Top Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-15
Figure 14. M1C1- Bending Strain at Bottom Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-16
Figure 15. M1C1- Von Mises Stress at Top Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-17
Figure 16. M1C1- Von Mises Stress at Bottom Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-18
Figure 17. M1C1- Bending Stress at Top Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-19
Figure 18. M1C1- Bending Stress at Bottom Fiber in Culvert- 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-20
MODEL 2- CANDIDATE 1 (M2C1) Model 2 represents a prototype of reinforced concrete box multi-cell culverts. Of three proposed candidates for Model 2 (per Quarterly Progress Report submitted on April 1, 2016), Candidate 1 is selected for this category. Geometry Geometry and layout of Model 2 Candidate 1 (M2C1) is presented in the Quarterly Progress Report and is presented here as Appendix B. Figure 19 (a) presents the section of the culvert and the equivalent geometry that is modeled in Lusas. The thickness of the top flange and side wall elements is set to the actual thickness of the members. Figure 19 (b) depicts the assigned thickness of the corner elements at the chamfered sections of the concrete box culvert. The Lusas model includes the entire length of the culvert. As shown in Figure 19 (a), the depth of model extends to 25â-6â. Laterally, the geometry extends to 39â on each side. Therefore, the cross section of model is 78âx25â-6â and the length is 31â. Also, the culvert has a 15o skew which is incorporated in the model. Material Properties The linear material properties of culvert are generated based on AASHTO LRFD Bridge Design Specifications for compressive strength of fâc = 5 ksi: modulus of elasticity (E) = 4074 ksi, Poissonâs ratio (ν) = 0.2, unit weight = 150 pcf, and coefficient of thermal expansion (α) = 10.8 e-6 1/C. Overlay and pavement is defined as a linear material with modulus of elasticity (E) = 4000 ksi, Poissonâs ratio (ν) = 0.35, and unit weight = 140 pcf. Table 2 presents the material properties of in-situ soil and backfill. In-situ soil is defined as an elastic material, while nonlinear material properties are considered for backfill, varying with depth. The values in Table 2 are adopted from previous study by McGrath et al. (2005). Mesh Quadrilateral quadratic thick shell elements are used to model the culvert. The thick shell elements are used for the culvert to incorporate the shear and bending of the culvert. Hexahedral quadratic solid elements are used to model the pavement (overlay), in-situ soil, and backfill. The mesh size around the culverts and in backfill is 1â-6â and expands to 6â at the boundaries. The mesh along the length of culvert varies between 6â at edges to 1â-6â at center. Boundary Condition At the end of the in-situ soil medium, perpendicular restraints are used for each boundary surface, i.e. lateral restraints at vertical faces and vertical restraints at the bottom of the in-situ soil. âTied Mesh Constraintsâ are assigned between the culvert and soil as well as the culvert and overlay to assure deformation compatibility. This option assures compatible deformation of adjacent shell elements and solid elements. No contact element or interaction properties are assigned. Load Cases Gravity is applied as a body force. Soil pressure is considered using vertical and lateral pressure (to provide in-situ conditions with close to zero deflections under soil self-weight). Live Load: Wheel load is modeled as a discrete patch load over a 10âx20â area. A load case with single axle load, and a load case with standard HL-93 truck moving load is applied to model. The truck load is moved across the culvert to capture the critical loading condition. The live load will be updated when the wheel load of the actual truck that is used in the experiment is determined. Appendix E - 3D Modeling Backup E-21
Results Figures 20 to 36 present the behavior of M2C1 in terms of displacement, strains and stresses under axle load at center of the culvert. Due to the skew, the axle loads are positioned so that the center of each axle passes through the centerline of culvert. Figures 37 to 53 presents the behavior of M2C1 when axle loads are applied at center of the left cell only. Because for nonlinear analysis, all loads must be applied sequentially, gravity and dead loads are applied first, then live load is applied and the final results are under both dead load and live load. Given that for experimental study, only the effect of live load is measured, a load combination is defined in Lusas that removes the effect of dead load by subtracting the results of âdead load analysisâ from the results after application of live load. It should be noted that maximum and minimum envelopes of results under moving loads are available, however, given that Lusas develops two separate envelopes for maximum and minimum, contour presentation may become misleading, unless both envelopes are compared side by side. This is especially important when the dead load effects (constant) are being deduced from the total âdead + live loadâ results. Results of envelop results of moving loads will be presented later where a specific entity or stage of loading is determined. Table 2. M2C1- Material Properties of Backfill and In-Situ Soil Properties Backfill: 0-1 ft Backfill: 1-6 ft Backfill: 6-11 ft In-Situ Soil Modulus of Elasticity, E (ksf) 230.4 576.0 864.0 864.0 Poissonâs Ratio (v) 0.4 0.29 0.24 0.25 Unit Weight (pcf) 121 121 121 127 Initial Cohesion (psf) 0.000144 0.000144 0.000144 - Initial Friction Angle 40 40 40 - Final Friction Angle 40 40 40 - Dilation Angle 10 10 10 - Cohesion Hardening (psf) 0 0 0 - Limiting Plastic Strain 0.001 0.001 0.001 - Appendix E - 3D Modeling Backup E-22
Figure 19. M2C1- Geometry and Culvert Thickness Assignment Appendix E - 3D Modeling Backup E-23
Figure 20. M2C1- Resultant Displacement of Solid Elements â 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-24
Figure 21. M2C1- Vertical Displacement of Solid Elements - 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-25
Figure 22. M2C1- Von Mises Strain of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-26
Figure 23. M2C1- Vertical Strain (EV) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-27
Figure 24. M2C1- Horizontal Strain (EX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-28
Figure 25. M2C1- Von Mises Stress of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-29
Figure 26. M2C1- Vertical Stress (SY) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-30
Figure 27. M2C1- Horizontal Stress (SX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-31
Figure 28. M2C1- Vertical Displacement of Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-32
Figure 29. M2C1- Von Mises Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-33
Figure 30. M2C1- Von Mises Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-34
Figure 31. M2C1- Bending Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-35
Figure 32. M2C1- Bending Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-36
Figure 33. M2C1- Von Mises Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-37
Figure 34. M2C1- Von Mises Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-38
Figure 35. M2C1- Bending Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-39
Figure 36. M2C1- Bending Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-40
Figure 37. M2C1- Resultant Displacement of Solid Elements â 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-41
Figure 38. M2C1- Vertical Displacement of Solid Elements - 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-42
Figure 39. M2C1- Von Mises Strain of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-43
Figure 40. M2C1- Vertical Strain (EV) of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-44
Figure 41. M2C1- Horizontal Strain (EX) of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-45
Figure 42. M2C1- Von Mises Stress of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-46
Figure 43. M2C1- Vertical Stress (SY) of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-47
Figure 44. M2C1- Horizontal Stress (SX) of Solid Elements- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-48
` Figure 45. M2C1- Vertical Displacement of Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-49
Figure 46. M2C1- Von Mises Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-50
Figure 47. M2C1- Von Mises Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-51
Figure 48. M2C1- Bending Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-52
Figure 49. M2C1- Bending Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-53
Figure 50. M2C1- Von Mises Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-54
Figure 51. M2C1- Von Mises Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-55
Figure 52. M2C1- Bending Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-56
Figure 53. M2C1- Bending Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Mid-Span of Left Cell Appendix E - 3D Modeling Backup E-57
MODEL 3- CANDIDATE 1 (M3C1) Model 3 represents a prototype of new precast concrete box culverts. Of three proposed candidates for Model 3 (per Quarterly Progress Report submitted on April 1, 2016), Candidate 1 is selected for this category. Geometry Geometry and layout of Model 3 Candidate 1 (M3C1) is presented in the Quarterly Progress Report and is presented here as Appendix C. Figure 54 (a) presents the section of the culvert and the equivalent geometry that is modeled in Lusas. The thickness of the top flange and side wall elements is set to the actual thickness of the members. Figure 54 (b) depicts the assigned thickness of the corner elements at the chamfered sections of the concrete box culvert. The Lusas model includes the entire length of the culvert. As shown in Figure 54 (a), the depth of model extends to 22â-9â. Laterally, the geometry extends to 24â on each side. Therefore, the cross section of model is 48âx22â-9â and the length is 36â. Also, the culvert has a 10o skew which is incorporated in the model. A one-foot bedding of coarse gravel is modeled under the culvert, per contract drawings. Also, the slope of backfill is assumed 1:1/2 vertical to horizontal. Material Properties The linear material properties of culvert are generated based on AASHTO LRFD Bridge Design Specifications for compressive strength of fâc = 5 ksi: modulus of elasticity (E) = 4074 ksi, Poissonâs ratio (ν) = 0.2, unit weight = 150 pcf, and coefficient of thermal expansion (α) = 10.8 e-6 1/C. Overlay and pavement is defined as a linear material with modulus of elasticity (E) = 4000 ksi, Poissonâs ratio (ν) = 0.35, and unit weight = 140 pcf. Table 3 presents the material properties of in-situ soil and backfill. In-situ soil is defined as an elastic material, while nonlinear material properties are considered for backfill, varying with depth. The values in Table 3 are adopted from previous study by McGrath et al. (2005). Mesh Quadrilateral quadratic thick shell elements are used to model the culvert. Thick shell elements are used for the culvert to incorporate the shear and bending of the culvert. Hexahedral quadratic solid elements are used to model the pavement (overlay), in-situ soil, and backfill. The mesh size is 1â around the culverts and in backfill and 4â at the boundaries. The mesh size along the length of culvert varies between 8â at edges to 2ââ at center. Boundary Condition At the end of the in-situ soil medium, perpendicular restraints are used for each boundary surface, i.e. lateral restraints at vertical faces and vertical restraints at the bottom of the in-situ soil. âTied Mesh Constraintsâ are assigned between the culvert and soil as well as the culvert and overlay to assure deformation compatibility. This option assures compatible deformation of adjacent shell elements and solid elements. No contact element or interaction properties are assigned. Load Cases Gravity is applied as a body force. Soil pressure is considered using vertical and lateral pressure (to provide in-situ conditions with close to zero deflections under soil self-weight). Live Load: Wheel load is modeled as a discrete patch load over a 10âx20â area. A load case with single axle load in two lanes and a load case with standard HL-93 truck moving load is applied to the model. The Appendix E - 3D Modeling Backup E-58
truck load is moved across the culvert to capture the critical loading condition. The live load will be updated when the wheel load of the actual truck that is used in the experiment is determined. Results Figures 55 to 71 present the behavior of M3C1 in terms of displacement, strains and stresses under axle load at center of the culvert. Due to the skew, the axle loads are positioned so that the center of each axle passes through the centerline of culvert. Because for nonlinear analysis, all loads must be applied sequentially, gravity and dead loads are applied first, then live load is applied and the final results are under both dead load and live load. Given that for experimental study, only the effect of live load is measured, a load combination is defined in Lusas that removes the effect of dead load by subtracting the results of âdead load analysisâ from the results after application of live load. It should be noted that maximum and minimum envelopes of results under moving loads are available, however, given that Lusas develops two separate envelopes for maximum and minimum, contour presentation may become misleading, unless both envelopes are compared side by side. This is especially important when the dead load effects (constant) are being deduced from the total âdead + live loadâ results. Results of envelop results of moving loads will be presented later where a specific entity or stage of loading is determined. Table 3. M3C1- Material Properties of Backfill and In-Situ Soil Properties Backfill: 0-1 ft Backfill: 1-6 ft Backfill: 6-11 ft In-Situ Soil Modulus of Elasticity, E (ksf) 230.4 576.0 864.0 864.0 Poissonâs Ratio (v) 0.4 0.29 0.24 0.25 Unit Weight (pcf) 121 121 121 127 Initial Cohesion (psf) 0.000144 0.000144 0.000144 - Initial Friction Angle 40 40 40 - Final Friction Angle 40 40 40 - Dilation Angle 10 10 10 - Cohesion Hardening (psf) 0 0 0 - Limiting Plastic Strain 0.001 0.001 0.001 - Appendix E - 3D Modeling Backup E-59
Figure 54. M3C1- Geometry and Culvert Thickness Assignment Appendix E - 3D Modeling Backup E-60
Figure 55. M3C1- Resultant Displacement of Solid Elements â 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-61
Figure 56. M3C1- Vertical Displacement of Solid Elements - 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-62
Figure 57. M3C1- Von Mises Strain of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-63
Figure 58. M3C1- Vertical Strain (EV) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-64
Figure 59. M3C1- Horizontal Strain (EX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-65
Figure 60. M3C1- Von Mises Stress of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-66
Figure 61. M3C1- Vertical Stress (SY) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-67
Figure 62. M3C1- Horizontal Stress (SX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-68
Figure 63. M3C1- Vertical Displacement of Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-69
Figure 64. M3C1- Von Mises Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-70
Figure 65. M3C1- Von Mises Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-71
Figure 66. M3C1- Bending Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-72
Figure 67. M3C1- Bending Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-73
Figure 68. M3C1- Von Mises Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-74
Figure 69. M3C1- Von Mises Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-75
Figure 70. M3C1- Bending Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-76
Figure 71. M3C1- Bending Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-77
MODEL 6- CANDIDATE 2 (M6C2) Model 6 represents a prototype of corrugated metal box culverts. Candidate 2 is selected for this category. Geometry Geometry and layout of Model 6 Candidate 2 (M6C2) is presented in Appendix D. Figure 72 presents the section of the culvert and the equivalent geometry that is modeled in Lusas. Thickness of the corrugated metal sheet and modulus of elasticity are adjusted to capture the behavior of the corrugated metal sheet. The Lusas model includes the entire length of the culvert. As shown in Figure 72, the span of culvert is 19â and the depth of the model extends to 23â-7.5ââ. Laterally, the geometry extends to 37â-6â on each side. Therefore, the cross section of model is 23â-7.5âx75â and the length is 44â-3â. A concrete 2âWx1.5âD footing is modeled at each end of the arch culvert. A 1â-6â deep pavement is assumed over the culvert, where the live load is applied to the structure. The slope of backfill is assumed 450. Material Properties Given that corrugated metal sheets have different axial and flexural behavior in two directions, orthotropic material properties are used to define the behavior of the culvert. For Model 6, a Lusas model using the appropriate corrugated aluminum sheet sections and type IV ribs was generated and a point load was applied at the center of the section. Using the model with the corrugations, a model with thin shell sections was generated and its material properties adjusted until deflections on both models were similar (Figure 74). Corrugated cross sections and simulated plate cross sections for top and bottom part of the culvert are shown in Figure 73. The following steps were taken to generate thin shell sections that will produce similar deflections: 1- Elastic modulus in the x direction was set as 9,940 ksi, which is the elastic modulus of aluminum. 2- Thickness of the thin shell element was adjusted until vertical deflections match vertical deflections of the corrugated sheet section model. The thickness values that would provide similar results were 3â for top sheets and 2.25â for side sheets. 3- Elastic modulus in the y direction was modified until deflections in this direction match deflections obtained from the corrugated sheet section model. The elastic modulus in the y direction was selected as 1/100,000 of the elastic modulus in the x direction. Overlay and pavement is defined as a linear material with modulus of elasticity (E) = 4000 ksi, Poissonâs ratio (ν) = 0.35, and unit weight = 140 pcf. The linear material properties of concrete footings are generated based on AASHTO LRFD Bridge Design Specifications for compressive strength of fâc = 5 ksi: modulus of elasticity (E) = 4074 ksi, Poissonâs ratio (ν) = 0.2, unit weight = 150 pcf, and coefficient of thermal expansion (α) = 10.8 e-6 1/C. Table 4 presents the material properties of in-situ soil and backfill. In-situ soil is defined as an elastic material, while nonlinear material properties are considered for backfill, varying with depth. The values in Table 4 are adopted from previous study by McGrath et al. (2005). Mesh Quadrilateral quadratic thin shell elements are used to model the culvert. Given that the corrugated metal sheet is quite thin, transferred shear through the section is minimal, hence thin shell element may effectively capture the behavior of the culvert. Appendix E - 3D Modeling Backup E-78
Hexahedral quadratic solid elements are used to model the pavement (overlay), footings, in-situ soil, and backfill. Due to limitation of number of elements and large dimensions for M7C1, the mesh size is set to 1â around the culverts and in backfill and 4â at the boundaries. The mesh size along the length of culvert is 5â- 6â. Boundary Condition At the end of the in-situ soil medium, perpendicular restraints are used for each boundary surface, i.e. lateral restraints at vertical faces and vertical restraints at the bottom of the in-situ soil. âTied Mesh Constraintsâ are assigned between the culvert and soil as well as the culvert and overlay to assure deformation compatibility. This option assures compatible deformation of adjacent shell elements and solid elements. No contact element or interaction properties are assigned. Load Cases Gravity is applied as a body force. Soil pressure is considered using vertical and lateral pressure (to provide in-situ conditions with close to zero deflections under soil self-weight). Live Load: Wheel load is modeled as a discrete patch load over a 10âx20â area. A load case with single axle load in three lanes and a load case with standard HL-93 truck moving load is applied to the model. The truck load is moved across the culvert to capture the critical loading condition. The live load will be updated when the wheel load of the actual truck that is used in the experiment is determined. Results Figures 77 to 93 present the behavior of M6C2 in terms of displacement, strains and stresses under axle load at center of the culvert. Due to the skew, the axle loads are positioned so that the center of each axle passes through the centerline of culvert, as shown in Figure 76. Because for nonlinear analysis, all loads must be applied sequentially, gravity and dead loads are applied first, then live load is applied and the final results are under both dead load and live load. Given that for experimental study, only the effect of live load is measured, a load combination is defined in Lusas that removes the effect of dead load by subtracting the results of âdead load analysisâ from the results after application of live load. It should be noted that maximum and minimum envelopes of results under moving loads are available, however, given that Lusas develops two separate envelopes for maximum and minimum, contour presentation may become misleading, unless both envelopes are compared side by side. This is especially important when the dead load effects (constant) are being deduced from the total âdead + live loadâ results. Results of envelop results of moving loads will be presented later where a specific entity or stage of loading is determined. Table 4. M6C2- Material Properties of Backfill and In-Situ Soil Properties Backfill: 0-1 ft Backfill: 1-6 ft Backfill: 6-11 ft In-Situ Soil Modulus of Elasticity, E (ksf) 230.4 576.0 864.0 864.0 Poissonâs Ratio (v) 0.4 0.29 0.24 0.25 Unit Weight (pcf) 121 121 121 127 Initial Cohesion (psf) 0.000144 0.000144 0.000144 - Initial Friction Angle 40 40 40 - Final Friction Angle 40 40 40 - Dilation Angle 10 10 10 - Cohesion Hardening (psf) 0 0 0 - Limiting Plastic Strain 0.001 0.001 0.001 - Appendix E - 3D Modeling Backup E-79
Figure 72. M6C2- Cross Section Appendix E - 3D Modeling Backup E-80
(a) Top Cross Section (b) Bottom Cross Section Figure 73. M6C2- Corrugated Cross Section and Simulated Plate Cross Section TYPE IV CORRUGATED SHEET THIN SHELL CORRUGATED SHEET THIN SHELL 3" 1'-6" 0.225" 0.125" 214" 1'-6" CORRUGATED SHEET THIN SHELL THIN SHELL CORRUGATED SHEET TYPE IV Appendix E - 3D Modeling Backup E-81
Figure 74. M6C2- Corrugation Simulation: Resultant Displacements â 1 kip Load at Center. Appendix E - 3D Modeling Backup E-82
Figure 75. M6C2- Corrugation Simulation: Von Mises Stress at Top Fiber â 1 kip Load at Center. Appendix E - 3D Modeling Backup E-83
Figure 76. M6C2- Positioning of Truck Axles in Two Lanes for Maximum Mid-span Deflection Appendix E - 3D Modeling Backup E-84
Figure 77. Resultant Displacement of Solid Elements â 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-85
Figure 78. Vertical Displacement of Solid Elements - 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-86
Figure 79. Von Mises Strain of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-87
Figure 80. Vertical Strain (EY) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-88
Figure 81. Horizontal Strain (EX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-89
Figure 82. Von Mises Stress of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-90
Figure 83. Vertical Stress (SY) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-91
Figure 84. Horizontal Stress (SX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-92
Figure 85. Vertical Displacement of Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-93
Figure 86. Von Mises Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-94
Figure 87. Von Mises Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-95
Figure 88. Bending Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-96
Figure 89. Bending Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-97
Figure 90. Von Mises Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-98
Figure 91. Von Mises Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-99
Figure 92. Bending Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-100
Figure 93. Bending Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-101
MODEL 7- CANDIDATE 1 (M7C1) Model 7 represents a prototype of deep corrugated metal culverts. Candidate 1 is selected for this category. Geometry Geometry and layout of Model 7 Candidate 1 (M7C1) is presented in Appendix E. Figure 94 presents the section of the culvert and the equivalent geometry that is modeled in Lusas. Thickness of the corrugated metal sheet and moduli of elasticity are adjusted to capture the behavior of the corrugated metal sheet. The Lusas model includes the entire length of the culvert. As shown in Figure 94, the span of culvert is 57â and the depth of the model extends to 64â. Laterally, the geometry extends to 97â on each side. Therefore, the cross section of model is 194âx64â and the length is 50â. A concrete 5Wx4D footing is modeled at each end of the arch culvert. A 2.5 ft deep pavement is assumed between the footings providing temporary road access through the culvert. Another 2.5 ft deep pavement is assumed over the culvert, where the live load is applied to culvert. The slope of backfill is assumed 1:2 vertical to horizontal. Material Properties Given that corrugated metal sheets have different axial and flexural behavior in two directions, orthotropic material properties are used to define the behavior of the culvert. However, according to Samanta and Mukhopadhyay (1997), Wennberg, et al. (2011), and Briassoulis (1985), both flexural and axial properties of the corrugated sheets are different, and by defining an orthotropic material, only one of the axial or flexural behavior may be adjusted. Given that the ratio of correction factors, for the existing model, material is defined so that the modulus of elasticity in weak axis (Ex) is adjusted for axial behavior, and in strong axis it is adjusted for flexural behavior. Other combinations of material properties are formulated and by using experimental data, the appropriate behavior may be selected. Formulation and adjustment factors are adopted from Samanta and Mukhopadhyay (1997). Originally, the thickness of the culvert elements was set to the actual value (0.2391â) and the moduli of elasticity were set accordingly. The corrugation effects and orthotropic behavior were captured perfectly. However, due to the very small thickness, the culvert showed localized deformations at the footing. Therefore, the thickness of the corrugation was increased to avoid the localized deformation and stress concentration issue. Finally, the moduli of elasticity were adjusted accordingly to represent the same behavior according to formulation of Samanta and Mukhopadhyay (1997). Overlay and pavement is defined as a linear material with modulus of elasticity (E) = 4000 ksi, Poissonâs ratio (ν) = 0.35, and unit weight = 140 pcf. The linear material properties of concrete footings are generated based on AASHTO LRFD Bridge Design Specifications for compressive strength of fâc = 5 ksi: modulus of elasticity (E) = 4074 ksi, Poissonâs ratio (ν) = 0.2, unit weight = 150 pcf, and coefficient of thermal expansion (α) = 10.8 e-6 1/C. Table 5 presents the material properties of in-situ soil and backfill. In-situ soil is defined as an elastic material, while nonlinear material properties are considered for backfill, varying with depth. The values in Table 5 are adopted from previous study by McGrath et al. (2005). Mesh Quadrilateral quadratic thin shell elements are used to model the culvert. Given that thickness of the corrugated metal sheet very small, transferred shear through the section is minimal, hence the thin shell element may effectively capture the behavior of the culvert. Hexahedral quadratic solid elements are used to model the pavement (overlay), footings, in-situ soil, and backfill. Due to limitation of number of elements and large dimensions for M7C1, the mesh size is set to 3â around the culverts and in backfill and 15â at the boundaries. The mesh along the length of culvert varies Appendix E - 3D Modeling Backup E-102
between 8â at edges to 2ââ at center. A sensitivity analysis in linear mode showed that the current mesh size provides comparable results with finer mesh. Boundary Condition At the end of the in-situ soil medium, perpendicular restraints are used for each boundary surface, i.e. lateral restraints at vertical faces and vertical restraints at the bottom of the in-situ soil. âTied Mesh Constraintsâ are assigned between the culvert and soil as well as the culvert and overlay to assure deformation compatibility. This option assures compatible deformation of adjacent shell elements and solid elements. No contact element or interaction properties are assigned. Load Cases Gravity is applied as a body force. Soil pressure is considered using vertical and lateral pressure (to provide in-situ conditions with close to zero deflections under soil self-weight). Live Load: Wheel load is modeled as a discrete patch load over a 10âx20â area. A load case with single axle load in three lanes and a load case with standard HL-93 truck moving load is applied to the model. The truck load is moved across the culvert to capture the critical loading condition. The live load will be updated when the wheel load of the actual truck that is used in the experiment is determined. Results Figures 95 to 111 present the behavior of M7C1 in terms of displacement, strains and stresses under axle load at center of the culvert. Because for nonlinear analysis, all loads must be applied sequentially, gravity and dead loads are applied first, then live load is applied and the final results are under both dead load and live load. Given that for experimental study, only the effect of live load is measured, a load combination is defined in Lusas that removes the effect of dead load by subtracting the results of âdead load analysisâ from the results after application of live load. It should be noted that maximum and minimum envelopes of results under moving loads are available, however, given that Lusas develops two separate envelopes for maximum and minimum, contour presentation may become misleading, unless both envelopes are compared side by side. This is especially important when the dead load effects (constant) are being deduced from the total âdead + live loadâ results. Results of envelop results of moving loads will be presented later where a specific entity or stage of loading is determined. Table 5. M7C1- Material Properties of Backfill and In-Situ Soil Properties Backfill: 0-1 ft Backfill: 1-6 ft Backfill: 6-11 ft In-Situ Soil Modulus of Elasticity, E (ksf) 230.4 576.0 864.0 864.0 Poissonâs Ratio (v) 0.4 0.29 0.24 0.25 Unit Weight (pcf) 121 121 121 127 Initial Cohesion (psf) 0.000144 0.000144 0.000144 - Initial Friction Angle 40 40 40 - Final Friction Angle 40 40 40 - Dilation Angle 10 10 10 - Cohesion Hardening (psf) 0 0 0 - Limiting Plastic Strain 0.001 0.001 0.001 - Appendix E - 3D Modeling Backup E-103
Figure 94. M7C1- Cross Section Appendix E - 3D Modeling Backup E-104
` Figure 95. Resultant Displacement of Solid Elements â 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-105
Figure 96. Vertical Displacement of Solid Elements - 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-106
Figure 97. Von Mises Strain of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-107
Figure 98. Vertical Strain (EV) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-108
Figure 99. Horizontal Strain (EX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-109
` Figure 100. Von Mises Stress of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-110
Figure 101. Vertical Stress (SY) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-111
Figure 102. Horizontal Stress (SX) of Solid Elements- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-112
Figure 103. Vertical Displacement of Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-113
Figure 104. Von Mises Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-114
Figure 105. Von Mises Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-115
Figure 106. Bending Strain at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-116
Figure 107. Bending Strain at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-117
Figure 108. Von Mises Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-118
Figure 109. Von Mises Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-119
Figure 110. Bending Stress at Top Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-120
Figure 111. Bending Stress at Bottom Fiber in Culvert- 2 Lane 32 k Axle at Center of Culvert Appendix E - 3D Modeling Backup E-121
Appendix F â Field Testing Plans Fâ1 Appendix F â Field Testing Plans This appendix provides the field testing plans developed for the seven culverts that were field tested for this project.Â
Appendix F â Field Testing Plans Fâ2 Model 1 â Testing Plan â Reinforced Concrete Box â Single Cell  Site/GeneralÂ ï· Single will be conducted â Instrumentation will be installed week of Aug 21, 2017 and load tested the following week. Gauges operation will be verified after installation and prior to test. ï· Test vehicles â Weighed test vehicle (Triaxle dump with raised axle) will be provided by PennDOT District forces. Each wheel of truck to be weighed. ï· PennDOT District will also provide traffic control during the test phase. No traffic control during gauge installation will be required. InstrumentationÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along a single line near the center of the travelway the culvert. If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the slab midspan locations. ï· Strain- 5 locations minimum as shown above, midspan of top and bottom slabs and at corners as close as possible to the edge of the haunch (measure actual distance). If time permits, mount backup redundant gauges. The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work, assisted by Baker. ï· String pot gauges, where possible, will be mounted to collect deflection data at slab midspan by mounting to a reference frame supported at locations unaffected by the truck loading. PreâtestÂ ï· Install instruments and test proper operation TrucksÂ ï· Trucks to be provided by PennDOT per cooperative letter. All trucks shall be consistent with design loadings. District indicated they can provide a dump truck with 3 rear axles ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. Primary gauge location Secondary gauge locationÂ
Appendix F â Field Testing Plans   Fâ3  TestÂ ï· Measure axle loads (see above) ï· Record air and pavement temperature (if still warm) ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Three vehicle paths will be established â one with a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) and the third with the wheel line 3 feet from the line of gauges and the second wheel line is 9 feet from the gauge line. Two passes will be made along each of these passes of the truck, stopping as each wheel/axle passes directly over a gauge TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day ï· Load testing â approx ½ day ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the PennDOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments Week of Aug 21, 2017 Load Test Week of Aug 28, 2017  Â
Appendix F â Field Testing Plans Fâ4 Testing Data General Location: State: Pennsylvania Route: 3020 Latitude-Longitude: 40.3538, -77.6488 (click link to open in browser) Actual Instrumentation Date: August 28-29, 2017 Actual Testing date: August 30, 2017 Weather/Other Test conditions: 61 F, Sunny Contractor Personnel: Dave Barrett, Chad Clancy (Modjeski & Masters) Mike Pichura, Mark Mlynarski (Michael Baker International) State Personnel/Contacts: George Helsey | Pennsylvania Department of Transportation District 2-0 George Prestash III, P.E. | District Bridge Engineer Pennsylvania Department of Transportation | Engineering District 2-0 70 PennDOT Drive | Clearfield, PA 16830
Appendix F â Field Testing Plans   Fâ5  Truck Wheel Load and Spacing Data/ Truck Positioning Data  Figure 1 â Wheel loads/configurations for Model 1âCandidate 1 (M1C1)  Â
Appendix F â Field Testing Plans Fâ6 Lift axle up runs CL of left wheel running on gauge line Wheel Position Time 1 1 10:21 1 2 10:22 1 3 10:23 1 4 10:24 1 5 10:24 2 1 10:27 2 2 10:27 2 3 10:28 2 4 10:29 2 5 10:30 3 1 10:33 3 2 10:34 3 3 10:35 3 4 10:36 3 5 10:36 CL of truck running on gauge line Wheel Position Time 1 3 10:40 2 3 10:41 3 3 10:42 Lift Axle Down runs CL of left wheel over CL gauge line Wheel Position Time 1 1 10:45 1 2 10:46 1 3 10:47 1 4 10:47 1 5 10:48 L 1 10:50 L 2 10:50 L 3 10:51 L 4 10:52Â
Appendix F â Field Testing Plans   Fâ7    5 10:52       2 1 10:54 2 2 10:54 2 3 10:55 2 4 10:56 2 5 10:56       3 1 10:59 3 2 10:59 3 3 11:00 3 4 11:01 3 5 11:01  CL of truck running on gauge line     Wheel Position Time 1 3 11:03 L 3 11:04 2 3 11:05 3 3 11:06       Left wheel on CL gauge line     Lift axle down     5 mph speed going across culvert     Time: 11:08    Wheel Position Descriptions (typ)  1 Wheel centered over inside face of culvert vertical wall 2 Wheel at first quarter point on top slab 3 Wheel centered over midspan (2nd quarter point) 4 Wheel at third quarter point on top of slab 5 Wheel centered over inside face of far culvert vertical wall      All wheels were spaced at 6ââ2â centerâcenter of wheel on each axle The front wheel was 13 inches wide  The Lift axle wheels were 2@8.5â wide with an outâout width of 22â The #2 axle (2nd from rear) wheels were 2@9â wide with an outâout width of 22.5â The #3 axle (rear) wheels were 2@9â wide with an outâout width of 22.5âÂ
Appendix F â Field Testing Plans Fâ8 Culvert Plans Figure 2 â Model 1, Candidate 1 (M1C1) â Plan and Typical SectionÂ
Appendix F â Field Testing Plans   Fâ9  Model 2 â Testing Plan â Reinforced Concrete Box â Twin Cell  Site/GeneralÂ Â ï· Instrumentation will be installed week of Dec 11, 2017 and load tested the same week. Gauges operation will be verified after installation and prior to test. ï· Test truck to be on site at 10am, traffic control needed starting at 9am ï· Test vehicles â Weighed test vehicle will be provided by Maryland DOT forces. Each wheel of truck to be weighed. ï· Maryland DOT will also provide traffic control during the test phase. No traffic control during gauge installation will be required, however, traffic control will be required 1 hour prior to testing to lay out load path line. Instrumentation Figure 3 â Instrumentation locations Primary gauge location Secondary gauge locationÂ
Appendix F â Field Testing Plans Fâ10 Figure 4 â Plan ViewÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the culvert segment (based on the orientation of the reinforcing, the line of sensors are to be installed along a line parallel to the traffic/outside edges of the culvert). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the slab midspan locations. ï· Strain- locations minimum as shown above, midspan of top and bottom slabs and at corners as close as possible to the edge of the haunches (measure actual distance). If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work, assisted by Baker. ï· String pot gauges, where possible, will be mounted to collect deflection data at slab midspans by mounting to a reference frame supported at locations unaffected by the truck loading. PreâtestÂ ï· Install instruments and test proper operation TrucksÂ ï· A loaded truck to be provided by Maryland DOT per cooperative letter. All trucks shall be consistent with design loadings. District indicated they can provide a dump truck ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. TestÂ ï· Measure individual wheel loads (Maryland DOT to work with State Police to obtain, see above) ï· Record air and pavement temperature
Appendix F â Field Testing Plans   Fâ11Â Â ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Vehicle paths will be established as shown in layout diagramâwith a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) Each wheel will be stopped over the vertical culvert wall, ¼ point and at midspan of the culvert top slab. In the event gauges are placed at the midspan locations of the second span, a wheel stop location will be placed at midspan of that cell. TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day ï· Load testing â approx ½ day ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the DOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments Week of Dec 11, 2017 Load Test Dec 14th (Rain date Dec 13th), 2017  Â
Appendix F â Field Testing Plans Fâ12 Testing Data General Location: State: Maryland DOT Route: SR 7 (Philadelphia RD) Latitude-Longitude: 39.411056, -76.409278 (click link to open in browser) Actual Instrumentation Date: December 12, 2017 Actual Testing date: December 13, 2017 Weather/Other Test conditions: 25 F, Sunny Contractor Personnel: Dave Barrett (Modjeski & Masters) Mike Pichura, Aaron Colorito (Michael Baker International) State Personnel/Contacts: Justin Mohr, P.E. MDOT Maryland State Highway Administration â Office of Structures 707 N. Calvert Street, MS â 203 Baltimore, MD 21202 410.545.8365 jmohr@sha.state.md.us
Appendix F â Field Testing Plans   Fâ13  Truck Wheel Load and Spacing Data/ Truck Positioning Data    Figure 5 â Wheel loads/configurations/testing times for Model 2âCandidate 1 (M2C1)  Â
Appendix F â Field Testing Plans Fâ14 Culvert Plans Figure 6 â Model 2, Candidate 1 (M2C1) â Plan and Typical SectionÂ
Appendix F â Field Testing Plans   Fâ15  Model 3 â Testing Plan â Reinforced Concrete Box â Single Cell Precast   Site/GeneralÂ Â ï· Instrumentation will be installed week of Nov 6, 2017 and load tested the same week. Gauges operation will be verified after installation and prior to test. ï· Test truck to be on site at 10am, traffic control needed starting at 9am ï· Test vehicles â Weighed test vehicle will be provided by PennDOT District forces. Each wheel of truck to be weighed. ï· PennDOT District will also provide traffic control during the test phase. No traffic control during gauge installation will be required, however, traffic control will be required 1 hour prior to testing to lay out load path line. Instrumentation Figure 7 â Instrumentation locationsÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the the culvert segment (see figure above and layout figure at the end of the testing plan). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the slab midspan locations. ï· Strain- locations minimum as shown above, midspan of top and bottom slabs and at corners as close as possible to the edge of the haunch (measure actual distance). If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski & Masters will perform this work, assisted by Baker. ï· String pot gauges, where possible, will be mounted to collect deflection data at slab midspan by mounting to a reference frame supported at locations unaffected by the truck loading. PreâtestÂ ï· Install instruments and test proper operation Primary gauge location Secondary gauge locationÂ
Appendix F â Field Testing Plans Fâ16 TrucksÂ ï· A loaded truck to be provided by PennDOT per cooperative letter. All trucks shall be consistent with design loadings. District indicated they can provide a dump truck ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. TestÂ ï· Measure individual wheel loads (PennDOT to work with State Police to obtain, see above) ï· Record air and pavement temperature ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Vehicle paths will be established as shown in layout diagramâwith a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) Each wheel will be stopped over the vertical culvert wall, ¼ point and at midspan of the culvert top slab. TimeÂ ï· Gauge/Target/Wiring installation and setup â approximately 1 day ï· Load testing â approximately ½ day ResultsÂ ï· Per NCHP policy, test results cannot be shared with the PennDOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments Week of Nov 6, 2017 Load Test Nov 7th (Rain date Nov 8th), 2017
Appendix F â Field Testing Plans   Fâ17  Figure 8 â Culvert Photo  Figure 9 â Layout diagramÂ
Appendix F â Field Testing Plans Fâ18 Figure 10 â Culvert Segments Figure 11 â Possible Truck Detour, if RequiredÂ
Appendix F â Field Testing Plans   Fâ19  Testing Data General Location: State: Pennsylvania Route: SR 281 Latitude-Longitude: 40.0513, -78.9943 (click link to open in browser)   Actual Instrumentation Date: 11/5/2017-11/6/2017 Actual Testing date: 11/7/2017 Weather/Other Test conditions: 36 F, Sunny Contractor Personnel: Dave Barrett (Modjeski & Masters) Mike Pichura, (Michael Baker International) Aaron Colorito (Michael Baker International) State Personnel/Contacts: Ralph DeStefano, P.E. District 9-0 Bridge Engineer William D. Oleksak, P.E. District Maintenance Manager Engineering District 9-0 1620 North Juniata Street Hollidaysburg, PA 16648 (814) 696-7129   Â
Appendix F â Field Testing Plans Fâ20 Truck Wheel Load and Spacing Data/ Truck Positioning Data Figure 12 â Wheel loads/configurations/testing times for Model 3âCandidate 1 (M3C1)Â
Appendix F â Field Testing Plans   Fâ21  Culvert Plans    Figure 13 â Model 3, Candidate 1 (M3C1) â Plan and Typical Section  Â
Appendix F â Field Testing Plans Fâ22 Model 4 â Testing Plan â Reinforced Concrete Arch Site/GeneralÂ ï· Instrumentation will be installed week of April 16, 2018 and load tested the same week. Gauges operation will be verified after installation and prior to test. ï· Test truck to be on site at 10am, traffic control needed starting at 9am ï· Test vehicles â Weighed test vehicle will be provided by Ohio DOT forces. Each wheel of truck to be weighed. Contact info: Shawn Rostorfer Highway Management Administrator District 6 400 E. William St., Delaware, OH 43015 740.833.8069 ï· Ohio DOT will also provide traffic control during the test phase. No traffic control during gauge installation will be required, however, traffic control will be required 1 hour prior to testing to lay out load path line. Instrumentation Figure 14 â M4C1 Instrumentation locationsÂ
Appendix F â Field Testing Plans   Fâ23   Figure 15 â M4C1 Load Traffic LineÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the culvert segment (based on the orientation of the reinforcing, the line of sensors are to be installed along a line parallel to the traffic/outside edges of the culvert). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the slab midspan locations. ï· Strain- locations minimum as shown above, midspan of top slabs and at corners as close as possible to the specified locations and measurements taken to record their exact position If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work, assisted by Baker. ï· String pot gauges, where possible, will be mounted to collect deflection data at slab midspans by mounting to a reference frame supported at locations unaffected by the truck loading.  PreâtestÂ ï· Install instruments and test proper operation TrucksÂ ï· A loaded truck to be provided by Ohio DOT per cooperative letter. All trucks shall be consistent with design loadings. ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. TestÂ ï· Measure individual wheel loads (Ohio DOT to work with State Police to obtain, see above) ï· Record air and pavement temperature
Appendix F â Field Testing Plans Fâ24Â ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Vehicle paths will be established as shown in layout diagramâwith a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) Each wheel will be stopped over the vertical culvert wall, ¼ point and at midspan of the culvert top slab. In the event gauges are placed at the midspan locations of the second span, a wheel stop location will be placed at midspan of that cell. TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day ï· Load testing â approx ½ day ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the DOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments Week of April 16, 2018 Load Test April 16, 2018
Appendix F â Field Testing Plans   Fâ25  Testing Data General Location: State: Ohio DOT Route: SR 669 Latitude-Longitude: 39.79083, -82.25111 (click link to open in browser)   Actual Instrumentation Date: 4/16/2018 Actual Testing date: 4/17/2018 Weather/Other Test conditions: 31 F, Snow Contractor Personnel: Dave Barrett (Modjeski & Masters) Mike Pichura, (Michael Baker International) Gerry Jones (Michael Baker International) State Personnel/Contacts: Shawn Rostorfer Highway Management Administrator District 6 400 E. William St., Delaware, OH 43015 740.833.8069   Â
Appendix F â Field Testing Plans Fâ26 Truck Wheel Load and Spacing Data Figure 16 â Wheel loads/configurations/testing times for Model 4âCandidate 1 (M4C1)Â
Appendix F â Field Testing Plans   Fâ27  Truck Positioning Data  MODEL 4 CULVERT NAME: SR 669 OVER CENTER BRANCH RUSH CREEK       DISTRICT/COUNTY : DISTRICT 5/ PERRY COUNTY BMS NO.:   BR KEY:   DATE: 4/17/2018           SNOW â 31 °F  0.00L = East end   NO LIFT AXLE ON TRUCK   TEST TRUCK â ON LOAD LINE QUARTER POINT WHEEL 1 2 3   0.00 L 9:53:55 AM 9:58:13 AM 10:01:45 AM   0.25 L 9:54:21 AM 9:58:48 AM 10:02:11 AM   0.50 L 9:54:46 AM 9:59:24 AM 10:02:35 AM   0.75 L 9:55:12 AM 9:59:53 AM 10:03:00 AM   1.00 L 9:55:40 AM 10:00:26 AM 10:03:28 AM    TEST TRUCK â CENTERED ABOUT LOAD LINE QUARTER  POINT WHEEL 1 2 3   0.00 L 10:10:46 AM 10:14:33 AM 10:17:47 AM   0.25 L 10:11:16 AM 10:14:55 AM 10:18:12 AM   0.50 L 10:11:40 AM 10:15:20 AM 10:18:39 AM   0.75 L 10:12:11 AM 10:15:47 AM 10:19:05 AM   1.00 L 10:12:35 AM 10:16:19 AM 10:19:30 AM       Â
Appendix F â Field Testing Plans Fâ28 Culvert Plans Figure 17 â Model 4, Candidate 1 (M4C1) â Plan and Typical SectionÂ
Appendix F â Field Testing Plans   Fâ29  Model 5 â Testing Plan â Metal Arch  Site/GeneralÂ ï· Instrumentation will be installed week of June 11, 2018 and load tested the same week. Gauges operation will be verified after installation and prior to test. ï· Test truck to be on site at 9am, traffic control needed starting at 8:30am ï· Test vehicles â Weighed test vehicle will be provided the township and weighed by PA State Police forces. Each wheel of truck to be weighed. Contact info: Greg Fisher â PA State Police 717-346-7330 Lower Paxton will also provide traffic control during the test phase. No traffic control during gauge installation will be required. Instrumentation Figure 18 â M5C1 Instrumentation locationsÂ
Appendix F â Field Testing Plans Fâ30 North Upstream Down stream Figure 19 â M5C1 Load Traffic LineÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the culvert segment (based on the orientation of the culvert span/ribs, the line of sensors are to be installed along a line parallel to the traffic/outside edges of the culvert). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the culvert midspan locations. ï· Strain- locations minimum as shown above, midspan of top of the metal culvert and at corners as close as possible to the specified locations and measurements taken to record their exact position If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work. See photos and time/data spreadsheet for arc length to gauges relative to the centerline of culvert gauge. ï· String pot gauges, where possible, will be mounted to collect deflection data at midspan by mounting to a reference frame supported at locations unaffected by the truck loading. PreâtestÂ ï· Install instruments and test proper operation
Appendix F â Field Testing Plans   Fâ31  TrucksÂ ï· A loaded truck to be provided by Lower Paxton Township per coordination Jeff Kline (717-364-9983). All trucks shall be consistent with design loadings. ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. TestÂ ï· Measure individual wheel loads (State Police to obtain, see above) ï· Record air and pavement temperature ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Vehicle paths will be established as shown in layout diagramâwith a wheel line directly over the gauges, if feasible, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) Each wheel will be stopped over the vertical culvert wall, ¼ point and at midspan of the culvert top. TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day Load testing â approx ½ day ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the DOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments June 11, 2018 Load Test June 12, 2018, Rain Date June 13  Â
Appendix F â Field Testing Plans Fâ32 Testing Data General Location: State: Pennsylvania Route: Latitude-Longitude: 40.300437, -76.8018666 (click link to open in browser) Actual Instrumentation Date: 6/11/2018 Actual Testing date: 6/12/2018 Weather/Other Test conditions: 82 F at 10:15 AM Contractor Personnel: Dave Barrett (Modjeski & Masters) Chad Clancy (Modjeski & Masters) State Personnel/Contacts: Jeff Kline Lower Paxton Township (717-364-9983) Greg Fisher â PA State Police 717-346-7330
Appendix F â Field Testing Plans   Fâ33  Truck Wheel Load and Spacing Data Wheel Loads       Axle Left Right  Tire widths Axle widths  1 (Front) 8450 lb 9250 lb  10.5" 90" outâout 2 9000 lb 11,600 lb  9" each and 22" outâout 95" outâout 3 (Rear) 9700 lb 10,700 lb  9" each and 22" outâout 95" outâout       Axle Spacings     14'â5" Axle 1 â Axle 2     4'â3" Axle 2 â Axle 3     Culvert Data     Curb height: 9.5 inches     Top of curb to top of headwall distance at south corners of headwall     Upstream Side 27"      Downstream Side 23"    CurbâCurb Roadway distance = 30'    Load Line description Load line 1 is centered over line of gauges and is parallel to the culvert ends (follows rib of corrugation).  Right wheel of truck is centered on load line. Load line 2 is parallel to load line 1 and offset 3 feet to the right.  This places approx center of truck centered over the centerline of gauges when right wheel is on this line.        Load Points Description      1 South edge of culvert     2 First quarter point     3 Midspan of culvert     4 Quarter point between midspan and north edge   5 North Edge of culvert     Arc distances to gauges:      1/2 â> 3/4 83.5 inches     3/4 â> 5/6 71 inches     5/6 â> 7/8 67.5 inches     7/8 â> 9/10 87 inches     Â
Appendix F â Field Testing Plans Fâ34 Figure 20 â Wheel loads/configurations for Model 5âCandidate 1 (M5C1) Truck Positioning Data Pass #1: Load Line 1  (Note: Passes 1 and 2 were repeated as 3 and 4 after removing charger that was causing extraneous signal noise) Load Point Axle No Time 1 1 9:29:40 2 1 9:30:20 3 1 9:30:55 4 1 9:31:28 5 1 9:31:58 1 2 9:33:25 2 2 9:33:50 3 2 9:34:15 4 2 9:34:48 5 2 9:35:22 1 3 9:38:38 2 3 9:39:43 3 3 9:40:09 4 3 9:40:34Â
Appendix F â Field Testing Plans   Fâ35  5 3 9:40:57 Pass #2: Load Line 2  (Note: Passes 1 and 2 were repeated as 3 and 4 after removing charger that was causing extraneous signal noise) Load Point Axle No Time 1 1 9:42:16 2 1 9:42:36 3 1 9:42:53 4 1 9:43:16 5 1 9:43:41       1 2 9:44:49 2 2 9:45:13 3 2 9:45:35 4 2 9:45:59 5 2 9:46:24       1 3 9:47:20 2 3 9:47:55 3 3 9:48:10 4 3 9:48:35 5 3 9:49:15       1 3 9:51:30 2 3 9:51:45 3 3 9:52:05 4 3 9:52:46 5 3 9:53:07   Â
Appendix F â Field Testing Plans Fâ36 Pass #3: Load Line 1  (Note: Passes 1 and 2 were repeated as 3 and 4 after removing charger that was causing extraneous signal noise) Load Point Axle No Time 1 1 10:01:00 2 1 10:01:25 3 1 10:01:50 4 1 10:02:20 5 1 10:02:45 1 2 10:03:57 2 2 10:04:23 3 2 10:04:45 4 2 10:05:08 5 2 10:05:30 1 3 10:06:30 2 3 10:06:52 3 3 10:07:10 4 3 10:07:30 5 3 10:07:50Â
Appendix F â Field Testing Plans   Fâ37  Pass #4: Load Line 2  (Note: Passes 1 and 2 were repeated as 3 and 4 after removing charger that was causing extraneous signal noise) Load Point Axle No Time 1 1 10:09:15 2 1 10:09:35 3 1 10:09:55 4 1 10:10:10 5 1 10:10:33       1 2 10:11:30 2 2 10:11:44 3 2 10:12:11 4 2 10:12:30 5 2 10:12:48       1 3 10:11:30 2 3 10:11:44 3 3 10:12:11 4 3 10:12:30 5 3 10:12:48    Â
Appendix F â Field Testing Plans Fâ38 Culvert Plans Figure 21â Model 5, Candidate 1 (M5C1) â Plan and Typical SectionÂ
Appendix F â Field Testing Plans   Fâ39  Model 6 â Testing Plan â Metal Arch  Site/GeneralÂ ï· Instrumentation will be installed week of May 2, 2018 and load tested the same week. Gauges operation will be verified after installation and prior to test. ï· Test truck to be on site at 10am, traffic control needed starting at 9am ï· Test vehicles â Weighed test vehicle will be provided by PA State Police forces. Each wheel of truck to be weighed. Contact info: Greg Fisher â PA State Police 717-346-7330 ï· Carroll Township will also provide traffic control during the test phase. No traffic control during gauge installation will be required, however, traffic control will be required 1 hour prior to testing to lay out load path line. Instrumentation  Figure 22 â M6C2 Instrumentation locationsÂ
Appendix F â Field Testing Plans Fâ40 Figure 23 â M6C2 Load Traffic LineÂ ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the culvert segment (based on the orientation of the culvert span/ribs, the line of sensors are to be installed along a line parallel to the traffic/outside edges of the culvert). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the culvert midspan locations. ï· Strain- locations minimum as shown above, midspan of top of the metal culvert and at corners as close as possible to the specified locations and measurements taken to record their exact position If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work. ï· String pot gauges, where possible, will be mounted to collect deflection data at midspan by mounting to a reference frame supported at locations unaffected by the truck loading.
Appendix F â Field Testing Plans   Fâ41  PreâtestÂ ï· Install instruments and test proper operation TrucksÂ ï· A loaded truck to be provided by Carroll Township per coordination with Bryon Cramer. All trucks shall be consistent with design loadings. ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic during testing. TestÂ ï· Measure individual wheel loads (State Police to obtain, see above) ï· Record air and pavement temperature ï· Read instruments pre-test ï· Truck positions for readings (as truck moves across span). Vehicle paths will be established as shown in layout diagramâwith a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) Each wheel will be stopped over the vertical culvert wall, ¼ point and at midspan of the culvert top. TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day Load testing â approx ½ day ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the DOT prior to publication ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: Operation Dates Install instruments May 2, 2018 Load Test May 3, 2018  Â
Appendix F â Field Testing Plans Fâ42 Testing Data General Location: State: Pennsylvania, Carroll Twp Route: Sleepy Hollow Rd. Latitude-Longitude: 40.359593, -77.142020 (click link to open in browser) Actual Instrumentation Date: 5/2/2018 Actual Testing date: 5/3/2018 Weather/Other Test conditions: 80 F at 9:30 AM Contractor Personnel: Dave Barrett (Modjeski & Masters) Chad Clancy (Modjeski & Masters) State Personnel/Contacts: Bryon Cramer Carroll Township Greg Fisher â PA State Police 717-346-7330
Appendix F â Field Testing Plans   Fâ43  Truck Wheel Load and Spacing Data  Axle Loads (lb) Left Right Axle spacing câc Front to rear Front 5850 5275 13'â1" Rear 10475 9550    Figure 24 â Wheel loads/configurations for Model 6âCandidate 1 (M6C2)  Â
Appendix F â Field Testing Plans Fâ44 Truck Positioning Data Points Axles (2âaxle Dump truck) 1 = Edge/Wall 1 = Front 2 = 1/4 Point 2 = Rear 3 = Midspan Axle No Point No Time 2 1 9:30:00 2 2 9:30:30 2 3 9:31:27 2 1 9:32:40 2 2 9:33:20 2 3 9:33:55 2 1 9:37:00 2 2 9:37:32 2 3 9:38:14 Test No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time (time format) (time format) (integer format) (integer format) 1 1 2 1 9:30:00 9:30:15 9.500 9.504 2 2 2 2 9:30:30 9:30:45 9.508 9.513 3 3 2 3 9:31:27 9:31:42 9.524 9.528 4 1 2 1 9:32:40 9:32:55 9.544 9.549 5 2 2 2 9:33:20 9:33:35 9.556 9.560 6 3 2 3 9:33:55 9:34:10 9.565 9.569 7 1 2 1 9:37:00 9:37:15 9.617 9.621 8 2 2 2 9:37:32 9:37:47 9.626 9.630 9 3 2 3 9:38:14 9:38:29 9.637 9.641 Time each location = 15 secondsÂ
Appendix F â Field Testing Plans   Fâ45  Culvert Plans   Figure 25â Model 6, Candidate 1 (M6C2) â Plan and Typical Section   Â
Appendix F â Field Testing Plans Fâ46 Model 7 â Testing Plan â Metal Arch Site/GeneralÂ ï· Two tests will be conducted â One test prior to paving with the trucks being run over the compacted pavement subgrade material and another test to be run after pavement is in place. It would be ideal if these tests could be conducted on the same day and or trip to the site but this is not necessary. ï· Sidefill/Backfill/Subgrade â sample materials â Dr. McGrath will obtain soil data from contractor/fabricator ï· Test vehicles (Provided by MassDOT â will need to coordinate with district, axle configurations, axle loads. Wheel loads will have to be weighed â coordinate with state police to weigh if possible. Alternatively use quarry scales to obtain individual axle loads). JF White will coordinate with MassDOT, MassDOT will coordinate with State Police for axle weighing ï· Surveying for actual depths of fill â obtain from contractor if possible Instrumentation Figure 26 â M6C2 Instrumentation locationsÂ ï· Instrumentation locations â strain gauges and deflection targets will be mounted at each of the primary gauge locations indicated in the figure above along a single line near the middle of the culvert. If time permits, additional gauges will be placed at the secondary locations. ï· Deflection â survey targets to be attached to culvert during assembly if possible. If feasible and time permits, string potentiometer gauges will be placed to back up the deflection data being obtained via surveying equipment. Note that the primary direction of deflections to be captured are vertical at the midspan location and horizontal at the corners. Modjeski will perform this work with surveying by CME. ï· Strain- 6 gauges minimum: 2 at each location (1 at outer crest of corrugation, 1 at trough â see figure below), 2 at each corner and 2 at midspan. If time permits, mount backup redundant gauges particularly in areas difficult to reach. The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work
Appendix F â Field Testing Plans   Fâ47  If gauges are to be mounted when culvert panel is in its final position a lift or ladders will be needed to mount the gauges.  Modjeski will supply ladders or will use contractorâs onâsite lifts if available.Â Â ï· Instrumentation locations â strain gauges will be mounted at each of the primary gauge locations indicated in the figure above along the âload lineâ near the center of the culvert segment (based on the orientation of the culvert span/ribs, the line of sensors are to be installed along a line parallel to the traffic/outside edges of the culvert). If time permits, additional gauges will be placed at the secondary locations. Where possible, string pot gauges will be mounted to capture deflections at the culvert midspan locations. ï· Strain- locations minimum as shown above, midspan of top of the metal culvert and at corners as close as possible to the specified locations and measurements taken to record their exact position If time permits, mount backup redundant gauges (redundant gauge at midspan is required). The strain gauges require small gauge electric wire cables to be run to a central location to be connected to the data acquisition device. Modjeski will perform this work. ï· String pot gauges, where possible, will be mounted to collect deflection data at midspan by mounting to a reference frame supported at locations unaffected by the truck loading. PreâtestÂ ï· Monitor sidefill/backfill (or collect records) ï· Install instruments TrucksÂ ï· Trucks to be provided by MassDOT per cooperative letter. All trucks shall be consistent with design loadings. Desired vehicles include a HS-20 truck (preferable) or alternatively a design tandem and a dump truck with 3 rear axles ï· During the test, at times when gauge readings are being taken, no other traffic can be on the culvert structure. Readings taken are for static loading so if it is necessary for a vehicle to traverse the structure, accommodations can be made. However, the structure will have to be closed to traffic in the paved condition during that phase of the testing. TestÂ ï· Measure axle loads (see above) ï· Record air and pavement temperature (if still warm) ï· Read instruments pre-test ï· Modjeski sub CME will provide surveying services to measure deflections ï· Truck positions for readings (as truck moves across span). Three vehicle paths will be established â one with a wheel line directly over the gauges, the second with the wheel line 3 feet transverse to the line of gauges (such that the truck is centered over the line of gauges) and the third with the wheel line 3 feet from the line of
Appendix F â Field Testing Plans Fâ48 gauges and the second wheel line is 9 feet from the gauge line. Two passes will be made along each of these passes of the truck, stopping as each wheel/axle passes directly over a gauge. TimeÂ ï· Gauge/Target/Wiring installation and setup â approx 1 day to occur after backfill and compacting, if possible. ï· Load testing â approx ½ day pre each of the two tests (with pavement and without pavement) ResultsÂ ï· Per NCHRP policy, test results cannot be shared with the contractor or MassDOT prior to publication in the final report. ScheduleÂ ï· Schedule is subject to change. Current preliminary schedule for setup and testing is as follows: ï· Schedule is subject to change to coincide with construction operations. Current preliminary schedule for setup and testing is as follows: Install instruments on/about 13 April 2017 to be confirmed by JFW 3 days in advance Load Test on subgrade on/about 14 April 2017 to be confirmed by JFW 3 days in advance Load Test on pavement on/about 27 April 2017 to be confirmed by JFW 3 days in advance
Appendix F â Field Testing Plans   Fâ49  Testing Data General Location: State: Massachusetts Route: I-95 over North Avenue Latitude-Longitude: 41.962574, -71.299294 (click link to open in browser)   Actual Instrumentation Date: May 1, 2017 (Stage A) June 1, 2017 (Stage B) Actual Testing date: May 3, 2017 (Stage A) June 2, 2017 (Stage B) Weather/Other Test conditions: Contractor Personnel: Dave Barrett (Modjeski & Masters) Travis Hopper (Modjeski & Masters) State Personnel/Contacts: Jim Cahill â JF White Dan Viera â Mass DOT 508-884-4223 Â
Appendix F â Field Testing Plans Fâ50 Gage Cluster Numbering Figure 27 â Model 7 â Gage Cluster Numbering (M7C1) Figure 28 â Model 7 â Plan View â Gage Numbering (M7C1) Figure 29 â Model 7 â Gage Location (M7C1)Â
Appendix F â Field Testing Plans   Fâ51  Truck Wheel Load and Spacing Data     Stage A â without pavement   Stage B â with pavement  Figure 30 â Wheel loads/configurations for Model 7âCandidate 1 (M7C1) Â
Appendix F â Field Testing Plans Fâ52 Truck Positioning Data (Stage A â Without pavement) Truck Positions Notation Description 1 Truck centered over centerline of culvert 2 Left wheel line centered on centerline of culvert 3 left wheel line offset 3 ft from centerline of culvert, right wheel line offset (3 ft + axle width) from centerline of culvert  N/S truck facing North or South Axle Numbering â Each axle was centered over each gauge line. Notation is as follows. Notation Description 1 Front Axle 2 Mid Axle 3 Rear Axle Gauge Locations â Each cluster of gauges was assigned a number. â Numbering was from South to North, numbers 1 through 5 as shown below. Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 0 500 zero 1 502 1N 1 1 13:12:15 13:12:30 1:12:15 PM 1:12:30 PM  2 503 1N 1 2 13:13:35 13:13:51 1:13:35 PM 1:13:51 PM  3 504 1N 2 1 13:14:55 13:15:06 1:14:55 PM 1:15:06 PM  4 505 1N 3 1 13:17:53 13:18:07 1:17:53 PM 1:18:07 PM  5 506 1N 1 3 13:19:20 13:19:42 1:19:20 PM 1:19:42 PM  6 507 1N 2 2 13:20:20 13:21:02 1:20:20 PM 1:21:02 PM  7 508 1N 3 2 13:21:33 13:21:53 1:21:33 PM 1:21:53 PM  8 509 1N 1 4 13:22:43 13:23:00 1:22:43 PM 1:23:00 PM  9 510 1N 2 3 13:23:30 13:23:47 1:23:30 PM 1:23:47 PM  10 511 1N 3 3 13:24:22 13:24:37 1:24:22 PM 1:24:37 PM  11 512 1N 1 5 13:25:12 13:25:28 1:25:12 PM 1:25:28 PM  12 513 1N 2 4 13:26:03 13:26:19 1:26:03 PM 1:26:19 PM  13 514 1N 3 4 13:26:55 13:27:11 1:26:55 PM 1:27:11 PM  14 515 1N 2 5 13:27:52 13:28:07 1:27:52 PM 1:28:07 PM  15 516 1N 3 5 13:28:40 13:28:55 1:28:40 PM 1:28:55 PM  16 517 2N 1 1 13:31:22 13:31:45 1:31:22 PM 1:31:45 PM  17 518 2N 1 2 13:32:28 13:32:45 1:32:28 PM 1:32:45 PM Â
Appendix F â Field Testing Plans   Fâ53  Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 18 519 2N 2 1 13:33:20 13:33:35 1:33:20 PM 1:33:35 PM   19 520 2N 3 1 13:34:11 13:34:30 1:34:11 PM 1:34:30 PM   20 521 2N 1 3 13:35:13 13:35:33 1:35:13 PM 1:35:33 PM   21 522 2N 2 2 13:36:06 13:36:22 1:36:06 PM 1:36:22 PM   22 523 2N 3 2 13:37:30 13:37:51 1:37:30 PM 1:37:51 PM   23 524 2N 1 4 13:38:35 13:38:57 1:38:35 PM 1:38:57 PM   24 525 2N 2 3 13:39:29 13:39:50 1:39:29 PM 1:39:50 PM   25 526 2N 3 3 13:40:30 13:40:55 1:40:30 PM 1:40:55 PM   26 527 2N 1 5 13:41:44 13:42:00 1:41:44 PM 1:42:00 PM   27 528 2N 2 4 13:42:30 13:42:48 1:42:30 PM 1:42:48 PM   28 529 2N 3 4 13:43:14 13:43:31 1:43:14 PM 1:43:31 PM   29 530 2N 2 5 13:44:07 13:44:24 1:44:07 PM 1:44:24 PM   30 531 2N 3 5 13:44:52 13:45:09 1:44:52 PM 1:45:09 PM   31 532       13:46:35 13:47:09 1:46:35 PM 1:47:09 PM zero 32 533 3N 1 1 13:48:12 13:48:30 1:48:12 PM 1:48:30 PM   33 534 3N 1 2 13:49:14 13:49:33 1:49:14 PM 1:49:33 PM   34 535 3N 2 1 13:50:01 13:50:19 1:50:01 PM 1:50:19 PM   35 536 3N 3 1 13:50:53 13:51:11 1:50:53 PM 1:51:11 PM   36 537 3N 1 3 13:51:49 13:52:32 1:51:49 PM 1:52:32 PM   37 538 3N 2 2 13:54:05 13:54:16 1:54:05 PM 1:54:16 PM   38 539 3N 3 2 13:54:41 13:54:54 1:54:41 PM 1:54:54 PM   39 540 3N 1 4 13:55:29 13:55:44 1:55:29 PM 1:55:44 PM hand written notes have 13:55:00 (not possible), assume start +15 sec 40 541 3N 2 3 13:56:07 13:56:26 1:56:07 PM 1:56:26 PM   41 542 3N 3 3 13:56:49 13:57:07 1:56:49 PM 1:57:07 PM   42 543 3N 1 5 13:57:42 13:58:03 1:57:42 PM 1:58:03 PM   43 544 3N 2 4 13:58:29 13:58:50 1:58:29 PM 1:58:50 PM   44 545 3N 3 4 13:59:15 13:59:32 1:59:15 PM 1:59:32 PM   45 546 3N 2 5 14:00:13 14:00:28 2:00:13 PM 2:00:28 PM   46 547 3N 3 5 14:01:35 14:01:52 2:01:35 PM 2:01:52 PM   47 548       14:02:57 14:03:17 2:02:57 PM 2:03:17 PM zero 48 549 1S 1 5 14:04:43 14:05:07 2:04:43 PM 2:05:07 PM   49 550 1S 1 4 14:05:41 14:05:54 2:05:41 PM 2:05:54 PM   50 551 1S 2 5 14:06:25 14:06:36 2:06:25 PM 2:06:36 PM   51 552 1S 3 5 14:07:14 14:07:33 2:07:14 PM 2:07:33 PM   52 553 1S 1 3 14:08:51 14:09:09 2:08:51 PM 2:09:09 PM   53 554 1S 2 4 14:09:45 14:10:03 2:09:45 PM 2:10:03 PM   54 555 1S 3 4 14:10:28 14:10:49 2:10:28 PM 2:10:49 PM  Â
Appendix F â Field Testing Plans Fâ54 Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 55 556 1S 1 2 14:11:23 14:11:41 2:11:23 PM 2:11:41 PM  56 557 1S 2 3 14:12:06 14:12:23 2:12:06 PM 2:12:23 PM  57 558 1S 3 3 14:12:50 14:13:05 2:12:50 PM 2:13:05 PM  58 559 1S 1 1 14:13:36 14:13:49 2:13:36 PM 2:13:49 PM  59 560 1S 2 2 14:14:15 14:14:32 2:14:15 PM 2:14:32 PM  60 561 1S 3 2 14:14:57 14:15:12 2:14:57 PM 2:15:12 PM  61 562 1S 2 1 14:15:42 14:15:56 2:15:42 PM 2:15:56 PM  62 563 1S 3 1 14:16:21 14:16:38 2:16:21 PM 2:16:38 PM  63 564 1S 14:17:23 14:17:37 2:17:23 PM 2:17:37 PM zero Truck Positioning Data (Stage B â With pavement) Truck Positions Notation Description 1 Truck centered over centerline of culvert 2 Left wheel line centered on centerline of culvert 3 left wheel line offset 3 ft from centerline of culvert, right wheel line offset (3 ft + axle width) from centerline of culvert  N/S truck facing North or South Axle Numbering â Each axle was centered over each gauge line. Notation is as follows. Notation Description 1 Front Axle 2 Mid Axle 3 Rear Axle Gauge Locations â Each cluster of gauges was assigned a number. â Numbering was from South to North, numbers 1 through 5 as shown below. Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 0 test 1 600 1N 1 1 12:06:25 12:06:46 12:06:25 PM 12:06:46 PM 2 601 1N 1 2 12:07:40 12:08:00 12:07:40 PM 12:08:00 PM 3 602 1N 2 1 12:08:56 12:09:13 12:08:56 PM 12:09:13 PM 4 603 1N 3 1 12:09:50 12:10:08 12:09:50 PM 12:10:08 PMÂ
Appendix F â Field Testing Plans   Fâ55  Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 5 604 1N 1 3 12:11:27 12:11:44 12:11:27 PM 12:11:44 PM  6 605 1N 2 2 12:12:21 12:12:39 12:12:21 PM 12:12:39 PM  7 606 1N 3 2 12:13:24 12:13:42 12:13:24 PM 12:13:42 PM  8 607 1N 1 4 12:14:38 12:14:57 12:14:38 PM 12:14:57 PM  9 608 1N 2 3 12:15:35 12:15:56 12:15:35 PM 12:15:56 PM  10 609 1N 3 3 12:16:38 12:16:57 12:16:38 PM 12:16:57 PM  11 610 1N 1 5 12:17:42 12:17:59 12:17:42 PM 12:17:59 PM  12 611 1N 2 4 12:19:59 12:20:19 12:19:59 PM 12:20:19 PM  13 612 1N 3 4 12:21:10 12:21:29 12:21:10 PM 12:21:29 PM  14 613 1N 2 5 12:22:32 12:23:04 12:22:32 PM 12:23:04 PM  15 614 1N 3 5 12:24:03 12:24:25 12:24:03 PM 12:24:25 PM  16 615 2N 1 1 12:29:05 12:29:25 12:29:05 PM 12:29:25 PM  17 616 2N 1 2 12:30:10 12:30:28 12:30:10 PM 12:30:28 PM  18 617 2N 2 1 12:31:04 12:31:21 12:31:04 PM 12:31:21 PM  19 618 2N 3 1 12:31:56 12:32:14 12:31:56 PM 12:32:14 PM  20 619 2N 1 3 12:32:56 12:33:14 12:32:56 PM 12:33:14 PM  21 620 2N 2 2 12:33:46 12:34:05 12:33:46 PM 12:34:05 PM  22 621 2N 3 2 12:34:36 12:34:52 12:34:36 PM 12:34:52 PM  23 622 2N 1 4 12:35:35 12:35:54 12:35:35 PM 12:35:54 PM  24 623 2N 2 3 12:36:37 12:36:54 12:36:37 PM 12:36:54 PM 25 624 2N 3 3 12:37:27 12:37:43 12:37:27 PM 12:37:43 PM  26 625 2N 1 5 12:38:22 12:38:40 12:38:22 PM 12:38:40 PM  27 626 2N 2 4 12:40:18 12:40:36 12:40:18 PM 12:40:36 PM  28 627 2N 3 4 12:41:14 12:41:31 12:41:14 PM 12:41:31 PM  29 628 2N 2 5 12:42:07 12:42:24 12:42:07 PM 12:42:24 PM  30 629 2N 3 5 12:42:54 12:43:12 12:42:54 PM 12:43:12 PM  31 630 3N 1 1 12:46:36 12:46:55 12:46:36 PM 12:46:55 PM  32 631 3N 1 2 12:47:36 12:47:57 12:47:36 PM 12:47:57 PM  33 632 3N 2 1 12:48:27 12:48:43 12:48:27 PM 12:48:43 PM  34 633 3N 3 1 12:49:21 12:49:38 12:49:21 PM 12:49:38 PM  35 634 3N 1 3 12:50:32 12:50:49 12:50:32 PM 12:50:49 PM  36 635 3N 2 2 12:51:14 12:51:38 12:51:14 PM 12:51:38 PM  37 636 3N 3 2 12:52:16 12:52:34 12:52:16 PM 12:52:34 PM  38 637 3N 1 4 12:53:14 12:53:32 12:53:14 PM 12:53:32 PM  39 638 3N 2 3 12:54:01 12:54:19 12:54:01 PM 12:54:19 PM  40 639 3N 3 3 12:54:49 12:55:05 12:54:49 PM 12:55:05 PM  41 640 3N 1 5 12:55:48 12:56:05 12:55:48 PM 12:56:05 PM  42 641 3N 2 4 12:56:45 12:57:02 12:56:45 PM 12:57:02 PM  43 642 3N 3 4 12:57:39 12:57:57 12:57:39 PM 12:57:57 PM  44 643 3N 2 5 12:58:33 12:58:51 12:58:33 PM 12:58:51 PM  45 644 3N 3 5 12:59:27 12:59:44 12:59:27 PM 12:59:44 PM Â
Appendix F â Field Testing Plans Fâ56 Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 46 645 1S 1 5 13:04:23 13:04:38 1:04:23 PM 1:04:38 PM originally recorded end time was 12:04:38 47 646 1S 1 4 13:05:47 13:06:12 1:05:47 PM 1:06:12 PM 48 647 1S 2 5 13:06:52 13:07:10 1:06:52 PM 1:07:10 PM 49 648 1S 3 5 13:07:51 13:08:14 1:07:51 PM 1:08:14 PM 50 649 1S 1 3 13:09:02 13:09:19 1:09:02 PM 1:09:19 PM 51 650 1S 2 4 13:09:59 13:10:18 1:09:59 PM 1:10:18 PM 52 651 1S 3 4 13:10:47 13:11:02 1:10:47 PM 1:11:02 PM 53 652 1S 1 2 13:11:40 13:11:56 1:11:40 PM 1:11:56 PM 54 653 1S 2 3 13:13:28 13:13:46 1:13:28 PM 1:13:46 PM 55 654 1S 3 3 13:14:20 13:14:37 1:14:20 PM 1:14:37 PM 56 655 1S 1 1 13:15:18 13:15:37 1:15:18 PM 1:15:37 PM 57 656 1S 2 2 13:16:10 13:16:33 1:16:10 PM 1:16:33 PM 58 657 1S 3 2 13:17:19 13:17:35 1:17:19 PM 1:17:35 PM 59 658 1S 2 1 13:18:14 13:18:31 1:18:14 PM 1:18:31 PM 60 659 1S 3 1 13:18:59 13:19:18 1:18:59 PM 1:19:18 PM 61 660 2S 1 5 13:22:17 13:22:36 1:22:17 PM 1:22:36 PM 62 661 2S 1 4 13:23:12 13:23:29 1:23:12 PM 1:23:29 PM 63 662 2S 2 5 13:24:02 13:24:19 1:24:02 PM 1:24:19 PM 64 663 2S 3 5 13:24:55 13:25:09 1:24:55 PM 1:25:09 PM 65 664 2S 1 3 13:25:45 13:26:03 1:25:45 PM 1:26:03 PM 66 665 2S 2 4 13:26:36 13:26:53 1:26:36 PM 1:26:53 PM 67 666 2S 3 4 13:27:21 13:27:39 1:27:21 PM 1:27:39 PM 68 667 2S 1 2 13:28:22 13:28:38 1:28:22 PM 1:28:38 PM 69 668 2S 2 3 13:29:13 13:29:32 1:29:13 PM 1:29:32 PM 70 669 2S 3 3 13:30:09 13:30:28 1:30:09 PM 1:30:28 PM 71 670 2S 1 1 13:31:05 13:31:22 1:31:05 PM 1:31:22 PM 72 671 2S 2 2 13:31:59 13:32:17 1:31:59 PM 1:32:17 PM 73 672 2S 3 2 13:32:55 13:33:13 1:32:55 PM 1:33:13 PM 74 673 2S 2 1 13:33:54 13:34:11 1:33:54 PM 1:34:11 PM 75 674 2S 3 1 13:34:47 13:35:07 1:34:47 PM 1:35:07 PM 76 675 3S 1 5 13:38:59 13:39:09 1:38:59 PM 1:39:09 PM 77 676 3S 1 4 13:40:15 13:40:53 1:40:15 PM 1:40:53 PM 78 677 3S 2 5 13:41:44 13:42:07 1:41:44 PM 1:42:07 PM 79 678 3S 3 5 13:42:44 13:43:03 1:42:44 PM 1:43:03 PM 80 679 3S 1 3 13:43:49 13:44:07 1:43:49 PM 1:44:07 PM 81 680 3S 2 4 13:45:45 13:46:09 1:45:45 PM 1:46:09 PM 82 681 3S 3 4 13:47:03 13:47:21 1:47:03 PM 1:47:21 PM 83 682 3S 1 2 13:48:07 13:48:24 1:48:07 PM 1:48:24 PM 84 683 3S 2 3 13:49:16 13:49:35 1:49:16 PM 1:49:35 PM 85 684 3S 3 3 13:50:07 13:50:22 1:50:07 PM 1:50:22 PM 86 685 3S 1 1 13:51:46 13:52:02 1:51:46 PM 1:52:02 PMÂ
Appendix F â Field Testing Plans   Fâ57  Test No. CME Survey Shot No. Truck Position Axle No. Gauge Location Start Time End Time Start Time End Time Notes 87 686 3S 2 2 13:52:42 13:52:59 1:52:42 PM 1:52:59 PM  88 687 3S 3 2 13:53:32 13:53:49 1:53:32 PM 1:53:49 PM  89 688 3S 2 1 13:54:45 13:55:06 1:54:45 PM 1:55:06 PM  90 689 3S 3 1 13:55:45 13:56:04 1:55:45 PM 1:56:04 PM    Â
Appendix F â Field Testing Plans Fâ58 Culvert Plans Figure 31â Model 7, Candidate 1 (M7C1) â Plan and Typical SectionÂ
G-1 Appendix G â Specification Backup Full Table of BrDR runs for Shear Capacity changes. The following table represents the AASHTOWare BrDR analysis runs for a select set of the Caltrans culverts for the change in the shear capacity. Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CD10x8;10 2002-Rev 1.5 Top Slab 2 0.6025 Top Slab 2 0.6025 1.1099 1.1789 0.9415 CD10x8;10 2002-Rev 1.9 Top Slab 2 0.6025 Top Slab 2 0.6025 1.1066 1.1835 0.9350 CD10x8;10 2002-Rev 2 Top Slab 2 0.6025 Top Slab 2 0.6025 1.1051 1.1051 1.0000 CD10x8;10 2002-Rev 4 Top Slab 2 0.6025 Top Slab 2 0.6025 1.7365 1.7365 1.0000 CD10x8;10 2002-Rev 7 Bottom Slab 1 9.46 Bottom Slab 1 9.46 1.5147 1.5147 1.0000 CD10x8;10 2010-Rev 1.5 Top Slab 2 0.6925 Top Slab 2 0.6925 1.4619 1.557 0.9389 CD10x8;10 2010-Rev 1.9 Top Slab 2 0.6925 Top Slab 2 0.6925 1.5025 1.5806 0.9506 CD10x8;10 2010-Rev 2 Top Slab 2 0.6925 Top Slab 2 0.6925 1.5521 1.5521 1.0000 CD10x8;10 2010-Rev 4 Top Slab 2 0.6925 Top Slab 2 0.6925 2.4874 2.4874 1.0000 CD10x8;10 2010-Rev 7 Bottom Slab 1 9.37 Bottom Slab 1 9.37 2.911 2.911 1.0000 CD10x8;16 1966-Rev 1.9 Top Slab 1 9.0893 Top Slab 1 9.0893 1.601 1.8908 0.8467 CD10x8;16 1966-Rev 2 Top Slab 1 9.0893 Top Slab 1 9.0893 1.5982 1.5982 1.0000 CD10x8;16 1966-Rev 2.5 Top Slab 1 9.0893 Top Slab 1 9.0893 1.9313 1.9313 1.0000 CD10x8;16 1966-Rev 3 Top Slab 1 9.0893 Top Slab 1 9.0893 2.2948 2.2948 1.0000 CD10x8;16 1966-Rev 3.5 Top Slab 1 9.0893 Top Slab 1 9.0893 2.6131 2.6131 1.0000 CD10x8;16 1966-Rev 4 Top Slab 1 9.0893 Top Slab 1 9.0893 2.8796 2.8796 1.0000 CD10x8;16 1966-Rev 7 Top Slab 1 9.0893 Top Slab 1 9.0893 4.0435 4.0435 1.0000 CD10x8;16 1966-Rev 9 Top Slab 1 9.0893 Top Slab 1 9.0893 3.7745 3.7745 1.0000 CD10x8;2 1966-Rev 0.5 Top Slab 1 9.3866 Top Slab 1 0.6354 1.0071 1.0407 0.9677 CD10x8;2 1966-Rev 1 Top Slab 1 9.3866 Top Slab 1 0.6354 1.0185 1.1017 0.9245 CD10x8;2 1966-Rev 1.5 Top Slab 1 9.3866 Top Slab 1 9.3866 1.0306 1.0946 0.9415 CD10x8;2 1966-Rev 1.9 Top Slab 1 9.3866 Top Slab 1 9.3866 1.0314 1.0873 0.9486 CD10x8;2 1966-Rev 2 Bottom Slab 1 9.475 Bottom Slab 1 9.475 1.2291 1.2291 1.0000 CD10x8;2 1966-Rev 3 Bottom Slab 1 9.475 Bottom Slab 1 9.475 1.2291 1.2291 1.0000 CD10x8;3 1952-Rev 1.5 Top Slab 1 8.8819 Top Slab 1 8 1.0699 1.3251 0.8074 CD10x8;3 1952-Rev 1.9 Top Slab 1 8.8819 Top Slab 1 8.8819 1.0888 1.3459 0.8090 CD10x8;3 1952-Rev 2 Top Slab 1 8.8819 Top Slab 1 8.8819 1.2148 1.2148 1.0000 CD10x8;3 1952-Rev 3 Bottom Slab 1 9.4 Bottom Slab 1 9.4 1.4473 1.4473 1.0000 CD10x8;3 1952-Rev 3.5 Bottom Slab 1 9.4 Bottom Slab 1 9.4 1.4692 1.4692 1.0000 CD10x8;3 1952-Rev 4 Bottom Slab 1 9.4 Bottom Slab 1 9.4 1.4456 1.4456 1.0000
Appendix G â Specification Backup G-2 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CD10x8;5 1948-Rev 1 Top Slab 1 8.9271 Top Slab 1 1.1034 1.1191 1.2936 0.8651 CD10x8;5 1948-Rev 1.5 Top Slab 1 8.9271 Top Slab 1 8.9271 1.1443 1.3417 0.8529 CD10x8;5 1948-Rev 1.9 Top Slab 1 8.9271 Top Slab 1 8.9271 1.1661 1.3478 0.8652 CD10x8;5 1948-Rev 2 Top Slab 1 8.9271 Top Slab 1 8.9271 1.3326 1.3326 1.0000 CD10x8;5 1948-Rev 3 Bottom Slab 1 9.1319 Bottom Slab 1 9.1319 1.5773 1.5773 1.0000 CD10x8;5 1948-Rev 4 Bottom Slab 1 9.1319 Bottom Slab 1 9.1319 1.5516 1.5516 1.0000 CD10x8;5 1948-Rev 5 Bottom Slab 1 9.1319 Bottom Slab 1 9.1319 1.4464 1.4464 1.0000 CD10x8;9 1948-Rev 1.5 Top Slab 1 8.8924 Top Slab 1 8.8924 1.3002 1.5054 0.8637 CD10x8;9 1948-Rev 1.9 Top Slab 1 8.8924 Top Slab 1 8.8924 1.3303 1.5218 0.8742 CD10x8;9 1948-Rev 2 Top Slab 1 8.8924 Top Slab 1 8.8924 1.5024 1.5024 1.0000 CD10x8;9 1948-Rev 4 Bottom Slab 1 8.9736 Bottom Slab 1 8.9736 2.415 2.415 1.0000 CD10x8;9 1948-Rev 6 Bottom Slab 1 8.9736 Bottom Slab 1 8.9736 2.3231 2.3231 1.0000 CD10x8;9 1948-Rev 8 Bottom Slab 1 8.9736 Bottom Slab 1 8.9736 2.0001 2.0001 1.0000 CD12x12;20 2010- Rev 1.9 Top Slab 2 1.227 Top Slab 2 1.227 3.1552 3.5462 0.8897 CD12x12;20 2010- Rev 2 Top Slab 2 1.227 Top Slab 2 1.227 3.1521 3.1521 1.0000 CD12x12;20 2010- Rev 2.5 Top Slab 2 1.227 Top Slab 2 1.227 3.1521 3.1521 1.0000 CD12x12;20 2010- Rev 3 Top Slab 2 1.227 Top Slab 2 1.227 4.395 4.395 1.0000 CD12x12;20 2010- Rev 3.5 Top Slab 2 1.227 Top Slab 2 1.227 4.9055 4.9055 1.0000 CD12x12;20 2010- Rev 4 Top Slab 2 1.227 Top Slab 2 1.227 5.3773 5.3773 1.0000 CD12x12;20 2010- Rev 5 Top Slab 2 1.227 Top Slab 2 1.227 6.426 6.426 1.0000 CD12x12;2 1966-Rev 1.5 Top Slab 1 11.252 Top Slab 1 11.252 1.3301 1.435 0.9269 CD12x12;2 1966-Rev 1.9 Top Slab 1 11.252 Top Slab 1 11.252 1.3323 1.4171 0.9402 CD12x12;2 1966-Rev 2 Bottom Slab 1 11.37 Bottom Slab 1 11.37 1.398 1.398 1.0000 CD12x12;2 1966-Rev 2.5 Bottom Slab 1 11.37 Bottom Slab 1 11.37 1.5088 1.5088 1.0000 CD12x12;2 1966-Rev 3 Bottom Slab 1 11.37 Bottom Slab 1 11.37 1.5887 1.5887 1.0000 CD12x12;2 1966-Rev 3.5 Bottom Slab 1 11.37 Bottom Slab 1 11.37 1.5659 1.5659 1.0000 CD12x12;2 1966-Rev 4 Bottom Slab 1 11.37 Bottom Slab 1 11.37 1.5203 1.5203 1.0000 CD12x8;9 1948-Rev 0 Top Slab 1 1.2486 Top Slab 1 1.2486 1.2529 1.2529 1.0000 CD12x8;9 1948-Rev 0.5 Top Slab 1 1.2486 Top Slab 1 1.2486 1.3022 1.3022 1.0000 CD12x8;9 1948-Rev 1 Top Slab 1 10.79 Top Slab 1 1.2486 1.2176 1.3535 0.8996 CD12x8;9 1948-Rev 1.5 Top Slab 1 10.79 Top Slab 1 10.79 1.2164 1.381 0.8808
Appendix G â Specification Backup G-3 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CD12x8;9 1948-Rev 1.9 Top Slab 1 10.79 Top Slab 1 10.79 1.2148 1.364 0.8906 CD12x8;9 1948-Rev 2 Top Slab 1 10.79 Top Slab 1 10.79 1.3333 1.3333 1.0000 CD12x8;9 1948-Rev 4 Top Slab 1 10.79 Top Slab 1 10.79 1.943 1.943 1.0000 CD12x8;9 1948-Rev 6 Top Slab 1 10.79 Top Slab 1 10.79 1.9194 1.9194 1.0000 CD12x8;9 1948-Rev 8 Bottom Slab 1 10.79 Bottom Slab 1 10.79 1.5434 1.5434 1.0000 CD12x8;9 1948-Rev 9 Bottom Slab 1 10.79 Bottom Slab 1 10.79 1.1156 1.1156 1.0000 CD12x8;9 1952-Rev 1.5 Top Slab 1 9.6 Top Slab 1 9.6 2.0712 2.1877 0.9467 CD12x8;9 1952-Rev 1.9 Top Slab 1 10.465 Top Slab 1 10.465 1.8899 2.2891 0.8256 CD12x8;9 1952-Rev 2 Top Slab 1 10.465 Top Slab 1 10.465 1.8811 1.8811 1.0000 CD12x8;9 1952-Rev 3.5 Top Slab 1 10.465 Top Slab 1 10.465 2.8637 2.8637 1.0000 CD12x8;9 1952-Rev 3 Top Slab 1 10.465 Top Slab 1 10.465 2.5928 2.5928 1.0000 CD12x8;9 1952-Rev 4 Top Slab 1 10.465 Top Slab 1 10.465 3.1016 3.1016 1.0000 CD14x13;10 2002- Rev 1.5 Top Slab 2 0.7525 Top Slab 2 0.7525 1.2995 1.3937 0.9324 CD14x13;10 2002- Rev 1.9 Top Slab 2 0.7525 Top Slab 2 0.7525 1.2622 1.3677 0.9229 CD14x13;10 2002- Rev 2 Top Slab 2 0.7525 Top Slab 2 0.7525 1.3325 1.3325 1.0000 CD14x13;10 2002- Rev 2.5 Top Slab 2 0.7525 Top Slab 2 0.7525 1.4176 1.4176 1.0000 CD14x13;10 2002- Rev 3 Top Slab 2 0.7525 Top Slab 2 0.7525 1.5063 1.5063 1.0000 CD14x13;10 2002- Rev 3.5 Top Slab 2 0.7525 Top Slab 2 0.7525 1.5443 1.5443 1.0000 CD14x13;10 2002- Rev 4 Top Slab 2 0.7525 Top Slab 2 0.7525 1.5649 1.5649 1.0000 CD14x9;10 2002-Rev 1.5 Top Slab 2 0.7525 Top Slab 2 0.7525 1.2781 1.3776 0.9278 CD14x9;10 2002-Rev 1.9 Top Slab 2 0.7525 Top Slab 2 0.7525 1.2383 1.3488 0.9181 CD14x9;10 2002-Rev 2 Top Slab 2 0.7525 Top Slab 2 0.7525 1.2947 1.2947 1.0000 CD14x9;10 2002-Rev 4 Top Slab 2 0.7525 Top Slab 2 0.7525 1.512 1.512 1.0000 CD14x9;10 2002-Rev 7 Bottom Slab 1 13.31 Bottom Slab 1 13.31 1.282 1.282 1.0000 CD14x9;10 2010-Rev 1.5 Top Slab 2 0.852 Top Slab 2 0.852 1.6473 1.7383 0.9477 CD14x9;10 2010-Rev 1.9 Top Slab 2 0.852 Top Slab 2 0.852 1.6197 1.7224 0.9404 CD14x9;10 2010-Rev 2 Top Slab 2 0.852 Top Slab 2 0.852 1.7144 1.7144 1.0000 CD14x9;10 2010-Rev 4 Top Slab 2 0.852 Top Slab 2 0.852 2.1355 2.1355 1.0000 CD14x9;10 2010-Rev 7 Top Slab 2 0.852 Top Slab 2 0.852 2.2762 2.2762 1.0000 CD8x8;10 1924-Rev 1 Top Slab 1 7.0713 Top Slab 1 7.0713 2.2342 2.4854 0.8989 CD8x8;10 1924-Rev 1.9 Top Slab 1 7.0713 Top Slab 1 7.0713 2.5273 2.8542 0.8855 CD8x8;10 1924-Rev 2 Top Slab 1 7.0713 Top Slab 1 7.0713 2.5427 2.5427 1.0000 CD8x8;10 1924-Rev 3 Top Slab 1 7.0713 Top Slab 1 7.0713 3.8408 3.8408 1.0000 CD8x8;10 1924-Rev 5 Bottom Slab 1 7.1546 Bottom Slab 1 7.1546 5.7973 5.7973 1.0000
Appendix G â Specification Backup G-4 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CD8x8;10 1933-Rev 1 Top Slab 1 7.0937 Top Slab 1 7.0937 2.0784 2.3505 0.8842 CD8x8;10 1933-Rev 1.9 Top Slab 1 7.0937 Top Slab 1 7.0937 2.3552 2.7004 0.8722 CD8x8;10 1933-Rev 2 Top Slab 1 7.0937 Top Slab 1 7.0937 2.3678 2.3678 1.0000 CD8x8;10 1933-Rev 3 Top Slab 1 7.0937 Top Slab 1 7.0937 3.5884 3.5884 1.0000 CD8x8;10 1933-Rev 3.5 Top Slab 1 7.0937 Top Slab 1 7.0937 4.1518 4.1518 1.0000 CD8x8;10 1933-Rev 4 Top Slab 1 7.0937 Top Slab 1 7.0937 4.565 4.565 1.0000 CD8x8;5 1924-Rev 1 Top Slab 1 7.2356 Top Slab 1 0.7722 1.6345 1.7773 0.9197 CD8x8;5 1924-Rev 1.5 Top Slab 1 7.2356 Top Slab 1 0.7722 1.7321 1.9571 0.8850 CD8x8;5 1924-Rev 1.9 Top Slab 1 7.2356 Bottom Slab 1 0.6055 1.821 2.0376 0.8937 CD8x8;5 1924-Rev 2 Top Slab 1 7.2356 Top Slab 1 7.2356 1.8472 1.8472 1.0000 CD8x8;5 1924-Rev 3 Bottom Slab 1 7.4023 Bottom Slab 1 7.4023 2.5361 2.5361 1.0000 CD8x8;5 1924-Rev 4 Bottom Slab 1 7.4023 Bottom Slab 1 7.4023 2.7612 2.7612 1.0000 CS10x8;10 1933-Rev 1.9 Top Slab 1 1.1503 Top Slab 1 1.1503 2.4883 2.4883 1.0000 CS10x8;10 1933-Rev 2 Top Slab 1 1.1503 Top Slab 1 1.1503 2.4912 2.4912 1.0000 CS10x8;10 1933-Rev 2.5 Top Slab 1 1.1503 Top Slab 1 1.1503 3.0667 3.0667 1.0000 CS10x8;10 1933-Rev 3 Top Slab 1 1.1503 Top Slab 1 1.1503 3.6997 3.6997 1.0000 CS10x8;10 1933-Rev 3.5 Top Slab 1 1.1503 Top Slab 1 1.1503 4.2713 4.2713 1.0000 CS10x8;10 1933-Rev 4 Bottom Slab 1 1.067 Bottom Slab 1 1.067 4.625 4.625 1.0000 CS10x8;10 1933-Rev 7 Bottom Slab 1 1.067 Bottom Slab 1 1.067 6.7502 6.7502 1.0000 CS10x8;10 1981-Rev 1.5 Top Slab 1 0.5425 Top Slab 1 0.5425 1.1412 1.2482 0.9143 CS10x8;10 1981-Rev 1.9 Bottom Slab 1 0.48 Top Slab 1 0.5425 1.1637 1.2681 0.9177 CS10x8;10 1981-Rev 2 Top Slab 1 0.5425 Top Slab 1 0.5425 1.322 1.322 1.0000 CS10x8;10 1981-Rev 4 Bottom Slab 1 0.48 Bottom Slab 1 0.48 1.9619 1.9619 1.0000 CS10x8;10 1981-Rev 7 Bottom Slab 1 0.48 Bottom Slab 1 0.48 2.2522 2.2522 1.0000 CS10x8;10 2002-Rev 1.5 Top Slab 1 0.5425 Top Slab 1 0.5425 1.2232 1.3337 0.9171 CS10x8;10 2002-Rev 1.9 Bottom Slab 1 0.48 Top Slab 1 0.5425 1.2561 1.3578 0.9251 CS10x8;10 2002-Rev 2 Top Slab 1 0.5425 Top Slab 1 0.5425 1.391 1.391 1.0000 CS10x8;10 2002-Rev 4 Bottom Slab 1 0.48 Bottom Slab 1 0.48 2.0835 2.0835 1.0000 CS10x8;10 2002-Rev 7 Bottom Slab 1 0.48 Bottom Slab 1 0.48 2.4697 2.4697 1.0000 CS10x8;10 2010-Rev 1.5 Top Slab 1 0.6325 Top Slab 1 0.6325 1.5199 1.7165 0.8855 CS10x8;10 2010-Rev 1.9 Top Slab 1 0.6325 Top Slab 1 0.6325 1.5698 1.7605 0.8917 CS10x8;10 2010-Rev 2 Top Slab 1 0.6325 Top Slab 1 0.6325 1.668 1.668 1.0000 CS10x8;10 2010-Rev 4 Top Slab 1 0.6325 Top Slab 1 0.6325 2.7829 2.7829 1.0000 CS10x8;10 2010-Rev 7 Bottom Slab 1 0.6 Bottom Slab 1 0.6 4.124 4.124 1.0000
Appendix G â Specification Backup G-5 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CS10x8;12 1952-Rev 1.9 Top Slab 1 1.116 Top Slab 1 1.116 1.6469 1.8724 0.8796 CS10x8;12 1952-Rev 2 Top Slab 1 1.116 Top Slab 1 1.116 1.6908 1.6908 1.0000 CS10x8;12 1952-Rev 4 Bottom Slab 1 0.6483 Bottom Slab 1 0.6483 2.4756 2.4756 1.0000 CS10x8;12 1952-Rev 7 Bottom Slab 1 0.6483 Bottom Slab 1 0.6483 3.4233 3.4233 1.0000 CS10x8;5 1922-Rev 1.5 Top Slab 1 1.6879 Top Slab 1 1.6879 2.5801 2.6162 0.9862 CS10x8;5 1922-Rev 1.9 Top Slab 1 1.6879 Top Slab 1 1.6879 2.7172 2.7663 0.9823 CS10x8;5 1922-Rev 2 Top Slab 1 1.6879 Top Slab 1 1.6879 2.7291 2.7291 1.0000 CS10x8;5 1922-Rev 2.5 Top Slab 1 8.327 Top Slab 1 8.327 3.3489 3.3489 1.0000 CS10x8;5 1922-Rev 3 Top Slab 1 1.673 Top Slab 1 1.673 4.0583 4.0583 1.0000 CS10x8;5 1922-Rev 3.5 Top Slab 1 1.673 Top Slab 1 1.673 4.7156 4.7156 1.0000 CS10x8;5 1922-Rev 4 Top Slab 1 1.673 Top Slab 1 1.673 5.2913 5.2913 1.0000 CS10x8;5 1933-Rev 1.5 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 1.4995 1.4995 1.0000 CS10x8;5 1933-Rev 1.9 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 1.5042 1.5042 1.0000 CS10x8;5 1933-Rev 2 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 1.5314 1.5314 1.0000 CS10x8;5 1933-Rev 2.5 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 1.754 1.754 1.0000 CS10x8;5 1933-Rev 3 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 2.0166 2.0166 1.0000 CS10x8;5 1933-Rev 3.5 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 2.207 2.207 1.0000 CS10x8;5 1933-Rev 4 Bottom Slab 1 0.7389 Bottom Slab 1 0.7389 2.3248 2.3248 1.0000 CS10x8;5 1952-Rev 1.5 Bottom Slab 1 0.51 Bottom Slab 1 0.51 0.96278 1.1542 0.8342 CS10x8;5 1952-Rev 1.9 Bottom Slab 1 0.51 Bottom Slab 1 0.51 0.95991 1.1504 0.8344 CS10x8;5 1952-Rev 2 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.0579 1.0579 1.0000 CS10x8;5 1952-Rev 3 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.3237 1.3237 1.0000 CS10x8;5 1952-Rev 4 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.4756 1.4756 1.0000 CS10x8;5 1952-Rev 5 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.5688 1.5688 1.0000 CS10x8;6 1948-Rev 1.5 Bottom Slab 1 0.576 Bottom Slab 1 0.576 1.3847 1.5789 0.8770 CS10x8;6 1948-Rev 1.9 Bottom Slab 1 0.576 Bottom Slab 1 0.576 1.3951 1.5891 0.8779 CS10x8;6 1948-Rev 2 Bottom Slab 1 0.576 Bottom Slab 1 0.576 1.5684 1.5684 1.0000 CS10x8;6 1948-Rev 3 Bottom Slab 1 0.576 Bottom Slab 1 0.576 2.0211 2.0211 1.0000 CS10x8;6 1948-Rev 4 Bottom Slab 1 0.576 Bottom Slab 1 0.576 2.3376 2.3376 1.0000 CS10x8;6 1948-Rev 5 Bottom Slab 1 0.576 Bottom Slab 1 0.576 2.6057 2.6057 1.0000
Appendix G â Specification Backup G-6 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CS10x8;8 1966-Rev 1.5 Top Slab 1 0.62 Top Slab 1 2 1.0366 1.2219 0.8484 CS10x8;8 1966-Rev 1.9 Top Slab 1 0.62 Top Slab 1 2 1.0618 1.291 0.8225 CS10x8;8 1966-Rev 2 Top Slab 1 0.62 Top Slab 1 0.62 1.2081 1.2081 1.0000 CS10x8;8 1966-Rev 4 Bottom Slab 1 0.555 Bottom Slab 1 0.555 1.7073 1.7073 1.0000 CS10x8;8 1966-Rev 6 Bottom Slab 1 0.555 Bottom Slab 1 0.555 2.0076 2.0076 1.0000 CS12x12;10 2002-Rev 1.5 Top Slab 1 0.6325 Top Slab 1 0.6325 1.2302 1.3203 0.9318 CS12x12;10 2002-Rev 1.9 Top Slab 1 0.6325 Top Slab 1 0.6325 1.2444 1.3195 0.9431 CS12x12;10 2002-Rev 2 Top Slab 1 0.6325 Top Slab 1 0.6325 1.3395 1.3395 1.0000 CS12x12;10 2002-Rev 2.5 Top Slab 1 0.6325 Top Slab 1 0.6325 1.4653 1.4653 1.0000 CS12x12;10 2002-Rev 3 Top Slab 1 0.6325 Top Slab 1 0.6325 1.6013 1.6013 1.0000 CS12x12;10 2002-Rev 3.5 Top Slab 1 0.6325 Top Slab 1 0.6325 1.7225 1.7225 1.0000 CS12x12;10 2002-Rev 4 Bottom Slab 1 0.6 Bottom Slab 1 0.6 1.8007 1.8007 1.0000 CS12x8;10 1952-Rev 10 Bottom Slab 1 0.7834 Bottom Slab 1 0.7834 3.4034 3.4034 1.0000 CS12x8;10 1952-Rev 1.5 Top Slab 1 1.3398 Top Slab 1 1.3398 1.7957 1.9911 0.9019 CS12x8;10 1952-Rev 1.9 Bottom Slab 1 0.7834 Top Slab 1 1.3398 1.8349 2.0668 0.8878 CS12x8;10 1952-Rev 2 Bottom Slab 1 0.7834 Bottom Slab 1 0.7834 1.8218 1.8218 1.0000 CS12x8;10 1952-Rev 3 Bottom Slab 1 0.7834 Bottom Slab 1 0.7834 2.3807 2.3807 1.0000 CS12x8;10 1952-Rev 4 Bottom Slab 1 0.7834 Bottom Slab 1 0.7834 2.6871 2.6871 1.0000 CS12x8;10 1952-Rev 7 Bottom Slab 1 0.7834 Bottom Slab 1 0.7834 3.2658 3.2658 1.0000 CS12x8;10 2010-Rev 1.5 Top Slab 1 0.6925 Top Slab 1 0.6925 1.5694 1.7585 0.8925 CS12x8;10 2010-Rev 1.9 Top Slab 1 0.6925 Top Slab 1 0.6925 1.5984 1.781 0.8975 CS12x8;10 2010-Rev 2 Top Slab 1 0.6925 Top Slab 1 0.6925 1.759 1.759 1.0000 CS12x8;10 2010-Rev 2.5 Top Slab 1 0.6925 Top Slab 1 0.6925 2.0268 2.0268 1.0000 CS12x8;10 2010-Rev 3 Top Slab 1 0.6925 Top Slab 1 0.6925 2.3093 2.3093 1.0000 CS12x8;10 2010-Rev 3.5 Top Slab 1 0.6925 Top Slab 1 0.6925 2.5235 2.5235 1.0000 CS12x8;10 2010-Rev 4 Top Slab 1 0.6925 Top Slab 1 0.6925 2.7149 2.7149 1.0000 CS12x8;5 1922-Rev 1.5 Top Slab 1 2.0204 Top Slab 1 2.0204 2.8244 2.8715 0.9836 CS12x8;5 1922-Rev 1.9 Top Slab 1 2.0204 Top Slab 1 2.0204 2.934 2.996 0.9793 CS12x8;5 1922-Rev 2 Top Slab 1 2.0204 Top Slab 1 2.0204 2.937 2.937 1.0000 CS12x8;5 1922-Rev 3 Top Slab 1 2.0204 Top Slab 1 2.0204 4.2056 4.2056 1.0000 CS12x8;5 1922-Rev 4 Top Slab 1 2.0027 Top Slab 1 2.0027 5.2324 5.2324 1.0000 CS12x8;5 1922-Rev 5 Top Slab 1 2.0027 Top Slab 1 2.0027 6.3741 6.3741 1.0000 CS14x14;10 2002-Rev 1.5 Bottom Slab 1 0.69 Bottom Slab 1 0.69 1.3813 1.4832 0.9313 CS14x14;10 2002-Rev 1.9 Bottom Slab 1 0.69 Bottom Slab 1 0.69 1.3527 1.46 0.9265
Appendix G â Specification Backup G-7 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CS14x14;10 2002-Rev 2 Top Slab 1 0.7225 Top Slab 1 0.7225 1.5401 1.5401 1.0000 CS14x14;10 2002-Rev 2.5 Top Slab 1 0.7225 Top Slab 1 0.7225 1.7043 1.7043 1.0000 CS14x14;10 2002-Rev 3 Top Slab 1 0.7225 Top Slab 1 0.7225 1.8188 1.8188 1.0000 CS14x14;10 2002-Rev 3.5 Bottom Slab 1 0.69 Bottom Slab 1 0.69 1.8584 1.8584 1.0000 CS14x14;10 2002-Rev 4 Bottom Slab 1 0.69 Bottom Slab 1 0.69 1.8852 1.8852 1.0000 CS14x9;10 2002-Rev 1.5 Top Slab 1 0.6325 Top Slab 1 0.6325 1.1166 1.2179 0.9168 CS14x9;10 2002-Rev 1.9 Top Slab 1 0.6325 Top Slab 1 0.6325 1.111 1.1973 0.9279 CS14x9;10 2002-Rev 2 Top Slab 1 0.6325 Top Slab 1 0.6325 1.2211 1.2211 1.0000 CS14x9;10 2002-Rev 4 Top Slab 1 0.6325 Top Slab 1 0.6325 1.4358 1.4358 1.0000 CS14x9;10 2002-Rev 7 Top Slab 1 0.6325 Top Slab 1 0.6325 1.3875 1.3875 1.0000 CS14x9;10 2010-Rev 1.5 Top Slab 1 0.7825 Top Slab 1 1.4 1.4648 1.7391 0.8423 CS14x9;10 2010-Rev 1.9 Top Slab 1 0.7825 Top Slab 1 0.7825 1.4714 1.7734 0.8297 CS14x9;10 2010-Rev 2 Top Slab 1 0.7825 Top Slab 1 0.7825 1.5539 1.5539 1.0000 CS14x9;10 2010-Rev 2.5 Top Slab 1 0.7825 Top Slab 1 0.7825 1.7586 1.7586 1.0000 CS14x9;10 2010-Rev 3 Top Slab 1 0.7825 Top Slab 1 0.7825 1.9669 1.9669 1.0000 CS14x9;10 2010-Rev 3.5 Top Slab 1 0.7825 Top Slab 1 0.7825 2.0896 2.0896 1.0000 CS14x9;10 2010-Rev 4 Top Slab 1 0.7825 Top Slab 1 0.7825 2.2055 2.2055 1.0000 CS16x12;0 1922 EAE-Rev 1.5 Top Slab 1 2.3528 Top Slab 1 2.3528 2.1968 2.2408 0.9804 CS16x12;0 1922 EAE-Rev 1.9 Top Slab 1 2.3528 Top Slab 1 2.3528 2.2376 2.3038 0.9713 CS16x12;0 1922 EAE-Rev 2 Top Slab 1 2.3528 Top Slab 1 2.3528 2.2285 2.2285 1.0000 CS16x12;0 1922 EAE-Rev 2.5 Top Slab 1 2.3528 Top Slab 1 2.3528 2.6235 2.6235 1.0000 CS16x12;0 1922 EAE-Rev 3 Top Slab 1 2.3315 Top Slab 1 2.3315 3.0002 3.0002 1.0000 CS16x12;0 1922 EAE-Rev 3.5 Top Slab 1 2.3315 Top Slab 1 2.3315 3.2459 3.2459 1.0000 CS16x12;0 1922 EAE-Rev 4 Top Slab 1 2.3315 Top Slab 1 2.3315 3.4994 3.4994 1.0000 CS16x8;5 1922 EAE- Rev 1.5 Top Slab 1 2.6645 Top Slab 1 2.6645 2.4898 2.5762 0.9665 CS16x8;5 1922 EAE- Rev 1.9 Top Slab 1 2.6645 Top Slab 1 2.6645 2.5454 2.6561 0.9583 CS16x8;5 1922 EAE- Rev 2 Top Slab 1 2.6645 Top Slab 1 2.6645 3.0398 3.0398 1.0000 CS16x8;5 1922 EAE- Rev 2.5 Top Slab 1 2.6645 Top Slab 1 2.6645 3.5048 3.5048 1.0000 CS16x8;5 1922 EAE- Rev 3 Top Slab 1 2.6645 Top Slab 1 2.6645 3.9755 3.9755 1.0000 CS16x8;5 1922 EAE- Rev 4 Top Slab 1 2.676 Top Slab 1 2.676 5.0277 5.0277 1.0000 CS7x7;10 2010-Rev 1.5 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.5433 1.5433 1.0000 CS7x7;10 2010-Rev 1.9 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.5855 1.5855 1.0000
Appendix G â Specification Backup G-8 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) CS7x7;10 2010-Rev 2 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.5806 1.5806 1.0000 CS7x7;10 2010-Rev 4 Bottom Slab 1 0.51 Bottom Slab 1 0.51 3.0855 3.0855 1.0000 CS7x7;10 2010-Rev 7 Bottom Slab 1 0.51 Bottom Slab 1 0.51 4.7945 4.7945 1.0000 CS8x8;10 2010-Rev 1.5 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.3655 1.3655 1.0000 CS8x8;10 2010-Rev 1.9 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.3896 1.3896 1.0000 CS8x8;10 2010-Rev 2 Bottom Slab 1 0.51 Bottom Slab 1 0.51 1.382 1.382 1.0000 CS8x8;10 2010-Rev 4 Bottom Slab 1 0.51 Bottom Slab 1 0.51 2.4193 2.4193 1.0000 CS8x8;10 2010-Rev 7 Bottom Slab 1 0.51 Bottom Slab 1 0.51 3.4916 3.4916 1.0000 Model 1- Candidate 1- Rev 1.5 Top Slab 1 1.8759 Top Slab 1 1.8759 1.4574 1.8193 0.8011 Model 1- Candidate 1- Rev 1.99 Top Slab 1 1.8759 Top Slab 1 1.8759 1.3847 1.726 0.8023 Model 1- Candidate 1- Rev 2 Top Slab 1 1.8759 Top Slab 1 1.8759 1.6066 1.6066 1.0000 Model 1- Candidate 1- Rev 2.1 Top Slab 1 1.8759 Top Slab 1 1.8759 1.6323 1.6323 1.0000 Model 1- Candidate 1- Rev 2.2 Top Slab 1 1.8759 Top Slab 1 1.8759 1.6575 1.6575 1.0000 Model 1- Candidate 1- Rev 2.4 Top Slab 1 1.8759 Top Slab 1 1.8759 1.7064 1.7064 1.0000 Model 1- Candidate 1- Rev 2.5 Top Slab 1 1.8759 Top Slab 1 1.8759 1.7241 1.7241 1.0000 Model 1- Candidate 1- Rev 3 Top Slab 1 1.8759 Top Slab 1 1.8759 1.7543 1.7543 1.0000 Model 1- Candidate 1- Rev 5 Top Slab 1 1.8759 Top Slab 1 1.8759 1.7624 1.7624 1.0000 Model 1- Candidate 1- Rev 7 Top Slab 1 1.8759 Top Slab 1 1.8759 1.5137 1.5137 1.0000 Model 2- Candidate 1- Rev 1.5 Top Slab 2 1.13 Top Slab 2 1.13 1.5227 1.698 0.8968 Model 2- Candidate 1- Rev 1.9 Top Slab 2 1.13 Top Slab 2 1.13 1.579 1.743 0.9059 Model 2- Candidate 1- Rev 2 Top Slab 2 1.13 Top Slab 2 1.13 1.634 1.634 1.0000 Model 2- Candidate 1- Rev 2.5 Top Slab 1 1.13 Top Slab 1 1.13 1.822 1.822 1.0000 Model 2- Candidate 1- Rev 3 Top Slab 1 1.13 Top Slab 1 1.13 2.2039 2.2039 1.0000 Model 2- Candidate 1- Rev 3.5 Top Slab 1 1.13 Top Slab 1 1.13 2.5422 2.5422 1.0000 Model 2- Candidate 1- Rev 4 Top Slab 1 1.13 Top Slab 1 1.13 2.8282 2.8282 1.0000 Model 2- Candidate 1- Rev 10 Bottom Slab 1 9.31 Bottom Slab 1 9.31 2.7384 2.7384 1.0000 Model 2- Candidate 1- Rev 7 Bottom Slab 1 9.31 Bottom Slab 1 9.31 3.4624 3.4624 1.0000 Model 3- Candidate 1- Rev 1.5 Top Slab 1 1.4337 Top Slab 1 1.4337 3.1686 3.4535 0.9175
Appendix G â Specification Backup G-9 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Op Rating Factor HL93 (After) Ratio (before/after) Model 3- Candidate 1- Rev 1.9 Top Slab 1 1.4337 Top Slab 1 1.4337 3.1686 3.4535 0.9175 Model 3- Candidate 1- Rev 2 Top Slab 1 1.4337 Top Slab 1 1.4337 3.2834 3.2834 1.0000 Model 3- Candidate 1- Rev 2.5 Top Slab 1 1.4337 Top Slab 1 1.4337 3.9636 3.9636 1.0000 Model 3- Candidate 1- Rev 3 Bottom Slab 1 1.2608 Bottom Slab 1 1.2608 4.5826 4.5826 1.0000 Model 3- Candidate 1- Rev 3.5 Bottom Slab 1 1.2608 Bottom Slab 1 1.2608 4.9611 4.9611 1.0000 Model 3- Candidate 1- Rev 4 Bottom Slab 1 1.2608 Bottom Slab 1 1.2608 5.2644 5.2644 1.0000 Model 3- Candidate 1- Rev 10 Bottom Slab 1 1.2608 Bottom Slab 1 1.2608 8.9506 8.9506 1.0000 Model 3- Candidate 1- Rev 7 Bottom Slab 1 1.2608 Bottom Slab 1 1.2608 6.9788 6.9788 1.0000
Appendix G â Specification Backup G-10 Full Table of BrDR runs for LL Surcharge vs Approaching Wheel Load changes. The following table represents the AASHTOWare BrDR analysis runs for a select set of the Caltrans culverts and project culverts for the change in the LL Surcharge vs. Approaching Wheel Load. Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-CD8x8;10 1924-Rev 1.0 ft Cover 0.41 0.531 0.41 0.531 1 1 LS-CD8x8;10 1924-Rev 1.9 ft Cover 0.579 0.751 0.579 0.751 1 1 LS-CD8x8;10 1924-Rev 2 ft Cover 0.596 0.773 0.596 0.773 1 1 LS-CD8x8;10 1924-Rev 3 ft Cover 1.27 1.646 1.27 1.646 1 1 LS-CD8x8;10 1924-Rev 5 ft Cover 0.919 1.191 1.453 1.883 0.632485 0.632501 LS-CD8x8;10 1933-Rev 1.0 ft Cover 0.466 0.605 0.466 0.605 1 1 LS-CD8x8;10 1933-Rev 1.9 ft Cover 0.657 0.851 0.657 0.851 1 1 LS-CD8x8;10 1933-Rev 2 ft Cover 0.676 0.876 0.676 0.876 1 1 LS-CD8x8;10 1933-Rev 3 ft Cover 1.388 1.8 1.388 1.8 1 1 LS-CD8x8;10 1933-Rev 3.5 ft Cover 1.625 2.106 1.739 2.254 0.934445 0.934339 LS-CD8x8;10 1933-Rev 4 ft Cover 1.496 1.939 2.119 2.746 0.705993 0.706118 LS-CD10x8;16 1966-Rev 1.9 ft Cover 0.723 0.937 0.736 0.954 0.982337 0.98218 LS-CD10x8;16 1966-Rev 2 ft Cover 0.692 0.897 0.753 0.976 0.918991 0.919057 LS-CD10x8;16 1966-Rev 2.5 ft Cover 0.549 0.712 0.652 0.845 0.842025 0.842604 LS-CD10x8;16 1966-Rev 3 ft Cover 0.401 0.52 0.51 0.661 0.786275 0.786687 LS-CD10x8;16 1966-Rev 3.5 ft Cover 0.249 0.323 0.337 0.437 0.738872 0.73913 LS-CD10x8;16 1966-Rev 4 ft Cover 0.093 0.121 0.134 0.174 0.69403 0.695402 LS-CS10x8;5 1922-Rev 1.5 ft Cover 1.001 1.298 1.001 1.298 1 1 LS-CS10x8;5 1922-Rev 1.9 ft Cover 0.973 1.261 0.973 1.261 1 1 LS-CS10x8;5 1922-Rev 2 ft Cover 0.958 1.242 0.958 1.242 1 1 LS-CS10x8;5 1922-Rev 2.5 ft Cover 1.036 1.343 1.036 1.343 1 1 LS-CS10x8;5 1922-Rev 3 ft Cover 1.102 1.429 1.102 1.429 1 1 LS-CS10x8;5 1922-Rev 3.5 ft Cover 1.13 1.465 1.13 1.465 1 1 LS-CS10x8;5 1922-Rev 4 ft Cover 1.122 1.454 1.122 1.454 1 1 LS-CS10x8;5 1933-Rev 1.5 ft Cover 0.566 0.734 0.569 0.738 0.994728 0.99458 LS-CS10x8;5 1933-Rev 1.9 ft Cover 0.456 0.591 0.494 0.64 0.923077 0.923438 LS-CS10x8;5 1933-Rev 2 ft Cover 0.429 0.556 0.473 0.613 0.906977 0.907015 LS-CS10x8;5 1933-Rev 2.5 ft Cover 0.293 0.379 0.35 0.454 0.837143 0.834802 LS-CS10x8;5 1933-Rev 3 ft Cover 0.157 0.204 0.203 0.263 0.773399 0.775665 LS-CS10x8;5 1933-Rev 3.5 ft Cover 0.023 0.03 0.032 0.041 0.71875 0.731707 LS-CS10x8;10 1933-Rev 1.9 ft Cover 1.297 1.681 1.297 1.681 1 1 LS-CS10x8;10 1933-Rev 2 ft Cover 1.282 1.661 1.282 1.661 1 1 LS-CS10x8;10 1933-Rev 2.5 ft Cover 1.409 1.827 1.409 1.827 1 1 LS-CS10x8;10 1933-Rev 3 ft Cover 1.559 2.021 1.559 2.021 1 1 LS-CS10x8;10 1933-Rev 3.5 ft Cover 1.69 2.191 1.69 2.191 1 1
Appendix G â Specification Backup G-11 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-CS10x8;10 1933-Rev 4 ft Cover 1.699 2.202 1.699 2.202 1 1 LS-CS10x8;10 1933-Rev 7 ft Cover 1.525 1.977 1.758 2.279 0.867463 0.867486 LS-CD12x8;9 1948-Rev 0.0 ft Cover 0.255 0.33 0.255 0.33 1 1 LS-CD12x8;9 1948-Rev 0.5 ft Cover 0.33 0.428 0.33 0.428 1 1 LS-CD12x8;9 1948-Rev 1.0 ft Cover 0.412 0.534 0.412 0.534 1 1 LS-CD12x8;9 1948-Rev 1.5 ft Cover 0.506 0.656 0.506 0.656 1 1 LS-CD12x8;9 1948-Rev 1.9 ft Cover 0.427 0.553 0.448 0.58 0.953125 0.953448 LS-CD12x8;9 1948-Rev 2 ft Cover 0.399 0.517 0.425 0.551 0.938824 0.938294 LS-CD12x8;9 1952-Rev 1.5 ft Cover 0.591 0.766 0.61 0.791 0.968852 0.968394 LS-CD12x8;9 1952-Rev 1.9 ft Cover 0.481 0.624 0.528 0.685 0.910985 0.910949 LS-CD12x8;9 1952-Rev 2 ft Cover 0.453 0.588 0.505 0.655 0.89703 0.89771 LS-CD12x8;9 1952-Rev 3 ft Cover 0.182 0.236 0.233 0.302 0.781116 0.781457 LS-CD12x8;9 1952-Rev 3.5 ft Cover 0.04 0.052 0.054 0.071 0.740741 0.732394 LS-CD12x12;20 2010-Rev 1.9 ft Cover 2.352 3.048 2.369 3.071 0.992824 0.992511 LS-CD12x12;20 2010-Rev 2 ft Cover 2.36 3.059 2.378 3.083 0.992431 0.992215 LS-CD12x12;20 2010-Rev 2.5 ft Cover 2.36 3.059 2.378 3.083 0.992431 0.992215 LS-CD12x12;20 2010-Rev 3 ft Cover 3.232 4.19 3.282 4.254 0.984765 0.984955 LS-CD12x12;20 2010-Rev 3.5 ft Cover 3.651 4.733 3.722 4.825 0.980924 0.980933 LS-CD12x12;20 2010-Rev 4 ft Cover 4.064 5.268 4.161 5.393 0.976688 0.976822 LS-CD12x12;20 2010-Rev 5 ft Cover 4.999 6.48 5.168 6.699 0.967299 0.967309 LS-CS12x8;5 1922-Rev 1.5 ft Cover 1.018 1.32 1.018 1.32 1 1 LS-CS12x8;5 1922-Rev 1.9 ft Cover 0.991 1.285 0.991 1.285 1 1 LS-CS12x8;5 1922-Rev 2 ft Cover 0.977 1.266 0.977 1.266 1 1 LS-CS12x8;5 1922-Rev 3 ft Cover 1.134 1.471 1.134 1.471 1 1 LS-CS12x8;5 1922-Rev 4 ft Cover 1.119 1.45 1.119 1.45 1 1 LS-CS12x8;5 1922-Rev 5 ft Cover 1.022 1.325 1.022 1.325 1 1 LS-CS12x8;10 1952-Rev 1.5 ft Cover 1.112 1.441 1.112 1.441 1 1 LS-CS12x8;10 1952-Rev 1.9 ft Cover 1.087 1.409 1.087 1.409 1 1 LS-CS12x8;10 1952-Rev 2 ft Cover 1.072 1.39 1.072 1.39 1 1 LS-CS12x8;10 1952-Rev 3 ft Cover 1.259 1.632 1.259 1.632 1 1 LS-CS12x8;10 1952-Rev 4 ft Cover 1.387 1.798 1.387 1.798 1 1 LS-CS12x8;10 1952-Rev 7 ft Cover 1.442 1.869 1.442 1.869 1 1 LS-CS12x8;10 1952-Rev 10 ft Cover 0.608 0.788 0.608 0.788 1 1 LS-CS12x8;10 2010-Rev 1.5 ft Cover 1.56 2.022 1.556 2.017 1.002571 1.002479 LS-CS12x8;10 2010-Rev 1.9 ft Cover 1.588 2.059 1.585 2.055 1.001893 1.001946 LS-CS12x8;10 2010-Rev 2 ft Cover 1.588 2.059 1.588 2.059 1 1 LS-CS12x8;10 2010-Rev 2.5 ft Cover 1.748 2.265 1.748 2.265 1 1 LS-CS12x8;10 2010-Rev 3 ft Cover 1.932 2.504 1.932 2.504 1 1
Appendix G â Specification Backup G-12 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-CS12x8;10 2010-Rev 3.5 ft Cover 2.088 2.707 2.088 2.707 1 1 LS-CS12x8;10 2010-Rev 4 ft Cover 2.219 2.876 2.219 2.876 1 1 LS-CS12x12;10 2002-Rev 1.5 ft Cover 1.191 1.544 1.192 1.545 0.999161 0.999353 LS-CS12x12;10 2002-Rev 1.9 ft Cover 1.17 1.516 1.183 1.533 0.989011 0.988911 LS-CS12x12;10 2002-Rev 2 ft Cover 1.238 1.605 1.249 1.619 0.991193 0.991353 LS-CS12x12;10 2002-Rev 2.5 ft Cover 1.334 1.73 1.349 1.749 0.988881 0.989137 LS-CS12x12;10 2002-Rev 3 ft Cover 1.49 1.932 1.505 1.951 0.990033 0.990261 LS-CS12x12;10 2002-Rev 3.5 ft Cover 1.563 2.026 1.571 2.037 0.994908 0.9946 LS-CS12x12;10 2002-Rev 4 ft Cover 1.613 2.091 1.613 2.091 1 1 LS-CS14x14;10 2002-Rev 1.5 ft Cover 1.261 1.634 1.281 1.66 0.984387 0.984337 LS-CS14x14;10 2002-Rev 1.9 ft Cover 1.227 1.591 1.249 1.619 0.982386 0.982705 LS-CS14x14;10 2002-Rev 2 ft Cover 1.381 1.79 1.381 1.79 1 1 LS-CS14x14;10 2002-Rev 2.5 ft Cover 1.5 1.944 1.504 1.95 0.99734 0.996923 LS-CS14x14;10 2002-Rev 3 ft Cover 1.636 2.121 1.636 2.121 1 1 LS-CS14x14;10 2002-Rev 3.5 ft Cover 1.693 2.194 1.693 2.194 1 1 LS-CS14x14;10 2002-Rev 4 ft Cover 1.736 2.251 1.736 2.251 1 1 LS-CD14x13;10 2002-Rev 1.5 ft Cover 1.28 1.659 1.28 1.659 1 1 LS-CD14x13;10 2002-Rev 1.9 ft Cover 1.265 1.64 1.265 1.64 1 1 LS-CD14x13;10 2002-Rev 2 ft Cover 1.255 1.627 1.255 1.627 1 1 LS-CD14x13;10 2002-Rev 2.5 ft Cover 1.381 1.79 1.381 1.79 1 1 LS-CD14x13;10 2002-Rev 3 ft Cover 1.525 1.976 1.525 1.976 1 1 LS-CD14x13;10 2002-Rev 3.5 ft Cover 1.581 2.049 1.581 2.049 1 1 LS-CD14x13;10 2002-Rev 4 ft Cover 1.606 2.082 1.606 2.082 1 1 LS-CS16x12;0 1922 EAE-Rev 1.5 ft cover 0.596 0.773 0.596 0.773 1 1 LS-CS16x12;0 1922 EAE-Rev 1.9 ft cover 0.541 0.701 0.541 0.701 1 1 LS-CS16x12;0 1922 EAE-Rev 2 ft cover 0.523 0.678 0.523 0.678 1 1 LS-CS16x12;0 1922 EAE-Rev 2.5 ft cover 0.54 0.7 0.54 0.7 1 1 LS-CS16x12;0 1922 EAE-Rev 3 ft cover 0.522 0.677 0.522 0.677 1 1 LS-CS16x12;0 1922 EAE-Rev 3.5 ft cover 0.432 0.56 0.432 0.56 1 1 LS-CS16x12;0 1922 EAE-Rev 4 ft cover 0.325 0.421 0.325 0.421 1 1 LS-CS16x8;5 1922 EAE-Rev 1.5 ft cover 0.112 0.145 0.112 0.145 1 1 LS-CS16x8;5 1922 EAE-Rev 1.9 ft cover 0.057 0.073 0.057 0.073 1 1 LS-CS16x8;5 1922 EAE-Rev 2 ft cover 0.042 0.054 0.042 0.054 1 1 LS-Model 1- Candidate 1-R 1.5 ft Cover 1.458 1.891 1.454 1.885 1.002751 1.003183 LS-Model 1- Candidate 1-R 1.99 ft Cover 1.386 1.796 1.383 1.793 1.002169 1.001673 LS-Model 1- Candidate 1-R 2.0 ft Cover 1.47 1.905 1.47 1.905 1 1 LS-Model 1- Candidate 1-R 2.1 ft Cover 1.486 1.927 1.486 1.927 1 1 LS-Model 1- Candidate 1-R 2.2 ft Cover 1.502 1.947 1.502 1.947 1 1
Appendix G â Specification Backup G-13 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-Model 1- Candidate 1-R 2.4 ft Cover 1.531 1.984 1.531 1.984 1 1 LS-Model 1- Candidate 1-R 2.5 ft Cover 1.538 1.994 1.538 1.994 1 1 LS-Model 1- Candidate 1-R 3.0 ft Cover 1.509 1.956 1.509 1.956 1 1 LS-Model 1- Candidate 1-R 5.0 ft Cover 1.147 1.487 1.147 1.487 1 1 LS-Model 1- Candidate 1-R 7.0 ft Cover 0.395 0.512 0.395 0.512 1 1 LS-Model 2- Candidate 1-R 1.5 ft cover 1.475 1.912 1.471 1.907 1.002719 1.002622 LS-Model 2- Candidate 1-R 1.9 ft cover 1.535 1.989 1.535 1.989 1 1 LS-Model 2- Candidate 1-R 2.0 ft cover 1.524 1.976 1.524 1.976 1 1 LS-Model 2- Candidate 1-R 2.5 ft cover 1.712 2.22 1.712 2.22 1 1 LS-Model 2- Candidate 1-R 3.0 ft cover 1.92 2.489 1.92 2.489 1 1 LS-Model 2- Candidate 1-R 3.5 ft cover 2.148 2.784 2.148 2.784 1 1 LS-Model 2- Candidate 1-R 4.0 ft cover 2.335 3.027 2.335 3.027 1 1 LS-Model 2- Candidate 1-R 7.0 ft cover 3.462 4.488 3.462 4.488 1 1 LS-Model 2- Candidate 1-R 10.0 ft cover 2.738 3.55 2.738 3.55 1 1 LS-Model 3- Candidate 1-R 1.5 ft cover 1.452 1.882 1.452 1.882 1 1 LS-Model 3- Candidate 1-R 1.9 ft cover 1.452 1.882 1.452 1.882 1 1 LS-Model 3- Candidate 1-R 2.0 ft cover 1.414 1.833 1.414 1.833 1 1 LS-Model 3- Candidate 1-R 2.5 ft cover 1.547 2.006 1.547 2.006 1 1 LS-Model 3- Candidate 1-R 3.0 ft cover 1.7 2.204 1.7 2.204 1 1 LS-Model 3- Candidate 1-R 3.5 ft cover 1.811 2.347 1.811 2.347 1 1 LS-Model 3- Candidate 1-R 4.0 ft cover 1.823 2.363 1.823 2.363 1 1 LS-Model 3- Candidate 1-R 7.0 ft cover 1.627 2.11 1.627 2.11 1 1 LS-Model 3- Candidate 1-R 10.0 ft cover 0.841 1.09 0.841 1.09 1 1 LS-TJM-10x10 1.5 ft Cover 0.639 0.828 0.639 0.828 1 1 LS-TJM-10x10 2.0 ft Cover 0.597 0.774 0.597 0.774 1 1 LS-CD8x8;5 1924-Rev 1.0 ft Cover 0.359 0.465 0.359 0.465 1 1 LS-CD8x8;5 1924-Rev 1.5 ft Cover 0.441 0.572 0.441 0.572 1 1 LS-CD8x8;5 1924-Rev 1.9 ft Cover 0.516 0.669 0.516 0.669 1 1 LS-CD8x8;5 1924-Rev 2 ft Cover 0.532 0.69 0.532 0.69 1 1 LS-CD8x8;5 1924-Rev 3 ft Cover 1.085 1.406 1.085 1.406 1 1 LS-CD8x8;5 1924-Rev 4 ft Cover 1.245 1.613 1.245 1.613 1 1 LS-CD10x8;9 1948-Rev 1.5 ft Cover 0.331 0.43 0.323 0.419 1.024768 1.026253 LS-CD10x8;9 1948-Rev 1.9 ft Cover 0.215 0.279 0.224 0.291 0.959821 0.958763 LS-CD10x8;9 1948-Rev 2 ft Cover 0.186 0.241 0.197 0.255 0.944162 0.945098 LS-CD10x8;10 2002-Rev 1.5 ft Cover 1.077 1.396 1.072 1.39 1.004664 1.004317 LS-CD10x8;10 2002-Rev 1.9 ft Cover 1.116 1.447 1.116 1.447 1 1 LS-CD10x8;10 2002-Rev 2 ft Cover 1.118 1.45 1.118 1.45 1 1 LS-CD10x8;10 2002-Rev 4 ft Cover 1.76 2.282 1.76 2.282 1 1
Appendix G â Specification Backup G-14 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-CD10x8;10 2002-Rev 7 ft Cover 1.609 2.086 1.609 2.086 1 1 LS-CD10x8;10 2010-Rev 1.5 ft Cover 1.466 1.9 1.466 1.9 1 1 LS-CD10x8;10 2010-Rev 1.9 ft Cover 1.506 1.953 1.506 1.953 1 1 LS-CD10x8;10 2010-Rev 2 ft Cover 1.558 2.019 1.558 2.019 1 1 LS-CD10x8;10 2010-Rev 4 ft Cover 2.512 3.256 2.512 3.256 1 1 LS-CD10x8;10 2010-Rev 7 ft Cover 3.01 3.902 3.01 3.902 1 1 LS-CD14x9;10 2002-Rev 1.5 ft Cover 1.283 1.663 1.283 1.663 1 1 LS-CD14x9;10 2002-Rev 1.9 ft Cover 1.248 1.618 1.248 1.618 1 1 LS-CD14x9;10 2002-Rev 2 ft Cover 1.259 1.632 1.259 1.632 1 1 LS-CD14x9;10 2002-Rev 4 ft Cover 1.531 1.985 1.531 1.985 1 1 LS-CD14x9;10 2002-Rev 7 ft Cover 1.36 1.763 1.36 1.763 1 1 LS-CD14x9;10 2010-Rev 1.5 ft Cover 1.656 2.147 1.656 2.147 1 1 LS-CD14x9;10 2010-Rev 1.9 ft Cover 1.629 2.112 1.629 2.112 1 1 LS-CD14x9;10 2010-Rev 2 ft Cover 1.735 2.249 1.735 2.249 1 1 LS-CD14x9;10 2010-Rev 4 ft Cover 2.155 2.793 2.155 2.793 1 1 LS-CD14x9;10 2010-Rev 7 ft Cover 2.318 3.005 2.318 3.005 1 1 LS-CS7x7;10 2010-Rev 1.5 ft Cover 1.528 1.981 1.529 1.982 0.999346 0.999495 LS-CS7x7;10 2010-Rev 1.9 ft Cover 1.536 1.992 1.536 1.992 1 1 LS-CS7x7;10 2010-Rev 2 ft Cover 1.521 1.972 1.521 1.972 1 1 LS-CS7x7;10 2010-Rev 4 ft Cover 2.533 3.284 2.533 3.284 1 1 LS-CS7x7;10 2010-Rev 7 ft Cover 3.835 4.972 3.835 4.972 1 1 LS-CS8x8;10 2010-Rev 1.5 ft Cover 1.345 1.744 1.345 1.744 1 1 LS-CS8x8;10 2010-Rev 1.9 ft Cover 1.325 1.717 1.325 1.717 1 1 LS-CS8x8;10 2010-Rev 2 ft Cover 1.309 1.697 1.309 1.697 1 1 LS-CS8x8;10 2010-Rev 4 ft Cover 1.821 2.36 1.821 2.36 1 1 LS-CS8x8;10 2010-Rev 7 ft Cover 2.435 3.156 2.435 3.156 1 1 LS-CS10x8;5 1952-Rev 1.5 ft Cover 0.691 0.896 0.691 0.896 1 1 LS-CS10x8;5 1952-Rev 1.9 ft Cover 0.663 0.859 0.663 0.859 1 1 LS-CS10x8;5 1952-Rev 2 ft Cover 0.65 0.842 0.65 0.842 1 1 LS-CS10x8;5 1952-Rev 3 ft Cover 0.729 0.945 0.729 0.945 1 1 LS-CS10x8;5 1952-Rev 4 ft Cover 0.762 0.988 0.762 0.988 1 1 LS-CS10x8;5 1952-Rev 5 ft Cover 0.731 0.948 0.731 0.948 1 1 LS-CS10x8;6 1948-Rev 1.5 ft Cover 0.912 1.182 0.912 1.182 1 1 LS-CS10x8;6 1948-Rev 1.9 ft Cover 0.89 1.153 0.89 1.153 1 1 LS-CS10x8;6 1948-Rev 2 ft Cover 0.877 1.136 0.877 1.136 1 1 LS-CS10x8;6 1948-Rev 3 ft Cover 1.024 1.327 1.024 1.327 1 1 LS-CS10x8;6 1948-Rev 4 ft Cover 1.1 1.425 1.1 1.425 1 1 LS-CS10x8;6 1948-Rev 5 ft Cover 1.047 1.357 1.047 1.357 1 1
Appendix G â Specification Backup G-15 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (After) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio LS-CS10x8;8 1966-Rev 1.5 ft Cover 0.91 1.18 0.91 1.18 1 1 LS-CS10x8;8 1966-Rev 1.9 ft Cover 0.886 1.149 0.886 1.149 1 1 LS-CS10x8;8 1966-Rev 2 ft Cover 0.873 1.132 0.873 1.132 1 1 LS-CS10x8;8 1966-Rev 4 ft Cover 1.137 1.474 1.137 1.474 1 1 LS-CS10x8;8 1966-Rev 6 ft Cover 1.219 1.58 1.219 1.58 1 1 LS-CS10x8;10 1981-Rev 1.5 ft Cover 1.133 1.469 1.129 1.464 1.003543 1.003415 LS-CS10x8;10 1981-Rev 1.9 ft Cover 1.15 1.491 1.152 1.493 0.998264 0.99866 LS-CS10x8;10 1981-Rev 2 ft Cover 1.179 1.528 1.179 1.528 1 1 LS-CS10x8;10 1981-Rev 4 ft Cover 1.648 2.136 1.648 2.136 1 1 LS-CS10x8;10 1981-Rev 7 ft Cover 1.814 2.351 1.865 2.417 0.972654 0.972693 LS-CS10x8;10 2002-Rev 1.5 ft Cover 1.215 1.575 1.211 1.57 1.003303 1.003185 LS-CS10x8;10 2002-Rev 1.9 ft Cover 1.242 1.61 1.244 1.612 0.998392 0.998759 LS-CS10x8;10 2002-Rev 2 ft Cover 1.246 1.615 1.246 1.615 1 1 LS-CS10x8;10 2002-Rev 4 ft Cover 1.761 2.283 1.761 2.283 1 1 LS-CS10x8;10 2002-Rev 7 ft Cover 2.106 2.729 2.156 2.795 0.976809 0.976386 LS-CS10x8;10 2010-Rev 1.5 ft Cover 1.51 1.957 1.505 1.951 1.003322 1.003075 LS-CS10x8;10 2010-Rev 1.9 ft Cover 1.558 2.02 1.555 2.016 1.001929 1.001984 LS-CS10x8;10 2010-Rev 2 ft Cover 1.655 2.146 1.655 2.146 1 1 LS-CS10x8;10 2010-Rev 4 ft Cover 2.442 3.166 2.442 3.166 1 1 LS-CS10x8;10 2010-Rev 7 ft Cover 3.611 4.681 3.611 4.681 1 1 LS-CS10x8;12 1952-Rev 1.9 ft Cover 1.1 1.426 1.1 1.426 1 1 LS-CS10x8;12 1952-Rev 2 ft Cover 1.086 1.407 1.086 1.407 1 1 LS-CS10x8;12 1952-Rev 4 ft Cover 1.489 1.931 1.489 1.931 1 1 LS-CS10x8;12 1952-Rev 7 ft Cover 1.806 2.341 1.806 2.341 1 1 LS-CS14x9;10 2002-Rev 1.5 ft Cover 1.106 1.434 1.103 1.429 1.00272 1.003499 LS-CS14x9;10 2002-Rev 1.9 ft Cover 1.084 1.406 1.083 1.403 1.000923 1.002138 LS-CS14x9;10 2002-Rev 2 ft Cover 1.188 1.539 1.19 1.542 0.998319 0.998054 LS-CS14x9;10 2002-Rev 4 ft Cover 1.355 1.756 1.366 1.771 0.991947 0.99153 LS-CS14x9;10 2002-Rev 7 ft Cover 1.28 1.659 1.294 1.677 0.989181 0.989267
Appendix H â Proposed Ballot Items Hâ1 Appendix H â Proposed AASHTO Ballot Items Proposed ballot items for AASHTO LRFD Bridge Design Specifications 1. Depth of live load, Article 3.6.1.2a 2. Live load distribution, Articles 3.6.1.2a, Article 4.6.2.10.2 3. Lateral Pressure Coefficient, Article 3.11.5.1 4. Approaching wheel load, Article 3.11.6.4.1 Proposed ballot items for AASHTO Manual for Bridge Evaluation: 1. LRFD Culverts, New Article 6A.10 2. ASD/LFD Culverts, New Article 6B.10
Appendix H â Proposed Ballot Items     Hâ2 Ballot LRFD-1 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Culverts â Depth of Fill and Consideration of Live Load TECHNICAL COMMITTEE:   T-5 Loads and Load Distribution, T-13 Culverts, T-18 Bridge Management Evaluation and Rehabilitation  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Revise the first paragraph of Article 3.6.1.2.6a-General in the Design Specifications as follows: The effects of live load may be neglected when the factored live load pressure at the surface of the culvert is less than 10% of the sum of the factored earth load plus factored live load pressure. OTHER AFFECTED ARTICLES: None BACKGROUND: Currently the AASHTO LRFD Specifications state: âFor single span culverts the effects of live load may be neglected where the depth of fill is more than 8.0 ft and exceeds the span length; for multiple span culverts the effects may be neglected where the depth of fill exceeds the distance between inside faces of end walls.â This provision requires consideration of live load until the depth exceeds the span; however, in the experience of some members of the research team the provision is often interpreted as ignoring live loads at depths of 8 ft and greater. At a depth of 8 ft, the live load is 36% of the total load and if dropped from design consideration, the net load factor (factored earth load/(service earth plus live load, in psf) is only 1.03. This low factor of safety likely occurred in part because the provision was developed under the Standard Specifications which used LLDF = 1.75. The proposed provision changes the depth of fill for dropping live load consideration to about 13 ft for the design tandem. At this depth the net load factor when not considering live load is 1.20 and is insensitive to overloaded live load vehicles.
Appendix H â Proposed Ballot Items     Hâ3 Also, the proposed revision provides a clear method for engineers to consider the depths at which permit vehicles and other non-standard loadings need not be considered in design or rating. REFERENCES: NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ.
Appendix H â Proposed Ballot Items     Hâ4 Ballot LRFD-2 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Live Load Distribution for Culverts TECHNICAL COMMITTEE:   T-5 Loads and Load Distribution, T-13 Culverts, T-18 Bridge Management and Evaluation  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Item #1 Article 3.6.1.2.6a Revise 2nd paragraph Live load shall be distributed to the top slabs of flat top three- or four-sided concrete culverts, three-sided arch top concrete culverts or concrete arch culverts over the area calculated in this Article, but not less than the dimensions calculated using the procedure specified in Article 4.6.2.10. Live load shall be distributed to concrete pipe culverts with 1.0 ft or more but less than 2.0 ft of cover in accordance with Article 4.6.2.10. Culverts other than concrete with 1.0 ft or more but less than 2.0 ft of cover shall be designed for a depth of 1.0 ft. Culverts with curved tops and less than 1.0 ft of cover shall be analyzed with more comprehensive methods. Delete 5th Paragraph Item #2 Revise Article 4.6.2.10.2 Modify 2nd paragraph and Equations Wheel loads shall be distributed to the top slab for determining moment, thrust, and shear as follows: Perpendicular to the span: E = 28 + td1 + 1.44 S (4.6.2.10.2-1) Parallel to the span: Espan = td2 + LLDF(H) (4.6.2.10.2-2)
Appendix H â Proposed Ballot Items     Hâ5 Add to notation td1 = tire dimension (lt or wt, see 3.6.1.2.6) perpendicular to the span td2 = tire dimension (lt or wt, see 3.6.1.2.6) parallel to the span Revise Article C4.6.2.10.2 Add new paragraph Strip widths for culverts are expressed in terms of wheel loads. Culvert spans are typically small and deign forces are controlled by single wheel effects. A flowchart illustrating the determination of the transverse distribution (strip width) for a single-axle load through fill is shown in Figure C4.6.2.10.2-1. Figure C4.6.2.10.2-1 - Single-Axle Transverse Distribution Through Fill
Appendix H â Proposed Ballot Items     Hâ6 Item #3 Revise Article 4.6.2.10.3 Traffic traveling perpendicular to the span shall consider multiple lane loadings with the appropriate multiple presence factor. When traffic travels perpendicular to the span, wheel loads shall be distributed to the top slab as specified here: Perpendicular to the span: E = ((Ax -1)* 48 + Axsp + td1 + 1.44 S)/Ax (4.6.2.10.2-3) Parallel to the span: Espan = td2 + LLDF(H) (4.6.2.10.2-4) where: Ax = No. of axles in axle group Axxp = Spacing of axles in axle group Revise Article C4.6.2.10.3 Add new paragraph: When vehicles travel perpendicular to the span, the wheel loads from adjacent axles (e.g. typical tandem and tridem axle configurations) interact. The equations in this section address this.  OTHER AFFECTED ARTICLES: BACKGROUND: This revision is based on recommendations made in the research report for NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ The current specifications for live load distribution through earth fill are discontinuous at a depth of 2 feet of fill due to the change from a slab bridge distribution procedure (Article 4.6.2.10) to a distribution through earth fill procedure (Article 3.6.1.2.6). The attached material investigates this discontinuity in live load distribution and provides a rational alternative to eliminate it. Further, the load distribution for traffic at depths less than 2.0 ft so that distributions in Articles 3.6.2.6 and 4.6.2.10 are both expressed in terms of wheel loads. The new equations in 4.6.2.10.3 provide the expressions necessary to address the interaction of adjacent axles for multi-axle configurations such as tandems and tridems. The NCHRP 15-54 report provides the rationale for this proposed change in further detail. ANTICIPATED EFFECT ON BRIDGES:
Appendix H â Proposed Ballot Items     Hâ7 This change will increase the distribution width for some culverts in some cases and in those cases will increase the load ratings due to the resulting increase in the capacity of the structure. REFERENCES: Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ OTHER:  Â
Appendix H â Proposed Ballot Items     Hâ8 Ballot LRFD-3 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Use of At-Rest Pressure Coefficient for Reinforced Concrete Box Culverts TECHNICAL COMMITTEE:   T-5 Loads and Load Distribution, T-18 Bridge Management Evaluation and Rehabilitation, T-13 Culverts  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Addition to Article 3.11.5.1 3.11.5.1-Lateral Earth Pressure: EH Add to existing Article: For the design of rectangular reinforced concrete culverts, the lateral pressure coefficient, ko, need not be taken greater than 0.5 for culverts embedded in granular soils. Add to existing commentary: C3.11.5.1 The lateral pressure on culverts is the same on both sides of the structure and produces small culvert forces relative to the forces due to vertical loads. The value of ko = 0.5 has long been used and produces safe designs. OTHER AFFECTED ARTICLES: None BACKGROUND: This revision is based on recommendations made in the research report for NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ.
Appendix H â Proposed Ballot Items     Hâ9 The proposed addition is intended to achieve consistency between the design and rating specifications. The existing provision for lateral earth pressure in the LRFD Bridge Design Specifications results in a higher pressure than what is specified in the Manual for Bridge Evaluation. The proposed revision is also based on successful past practice for the design of reinforced concrete box culverts that are performing well in the field. ANTICIPATED EFFECT ON BRIDGES: The proposed provision will reduce the lateral earth pressure for some culverts to a level consistent with what many of them were designed for. Without such a change culverts designed for this level of earth pressure but rated for the higher at-rest earth pressure may have been deficient. REFERENCES: NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ. OTHER:  Â
Appendix H â Proposed Ballot Items     Hâ10 Ballot LRFD-4 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Use of At-Rest Pressure Coefficient for Reinforced Concrete Box Culverts TECHNICAL COMMITTEE:   T-5 Loads and Load Distribution, T-13 Culverts, T-18 Bridge Management, Evaluation and Rehabilitation  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Add new title to Article 3.11.6.4.1 Article 3.11.6.4.1 Walls (section otherwise unchanged) Add new article: Article 3.11.6.4.2 Culverts Concrete box culverts and three-sided flat-topped culverts with a depth of fill less than 2 ft shall be subjected to an approaching wheel load in the form of a lateral soil pressure representing a vehicle approaching the culvert. The pressure shall decrease with increasing depth of fill in accordance with Eq. 3.11.6.4.2-1: âp(hd) = 700/hd ⤠800 psf Eq. 3.11.6.4.2-1 Where âp (hd) = lateral soil pressure at depth hd, psf hd = depth of fill at which pressure is calculated, ft The calculated pressure shall be applied to both sides of the culvert model. This load need not be applied to culverts with a depth of fill over the top slab greater than 2 ft nor to concrete culverts with round tops or metal, thermoplastic or fiberglass culverts. Add new commentary: Article C3.11.6.4.1
Appendix H â Proposed Ballot Items     Hâ11 Retaining walls have historically been designed considering a lateral live load surcharge pressure to represent the additional load applied by a vehicle located near the wall. This loading was historically applied to culverts as well. However, while a lateral load on a wall increases the overturning moment, such a load on a culvert is transmitted through the culvert, largely through compressive thrust and minimal bending moments. The approaching wheel load replaces the live load surcharge for culverts. OTHER AFFECTED ARTICLES: None BACKGROUND: This revision is based on recommendations made in the research report for NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ. ASTM standards for precast reinforced concrete box sections (ASTM C1577) with depths of fill less than two feet have been designed for the proposed lateral pressure resulting from an approaching vehicle since the standards were first developed and the loading is also used in AASHTO Standard M273. The figure below includes results from FEM models of culverts analyzed during NCHRP Project 15-54 which show high pressure near the surface that reduce quickly with increasing depth of fill. The design pressure used for precast box sections (ASTM C1577, identical to AASHTO M273) show a similar trend, while the LRFD live load surcharge pressure is constant with depth based on the assumption of an additional depth of fill. While the FEM pressures exceed both the ASTM and LRFD pressures at the surface, this is not a design issue for several reasons. ï· The pressure, shown in the figure are the peak pressures and decrease away from the wheel location. ï· The load is primarily transmitted as a thrust through the top slab, reacting with the soil on the far side of the culvert. The moments resulting from this pressure are small. ï· The research team is unaware of any structural issues in a box culvert due to lateral load from vehicles. As the load pressure decreases rapidly with increasing depth of fill, it is proposed to require the ASTM approaching wheel load for culverts with depths of fill less than 2 ft and no lateral surcharge for deeper culverts.
Appendix H â Proposed Ballot Items     Hâ12 ANTICIPATED EFFECT ON BRIDGES: The current LRFD specifications do not explicitly exclude the use of LS for culverts under large fill depths so there is inconsistency in the application of the current provisions while it is known that the effects of LS decrease quickly as the depth of fill increases. The proposed change provides for a more rationally based application of LS to the design and analysis of box culverts. While this amounts to a reduction or elimination of LS for culverts under fill, the effects of LS become negligible under such conditions. REFERENCES: NCHRP Project 15-54, âProposed Modifications to AASHTO Culvert Load Rating Specificationsâ. ASTM C1577-19 Standard Specification for Precast Reinforced Concrete Monolithic Box Sections for Culverts, Storm Drains, and Sewers Designed According to AASHTO LRFD AASHTO M 273, Standard Specification for Precast Reinforced Concrete Box Sections for Culverts, Storm Drains, and Sewers with Less Than 2 ft of Cover Subjected to Highway Loadings OTHER:   â18 â16 â14 â12 â10 â8 â6 â4 â2 0 â1200 â1000 â800 â600 â400 â200 0 200 400 600 De pt h (ft ) Lateral Pressure Distribution on Wall, psf Axle @  3'â1" from CL wall Axle @  2'â0" from CL wall Axle @  1'â3" from CL wall ASTM Wall Pressure AASHTO LL Surcharge Culvert
Appendix H â Proposed Ballot Items     Hâ13 Ballot MBE-1 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Rating and Condition Evaluation of Culverts TECHNICAL COMMITTEE:   T-18 Bridge Management, Evaluation and Rehabilitation, T-13 Culverts  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Item #1 Delete Article 6A.5.12  As noted, portions of this Article are incorporated into the proposed new Article 6A.10 Item #2 Add new Article 6A.10 Rating of Culverts 6A.10.1-Scope This Article incorporates provisions specific to the load rating culvert of types designed using the AASHTO LRFD methodology and it provides a load rating that is consistent with that approach. This Article assumes culverts have been inspected prior to rating and that the current condition of the culvert can be properly accounted for. C6A.10.1 Good structural performance of culverts results from interaction of the culvert and the soil it is embedded in. Further, culverts are often designed by product specific methods developed by industry and adopted by AASHTO. This Article addresses the issues specific to culverts. Metal and concrete culverts are often constructed in sizes where rating is mandatory. Thermoplastic, fiberglass, and many metal and concrete culverts are typically not rated; however, brief guidance is provided here for those organizations that rate all culvert types. Older culverts designed using ASD and LFD can also be load rated using these provisions. In cases where the resulting ratings show deficiencies, consideration may be given to rating the culvert using the specifications for which it was designed. It is common practice for most of the culvert specific variables to be taken directly from the construction documents or standard plans. They include culvert dimensions, materials and material properties, and installation methods. The data from construction documents, including culvert dimensions, materials and
Appendix H â Proposed Ballot Items     Hâ14 material properties, and installation methods should be confirmed during a visual inspection of the culvert and any discrepancies from the construction documents should be addressed. 6A.10.2-General Rating Requirements Culvert ratings should recognize that these structures experience several loadings that are not applicable to most bridge superstructures, including vertical and horizontal soil loads and approaching wheel load. Culverts shall be evaluated for the Limit States required in design in Article 12 of the AASHTO LRFD Specifications as modified for specific structures herein. Load ratings shall be calculated at critical sections for each load effect to establish the controlling load rating. 6A.10.3-Structural Analysis of Culverts The analysis of culverts may be based on any rational method acceptable to the owner and consistent with the methods used for design in the AASHTO LRFD Specifications. C6A.10.3 Analysis procedures for culverts in the AASHTO LRFD Specifications vary widely depending on the culvert shape and material. Concrete box culverts and three-sided culverts are primarily analyzed and designed with computer programs such as simple frame or finite element models. Other shapes and materials are often analyzed through simple empirical procedures, often developed independently by manufacturerâs trade associations, and adopted by AASHTO into the LRFD Design Specifications. 6A.10.3.1 Rectangular Concrete Culverts Rectangular concrete culverts include box culverts and three-sided, flat-top culverts. Structural analysis for rectangular concrete culverts is most often completed with frame models subjected to uniform pressures, but finite element modeling is acceptable. For box culverts analyzed with frame models, culvert-soil interaction can be mimicked in part by supporting the bottom slab with springs that simulate actual soil support and allowing the soil load to redistribute, much like a beam on elastic foundation. This redistribution of pressure typically reduces the moment and shear forces in the bottom slab as compared to traditional uniformly applied bedding pressure. Spring constants, in the form of moduli of subgrade reaction values, must be selected by a qualified geotechnical engineer based on available site information. General values are presented in Table 6A.10.3.1-1 for consideration. For conditions where a bedding layer is placed over undisturbed native soils, the design value should represent the combined stiffness of the two layers. The native soil layer may have more effect on the combined stiffness than the bedding soil.
Appendix H â Proposed Ballot Items     Hâ15 Table 6A.10.3.1-1 Modulus of Subgrade Reaction for Bedding Support of Rectangular Concrete Culverts Soil Range2 (pci) Rating Value3 (pci) Loose sand 15-60 30 Medium dense sand 35-290 115 Dense sand 230-460 290 Clayey medium dense sand 115-290 200 Silty medium dense sand 85-170 145 Clayey Soils1 qu ⤠4 ksf 40-85 60 8 ksf ⤠qu ⤠4 ksf 85-170 155 qu Ë 8 ksf 170 > 230 1. qu = unconfined compression strength 2. Values for undisturbed native soils can be much higher. 3. Suggested values. Rating engineers must use field data to make a final determination for analysis. Based on: Bowles, J.E. (1996) Foundation Analysis and Design, 5th Ed., McGraw Hill, New York. C6A.10.3.1 For cases where springs are modeled, there should be at least 10 support points for springs. Analysis and computations required to rate concrete box culverts is completed with the use of computer programs written for that purpose. A number of programs have been developed over the years; however, these programs often make different assumptions for the analysis model and design. Further, some programs used for design of box sections do not have the features necessary to rate them. Thus, it is possible that a box culvert could be designed with one set of assumptions and rated with another. If the rating program makes more conservative assumptions than the design program, unnecessarily conservative rating factors will result. This section provides guidance for analysis and design features that engineers should evaluate when selecting rating software. Analysis methods used in these programs fall into two and perhaps three categories: ï· Two-dimensional frame (2-D Frame) models â In these programs, a two-dimensional frame model is created and subjected to uniform or linearly varying pressure distributions representing the applied earth, live, and, water (external only for rating) loads. Some programs allow the use of springs to model bottom soil support which mimics culvert-soil interaction and produces some of the benefits of FE modeling discussed next. ï· Two-dimensional finite element models â Finite element analysis programs model the box culvert and soil as a continuum of discrete elements each assigned appropriate properties. The inclusion of soil in the model allows a realistic evaluation of culvert-soil interaction. These models often result in pressure distributions that peak at the corners and are reduced at mid-span, thus reducing moment and shear forces relative to frame models. Rating with finite element models should only be conducted by engineers experienced with this type of analysis. See discussion of the CANDE finite element model in C6A10.3.3. ï· Three-dimensional finite element (3-D FE) models â Currently, full three-dimensional modeling of box culverts is used almost exclusively for research studies as the modeling takes considerable
Appendix H â Proposed Ballot Items     Hâ16 time, expertise, and computer capacity. It is included here as it provides the most complete and accurate model currently possibly of soil-culvert interaction and does not require external decisions on how to apply and distribute live loads to account for the three-dimensional load spreading that occurs as load is transmitted through the soil. Specific modeling and design assumptions that engineers should evaluate include the following. ï· 2-D Frame vs 3-D FE â 2-D frame models distribute loads as uniform pressures while 3-D FE models include the soil in the model and allow the soil and live loads on the culvert to redistribute due to the flexibility of the culvert and shear strength of the soil. This redistribution results in higher pressures at the corners and lower pressures at midspan which reduces design moment and shear forces. ï· 45o Haunches â The use of haunches in the corners of box culverts has varied over time. Older culverts were primarily constructed with cast-in-place methods and used small or no haunches. Newer culverts, and, in particular, precast box culvert sections, almost always use 45o haunches with dimensions often equivalent to the thickness of the culvert slabs. The structural effect of haunches should be considered in analysis. A haunch stiffens the corner of the model resulting in higher moments at the corners and lower moments at midspan. The higher corner moments do not increase the design moment as discussed below. ï· Non-45o haunches â Some box sections include haunches that extend further out into the slabs than down the sidewalls. These haunches produce the beneficial stiffening effect noted above, but the critical design section may occur at the tip of the haunch or at the face of the wall. Some 3-sided box sections (no bottom slab) include non-45o haunches. ï· Critical design locations â As noted above, the presence of haunches shifts critical design locations. Reinforcement for box culvert corners should be determined based on the moment and thrust at the tip of the haunch. Shear capacity should be based on the moment, thrust, and shear forces at the location d, or dv from the tip of the haunch. ï· Thrust forces â It is common to think of culvert elements as flexural members to be designed considering only the applied moment. However, thrust forces in culverts can be considerable, particularly in the sidewall of deeper box culverts as about 50% of compressive thrust reduces the tension in the reinforcement. Consideration of this thrust produces more economical designs and higher rating factors. 6A.10.3.2 Concrete Arches, Metal, Thermoplastic, and Fiberglass Pipe and Other Metal Culvert Types Most metal and all thermoplastic, and fiberglass pipe are typically analyzed and rated by the empirical procedures embodied in the LRFD Specifications or by rigorous methods such as finite element models. 6A.10.3.3 â Finite Element Modeling Finite element-based computer modeling is used routinely for analysis of concrete arch culverts and deep corrugated metal culverts. It may be used for any culvert. Finite element modeling should only be undertaken by engineers experienced in the use of such programs for culvert analysis.
Appendix H â Proposed Ballot Items     Hâ17 Finite element analysis should consider loadings to mimic reduced lateral pressure as is done for rectangular concrete culverts in frame models. This can be accomplished by adjusting the soil properties, such as by reducing the backfill density. C6A.10.3.3 The most commonly used program for finite element analysis of culverts is CANDE. Originally developed by the FHWA and upgraded through NCHRP Projects, CANDE offers many features that aid in analyzing and rating culverts, and some that improve rating but are not allowed in the LRFD Design specifications, including: ï· Continuous load scaling (CLS) â this feature permits a live load to spread longitudinally as it is transferred from the top of the culvert to the bottom slab. This feature is appropriate and useful for single lane loadings and not typically available in two-dimensional finite element programs. For multiple lane loadings the LRFD Design specifications require that the same live load pressure applied to the top slab be applied as reaction on the bottom slab with a multiple presence factor, m = 1.2. This approach has been shown to be controlling over multiple lane loadings with m = 1.0. Thus, for multiple lane designs, analyze for a single lane without using the CLS feature. ï· Soil models â CANDE includes options for several soil models. It is most common to use linear properties for in situ soils, but soft in situ soils may require using a non-linear model. While there is no âcorrectâ non-linear model, most AASHTO culvert specifications are based on the Duncan soil model with the Selig hyperbolic bulk modulus Engineers should understand the implications of any finite element program feature prior to applying it to culvert rating. 6A.10.4 Load Rating Equation for Culverts Load rating of culverts shall be carried out for each load effect using the following rating factor expression with the lowest value determining the controlling rating factor. Limit states and load factors for load rating shall be selected from Table 6A.10.5-1. ð ð¹ (6A.10.4-1) In which, for the strength limit states: ð¶ ð ð ðð (6A.10.4-2) Where:
Appendix H â Proposed Ballot Items     Hâ18 RF = rating factor C = capacity Rn = nominal member resistance (as inspected) DC = dead load effect due to structural components and attachments DW = dead load effect due to wearing surface and utilities EV = vertical earth pressure EH = horizontal earth pressure ES = uniform earth surcharge LL = live load effect IM = dynamic load allowance AW = approaching wheel load γDC = LRFD load factor for structural components and attachments γDW = LRFD load factor for wearing surfaces and utilities γEV = LRFD load factor for vertical earth pressure γEH = LRFD load factor for horizontal earth pressure γES = LRFD load factor for earth surcharge γLL = evaluation live load factor γAW = LRFD load factor for approaching wheel load Ïc = condition factor Ïs = system factor Ï = LRFD resistance factor The product of Ïc and Ïs shall not be taken less than 0.85. Components subject to combined load effects shall be load rated considering the interaction of load effects. C6A.10.4 The approaching wheel load replaces the live load surcharge as more appropriate for culverts. 6A.10.5 â Limit States Culverts shall be load rated for the Strength I load combination for the design and legal loads and the Strength II load combination for permit loads. The applicable loads and their combinations for evaluation are specified in Table 6A.10.5-1 and in Articles 6A.10.6 through 6A.10.10. Service limit state for crack width control need not be checked when load rating concrete culverts if internal inspection does not indicate reinforcement corrosion. C6A.10.5 Maximum and minimum load factors for different loads should be combined to produce the largest load effect. The load cases should be selected to generate the critical combinations of moment, shear, and thrust demands at all critical sections for each load case. It is prudent to also perform an evaluation of the culvert under permanent loads only if the depth of earth fill over the culvert has changed since the original construction.
Appendix H â Proposed Ballot Items      Hâ19 Table 6A.10.5-1 Limit States and Load Factors for Culvert Load Rating (Modified from current MBE Table 6A.5.12.5-1)
Appendix H â Proposed Ballot Items      Hâ20 6A.10.6-Resistance Factors Resistance factors for culverts shall be taken as specified in LRFD Design Article 12.5.5. 6A.10.7-Condition Factors Use of condition factors as presented in Table 6A.4.2.3-1 may be considered optional based on an agencyâs load rating practice. 6A.10.8-System Factor: Ïs The system factor for strength limit states for culverts shall be taken as 1.0 6A.10.9-Materials No change from current Article 6A.5.12.9 C6A.10.9 No change from current Article C6A.5.12.9 6A.5.12.10-Loads for Evaluation 6A.5.12.10.1-Dead Loads No change from current Article 6A.5.12.9 6A.5.12.10.2- Earth Pressure 6A.5.12.10.2a-Vertical Earth Pressure: EV The unit weight of the soil may be taken as shown in LRFD Design Table 3.5.1-1 or in accordance with agency design practice. Weight of earth shall be modified for culvert-soil interaction in accordance with the LRFD Design Specifications for the culvert material being analyzed. 6A.5.12.10.2b-Horizontal Earth Pressure: EH Lateral earth pressure is only explicitly applied to rectangular concrete culverts analyzed with frame models. It shall be assumed linearly proportional to the depth of soil based on the at rest pressure coefficient as shown in LRFD Design Article 3.11.5.2. The coefficient for the maximum condition need not be taken greater than 0.5 and the coefficient for the minimum condition need not be taken less than 0.25. Lateral pressure for non-rectangular culverts is embedded in the material specific LRFD design methods and no additional evaluation is required. Culverts rated with finite element programs automatically consider lateral soil pressures as part of the culvert-soil interaction. If inspection of flexible culverts shows high deflections, the backfill conditions must be modeled to match those deflections during rating analysis. 6A.5.12.10.2c-Uniform Surcharge Loads: ES Typically, uniform surcharge loads are not considered in culvert design or rating unless temporary fill will be added over the culvert during or after construction. If applied, the culvert shall be evaluated both with and without the surcharge load.
Appendix H â Proposed Ballot Items     Hâ21 6A.10.10.3-Live Loads No change from current Article 6A.5.12.10.3 C6A.10.10.3 No change from current Article C6A.5.12.10.3 C6A.5.10.10.3a-Live Load Distribution Current specification Article 6A.5.12.10.3a with proposed changes listed below. Change 1- Replace deleted sentence with: Culverts where design for live load is not required per the LRFD Design Specifications Article 3.6.1.2.6a do not require rating for live loads. Change 2 â Deleted sentence. No replacement. Change 3 â Replace deleted sentence with:
Appendix H â Proposed Ballot Items     Hâ22 Distribution parallel to the span with increasing depth is accomplished by adding LLDF * Depth of fill to the tire dimension. Per LRFD Design Specifications Article 4.6.2.10. Change 4 â Replace deleted sentence with: Lane loads are only considered for culverts with spans greater than 20 ft. Change 5 - Delete entire paragraph (only a portion of the deleted paragraph is shown above). No replacement. 6A.10.10.3b-Dynamic Load Allowance: IM No change from current Article 6A.5.12.10.3b C6A.5.12.10.3b No change from current Article C6A.5.12.10.3b 6A.10.10.3c â Approaching Wheel Load Rectangular concrete culverts with less than or equal to 2 ft of cover shall be loaded with a lateral pressure distribution to produce the effects of a truck axle just before going over the culvert. This pressure shall be computed using Eq. 6A.10.10.3c-1 and shall be applied to both sides of the culvert. p-lat(hd) = 700/hd â¤800 psf Eq. 6A.10.10.3c-1 where: p-lat(hd) = lateral soil pressure resulting from an approaching wheel load at depth hd, psf hd = depth of fill to depth where pressure is calculated, ft The approaching wheel load need not be considered for culverts with more than 2 ft of fill from top of culvert to top of pavement. C6A.10.10.3c Culverts have traditionally been evaluated for a live load surcharge that is appropriate for earth retaining structures. The live load surcharge is not appropriate for rectangular culverts for the following reasons: ï· Unlike retaining walls, where a vehicle load near a wall increases the overturning moment, a vehicle approaching a culvert produces a small lateral pressure that is resisted by the soil on the far side of the culvert. ï· Lateral pressure near the mid-height of the wall will result in an increase in positive moments in the sidewall and negative moments at the corners and a decrease in positive moments in the slabs. Lateral pressure near the top of a shallow culvert primarily results in a thrust in the top slab which has almost no effect on the moments, and hence the reinforcement requirements. This approaching wheel load has been used in AASHTO and ASTM standards for precast concrete box culverts for over 40 years. It was first proposed by Heger, F.J. and Long, K.N. (1976) Structural Design
Appendix H â Proposed Ballot Items     Hâ23 of Precast Concrete Box Sections for Zero to Deep Cover Earth Cover Conditions and Surface Wheel Loads, Concrete Pipe and the Soil-Structure System, ASTM STP 630. 6A.10.10.3d - Pavements Pavements are used to spread the effects of wheel loads over a greater area and thus reduce soil stresses below the pavement. Rating engineers may consider the effects of asphalt or concrete pavements in reducing the loads applied to culverts. This can be completed using finite element soil structure interaction analyses which can directly model the pavement layer, or with elasticity based or empirical procedures. Such analyses must consider the current and expected future condition of the pavement. Analysis of asphalt pavements must consider anticipated temperature effects on properties. C6A.10.10.3d Most culverts are designed without consideration of the improved load distribution resulting from pavements over the culvert. The only exception to this is some metal box section designs as detailed in LRFD Article 12.9.4.6. The effect of pavements is ignored primarily to allow for construction loads prior to placement of pavement. The finite element analysis culvert program most commonly used for analysis, design, and rating of culverts is CANDE, originally developed by FHWA and later updated by AASHTO through the NCHRP Program. Empirical procedures for considering pavements include elasticity theory procedures for layered systems and the Westergaard procedure for distributing live loads through concrete pavements as embodied in the American Concrete Pipe Associationâs Concrete Pipe Handbook. Table C6A.10.10.3d-1 presents guidance on the conditions and locations where pavements are effective in reducing loads on culverts. Table C6A.10.10.3d-1 Pavement Effect in Distributing Live Load on Culverts Pavement thickness, in. Asphalt stiff subgrade Asphalt soft subgrade Concrete stiff subgrade Concrete soft subgrade E1/E2 ~3 E1/E2 ~ 35 E1/E2 ~ 400 4 NB NB 0.50 / 5 ft 8 NB 0.60 / 6 ft 0.25 / 6 ft 16 0.75 / 6 ft 0.50 / 7 ft 0.15 / 8 ft Where: - E1 = modulus of pavement layer - E2 = modulus of soil subgrade - NB = no benefit - The data lines, such as 0.50 / 5 ft indicate the reduction that may be applied to the live load at the surface of the pavement and the depth at which no benefit is derived in reducing pavement load. Table C6A.10.10.3d-1 is derived from an elastic solution derived by Fox and presented in Poulos, H.G., and Davis, E.H. (1991) Elastic Solutions for Soil and Rock Mechanics, which is available at http://research.engr.oregonstate.edu/usucger/PandD/PandD.htm, and uses the following assumptions:
Appendix H â Proposed Ballot Items     Hâ24Â ï· E-concrete pavement = 4,000 ksi ï· E-asphalt pavement = 0.3 ksi ï· E-soft subgrade approximately 8 ksi ï· E-stiff subgrade approximately 100 ksi One relationship between the soil modulus and the common parameters, as recommended by the Federal Aviation Administration Advisory Circular 150/5320-6F, 2016, are: E = 1,500 CBR Eq. C6A.10.10.3d-1 E = 20.15 k1.284 Eq. C6A.10.10.3d-2 Where: E = modulus of elasticity of subgrade, psi CBR = California bearing ratio k = modulus of subgrade reaction, pci Note that Eqs.C 6A.10.10.3d-1 and C6A.10.10.3d-2 provide values of subgrade modulus considerably higher than typically used in culvert backfill design. As an example, for an 8 in. concrete pavement with a soft subgrade, the live load could be reduced to 25% of the applied load for a culvert directly under the pavement and there would be no reduction if the culvert is more than 5 ft below the pavement. Linear extrapolation can be used to determine the reduction for intermediate depths. 6A.10.11 - Concrete Culverts 6A.10.11.1 Design for Shear The shear strength of culverts without prestressing and with less than 2.0 ft of cover that are performing well based on inspection can be evaluated with a modified approach to shear capacity. Use the General Procedure for shear strength in LRFD Design Specifications Article 5.7.3.4.2, substituting the following procedure to compute the strain in the reinforcement: ð | | . | | Eq. 6A.10.11.1-1 Where Mu-mod is the factored moment at the critical shear design location, which may be modified as follows if it is a negative moment: ð ð . . Eq. 6A.10.11.1-2 where: S = clear span of the culvert (ft) â (same value as used in 4.6.2.10.2-1) Use the unmodified Mu if the controlling moment is positive. Further, the limitation that the minimum value of Mu = Vu dv does not apply. This expression can be applied to box sections analyzed and designed with two-dimensional frame or finite element models.
Appendix H â Proposed Ballot Items     Hâ25 The use of springs to represent bedding pressure noted in Article 6A.10.3.1 results in reduced shear and moments. The rating factors for the lower half of box culverts analyzed in this manner may be applied to the locations in the upper half of the culvert provided the following conditions are met: ï· The culvert is installed at a depth where live load is not considered. ï· The reinforcing in the upper half of the culvert matches that in the lower half. C6A.10.11.1 Many concrete culverts that have been in service and performed well for many years have rating values less than 1.0 due to computing shear strength by current procedures. There are two primary reasons for this: ï· Past editions of AASHTO specifications have allowed designers to assume shear strength is adequate if the section is properly designed for flexure. ï· Frame models of box sections are inherently conservative due to the assumption of uniform pressures to model vertical loads. The equations in this section provide a moderately increased shear capacity to reflect this history. The reduction in negative moment at the critical section is based on: McGrath, T.J., A.A. Liepins, and J.L Beaver, âLive Load Distribution Widths for Reinforced Concrete Box Sectionsâ, Transportation Research Record: Journal of the Transportation Research Board, CD 11-S, Transportation Research Board of the National Academies, Washington, DC, 2005, pp 99-108. Culvert inspections should evaluate flexural cracking or concrete crushing which could indicate the culvert is carrying more load than considered in design. C6A.10.12 - Metal Culverts Metal culverts should only be rated after a field inspection has documented the culvert shape and condition. Metal Culverts should be analyzed for service and factored forces in accordance with the LRFD Design Specifications and appropriate provisions of this Manual. Suitable adjustments should be included to consider the current condition of the culvert. Metal culverts that are designed using finite element modeling must be rated with the same analysis method. Modeling must consider installation conditions that produce the culvert shape observed in the field.
Appendix H â Proposed Ballot Items     Hâ26 C6.A.10.12 The long-term performance of these culverts is dependent on the performance of the backfill soil around the culvert. The culvert shape is a key indicator of backfill quality and careful measurements in the field are warranted. National Corrugate Steel Pipe Association (NCSPA) Design Data Sheet No. 19 provides recommended procedures for rating metal culverts and suggested adjustments based on existing conditions. Rating engineers should note that the design methods and load factors for the several types of metal culverts are quite different as they are often empirical or semi-empirical. In addition to loss of section due to corrosion, the field inspection should document the shape of the culvert. 6.A.10.13 -Thermoplastic and Fiberglass Culverts Thermoplastic and fiberglass culverts should only be rated after a field inspection has documented the culvert shape and condition. Such culverts should be analyzed for service and factored forces in accordance with the LRFD Design Specifications and appropriate provisions of this Manual. Suitable adjustments should be included to consider the current condition of the culvert. The effect of the observed deflected shape on culvert forces must be considered. C6A.10.13 Thermoplastic and fiberglass culverts are both considered flexible. The long-term performance of these culverts is dependent on the performance of the backfill soil around the culvert. The culvert shape is generally a key indicator of backfill quality and careful measurements in the field are required.   Â
Appendix H â Proposed Ballot Items     Hâ27 Ballot MBE-2 2019 AASHTO BRIDGE COMMITTEE AGENDA ITEM:  Click here to enter text SUBJECT:  Rating and Condition Evaluation of Culverts TECHNICAL COMMITTEE:   T-18 Bridge Management, Evaluation and Rehabilitation, T-13 Culverts  â REVISION â ADDITION â NEW DOCUMENT â DESIGN SPEC â CONSTRUCTION SPEC â MOVABLE SPEC â MANUAL FOR BRIDGE â SEISMIC GUIDE SPEC â MANUAL BRIDGE ELEMENT INSP EVALUATION â OTHER Research  DATE PREPARED: 7/3/2019 DATE REVISED: Click here to enter a date AGENDA ITEM: Item #1 Add New Article 6B.9 Article 6.B.9 Culverts may be load rated in accordance with the current LRFD Specifications or with the Specifications under which they were originally design. Culvert ratings based on older specifications must be inspected prior to rating and the current conditions must be considered. C6.B.9 Concrete pipe, metal, thermoplastic, and fiberglass pipe are essentially designed by the same methods as were incorporated into prior bridge design specifications and, thus, most should rate in accordance with the current LRFD Specifications. Reinforced concrete box sections have been designed under AASHTO specifications for many years and the provisions have changed such that many do not meet current standards. This is particularly true for shear strength, as some editions of AASHTO specifications did not require design for shear in slabs, such as the top and bottom slab of box culverts. This article allows rating engineers to take advantage of the less demanding older specifications provided the culvert has demonstrated good performance and the loading has not changed since prior ratings. Article 6A.10 provides several provisions for analysis and rating that will assist engineers using older specifications for rating.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL Iâ1 Appendix I â Improving AASHTO LRFD/LRFR Specifications for 2D Analysis of Buried Culverts Under Live Load This appendix provides a white paper prepared by Dr. Katona for Live Load Distribution. Â
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ2      WHITE PAPER IMPROVING AASHTO LRFD/LRFR SPECIFICATIONS FOR TWOâDIMENSIONAL ANALYSIS OF BURIED CULVERTS UNDER LIVE LOAD Dr. Michael Katona Â
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ3  A White Paper on Improving AASHTO LRFD/LRFR Specifications for Two-dimensional Analysis of Buried Culverts under Live Loads INTRODUCTION Background. Buried culverts, due to their long prismatic configuration, are generally designed and analyzed as two-dimensional (2D) systems because the earth pressure acting on the culvert is nearly constant in the longitudinal direction and well represented by 2D models. Comprehensive plane-strain finite element (FEM) programs such as CANDE simulate a representative cross-sectional slice of both soil and culvert to simultaneously determine soil-structure interaction loads and structural responses of the culvert. Design-oriented programs such as BOXCAR and AASHTOWare-BrR use 2D frame models to simulate the culvert without explicitly modeling the soil; rather, approximate methods are used to prescribe the loading on the culvert as specified by AASHTO LRFD Bridge Design Specifications. Liveâload issue. A major difficulty with all 2D models is determining the pressures transmitted to the culvert from live loads acting on the soil surface (wheel footprints). For 2D FEM plane-strain analysis, the live-load pressure automatically spreads in the transverse direction (plane of the culvert span); however, the live-load pressure in the longitudinal direction (out-of-plane) is restrained from spreading due to the limitations of 2D plane-strain geometry. Consequently, longitudinal load-spreading approximations such as recommended by AASHTO are used to avoid overly conservative loading conditions. For 2D frame models, load spreading approximations are required for both transverse and longitudinal directions. Another, but less understood, problem is that 2D live-load analysis underestimates the culvertâs actual stiffness that arises from 3D deformation patterns caused by short-width longitudinal loads. Said another way, 3D deformation patterns caused by short load widths produce additional 3D stiffness effects that are not accounted for by the one-way bending stiffness inherent in 2D analysis. The current AASHTO LRFD specifications recognizes this 3D-stiffness phenomenon for shallow burial of reinforced concrete boxes and arches but not for âgeneral culvertsâ of other shapes and materials. Specifically, AASHTO provides special equations to account for 3D stiffness effects of r/c boxes and arches under less than 2 feet of fill. Scope. This white paper focuses on the little-understood 3D stiffness effects that gives rise to the special AASHTO longitudinal distribution widths that are intertwined with the better-understood longitudinal distribution representing load-spreading through the soil. The white paper is divided in two parts. Part I includes a review of AASHTO equations originating from the PennDOT study along with a new conceptual model that explains the 3D stiffness effects using a new parameter called Wcritical, Part II defines a mechanistic model representing the top slab of a box culvert, provides a solution based on the
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ4  Ritz Technique, and compares and contrasts results with current AASHTO methods. The paper concludes with a summary of findings and list of recommendations. PART I ââ REVIEWS, CONCEPTS AND ISSUES REVIEW OF AASHTO DISTRIBUTION WIDTHS  General Culverts. The intuitive AASHTO LRFD model for load-spreading through soil is applicable to all culverts. It assumes the wheelâs surface footprint dimensions (L0 x W0) spreads with soil depth at a specified angle (typically 30 degrees) in both transverse and longitudinal directions. Further it is assumed the pressure remains uniform so that vertical force equilibrium dictates the pressure decreases in proportion to increased area. Equation 1 is from AASHTO Section 3.6.1.2.6 and represents the expanded footprint length or distribution width in the longitudinal direction for soil depth H. Long 0 intE = W + LLDF H for H < Hïª ï® Equation 1 where, ELong = Longitudinal distribution width for 1-wheel load (inches). H = Soil depth from surface, usually H = cover depth (inches). W0 = Wheel longitudinal footprint width on surface (typically 20â). LLDF = Live-load distribution factor = 2tan(300) = 1.15. When H < Hint, only one wheel (½ axle load) contributes to the line load magnitude. Thus, the 2D line load for one wheel is given by, p1 = ½ axle load/ELong. Hint is called the 2-wheel interaction soil depth and is dependent on the spacing between the axleâs wheels. When H > Hint both wheels (full axle load) contributes to the line load magnitude and the distribution width is redefined as, Long axle 0 intE = S +W + LLDF H for H > Hïª ï® Equation 2 where, ELong = Longitudinal distribution width for 2-wheel load (inches) Saxle = center-to-center wheel spacing on axle (typically 72â). Hint = (Saxleâ W0)/LLDF (usually computes to 45.2â) Since Equation 2 applies to the full axle load (2 wheels), the 2D line load for two wheels is given by, p2 = axle load/ELong. Note that the line-load magnitude is a continuous function of H when transitioning from Equation 1 to Equation 2, i.e.; p1 = p2 for H = Hint. Reinforced Concrete Box and Arch Culverts. Equations 1 and 2 generally apply to all culverts materials and shapes. However, for reinforced concrete box and arch culverts, AASHTO Section 4.6.2.10 specifies Equation 3 to replace Equation 1 for cover heights less than 2 feet with the understanding this distribution width applies to the full axle load (2 wheels). LongE = 96" +1.44 Span(ft) special r/c case, for H < 2 feetïª ï® Equation 3 where, ELong = Longitudinal distribution width for 2-wheel loading (inches) Span = Reinforced concrete box or arch span measured in feet.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ5  The reason for the change from Equation 1 to Equation 3 is because analytical studies revealed that Equation 1 is too conservative when H is less than 2 feet particularly for box culverts that are sometimes installed with zero soil cover. For precast boxes and arches, AASHTO sections 12.11.2.1 and 12.14.5.2 infer that ELong should not exceed two lay lengths. Before discussing the origin and implications of Equation 3, it is instructive to compare Equations 3 with Equations 1 & 2 in the context of the reduced- surface-load (RSL) method. RSL is the most common 2D method for reducing the actual longitudinal line load under the wheel(s) to account for longitudinal load spreading at depth H and 3D stiffness effects. The reduction factor r is determined by preserving force equilibrium at the surface and at soil depth H. Given that the surface force is the surface line-load p0 times the longitudinal width E0, and the force at depth H is line-load pH times ELong, then the reduction factor which is defined as r = pH/p0 is also given by the geometric ratio, 0 Long Er E ï½ Equation 4 where, r = reduction factor applied to surface line load under wheel(s). E0 = distribution width on surface (H=0) dependent 1 or 2 wheels: ï· E0 = W0 for 1 wheel. (Equation 1) ï· E0 = 2W0 for 2 wheels. (Equation 2 or 3) ELong = distribution width at depth H as defined in Equation 1, 2 or 3. Figure 1 shows RSL reduction factors versus soil depth for three example culverts: (1) general culvert. (Eq. 1 for 0 ⤠H < Hint, and Eq. 2 for H ⥠Hint.) (2) r/c box culvert with 10-foot span. (Eq. 3 for 0 ⤠H < 2â, and Eqs. 1 & 2 for H ⥠2â.) (3) r/c arch culvert with 50-foot span. (Eq. 3 for 0 ⤠H < 2â, and Eqs. 1 & 2 for H ⥠2â.)
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ6  Figure 1. Reduction factor versus soil depth for three example culverts. Three observations from Figure 1 are worth noting for future reference; 1. For general culverts, the reduction factor is 1.0 at the surface, which is in keeping with Equation 1 because there is no soil depth to spread the load. At 2 feet of fill the reduction factor rapidly but smoothly reduces to 0.42 and continues to smoothly decrease until the 2-wheel interaction depth wherein the slope of reduction factor curve increases, but remains continuous. 2. In contrast, the reinforced concrete box and arch culverts have reduction factors at the surface equal to 0.36 and 0.24, respectively, and remain constant until H = 2â. Clearly these reduction factors are not attributed to longitudinal load spreading through soil, rather they are attributed to additional 3D stiffness effects that are not captured in 2D models. A major objective of this report is to fully explain and investigate the meaning behind these 3D stiffness effects. 3. There are obvious discontinuities in the reduction curves for the r/c box and r/c arch when transitioning through H = 2â due to shifting from Equation 3 to Equation 1. Using the r/c arch as an example, we see that r = 0.24 at H = 1.999â but jumps to r = 0.42 at H = 2.001â, a 75% increase over an infinitesimal distance. The consequence of this discontinuity, is that an engineer would design for 75% more load for a cover height H = 2.001â than he would for the same culvert
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ7  with H = 1.999â. This is a serious problem and needs to be rectified in future AASHTO specifications. PennDOT Report â AASHTO Equation 3. Equation 3 (i.e., AASHTO LRFD 4.6.2.10.2-1) originates from the well-documented PennDOT study, Live Load Distributions for Design of Box Culverts (2004), conducted by Tim McGrath and engineers from SGH under the sponsorship of Pennsylvania Department of Transportation. The PennDOT study builds upon previous work from NCHRP Project 12-26 Distribution of Wheel Loads on Highway Bridges in which the basic assumption is the top slab of shallowly buried box culverts behaves like reinforced concrete bridge-deck slabs. The PennDOT study used NASTRAN to obtain 3D finite element solutions of reinforced concrete box culverts subject to HS20 two-wheel axle loadings. Overall, 31 linear box and slab model configurations were constructed including a range of haunch dimensions, slab and wall thicknesses, and transverse- traveling HS20 loads applied along the mid-length plane and also along the free-edge plane. Variations of the major system dimensions are listed below: ï· Cover height; H = 0â and 2â. ï· Span lengths; S = 8â, 16â and 24â. ï· Rise height; R = 0â (4 slab models) and 8â (27 box models). ï· Longitudinal length; L = 30â (fixed for all 31 models). Longitudinal distribution widths for each r/c box model were computed for maximum positive moment, maximum negative moment, and maximum shear. As inferred in the PennDOT report, the computed distribution widths provide reduction factors (Equation 4) that produce 2D responses equivalent to the 3D NASTRAN solutions. As expected, the controlling distribution widths for maximum shear occurs when the HS20 axle is located near the wall-supported edges of the span, and the controlling distribution widths for maximum moments occurs when the HS20 axle is located in the central region of the span. In all cases the distribution widths tend to increase as the box span increases from 8â to 24â. Figure 2, as copied from the PennDOT report, shows the distribution widths under 1 wheel for 15 PennDOT box-culvert models that have zero soil cover (H = 0) and HS20 axle loads applied symmetrically along the mid-length plane. Also shown are the recommended AASHTO distribution widths for 1-wheel loading as specified in the then-current AASHTO Standard and LRFD Specifications wherein the distribution-width equations are multiplied by ½ to reflect width under 1-wheel.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ8  Figure 2. Longitudinal distribution widths for 1-wheel load versus span as tabularized below: Source of distribution widths Distribution-width symbols Relationships/Equations PennDOT 3D FEM solutions 2004 bM+ = max positive moment bM- = max negative moment bQx = maximum edge shear Discrete data points for 8â, 12â & 24â spans with separate symbols for each maximum force effect. AASHTO Standard Specifications 2002 ------- Standard E = ½(96â + 1.44Span) One equation for all force effects. ASSHTO LRFD Specifications 1998 with 2002 update M+ = max pos. moment, Span ⤠15â M- = max neg. moment, Span ⤠15â LRFD = all force effects, Span > 15â E = ½(26â + 6.6*Span) E = ½(48â + 3*Span) E = ½(10â + 5*(Span*Length)½) Upon inspecting the PennDOT data points in Figure 2, it is seen that the minimum distribution widths (most conservative) are associated the maximum shear criterion. Remarkably, the distribution-width equation from the 2002 Standard AASHTO Specification was observed to provide a reasonable lower bound to PennDOT maximum shear data points. Accordingly, the PennDOT report recommended that the new AASHTO LRFD Specification adopt the equation from the Standard Specification. This provides a brief history behind the origin of Equation 3, but not a meaningful explanation of the physics behind it.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ9  Two other parametric studies from the PennDOT report reveal how distribution widths are influenced by loading along the free edge and by orthotropic properties of the top slab. Not too surprisingly, when the transverse-traveling HS20 load was relocated from the slab center to the free-edge, the computed distribution widths decreased due to less 3D stiffness support. Also, when the longitudinal elastic modulus of the top slab was reduced by 30% in comparison to the transverse modulus, the distribution widths decreased by about 5%. Review Summary and Issues. Equations 1, 2 and 3 have one common purpose, which is to reduce the magnitude of the surface line so that a 2D solution is not overly conservative, i.e., the RSL method. Said another way, if a 3D solution methodology is being used there is no need for Equations 1, 2 and 3, or the RSL method. Even though the three equations have a common purpose, Equation 3 is fundamentally and physically different than Equations 1 and 2. The latter equations represent an intuitive physical model for an expanding longitudinal distribution width through the soil with cover depth H. In contrast, Equation 3 accounts for a 3D stiffness effect that is missing in 2D analysis. Specifically, the RSL reduction factor as computed from Equation 3 and applied to the surface strip load compensates for the additional longitudinal bending and twisting stiffnesses that are not realized with 2D models. The PennDOT study resulted in significant improvements in the AASHTO LRFD specifications; however, as listed below, there remain several issues in need of additional research and/or clarification. (1) Continuity of distribution widths with soil depth. As was shown in Figure 1, there is a discontinuity in distribution widths at the soil depth H = 2â that is slight or modest for small spans but becomes significant as the span increases. Clearly, a smooth transition methodology needs to be developed. (2) Influence of culvert length. The PennDOT study used a fixed culvert length of 30â for all finite element models, which may be appropriate for cast-in-place culverts. However, precast box culverts have lay lengths of 8â or less, and precast arches have lay lengths as small as 4â. Although it has been demonstrated that small depths of soil cover negate the need for shear connectors between adjacent units, the lack of moment continuity between adjacent units reduces the 3D stiffness effects. Therefore, the influence of culvert length on distribution widths need to be investigated. It is interesting to note that the 1998 LRFD AASHTO specifications included lay length in the equations for distribution width for spans > 15â. (3) Limit on spanâs linear influence. The PennDOT study investigated box culvert spans of 8â, 16â and 24â with the result that distribution widths appear to increase linearly with span as exemplified by Equation 3. However, since precast arches have spans up to 72â, it is reasonable to extend the investigation to see if there is a limiting span length beyond which the span does not increase the distribution width. (4) Verification of procedure for computing distribution widths. Distribution widths were computed from 3D NASTRAN solutions by numerically integrating the force effect (moment or shear) over the culvert length along the loading line and then dividing the result by the peak value of the force effect. Although the PennDOT report succinctly describes this mathematical procedure, the underlying physics is not clear. Verification of the PennDOT procedure with the procedure proposed in this white paper should be undertaken.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ10  (5) Justification for applying r/c box culvert results to r/c arches. The PennDOT finite element models simulated r/c box-shaped culverts, not precast arches like Con/Span or Bebo. However, AASHTO LRFD specifications (sections 12.14.5.2 and section 4.6.2.10) assign the distribution width developed for box culverts (Equation 3) to arch culverts as well. Since Equation 3 reflects the maximum shear criterion in a box slab loaded near the supporting wall, it is not likely the arch shape will experience the same level of shear. Additional studies are needed to either verify the validity of Equation 3 for arches or propose new distribution widths. (6) Potential 3D-effects for all culvert materials and shapes. Based on the PennDOT study a natural question is, âWhy shouldnât all culvert materials and shapes exhibit some level of 3D effects that could be taken advantage of in 2D analysis?â Perhaps the corrugated nature of steel and aluminum culverts result in orthotropic stiffness properties such that the longitudinal bending stiffness does not provide sufficient 3D-stiffness enhancement. In any event this question should be researched. OBJECTIVES This white paper is not intended to provide the final answer to the six issues above. Rather the intent of this paper is to provide a framework of concepts, ideas and mechanistic models that offer guidelines and direction for additional 3D finite element studies like the PennDOT study. To this end, this white paper has the following objectives. 1. Develop a flat plate model that illustrates 3D stiffness effects and explicitly provides the functional influence of culvert length, span and orthotropic bending properties in determining distribution widths applicable to 2D analysis. 2. Show graphs of distribution widths as a function of slab properties and compare results with the PennDOT study for the purpose of guiding future 3D investigations. 3. Present an overall strategy on applying distribution widths for 2D analysis using either the reduced surface load (RSL) technique or the new continuous load scaling (CLS) technique 4. Revisit the six issues listed above and offer suggestions on addressing these problems based on the above findings. CONCEPTUAL MODEL AND INSIGHTS Description. Figure 3 portrays a rectangular flat plate representing the top slab of a box culvert with fixed-end boundary conditions along the left and right sides and free to deflect at each end. The x,y,z coordinate system originates from the plateâs center where a variable-length line load of magnitude p is applied symmetrically along the z-axis. Spatial variables are denoted as, ï· W* = width of line load acting on slab (culvert) ï· S = Span of slab (culvert) ï· L = length of slab (culvert)
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ11  Figure 3. View of rectangular plate model with line-load (lbs./inch). Bigâpicture Overview and Concepts. In Part II a closed form solution of the plate model is developed. However, for present purposes, the objective is to illustrate conceptually how this model is useful for shedding light on the special ASSHTO distribution width and providing a clear understanding of the 3D stiffness effects. To this end, let us temporarily assume that the plateâs span, length, line-load magnitude and stiffness properties are fixed, and the only variable parameter is the line-load width W*. With this understanding, the plateâs displacement function is symbolically expressed as, ( , , *)f x z Wï ï½ Equation 5 The Î-function provides a wide range of displaced 3D shapes because W* may range from 0 to L (or 0 ⤠W*/L ⤠1). For the special case W*= L, a uniform 2D response is produced because the entire plate deforms in one-way bending like a fixed-end beam. In short, W*/L = 1 produces a uniform, maximum deflected shape independent of z, exactly equivalent to a 2D model using beam theory. Functionally, this maximum displacement profile is denoted by, , ( * )M ax f x W Lï ï½ ï½ Equation 6 Figure 4 shows the symmetric half of the uniform displacement profile ÎMax from z = 0 to z = L/2 plotted along the plate centerline through the origin.  Span = S x y zp
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ12  0.0 0.1 0.2 0.3 0.5 0.70.4 0.6 0.8 0.9 1.0          100% 25% 50% 75% Ce nt er lin e de fle ct io n,  %  Πm ax W*< Wcritical Position along plateâs positive zâaxis,  z/(½L) ÎMax W*=L Îcritical W*=Wcritical W*> Wcritical Figure 4. Deflection profiles (symmetric half) for four key choices of W*. Also illustrated in Figure 4 is a very special line-load width called the critical distribution width, symbolically expressed as Wcritical. Physically, Wcritical is the minimum distribution width producing a peak 3D displacement at z = 0 that is equal to the uniform maximum 2D displacement, ÎMax. Wcritical is determined by forming the displacement ratio shown below and incrementally increasing the value of W* until the ratio is equal to 1. 0 0Ratio 0 ( *) ( , , *)( *) ( , )Max W f WW f L ï ï½ ï½ ï Equation 7 Wcritical = critical distribution width, i.e., minimum W* producing Ratio(W*) = 1 Note that Wcritical is a physical property of the plate (culvert) irrespective of the soil or burial depth. Moreover, since Wcritical is determined from the ratio of two solutions, Wcritical is not influenced by linear plate parameters such as plate stiffness because these parameters cancel out in the ratio. For an isotropic plate, Wcritical is only dependent on span S and length L. Wcritical is used to determine whether or not the actual loading length W* generates 3D stiffness effects that need to be accounted for in 2D solutions. First consider the case W* > Wcritical in which W* is the line-load width impinging on the slab at soil depth H. As shown in Figure 4, the maximum 3D displacement coincides with maximum 2D displacement in a region about z = 0. Within this region both 2D and 3D solutions using the same line-load magnitude produce the same structural distress (i.e., transverse deformations in the plane of the span). Consequently, no adjustment is required for 2D analysis to account for 3D stiffness effects when W* > Wcritical.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ13  Next consider the 3D deflection profile for the case W* < Wcritical. As shown in Figure 4 the peak 3D deflection at z = 0 is well below the 2D displacement (ÎMax) with the same line-load magnitude. The reduced 3D deflection is due to resistance from longitudinal bending stiffness and plate twisting stiffness in portions of the slab beyond the loading width W*. In order to better understand the 3D stiffness effect, imagine the slab (or culvert) to be cut into many beam-like slices parallel to the x-axis, thereby dismantling the 3D stiffness effect by creating 2D slices. If the sliced system is line-loaded over a width W*, then those loaded slices beneath W* will deflect to the maximum 2D amount (ÎMax) whereas the unloaded slices remain un-deflected (zero), i.e., no stiffness interaction between loaded and unloaded slices. Hence, it is evident that 2D models lack the additional 3D stiffness that actually exist in contiguous systems. Consequently, some corrective adjustment is required for 2D analysis to account for 3D stiffness effects when W* < Wcritical. The traditional and most common method of adjusting the 2D analysis is the reduced surface load (RSL) method previously introduced in the AASHTO review. A second and more accurate method is called continuous load scaling (CLS). Both methods are discussed in the following next two sections to complete the big-picture overview. Reduced Surface Load (RSL). The RSL method proposed herein is similar to existing AASHTO approach (Equations 1-to-4 and Figure 1) except for two important aspects. First, the discontinuity at H = 2 feet is corrected in a logical manner, and second, all distribution widths are referenced to 1-wheel load to avoid the confusion of dealing with axle and 1-wheel loads in the same set of equations. Although the distribution widths are referenced to 1-wheel load, the size of the distribution widths are influenced by both wheel-loads on the axle. Figure 5 shows a longitudinal view of a culvert shallowly buried at depth H1 and in deeper burial at depth H2. For both burial depths the soil surface is loaded with one wheel so that the longitudinal line-load beneath the wheel on the surface is given by, 0 0 Wheel-load W p ï½ Equation 8 where, p0 = surface line load beneath wheel (lbs./inch) Wheel-load = specified weight of 1 wheel (lbs.) W0 = wheelâs longitudinal footprint (typically 20 inches) Shown with red lines is the culvertâs critical distribution width Wcritical that remains constant with soil depth, and shown with green lines the expanding soil-spreading distribution width W(H) representing any valid load-spreading theory. For present purposes, the AASHTO load-spreading theory, as defined in Equations 1 and 2 is adopted, and restated here in terms of 1-wheel load but including the influence of two-wheel axles loads, i.e., 0 int axle 0 int 1 2 W + LLDF H for H < H W(H) = [S +W + LLDF H] for H > H ïª ï®ï¬ ï¯ ï ïª ï®ï¯ï® Equation 9 where, W(H) = distribution width under 1-wheel, continuous function of H (inches) H = soil depth from surface, usually H = cover depth (inches). LLDF = live-load distribution factor = 2tan(300) = 1.15.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ14  Saxle = center-to-center wheel spacing on axle (usually 72 inches) Hint = two-wheel interaction soil depth = (Saxleâ W0)/LLDF (inches) W0 H W(H) wcritical Culvert Length = L p0=Wheelâload/W0 (1) Culvert (2) Culvert HT pH1= p0(W0/Wcritical) pH2 = p0(W0/W(H2)) H1 H2 Figure 5. Longitudinal loading on a culvert buried above and below the transition depth, HT For shallow burial depth H1 the above figure indicates that Wcritical > W(H1), therefore Wcritical is the controlling distribution width as explained in the previous section. Preserving the wheel-load force, the reduced surface line load is given by, 1 1 0H Hp r pï½ = reduced surface load applicable to H1 Equation 10 where, 01H critical Wr W ï½ = reduction factor for depth H1 It is worth restating that pH1 is not the actual line-load acting on the culvert at depth H1; rather it is a pseudo value to account for the real 3D stiffness effects that are invisible in 2D analysis. At deeper burial depth H2 the figure shows W(H2) > Wcritical; therefore, W(H2) is the controlling distribution width, and the reduced surface line load is given by, 2 2 0H Hp r pï½ = reduced surface load applicable to H2 Equation 11 where, 02 2( ) H Wr W H ï½ = reduction factor for depth H2
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ15  The general equation for reduced surface pressure for an arbitrary burial depth H is easily deduced from Equations 10 and 11 as, 0H Hp r pï½ = reduced surface load applicable to any depth H. Equation 12 where, 0 0( , ) ( )H critical W Wr Minimum W W H ï½ = reduction factor for any depth H. The above equation for rH provides a logical and continuous reduction factor for all H; hence, it is recommended as a replacement to the discontinuous AASHTO approach (Equation 4) As illustrated in Figure 5, the smooth transition occurs at soil depth HT where red lines intersect the green lines. Simply put, HT is determined from Equation 9 by setting W(HT) = Wcritical; consequently, HT is not a fixed depth like 2 feet, but rather a variable depth dependent on culvert properties that define Wcritical. Although it is not necessary to actually compute HT, the equation is provided below for reference. 0 int 0 int ( - ) / (2 - - ) / critical T T critical axle T W W LLDF if H H H W S W LLDF if H H ï® ï£ï¬ ï½ ï ï® ï¾ï® Equation 13 where, HT = transition soil depth between governing distribution widths (Wcritical & W(H)) LLDF = live-load distribution factor = 2tan(300) = 1.15. Saxle = center-to-center wheel spacing on axle (usually 72 inches) Hint = two-wheel interaction soil depth = (Saxleâ W0)/LLDF (inches) In summary the proposed RSL method reduces the surface line load p0 by the reduction factor rH as defined by Equation 12 where H is the soil cover depth. Using the reduced line-load on the surface of the 2D model produces structural distress equivalent to 3D analysis. Continuous Load Scaling (CLS). As presented in the 2017 TRB paper cited below, the CLS method simulates longitudinal load spreading through the soil and structure system by increasing every elementâs unit thickness by an amplification factor, which is dependent on each elementâs depth. The amplification factor is simply the inverse of the reduction factor expressed as a variable function of soil depth H, i.e., ï¨ ï© ï¨ ï© 0 elel W H W Hï¡ ï½ Equation 14 where, Hel = individual cover depth to each soil and culvert element. W(Hel) = load spreading width at element level (computed by Equation 9) α(Hel) = amplification factor assigned to each individual element. Equation 14 gives α(0) = 1.0 on the surface, and α(Hel) steadily increases as element depth increases. Thus, unlike RSL that reduces loading based on a single choice of H (usually H= soil cover), CLS reduces the load continuously with soil depth as actually occurs in nature. For details see TRB paper, âContinuous Load Scaling: A New Method to Simulate Longitudinal Live-load Spreading for 2D Finite Element Analysis of Buried Culverts, Transportation Research Record: Journal of the Transportation Research Board, No. 2642, 2017 by M. G. Katona.â
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ16  As originally presented, the CLS method only corrects for longitudinal load spreading. It did not address the problem of additional 3D stiffness effects in the culvert structure. Fortunately, CLS methodology is well suited to also correct for the missing 3D stiffness effect by modifying the original algorithm as follows. For all culvert elements (not soil elements) whose depths Hel are less than the transition depth HT, the amplification factor is constant and is defined as, critical 0 for H H (or W(H ) W( ) )criticalel el T el WH W ï¡ ï½ ï® ï£ ï£ Equation 15a Otherwise if the culvert elementâs depth is greater the transition depth, then the original load-spreading amplification factor applies, i.e., critical 0 for H H (or W(H ) W( )( ) )elel el T el W HH W ï¡ ï½ ï® ï¾ ï¾ Equation 15b Equations 15a&b apply to culvert elements only. All soil elements and other types of elements are amplified by the original CLS procedure (Equation 14). CRITICAL DISTRIBUTION WIDTH SUMMARY (WCRITICAL)   To account for 3D stiffness effects using either RSL or CLS methodology, it is evident that Wcritical must be known for the particular culvert being analyzed for live loads. To this end, it is useful to summarize essential features of Wcritical as developed thus far in the white paper. ï· Wcritical is the minimum longitudinal distribution width acting on the surface of a 3D culvert that produces the same in-plane deformation as a 2D culvert with same line-load magnitude. ï· By convention Wcritical is the longitudinal distribution width beneath 1-wheel, not an axle. However, the physical width of Wcritical is influenced by both wheels on the axle. ï· Equation 7 describes how Wcritical can be determined from 3D culvert models by forming the displacement ratio = Î(W*)/Î(L), and then finding the minimum value of W* such that ratio = 1. Clearly Wcritical is a culvert property independent of the soil and only dependent on those culvert properties that donât cancel out of the displacement ratio. ï· As will be shown, Wcritical is strongly dependent on culvert span and length (S and L). Other factors influencing Wcritical include the degree of orthotropic stiffness and the location of the line- load relative to fixed or free edges. ï· Currently, the only existing expression representing Wcritical comes from the PennDOT study, and adopted in the current AASHTO LRFD specifications for r/c boxes and arches. By setting Wcritical = ½ Elong where the ½ factor implies 1-wheel load instead of an axle load, we get, 1W = [96" +1.44 Span(ft)] 2critical ïª inches
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ17  Using the above expression for Wcritical in the proposed RSL or CLS methods results in the same 2D analysis prediction as the current AASHTO methodology except soil depths in the range 2â < H < HT wherein the new procedure provides a smooth transition without discontinuities. The second half of this white paper is devoted to developing a rational framework to quantify Wcritical based on a plate model representing the top slab of a r/c box culvert. Verification and calibration from 3D finite models are needed to transform the framework into useful equations for AASHTO specifications. PART II ââ PLATE MODEL DEVELOPMENT AND SOLUTION PLATE MODEL FORMULATION  Configuration. As previously presented in Figure 3, the plate model simulates the top slab of a reinforced concrete box culvert. By taking advantage of double symmetry, the analytical model only requires one quadrant of the full plate as shown in Figure 6. Since the origin of the coordinate system is at the center of the full plate, the quadrantâs x and z dimensions are ½Span and ½Length, respectively. x z y, v(x,z) s = ½Span Boundary condition â fixed: ï·ï v(s,z) = 0  (No displacement) ï·ï v,x(s,z) = 0 (No slope) Boundary condition â symmetric: ï·ï v,z(x,0) = 0 Boundary condition â symmetric: ï·ï v,z(x,l) = 0 p = ½PL Boundary condition â symmetric: ï·ï v,x(0,z) = 0 Figure 6. Flat plate model quadrant exploiting double symmetry. For convenience all half-dimensions are denoted by lower-case letters representing half measures of the full-plate dimensions listed below.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ18Â Â ï· s = ½S = half Span of plate (slab) ï· l = ½L = half Length of plate (slab) ï· w* = ½W* = half longitudinal load width. Although Figure 6 appears to be an isotropic plate with uniform thickness h, the following formulation allows for orthotopic moment of inertia values Ix and Iz in the two orthogonal directions. Formulation. Kirchhoff plate theory is adopted for this study wherein the two basic assumptions are; (1) lines normal to the mid-surface remain straight and normal upon plate bending, and (2) stress and strain through plate thickness is negligible (Ïyy = εyy = 0). The above assumptions lead to the following kinematic approximations used in Kirchhoff plate theory (similar to Bernoulli-Euler beam theory), ( , ) ( , , ) , ( , , ) , x z v v x z u u x y z yv w w x y z yv ï½ ï½ ï½ ï ï½ ï½ ï Equation 16 where, v = vertical displacement of plate, i.e., the primary unknown function. u, w = in-plate displacement functions, related to gradients of v. and, 2 2 3 2 3 and ; higher partial are , , , , , , , , .x z xx xz zzz v v v v vv v v v v etc x z x x z z ï¶ ï¶ ï¶ ï¶ ï¶ ï½ ï½ ï½ ï½ ï½ ï¶ ï¶ ï¶ ï¶ ï¶ ï¶ Shear forces per unit length are defined by integrating the shear stresses over the plate thickness from y = -½h to y = ½h. /2 /2 h x xy h Q dyï´ ï ï½ ï² = downward shear force per unit length dz acting on the x-face /2 /2 h z zy h Q dyï´ ï ï½ ï² = downward shear force per unit length dx acting on the z-face Moments per unit length are defined by integrating stress components with moment-arm y over the plate thickness from y = -½h to y = ½h. /2 /2 h x xx h M ydyï³ ï ï½ ï² = bending moment per unit length dz acting on the x-face (about z-axis) /2 /2 h z zz h M ydyï³ ï ï½ ï² = bending moment per unit length dx acting on the z-face (about x-axis). /2 /2 h xz xz h M ydyï´ ï ï½ ï² = twisting moment per unit length dz acting on the x-face (about x-axis). /2 /2 h zx zx h M ydyï´ ï ï½ ï² = twisting moment per unit length dx acting on the z-face (about z-axis).
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ19  By expressing stresses in terms of displacement gradients via stress-strain and strain-displacements relationships, the y integrations are performed over the two differential faces dxdy and dzdy, wherein different stiffness properties are allowed on the x-face and y-face. This operation results in the following moment-to-curvature equations, /2 2 /2 /2 2 /2 /2 2 /2 1 2 ( , , ) 1 ( , , ) 1 (1 ) (1 ) , 1 h x x xx xx zz h h x z zz zz xx h h x x z zx xz x z h EIM ydy v v EIM ydy v v EI M M ydy v ï³ ï ï ï¡ï³ ï ï ï¡ ï´ ï ï ï ï ï ï½ ï½ ï ï« ï ï½ ï½ ï ï« ï ï« ï½ ï½ ï½ ï ï ï ï² ï² ï² Note: Iz = α Ix Equation 17 where E = Youngâs modulus of material μ = Poisson ratio Ix = 2nd moment of inertia on x-face of plate thickness. Iz = 2nd moment of inertia on z-face of plate thickness = αIx α = Iz/Ix = orthotropic ratio (isotropic if α = 1) Equilibrium of moments about the x and z axis and vertical force equilibrium lead to the following 3 equilibrium equations, x x,x zx,zQ = M + M Equation 18 z z,z xz,xQ M + Mï½ Equation 19 x,xx xz,xz z,zzM + 2M M + q(x,z) 0ï« ï½ Equation 20 where q(x,z) = applied surface pressure on plate interior. Finally, inserting the moment-curvature expressions into the governing equilibrium equation leads to the governing partial differential equation for an orthotropic plate, 1 [ , ( ) , , ] ( , )X xxxx xzxz zzzzD v v v q x zï¡ ï¡ï« ï« ï« ï½ Equation 21 where, DX = EIX/(1-μ2) = plate bending stiffness for x-face per unit length in z direction. DZ = αDX = plate bending stiffness for z-face per unit length in x direction α = IZ/ IX = ratio of in-plane to out-of-plane flexural stiffness for orthotropic plates. q(x,z) = 0, No interior surface pressure per Figure 6.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ20  Interior plate pressure loading is zero, q(x,z) = 0, because loading is applied through the shear-force boundary condition as discussed next. Boundary Conditions (BC). Along with the above partial differential, boundary conditions must be specified along the four sides of the plate quadrant as portrayed in Figure 6. Each side of the quadrant requires two valid boundary conditions. A valid boundary condition is called âridgedâ if it prescribes displacements or slopes. Alternatively, it is called ânaturalâ if it prescribes shears or moments. Table 1 identifies the two boundary conditions assigned to each of the 4 quadrant sides. Table 1. Specified boundary conditions as portrayed in Figure 6 B.C. set number Quadrant side: (xa,za) to (xb,zb) Rigid B.C. Natural B.C. 1 z-face along front side, (0,0) to (s,0) v,z(x,0) = 0 Symmetric condition, no slope Qz = 0, No shear 2 x-face along left side (0,0) to (0,l) v,x(0,z) = 0 Symmetric condition, no slope Qx = p, shear 0 ⤠z ⤠w* Qx = 0, No shear w* ⤠z ⤠l 3 z-face along back side (0,l) to (s,l) v,z(x,l) = 0 Symmetric condition, no slope Qz = 0, No shear 4 x-face along right side (s,0) to (s,l) v(s,z) = 0 (no displacement) v,x(s,z) = 0 (no slope) None BC sets #1 and #2 are the double-symmetry assumption, which is enforced by specifying zero slope normal to the boundary side and specifying the value of boundary shear load, zero or otherwise. In particular, BC set #2 prescribes the non-zero shear load p acting over a chosen longitudinal width w*, where p is the line-load magnitude, 1 1 2 2 2* * Wheel load Wheel loadp W w ï ï ï½ ï½ Equation 22 The above ½ factor implies the full-plate line load P is split into p half-values for each half plate. As a consequence of the BC set #1 the bottom half of the full plate responds as the mirror image of the top half, and BC set # 2 the left side of the full plate responds as the mirror image of the right half. BC set #3 is a special choice that needs explanation. Ordinarily the free end of the culvert would be assigned the natural boundary conditions enforcing shear and moment to be zero (Qz = Mz = 0). However, BC set #3 is assigned a symmetry condition inferring that plate repeats indefinitely in periodic lengths L wherein each periodic length experiences the same shear line-loading defined in BC set #2. For long culvert lengths, say L ⥠30â, the periodic longitudinal loading has negligible influence on the deformation in the primary plate, i.e., Saint-Venantâs principle. However, for shorter lay lengths, say 4â to 8â lengths typical of precast culverts, the periodic loading causes additional deformation in the primary length, more so for 4â than 8â lengths, but conservative results in either case. Since it is known from the PennDOT study that loading the slabâs free end produces more deformation than loading the slabâs central region, BC set #3 is intentionally chosen to produce additional deformation in short-length culverts because they are more likely experience free edge loading than longer length culverts. Thus, BC set #3 appears to be a reasonable representation for all lay lengths. Finally, BC set #4 represents a fixed connection where the top slab is connected to the side walls allowing neither rotation or displacement. This choice is deemed more realistic for a box culvert than a pinned
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ21  connection. Moreover, it is postulated that the ratio-forming procedure used to compute the critical distribution width Wcritical is relatively insensitive to the choice of slab-to-wall connection. RITZ SOLUTION METHODOLOGY  After an extensive literature search, a closed form solution for the flat palate portrayed in Figure 6 with boundary conditions shown in Table 1 could not be found even for an isotopic plate, let alone an orthotopic case. Accordingly, the author proceeded to develop an approximate closed-form solution based on virtual work together with the Ritz method. Highlights of the development are provided below and detailed developments are presented in the addendum to this report. Virtual work and Ritz method. Shown below is the virtual work statement that is equivalent to the partial differential equation in Equation 21 and the natural boundary conditions in Table 1. * 0 0 0 { , ( , , ) , ( , , ) (1 )(1 ) , , } ( ) 0 x s z l z w x xx xx zz zz zz xx x z x z x z z D v v v v v v v v dxdz v p dzï¤ ï ï¡ï¤ ï ï¡ ï ï¤ ï¤ ï½ ï½ ï½ ï½ ï½ ï½ ïï« ï« ï« ï« ï« ï ï½ï² ï² ï² where δ is the virtual variation symbol and all other symbols are as defined in the previous formulation. The Ritz method requires choosing a trial function for v(x,z) composed of linearly independent functions in x and z with unknown coefficients. The first requirement is that the trial function must satisfy all rigid boundary conditions, thereby determining values for some of the unknown coefficients. The remaining unknown coefficients are determined by satisfying the virtual work expression, which produces a set of coupled algebraic equations based on the independent virtual variation of each unknown coefficient. As the number of selected linearly independent functions increases, the Ritz solution is more and more accurate and becomes the exact solution in the limit. For a finite set of linearly independent functions, the Ritz solution is equivalent to minimizing strain energy, but generally reacts a little stiffer than the exact solution. Ritz trial function. The trial function adopted in this study is separable in x and z as expressed below. ï¨ ï© ï¨ ï© ï¨ ï© ,v x z X x Z zï½ Equation 23 where 2 3 1 2 32 3( ) 1 x x xX x C C C s s s ï½ ï« ï« ï« Unknown coefficients: C1, C2, and C3 2 3 4 0 1 2 3 42 3 4( ) z z z zZ z B B B B B l l l l ï½ ï« ï« ï« ï« Unknown coefficients B0, B1, B2, B3, and B4. Upon enforcing the 5 rigid boundary conditions listed in Table 1, the Ritz trial function is reduced to the following expression with 3 unknown parameters B0, B2 and B3 as expressed below, 2 3 2 4 3 4 0 2 32 3 2 4 3 4 31 2 2 4 3 1( , ) [ ][ ( ) ( ) ]x x z z z zv x z B B B s s l l l l ï½ ï« ï« ï ïï ï« Equation 24 Finally, introducing the reduced trial function into the virtual work statement provides three algebraic equation for determining B0, B2 and B3. This operation is extremely labor-intensive requiring hundreds of
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ22  integrations and mathematical manipulations. After several ill-fated attempts, the following results are believed to be accurate. Ritz solution of plate model. The final Ritz solution for the plateâs displacement function due to a single wheel line-load in the middle of the full plate is summarized below: 2 3 2 4 3 4 1 2 32 3 2 4 3 4 3 1 31 2 2 4 3( , ) [ ][ ( ) ( )] x x x z z z zv x z Q Q Q s s l lD l p l s ï½ ï« ï« ï ï« ïï Equation 25 where, v(x,z) is plate displacement function x, z = spatial coordinates with origin at plate center s = ½ Span of plate in x-direction l = ½ Length of plate in z-direction. p = magnitude of line-load over width w* Dx = plate stiffness parameter in x-direction Q1, Q2, Q3 = solution parameters as determined below. The three Q parameters are dependent on loading components P1, P2 and P3 and system parameters a, b, c and d as shown below: 3 2 3 2 2 3 1 1 2 3 1 1 7 1 30 10 ( ) ( ) Q cP aP ad bc Q dP bP ad bc Q P Q Q ï½ ï ï« ï ï½ ï ï ï ïï½ Equation 26 The three loading components P1, P2 and P3 are dependent on the fraction of culvert length that is loaded by the longitudinal width, w*/l. as expressed below. 1 3 5 2 3 5 4 5 3 4 5 1 12 1 7 10 3 30 1 2 5 3 20 *( ) * * *( ) * * *( ) wP l w w wP l l l w w wP l l l ï½ ï½ ï ï« ï ï½ ï ï« ï Equation 27 Finally, the system parameters a, b, c and d are defined below and are dependent on span-to-length ratio s/l and orthotropic stiffness ratio α = Dz/Dx,
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ23  2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 64 131 1 175 4 33 43 391 175 44 11 33 43 391 175 44 11 18 11 131 175 12 3 [( ) ( )] [( ) ( )] [( ) ( )] [( ) ( )] s s sa l l l s s sb l l l s s sc l l l s s sd l l l ï¡ ï¡ ï¡ ï¡ ï½ ï« ï« ï« ï½ ï« ï« ï« ï½ ï« ï« ï« ï½ ï« ï« ï« Equation 28 RITZ 1âWHEEL SOLUTION VERIFICATION AND INSIGHTS Verification of 1âwheel Ritz solution for oneâway bending. When the culvert length is fully loaded so that W*/L = 1, the above equations yield P1 = 1/12 and P2 = P3 = 0, which in turn dictates that Q1 = 1/12 and Q2 = Q3 = 0. Consequently, the displacement profile is independent of z, which indicates a 2D response with one-way bending like a beam, i.e., 2 3 2 3 3 1 231 12 ( ) ( ) x xp D xv x s s s ï«ïï½ Equation 29a The maximum displacement occurs all along the plate centerline where x= 0.0, so that the maximum 2D displacement used to normalize the 3D Ritz 1-wheel solutions is given by, 310 12 ( )Max x v p D s ï ï½ ï½ Equation 29b As desired, the above equation is identical to the 2D-plane strain displacement profile of a fixed-end beam of length = 2s with unit width and central load 2p. Therefore, the Ritz solution is awarded a degree of confidence that is further bolstered by additional checks that reveal that net shear and moment equilibrium are maintained for all variations of the system parameters. Nonetheless, the Ritz solution is only an approximate solution due to the restricted number of independent Ritz trial functions. Span and Length Measures for Concrete Culvert Products. The span-to-length ratio (S/L) is a key parameter influencing the longitudinal displacement profile when W*/L is less than 1. Table 2 lists the span and lay length measures for typical concrete culvert products. Precast r/c products are available in well-defined span and lay-length combinations from manufacturers. On the other hand, cast- in-place products are generally continuous for the entire culvert length. However, 30 feet is considered a reasonable upper limit to retain moment continuity due to cold joints and micro cracking.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ24  Table 2. Spans and associated lay lengths for R/C culverts. R/C Culvert Product Span range 4-10 feet Span range 12-24 feet Span range 26-42 feet Span range 44-72 feet Precast arch NA* L = 8 ft L = 6 ft L = 4 ft Precast box L = 8 ft L = 4 ft NA NA Pipes L = 8 ft L = 4 ft NA NA Cast-in-place NA L = 30 ft L = 30 ft L = 30 ft S/L range 0.5 to 1.3 0.4 to 6.0 0.9 to 7.0 1.5 to 18.0 NA = Generally not available or constructed. Plots and Insights from 1âwheel loading. The 1-wheel Ritz solution, which is given by Equations 25 to 28, requires graphical plots to gain an understanding of how the displacement profiles are influenced by the parametric ratio S/L. Guided by Table 2, a realistic set of three values are chosen to show how S/L ratios influences displacement patterns. Figures 7a, b & c show longitudinal displacement profiles for the S/L = 0.4, 0.8 and 2.0, respectively. Each figure shows five displacement profiles representing increased load lengths; W*/L = 0.1, 0.25, 0.50, 0.75 and 1.00. Each profile starts at the load center (x = 0, z = 0) and continues along the centerline to the plate edge (x = 0, z = l). Displacements are normalized by dividing by the corresponding 2D solution, i.e., ÎMax in Equation 29b. Isotropic plate properties are assumed in all cases, α = Dy/Dx = 1. Figure 7a. Normalized displacement profiles for S/L = 0.4
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ25  Figure 7b. Normalized displacement profile for S/L = 0.8
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ26  Figure 7c. Normalized displacement profile for S/L =2.0 Figures 7a shows that when S/L is less than 0.5 the deflection profiles have pronounced peaks under the load, and the value of Wcritical/L is approximately 0.5 or less. Wcritical/L is the W*/L ratio producing the first peak approaching ÎMax. Conversely, Figure 7c illustrates that when S/L is greater than 1.5 the defection profiles become uniformly flattened and Wcritical/L is approximately 1.0. Figure 8 is a useful and pragmatic graph of Wcritical/L versus S/L with many data points for S/L and W*/L. Wcritical/L is determined by special spreadsheet programming to find the first W*/L value producing a peak displacement equal to 90% of ÎMax. The reduced value of 90% instead of 100% ÎMax was chosen for three reasons; (1) 90% ÎMax produces slightly conservative values for Wcritical/L, (2) 90% ÎMax compensates for inherently over-stiff Ritz solution, and (3) 90% ÎMax mitigates the numerical asymptotic error inherent with 100% ÎMax. Figure 8. Wcritical/Length vs Span/Length for 1-wheel loading at slab center (isotropic slab) The above curve provides a complete solution for Wcritical for all span and length dimensions assuming the slab is loaded by only 1-wheel at the slab center. Here it is observed that Wcritical/L increases as S/L increases up to a limit of S/L â 1.5. Thereafter, Wcritical /L remains effectively constant at Wcritical /L = 0.9. Since Figure 8 only applies to 1-wheel load located at the slab center, the curveâs pragmatic utility is restricted to lay lengths 6 feet or less because lay lengths greater than 6 feet are subjected to loading from
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ27  both wheels on the truckâs axle. In the next section, the solution to the 2-wheel problem is approximated by superposition of the 1-wheel Ri RITZ 2âWHEEL SOLUTION BY SUPERPOSITION  Given that truck axles have two wheels, which are typically spaced at 6 feet, the second wheel may also contribute to the culvertâs displacement profile depending on the culvertâs lay length. In particular, if the culvert lay length is greater than 6 feet, then the displacement profile induced by the second wheel needs to be added (superimposed) to the deflection profile from first wheel. In this study the second deflection profile is approximated by rigidly shifting the 1-wheel deflection profile 6 feet (spacing along axle) to the right of the slab center. This approach requires that the culvert must be at least 12 feet long or more in order that the shifted profile makes physically sense for two full wheel loading. To summarize, the 1-wheel Ritz solution applies to culverts 6 feet or less, and the 2-wheel superposition solution applies to culverts 12 feet or more. For lay lengths between 6 and 12 feet, the solutions are interpolated from the 6-foot and 12-foot lay length solutions. Plots and insights from 2âwheel loading. An illustration of the superposition procedure is shown below for a culvert length L=15 feet, span S = 10 feet, and loading-length ratio W*/L = 0.40. Figure 9. Displacement profiles 2-wheel loading for L= 15 ft, S = 10 ft and W*/L = 0.4 Since the displacement profile of the first wheel peaks at the origin and is symmetric about the origin, the 2nd wheel displacement profile peaks and is symmetric about the 6-foot offset position due to the ridged shift approximation. Superimposing the two curves to produce the combined 2-wheel deflection profile usually produces a peak displacement midway between the wheels as illustrated by the red curve at the 3- foot mark. In this example S/L = 0.667; however, in cases when S/L is smaller, the peak combined displacement may occur at both wheel locations.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ28  One last observation from Figure 9 is the 2-wheel peak displacement happens to be slightly greater than 90% of ÎMax (i.e. 90% of Normalized Displacement), which means Wcritical/L is slightly less than the chosen ratio W*/L = 0.4. It is important to remember that in this study W*/L is defined as the loading- length ratio beneath one wheel only. Hence, 2-wheel loading on the slab requires a smaller critical loading-length ratio Wcritical/L than does just 1-wheel loading. Similar to Figure 8, Figure 10 presents graphs of Wcritical/L versus S/L that includes 2-wheel loading for culvert lengths up to 30 feet. As before, Wcritical/L is determined by special spreadsheet programming to find the first W*/L value producing a peak displacement equal to 90% of ÎMax. Of course, the superposition procedure is more complex because the 2-wheel peak displacement may occur at the slab center or between the two wheels depending on the S/L ratio and the physical length L. Table 3 summarizes how the parametric-length curves in Figure 10 are generated. Figure 10. Complete set of graphs for Wcritical/L versus S/L for parametric slab lengths. Table 4. Procedure used to generate parametric-length curves in Figure 10. Culvert length L feet Procedure to determine Wcritical/L vs S/L for L-dependent curves L ⤠6 ft Ritz 1-wheel solution. (Applies to lengths ⤠6 ft, only 1wheel fits) 7 ft ⤠L ⤠11 ft Interpolated between L = 6â & L= 12â. (Transition 1 to 2 wheels). L ⥠12 ft Superposition for 2-wheels. (Applies to lengths ⥠12 ft, 2 wheels fit)
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ29  Given the length and span dimensions for any slab (culvert), Figure 10 provides the means to compute Wcritical to account for the 3D stiffness effect of that particular culvert. It is interesting to note for culverts with lengths of 12 feet or less, the Wcritical/L vs S/L curves are identical in the range 0 ⤠S/L ⤠0.4, and thereafter the curves diverge. This is because corresponding displacement profiles for S/L ⤠0.4 have pronounced bell shapes such as shown in Figure 7a so the 2nd wheel does not contribute to the peak deflection. As S/L increases all curves approach an asymptotic limit between 0.9 for L ⤠6 feet and 0.45 for L ⥠0.45. COMPARE RITZ SOLUTION WITH PENNDOT SOLUTION (L= 30â) Recall the PennDOT study presented âdistribution widthsâ (i.e., Wcritical) for box culverts and slabs for a fixed culvert length = 30 ft and three span dimensions, S = 8, 16 and 24 ft. From PennDOTâs set of 31 finite element models, 5 models have loading conditions that conform to the assumptions of the Ritz solution. Specifically, PennDOT box models #1, #9, #17 corresponding to spans of 8, 16, 24 ft and slab models #28 and #30 corresponding to spans of 8 & 16 feet. Like the Ritz model assumptions, these PennDOT models have no soil cover and are loaded with 2 wheels, symmetrically placed about the slab center. Figure 11 compares PennDOT and Ritz predictions for Wcritical as a function of span. Figure 11. Comparison of compatible PennDOT predictions with Ritz predictions for L = 30 ft. Remarkably the PennDOT data points for the box culvert are very close to Ritz fixed-slab solution. The PennDOT slab model, which assumes a pinned condition, predicts higher distribution widths than the box model. This indicates that a fixed-slab model better represents the box culvert behavior than does a pinned-slab model. Also shown for reference is the current AASHTO specification for distribution width
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ30  based on PennDOTâs solution for shear control when the loading location is shifted near the supporting wall of the box. Unfortunately, the Ritz model is only applicable to centrally loaded slabs that produce maximum positive moments and deflections; hence, no direct comparison with the AASHTO specification is meaningful. The significant finding is that the PennDOT prediction for centrally loaded box culverts is in good agreement with fixed-slab Ritz model for the case when culvert length L = 30 feet. In the next section, the Ritz model is used to examine the influence of culvert length, which is not considered in the PennDOT study. GENERAL RITZ SOLUTION AS FUNCTION OF LENGTH AND SPAN Figure 12 shows Wcritical (feet) as a continuous function of culvert span (feet) for a discrete set of practical culvert lengths, L = 4, 6-to-12, 18 and 30 ft. These parametric curves are identical to the general Ritz solutions presented in Figure 10 except the curves are converted to physical units of Wcritical versus Span instead of the ratios Wcritical/L versus Span/L. As a result of converting to physical units, all culvert lengths between 6 and 12 ft collapse into a single curve as shown by the solid red line below. The collapse into a single curve occurs during the transition from 1-wheel loading to 2-wheel loading wherein the structural benefit of increased slab length is offset by a proportional increase in wheel loading. Figure 12. Wcritical versus span for a set of parametric culvert lengths assuming an isotropic slab.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ31  Figure 12 reveals three significant findings for centrally loaded culverts: 1. Culvert length L has a significant impact on Wcritical except in the range, 6 ⤠L ⤠12 ft. 2. For culvert lengths L ⤠12 feet, Wcritical is not influenced by the culvert span. 3. For culvert lengths L > 12 feet, Wcritical increases as span and/or length increases. Recalling from Table 2 that all precast r/c products have lay-lengths less than 12 feet, the consequence of the above findings is that Wcritical is independent of culvert span and only dependent on culvert length. Thus for all culvert lengths L ⤠12 feet, Wcritical is given by the following equation. 0.9 6 5.4 6 12 critical L if L ft W ft if L ft ï® ï£ï¬ ï½ ï ï® ï£ ï£ï® Equation 30 where, L = lay length of precast culvert or cast-in-place culvert with L ⤠12 ft. For cast-in-place culverts whose continuous length are greater than 12 feet, the culvert span as well as the culvert length influences Wcritical as can be observed in Figure 12 for L = 18 and 30 ft. For these cases Wcritical can be approximated by two straight lines. The first line goes from the origin (S = 5 ft, L = 5.4 ft) to the maximum Wcritical value on the L-curve where occurs at S = 2L. Thereafter, as S increases Wcritical remains constant at maximum value. With the above understanding, Equation 31a&b represent straight-line approximations to predict Wcritical as a function of S and L. 5.4 ' ( 5 ') 5' S 2 2critical critical m S if L W MaxW if S L ï« ï ï® ï£ ï£ï¬ ï½ ï ï® ï¾ï® Equation 31a where m is the straight-line slope and Max-Wcritical is the maximum of value of Wcritical, both dependent L. 0.46120 087 6 5 4 2 5 '. ' . ' ( ')critical Lm MaxW m L ïï¦ ï¶ï½ ï§ ï· ï¨ ï¸ ï½ ï« ï Equation 31b For reference, Figure 12 also shows the shear-based AASHTO distribution width, which is purportedly applicable to all r/c box and arch culvert lengths even though that the underlying PennDOT study used a fixed length L = 30 foot. Given that the Ritz predictions assume central-slab loading and AASHTO predictions assume side-slab loading, there is no expectation of agreement between ASSHTO and Ritz predictions even for L = 30 ft. Nonetheless, the AASHTO and Ritz predictions are compared and contrasted in the following bullets for the purpose of ultimately improving the AASHTO methodology. ï· The main lesson learned from the Ritz solutions is that culvert length L has a pronounced influence on Wcritical, even more so than culvert span S. Clearly, follow-on studies like the PennDOT study need to be undertaken for a range of culvert lengths.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ32Â Â ï· Because the Ritz and the PennDOT predictions for Wcritical show good agreement for centrally loaded slabs for the case L = 30 feet, it is tentatively concluded that the Ritz slab model is a viable surrogate for all centrally loaded box culverts. However, this conclusion needs to be validated with 3D FEM models with smaller culvert lengths. ï· The curved geometry of concrete arches is significantly different from the flat geometry of slabs and box culverts. Consequently, 3D finite element models of typical concrete arches need to be undertaken to assess the influence of curvature on Wcritical, if any. It is expected that the Ritz predictions for Wcritical as shown in Figure 12 and quantified by Equations 30 and 31 will need to be adjusted based on future 3D finite element analysis. The true value of Ritz solution is to illustrate the effect of culvert length and span and to establish a template to build upon. INFLUENCE OF ORTHOTROPIC SLAB PROPERTIES. Up to this point, all Ritz solutions have assumed the slab is isotropic with the same bending stiffness in the longitudinal plane as the transverse plane, i.e., DZ = DX, where DZ = EIZ/(1-μ2) and DX = EIX/(1-μ2) are the plate stiffness parameters in the longitudinal and transverse planes, respectively. The bold black curve in Figure 13 is Wcritical/L versus S/L for isotropic case DZ/DX = 1 as previously shown in Figure 8 for 1-wheel loading. Also shown in Figure 13 is a family of curves for DZ/DX = 0.01, 0.1, 0.5 and 2.0, representing a realistic range of orthotropic properties that may be experienced in rigid or flexible culverts. Figure 13. Wcritical/L versus S/L for several orthotopic stiffness ratios DZ/DX, (1-wheel loading).
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ33  For any particular S/L ratio, the above curves reveal the comparative change in Wcritical/L when an isotropic slab is compared to an orthotropic slab. The relative change applies to 2-wheel loading as well as 1-wheel loading because 2-wheel loading is achieved by superposition of 1-wheel loading. To illustrate utilizing the above chart, begin by inspecting Figure 12, which is the general 2-wheel Ritz solutions for Wcritical for isotropic slabs. Choosing a specific slab dimensions, say S = 18 ft and L = 18 ft, we find Wcritical â 7.2 ft for the isotropic case. Next, to get the value of Wcritical for the orthotropic case DZ/DX = 0.5, enter the above chart for S/L = 18/18 = 1 and read Wcritical/L â 0.82 from the curve DZ/DX = 0.5 and also read Wcritical/L â 0.86 from the isotropic curve. Forming the ratio 0.82/0.86 = 0.95 and multiplying it by original isotropic Wcritical value, we arrive at the orthotropic value for Wcritical = 6.9 ft. With regard to reinforced concrete culverts, longitudinal cracks reduce the transverse stiffness DX, and circumferential cracks reduce longitudinal stiffness DZ as may be predicted from cracked-transformed section properties. If the degree of concrete cracking (or lack of cracking) is relatively the same for longitudinal and circumferential cracks, then an isotropic assumption is reasonable, DZ/DX = 1.0. Field observations of concrete culverts subject to dead and live loads typically show that longitudinal cracks are significantly more prevalent than circumferential cracks so that DZ/DX = 2.0 may be a reasonable orthotropic assumption. However, this assumption results in higher values for Wcritical and, hence, less conservative. Consequently, it is generally recommended to assume isotopic conditions for r/c culverts, DZ/DX = 1.0 In contrast to r/c culverts, corrugated metal and corrugated plastic culverts have fixed section properties where DX is 1 to 2 orders of magnitude larger than DZ dependent on the corrugation geometry. Consequently, the curves for DX/DZ = 0.1 and 0.01 are appropriate for corrugated flexible culverts. Although this white paper is focused on r/c culverts, one of the issues listed at the beginning of this paper asked the question why is the 3D-stiness effect only applicable to reinforced concrete culverts and not flexible culverts. Figure 13 provides a partial answer because Wcritical for corrugated culverts are significantly smaller than for isotropic r/c culverts. A final point of interest is that the curve DZ/DX = 0 (not shown) is indistinguishable from the curve DZ/DX = 0.01. Hence, even if there is no longitudinal stiffness DZ = 0 (i.e. IZ= 0), there still exists a small 3D stiffness effect due to twisting momenta whose stiffness are a combination of DX and DZ. SUMMARY Part I of this white paper reviewed the AASHTO LRFD distribution-width equations that are used to reduce the magnitude of 2D live loads to account for 3D effects in the longitudinal direction. Equations 1 and 2 are the AASHTO distribution widths that account for the longitudinal load spreading through the soil. These long-standing equations are a function of soil depth H and apply to all culvert sizes, shapes and materials. Equation 3 is a special distribution width that only applies to reinforced concrete box and arch culverts with less than 2 feet of soil cover. This equation originated from the PennDOT study wherein numerous 3D finite element models of r/c box culverts were analyzed to develop a span- dependent, distribution-width equation so that 2D analysis predicts structural responses similar to 3D analysis. Part I also introduces a conceptual plate model that illustrates the underlying physics behind the special distribution width associated with Equation 3. The physical reason is that there exists a real-world 3D
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ34  stiffness effect that is not captured by 2D culvert models subject to live loads at shallow burial depths. More precisely, a 2D model underrepresents the actual 3D stiffness whenever the width of the longitudinal line-load impinging on the plate (culvert) is less than a culvert-specific parameter called the critical distribution width, Wcritical. Pragmatically, Wcritical plays the same role as Elong in Equation 3, except rather than axle load, Wcritical applies to one-wheel load, i.e., Wcritical = ½ Elong. At the conclusion of Part I, a very useful concept is presented in Figure 5 that illustrates a logical methodology to smoothly transition from the fixed distribution width Wcritical to the soil-spreading distribution width. In addition, step-by-step procedures are described for 2D live-load analysis based on the Reduced Surface Load (RSL) technique or the Continuous Load Scaling (CLS) technique. In either case Wcritical plays the pivotal role. Whereas Part I, deals with concepts and big picture ideas, Part II is focused on obtaining quantifiable insights from a mechanistic model. Specifically, a 3D elastic plate is defined to represent the top slab of an r/c box culvert with a longitudinal strip load placed symmetrically about the slab center as depicted in Figure 6 for a symmetric quadrant of the slab. The associated differential equation and boundary conditions are solved by the Ritz technique to provide an approximate solution for displacements and structural responses. Spread sheet calculations are used to process the Ritz solution to compute Wcritical for 1- and 2-wheel loading conditions. Solution plots are shown as a function of slab span, length and degree orthotropic stiffness. Figure 11 compares values of Wcritical from the Ritz model with the corresponding distribution widths from the PennDOT as a function of slab span with fixed slab length L = 30 feet. Remarkably, the correlations are surprisingly close; thereby suggesting the Ritz slab model is a viable surrogate for a centrally loaded r/c box culvert. Figure 12 portrays the general Ritz solution for Wcritical as a function of span S and length L assuming isotropic slab stiffness properties. Surprisingly, the culvert length L has a pronounced influence on Wcritical even more so than the culvert span S. Since the PennDOT study did not vary the box culvert length, this finding has important consequences on the future AASHTO distribution-width equations. Figure 13 shows that Wcritical becomes smaller as the orthotropic plate stiffness ratio DZ/DX becomes smaller. Since corrugated flexible culverts have very small stiffness ratios DZ/DX < 0.1, it is evident that corrugated flexible culverts do not produce 3D stiffness effects as large as rigid r/c culverts whose stiffness ratio are approximately DZ/DX â 1.0. Perhaps this explains why AASHTOâs special distribution width equations only apply to reinforced concrete and not to other culvert materials. To conclude this summary, the original six issues listed on page 6 are re-visited in light of the concepts and findings presented in Parts I and II. The six issues are addressed below. 1. Continuity of distribution widths with soil depth. As shown in Figure 1, the current AASHTO distribution width equations are discontinuous at the soil depth H = 2 ft. In Part I, a logically smooth transition method is illustrated in Figure 5 using a variable transition soil depth HT, which is dependent on critical distribution width Wcritical. Said another way, there is no apparent engineering logic behind the current AASHTO stipulation that all transitions occur at H = 2 ft whereas the variable transition depth is physically logical.
Appendix I â Improving AASHTO LRFD/LRFR Specs for 2D for Buried Culverts under LL  Iâ35  2. Influence of culvert length. The PennDOT study used a fixed culvert length of 30 feet for all finite element models; consequently, Equation 3 is only dependent on culvert span. In sharp contrast, results from Ritz slab model reveals that length L has a pronounced influence on Wcritical even more so than the culvert span S. 3. Influence of culvert span. The PennDOT study investigated box culvert spans of 8, 16 and 24 ft with a fixed length L = 30 ft thereby finding that Elong is a linearly increasing function of span. In contrast, the Ritz slab model found that Wcritical is not influenced by the span S if L ⤠12 feet, which includes all precast culverts. For cast-in-place culverts with L > 12 feet, Wcritical increases with span but not in a linear fashion. Rather Wcritical increases on an asymptotic curve as shown in Figure 12. 4. Verification of procedure for computing distribution widths. Figure 11 shows remarkably close correlation between the PennDOT and Ritz predictions for distribution widths based on centered 2-wheel loading. Nonetheless, the PennDOT procedure, which is based on integrating force-effect distributions, is significantly different than the Ritz procedure, which is described by Equation 7. 5. Justification for applying r/c box culvert results to r/c arches. Neither the PennDOT study nor this white paper considered curved models representative r/c arches. Nonetheless Equation 3 (developed for box culverts) also applies to reinforced concrete arches according to the ASSHTO specifications. 6. Potential 3D-effects for other culvert materials and shapes. Both the PennDOT study and Ritz model indicate that 3D stiffness effects are a real phenomenon and potentially applicable to all culvert materials and shapes to some degree. Figure 13 illustrates that orthotropic stiffness ratios representative of corrugated flexible culverts do indeed exhibit 3D stiffness effects but to a lesser degree than isotropic stiffness properties assumed for rigid culverts. Â
Appendix J â Data Mining BrDR Regression Data Jâ1 Appendix J â Plots Mined from BrDR Regression Data â Caltrans Double Box This appendix shows plots mined from BrDR regression data for Caltrans double cell culverts. The plots show the RF and itâs contributing components.Â
Appendix J â Data Mining BrDR Regression Data   Jâ2  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)   CD12x10;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 3 of 6)  Â
Appendix J â Data Mining BrDR Regression Data   Jâ3  CD12x10;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 3 of 6)   CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 5 of 6)  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF: FLAG for Hand Calculations Â
Appendix J â Data Mining BrDR Regression Data   Jâ4  CD12x10;14 1966:MMâLRFRâCulvert: Shear RF: FLAG for Hand Calculations  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 2 of 6)  CD12x10;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 2 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ5  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x10;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x10;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 6 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ6  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 3 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ7  CD12x12;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 3 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 5 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF: FLAG for Hand Calculations CD12x12;14 1966:MMâLRFRâCulvert: Shear RF: FLAG for Hand CalculationsÂ
Appendix J â Data Mining BrDR Regression Data   Jâ8   CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 2 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 2 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ9  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x12;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 6 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ10  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 3 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ11  CD12x6;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 3 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 5 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF: FLAG for Hand Calculations Â
Appendix J â Data Mining BrDR Regression Data   Jâ12  CD12x6;14 1966:MMâLRFRâCulvert: Shear RF: FLAG for Hand Calculations  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 2 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 2 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ13  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x6;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 6 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ14  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 3 of 6) Â
Appendix J â Data Mining BrDR Regression Data   Jâ15  CD12x7;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 3 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 5 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF: FLAG for Hand Calculations Â
Appendix J â Data Mining BrDR Regression Data Jâ16 CD12x7;14 1966:MMâLRFRâCulvert: Shear RF: FLAG for Hand Calculations CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 2 of 6) CD12x7;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 2 of 6)Â
Appendix J â Data Mining BrDR Regression Data   Jâ17  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Shear RF:  R_Soil 2: 120V; 60H (MDL 4 of 6)  CD12x7;14 1966:MMâLRFRâCulvert: Moment RF:  R_Soil 2: 120V; 60H (MDL 6 of 6) Â
Appendix J â Data Mining BrDR Regression Data Jâ18 CD12x8;14 1966:MMâLRFRâCulvert: Moment RF:  D_Soil 1: 120V; 36H (MDL 1 of 6) CD12x8;14 1966:MMâLRFRâCulvert: Shear RF:  D_Soil 1: 120V; 36H (MDL 1 of 6)Â
Appendix K â Calibration Information Kâ1 Appendix K â Calibration InformationÂ
Appendix K â Calibration Information Kâ2 1 Introduction This appendix contains the calibration summaries for the seven models load tested for this research. 1.1 Calibration Summary â Model 1, Candidate 1 Model 1, Candidate 1 consists of a singleâcell precast concrete culvert located in Juniata County, Pennsylvania.  Additional details of the testing plan and instrumentation can be found in Appendix F of this document. The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 1, Candidate 1 under the truck load that was used in the experimental program. The field test loading consisted of two main phases: Phase 1 loading as based on the culvert being loaded with the lift axle of the truck in the up position; and Phase 2 loaded the culvert with the lift axle down. The first phase included four main sets of loading where the marked points are the locations on the slab directly above the line of strain gauge installations: - Uâ1:  the center of left wheel of Axle 1 of truck over the marked points (see Figure 4). - Uâ2:  the center of left wheel of Axle 2 of truck over the marked points (see Figure 4). - Uâ3:  the center of left wheel of Axle 3 of truck over the marked points (see Figure 4). - Uâ4:  the center of each axle of the truck over the centerline of the line of gauges. The second phase included five main sets of loading: - Dâ1:  the center of left wheel of Axle 1 of truck over the marked points (see Figure 4). - Dâ2:  the center of left wheel of Axle 2 of truck over the marked points (see Figure 4). - Dâ3:  the center of left wheel of Axle 3 of truck over the marked points (see Figure 4). - Dâ4:  the center of each axle of the truck over the centerline of the line of gauges. - DâL:  the center of left wheel of Lift Axle of truck over the marked points (see Figure 4). Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 5. The load configuration of the experimental truck for both phases is shown in Figure 6 and Figure 7. Â
Appendix K â Calibration Information Kâ3 Figure 1 â Culvert Plan and Elevation Figure 2 â Culvert Typical SectionÂ
Appendix K â Calibration Information Kâ4 1.1.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 3 below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 3 â Model 1 (M1C1) Isometric 3D LUSAS Model Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 8 through Figure 16.  The table below provides a more detailed notation and descriptions of the stress and displacement figures than the abbreviated keys for each these figures.  In each of the graphs, the vertical axis represents either the stress (for strain gauge locations) or displacement (for string potentiometer locations).  The horizontal axis represents the load locations for each of the five load positions shown in Figure 4.  For all gauge locations, see Figure 5.Â
Appendix K â Calibration Information Kâ5 Notation Description G1 Gage 1 â 3D LUSAS model results G1 â Data Gage 1 â Field testing data results G2 Gage 2 â 3D LUSAS model results G2 â Data Gage 2 â Field testing data results G3 Gage 3 â 3D LUSAS model results G3 â Data Gage 3 â Field testing data results G4 Gage 4 â 3D LUSAS model results G4 â Data Gage 4 â Field testing data results G5 Gage 5 â 3D LUSAS model results G5 â Data Gage 5 â Field testing data results POTâ2 String Potentiometer 2 â 3D LUSAS model results POTâ2âData String Potentiometer 2 â Field testing data results POTâ3 String Potentiometer 3 â 3D LUSAS model results POTâ3âData String Potentiometer 3 â Field testing data results Figure 8 through Figure 11 are for the lift axle up configuration showing each axle placed over each of the marked points with the left wheel centered on the gauge line and then with the center of the truck centered over the gauge line. Figure 12 through Figure 16 are for the lift axle down configuration showing each axle placed over each of the marked points with the left wheel centered on the gauge line and then with the center of the truck centered over the gauge line. As can be seen in Figure 8 through Figure 16, at axle load locations that produce the peak positive and negative moment stresses, good agreement is seen in the negative moment stresses at the corner of the culvert (gauge locations G3 and G4) and at the quarterâpoint gauge location (G4). Displacement at the midspan of the top slab (Pot 3) also shows good agreement whereas the stresses predicted by the model at that location are significantly less than what was measured in the field.  Â
Appendix K â Calibration Information Kâ6 Figure 4 â Location of Marks (Location of Axles for each Load Case) (M1C1) Figure 5 â Location of Strain Gages and String Potentiometers  (M1C1)Â
Appendix K â Calibration Information Kâ7 Figure 6 â Load Truck Configuration for Phase 1 (lift axle up) (M1C1) Figure 7 â Load Truck Configuration for Phase 2 (lift axle down)(M1C1)Â
Appendix K â Calibration Information Kâ8 Figure 8 â Load Case Uâ1: Lift Axle Up and Axle 1 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ9 Figure 9 â Load Case Uâ2: Lift Axle Up and Axle 2 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ10 Figure 10 â Load Case Uâ3: Lift Axle Up and Axle 3 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ11 Figure 11 â Load Case Uâ4: Lift Axle Up and Center of each Axle over Midspan (M1C1)Â
Appendix K â Calibration Information Kâ12 Figure 12 â Load Case Dâ1: Lift Axle Down and Axle 1 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ13 Figure 13 â Load Case Dâ2: Lift Axle Down and Axle 2 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ14 Figure 14 â Load Case Dâ3: Lift Axle Down and Axle 3 Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ15 Figure 15 â Load Case DâL: Lift Axle Down and Lift Axle Left Wheel over Marked Points (M1C1)Â
Appendix K â Calibration Information Kâ16 Figure 16 â Load Case Dâ4: Lift Axle Down and Center of each Axle over Midspan (M1C1)Â
Appendix K â Calibration Information Kâ17 1.2 Calibration Summary â Model 2, Candidate 1 Model 2, Candidate 1 consists of a twoâcell castâinâplace reinforced concrete culvert located in the state of Maryland and owned by the Maryland DOT (Structure Number 0329500).  Additional details of the testing plan and instrumentation can be found in Appendix F of this document.   The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 2, Candidate 1 under the truck load that was used in the experimental program. The field test loading consisted of two main phases: Phase 1 loading as based on the culvert being loaded with the lift axle of the truck in the up position; and Phase 2 loaded the culvert with the lift axle down. The wheel line of the truck was first run over the line of gauges below.  Next, the tests in each phase were also repeated for the case where the truck centerline coincided with the line of gauges.  The table below summarizes the loading cases. Test Load Case Drop Axle Configuration Axle of Truck Placed on each Load Point* Wheel Or Truck Centerline Placed Over Line of Gauges 1 Up 1 Wheel 2 Up 3 Wheel 3 Up 4 Wheel 4 Down 1 Wheel 5 Down 2 Wheel 6 Down 3 Wheel 7 Down 4 Wheel 8 Up 1 Truck 9 Up 3 Truck 10 Up 4 Truck 11 Down 1 Truck 12 Down 2 Truck 13 Down 3 Truck 14 Down 4 Truck *Axles numbered consecutively from steering axle to rear axle Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 21. The load configuration of the experimental truck for both phases is shown in Figure 22 and Figure 23. Â
Appendix K â Calibration Information Kâ18 Figure 17 â Culvert Plan View (Skewed) Figure 18 â Culvert Typical SectionÂ
Appendix K â Calibration Information Kâ19 1.2.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 19 below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 19 â Isometric View of 3D LUSAS Model (M2C1) Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 24 and Figure 25.  In each of the graphs, the vertical axis represents either the stress at strain gauge locations.  The horizontal axis represents the load locations for each of the six load positions shown in Figure 20.  For all gauge locations, see Figure 30.  In the graphs, the dashed lines represent fieldâcollected data while the solid lines represent the results obtained from the 3D model. Figure 22 and Figure 23 are for the lift axle up and down configurations, respectively, showing each axle placed over each of the marked points with the centerline of the truck centered on the gauge. As can be seen in the representative results shown, the 3D model is significantly conservatively overestimating the stresses, particularly for loads placed over the first cell of the culvert.  It should be noted that the redundant sets of gauges generally produced similar results to one another.Â
Appendix K â Calibration Information Kâ20 Figure 20 â Location of Marks (Location of Axles for each Load Case) (M2C1) Figure 21 â Location of Strain Gages and String Potentiometers (M2C1) Figure 22 â Load Truck Configuration for Phase 1 (lift axle up) (M2C1) Figure 23 â Load Truck Configuration for Phase 2 (lift axle down) (M2C1)Â
Appendix K â Calibration Information Kâ21 Figure 24 â Load Case 10: Lift Axle Up and Axle 4 Truck Centerline over Marked Points (M2C1) â8 â6 â4 â2 0 2 0 0.25 0.5 0.75 1 1.25 1.5 L Test 10, Gauges 1â2 Gauge 1 Gauge 2 Model â15 â10 â5 0 0 0.25 0.5 0.75 1 1.25 1.5 L Test 10, Gauges 5â6 Gauge 5 Gauge 6 Model â5 0 5 10 15 20 0 0.25 0.5 0.75 1 1.25 1.5 L Test 10, Gauges 7â8 Gauge 7 Gauge 8 Model
Appendix K â Calibration Information Kâ22 Figure 25 â Load Case 14: Lift Axle Down and Axle 4 Truck Centerline over Marked Points (M2C1) â8 â6 â4 â2 0 2 4 0 0.25 0.5 0.75 1 1.25 1.5 L Test 14, Gauges 1â2 Gauge 1 Gauge 2 Model â15 â10 â5 0 5 0 0.25 0.5 0.75 1 1.25 1.5 L Test 14, Gauges 5â6 Gauge 5 Gauge 6 Model â5 0 5 10 15 20 0 0.25 0.5 0.75 1 1.25 1.5 L Test 14, Gauges 7â8 Gauge 7 Gauge 8 Model
Appendix K â Calibration Information Kâ23 1.3 Calibration Summary â Model 3, Candidate 1 Model 3, Candidate 1 consists of a singleâcell precast concrete culvert located in Somerset County Pennsylvania and owned by PennDOT (Structure BRKEY 48389).  Additional details of the testing plan and instrumentation can be found in the testing plan document.  Additional details of the testing plan and instrumentation can be found in Appendix F of this document. The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 3, Candidate 1 under the truck load that was used in the experimental program. The field test loading consisted of two main phases: Phase 1 loading as based on the culvert being loaded with the lift axle of the truck in the up position; and Phase 2 loaded the culvert with the lift axle down. The wheel line of the truck was first run over the line of gauges below.  Next, the tests in each phase were also repeated for the case where the truck centerline coincided with the line of gauges.  The table below summarizes the loading cases. Test Load Case Drop Axle Configuration Axle of Truck Placed on each Load Point* Wheel Or Truck Centerline Placed Over Line of Gauges 1 Up 1 Wheel 2 Up 3 Wheel 3 Up 4 Wheel 4 Down 1 Wheel 5 Down 2 Wheel 6 Down 3 Wheel 7 Down 4 Wheel 8 Down ** Truck 9 Up ** Truck *Axles numbered consecutively from steering axle to rear axle **Each axle of the truck was placed over the midspan point on the culvert for these tests Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 30. The load configuration of the experimental truck for both phases is shown in Figure 31 and Figure 32. Â
Appendix K â Calibration Information Kâ24 Figure 26 â Culvert Plan View (Skewed) (M3C1) Figure 27 â Culvert Typical Section (M3C1)Â
Appendix K â Calibration Information Kâ25 1.3.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 28  below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 28 â Isometric View of 3D LUSAS Model Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 33  through Figure 33 .  In each of the graphs, the vertical axis represents either the stress (for strain gauge locations) or displacement (for string potentiometer locations).  The horizontal axis represents the load locations for each of the six load positions shown in Figure 29.  For all gauge locations, see Figure 30.  In the graphs, the dashed lines represent fieldâcollected data while the solid lines represent the results obtained from the 3D model. Figure 33 shows some representative results for the lift axle up configuration showing each axle placed over each of the marked points with the left wheel centered on the gauge line and then with the center of the truck centered over the gauge line. Figure 34 shows results for the lift axle down configuration showing each axle placed over each of the marked points with the left wheel centered on the gauge line and then with the center of the truck centered over the gauge line. As can be seen in Figure 33 and  Figure 34, stresses for the gauge clusters at the top slab show fairly good agreement with more disparity seen at the lower gauge of clusters near the bottom slab.  At that location, the stresses predicted by the 3D model are conservatively higher than what was observed in the field measurements suggesting that more load spreading is occurring than is predicted by the model. Â
Appendix K â Calibration Information Kâ26 Figure 29 â Location of Marks (Location of Axles for each Load Case) (M3C1) Figure 30 â Location of Strain Gages and String Potentiometers (M3C1)Â
Appendix K â Calibration Information Kâ27 Figure 31 â Load Truck Configuration for Phase 1 (lift axle up) (M3C1) Figure 32 â Load Truck Configuration for Phase 2 (lift axle down) (M3C1)Â
Appendix K â Calibration Information Kâ28 Figure 33 â Model 3 Results for Test 2 (Axle 3), Lift Axle Up (M3C1) â10 â5 0 5 10 15 20 25 30 0 0.25 0.5 0.75 1 L Test 2, Gauges 1â2 Gauge 1 Gauge 2 Model â10 â5 0 5 10 15 0 0.25 0.5 0.75 1 L Test 2, Gauges 3â4 Gauge 3 Gauge 4 Model â15 â10 â5 0 5 0 0.25 0.5 0.75 1 L Test 2, Gauges 7â8 Gauge 7 Gauge 8 Model
Appendix K â Calibration Information Kâ29 Figure 34 â Model 3 Results for Test 6 (Axle 3), Lift Axle Down (M3C1) â30 â25 â20 â15 â10 â5 0 5 10 15 20 0 0.25 0.5 0.75 1 L Test 6, Gauges 1â2 Gauge 1 Gauge 2 Model â10 â5 0 5 10 0 0.25 0.5 0.75 1 L Test 6, Gauges 3â4 Gauge 3 Gauge 4 Model â12 â10 â8 â6 â4 â2 0 0 0.25 0.5 0.75 1 L Test 6, Gauges 7â8 Gauge 7 Gauge 8 Model
Appendix K â Calibration Information Kâ30 1.4 Calibration Summary â Model 4, Candidate 1 Model 4, Candidate 1 consists of a threeâsided precast concrete arch culvert (CONSPANâtype) located in the state of Ohio and owned by the Ohio DOT.  Additional details of the testing plan and instrumentation can be found in Appendix F of this document.   The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 4, Candidate 1 under the truck load that was used in the experimental program. The wheel line of the truck was first run over the line of gauges below (Test   1â3).  Next, the tests in each phase were also repeated for the case where the truck centerline coincided with the line of gauges (Test Load Cases 4â6).  The table below summarizes the loading cases. Test Load Case Drop Axle Configuration Axle of Truck Placed on each Load Point* Wheel Or Truck Centerline Placed Over Line of Gauges 1 N/A 1 Wheel 2 N/A 2 Wheel 3 N/A 3 Wheel 4 N/A 1 Truck 5 N/A 2 Truck 6 N/A 3 Truck *Axles numbered consecutively from steering axle to rear axle Plan and crossâsectional views are shown in Figure 35 and Figure 36, respectively. Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 39. The load configuration of the experimental truck for both phases is shown in Figure 40.Â
Appendix K â Calibration Information Kâ31 Figure 35 â Culvert Plan View  Figure 36 â Culvert Typical SectionÂ
Appendix K â Calibration Information Kâ32 1.4.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 37 below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 37 â Isometric View of 3D LUSAS Model (M4C1) Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 41 through Figure 46. In each of the graphs, the vertical axis represents experimentally measured or modeled stress.  The horizontal axis represents the load locations for each of the five load positions shown in Figure 38.  For all gauge locations, see Figure 39.  In the graphs, the dashed lines represent fieldâcollected data while the solid lines represent the results obtained from the 3D model. As can be seen, good agreement is seen in the axial gauges (1 & 2) with the axles at midspan although significant differences are seen with the lead axle at the ¾ point.  At gauges 5 and 6 where a combination of axial and flexural stresses exist, good agreement is observed at all loading points.  Â
Appendix K â Calibration Information Kâ33 Figure 38 â Location of Marks (Location of Axles for each Load Case) (M4C1) Figure 39 â Location of Strain Gages (M4C1)Â
Appendix K â Calibration Information Kâ34 Figure 40 â Load Truck Configuration for Phase 1 (No lift axle) (M4C1)Â
Appendix K â Calibration Information Kâ35 Figure 41 â Load Test 4 (Gauges 1â6) (: Axle 1 over Marked Points (Truck Centered) (M4C1) â20 â15 â10 â5 0 5 0 0.25 0.5 0.75 1 L Test 4, Gauges 1â2 Gauge 1 Gauge 2 Model â20 â10 0 10 20 30 0 0.25 0.5 0.75 1 L Test 4, Gauges 3â4 Gauge 3 Gauge 4 Model â20 â10 0 10 20 0 0.25 0.5 0.75 1 L Test 4, Gauges 5â6 Gauge 5 Gauge 6 Model
Appendix K â Calibration Information Kâ36 Figure 42 â Load Test 4 (Gauges 7â10) (: Axle 1 over Marked Points (Truck Centered) (M4C1) â20 0 20 40 0 0.25 0.5 0.75 1 L Test 4, Gauges 7â8 Gauge 7 Gauge 8 Model â20 â15 â10 â5 0 5 0 0.25 0.5 0.75 1 L Test 4, Gauges 9â10 Gauge 9 Gauge 10 Model
Appendix K â Calibration Information Kâ37 Figure 43 â Load Test 5 (Gauges 1â6): Axle 2 over Marked Points (Truck Centered) (M4C1) â20 â15 â10 â5 0 5 10 15 0 0.25 0.5 0.75 1 L Test 5, Gauges 1â2 Gauge 1 Gauge 2 Model â30 â20 â10 0 10 20 0 0.25 0.5 0.75 1 L Test 5, Gauges 3â4 Gauge 3 Gauge 4 Model â15 â10 â5 0 5 10 15 0 0.25 0.5 0.75 1 L Test 5, Gauges 5â6 Gauge 5 Gauge 6 Model
Appendix K â Calibration Information Kâ38 Figure 44 â Load Test 5 (Gauges 7â10): Axle 2 over Marked Points (Truck Centered) (M4C1) â20 â10 0 10 20 30 0 0.25 0.5 0.75 1 L Test 5, Gauges 7â8 Gauge 7 Gauge 8 Model â20 â15 â10 â5 0 5 10 0 0.25 0.5 0.75 1 L Test 5, Gauges 9â10 Gauge 9 Gauge 10 Model
Appendix K â Calibration Information Kâ39 Figure 45 â Load Test 6 (Gauges 1â6): Axle 3 over Marked Points (Truck Centered) (M4C1) â15 â10 â5 0 5 10 15 20 0 0.25 0.5 0.75 1 L Test 6, Gauges 1â2 Gauge 1 Gauge 2 Model â20 â10 0 10 20 30 0 0.25 0.5 0.75 1 L Test 6, Gauges 3â4 Gauge 3 Gauge 4 Model â20 â10 0 10 20 0 0.25 0.5 0.75 1 L Test 6, Gauges 5â6 Gauge 5 Gauge 6 Model
Appendix K â Calibration Information Kâ40 Figure 46 â Load Test 6 (Gauges 7â10): Axle 3 over Marked Points (Truck Centered) (M4C1) â20 â10 0 10 20 30 40 0 0.25 0.5 0.75 1 L Test 6, Gauges 7â8 Gauge 7 Gauge 8 Model â20 â15 â10 â5 0 5 10 0 0.25 0.5 0.75 1 L Test 6, Gauges 9â10 Gauge 9 Gauge 10 Model
Appendix K â Calibration Information Kâ41 1.5 Calibration Summary â Model 5, Candidate 1 Model 5, Candidate 1 consists of a corrugated steel arch culvert with a span of 23 feet located in the Lower Paxton Township, Pennsylvania in a private housing development. Additional details of the testing plan and instrumentation can be found in Appendix F of this document. The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 5, Candidate 1 under the truck load that was used in the experimental program. The wheel line of the truck was first run over the line of gauges below.  Next, the tests in each phase were also repeated for the case where the truck centerline coincided with the line of gauges.  The table below summarizes the loading cases. Test Load Case Drop Axle Configuration Axle of Truck Placed on each Load Point* Wheel Or Truck Centerline Placed Over Line of Gauges 1 N/A 1 Wheel 2 N/A 2 Wheel 3 N/A 3 Wheel 4 N/A 1 Truck 5 N/A 2 Truck 6 N/A 3 Truck *Axles numbered consecutively from steering axle to rear axle Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 62. The load configuration of the experimental truck is shown in Figure 52. Â
Appendix K â Calibration Information Kâ42 North Upstream Down stream Figure 47 â Culvert Plan View Schematic (Skewed) (M5C1) Figure 48 â Culvert Typical Section (M5C1)Â
Appendix K â Calibration Information Kâ43 1.5.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 49  below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 49 â Isometric View of 3D LUSAS Model (M5C1) Calibration Results The results shown in Figure 53 through Figure 54 are for the second series of test loadings for Model 5.  The calibration for this model shows good agreement in the shape of the response curves for the various load points.  Good agreement was obtained in the displacements between the 3D analyses and the field test results but as discussed herein, greater differences were observed in the stress value comparisons. Figure 50 â Location of Marks (Location of Axles for each Load Case) (M5C1)Â
Appendix K â Calibration Information Kâ44 Figure 51 â Location of Strain Gages and String Potentiometers (M5C1) Figure 52 â Load Truck Configuration (M5C1)Â
Appendix K â Calibration Information Kâ45 Figure 53 â Load Case 2: Gauges 1 and 3 (M5C1)Â
Appendix K â Calibration Information Kâ46 Figure 54 â Load Case 2: Gauges 5, 7, and 9 (M5C1)Â
Appendix K â Calibration Information Kâ47 1.6 Calibration Summary â Model 6, Candidate 2 Model 6, Candidate 2 consists of a corrugated aluminum arch culvert Carroll Township, PA.  Additional details of the testing plan and instrumentation can be found in Appendix F of this document.  The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 6, Candidate 2 under the truck load that was used in the experimental program. The wheel line of the truck was run over the line of gauges below.  Due to the heavy skew and the narrow roadway between guardrails, the load configuration with the centerline of the truck could not be included for this model.  Furthermore, only the heavy rear axle could be located over each of the quarterâpoint loading locations.  For a culvert of such a short span, this is expected to be the controlling loading case.  Due to the limited number of loadings to be applied in this single load case, the tests were repeated three times. Test Load Case Drop Axle Configuration Axle of Truck Placed on each Load Point* Wheel Or Truck Centerline Placed Over Line of Gauges 1 N/A 1 Wheel *Axles numbered consecutively from steering axle to rear axle Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 59. The load configuration of the experimental truck is shown in Figure 60. Figure 55 â Culvert Plan View Schematic (Skewed) (M6C2)Â
Appendix K â Calibration Information Kâ48 Figure 56 â Culvert Typical Section (M6C2) 1.6.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 57 below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 57 â Isometric View of 3D LUSAS Model (M6C2) Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 61. In each of the graphs, the vertical axis represents either the stress at strain gauge locations.  The horizontal axis represents the load locations for each of the three load positions shown in Figure 58.  For all gauge locations, see Figure 59.  In the graphs, the dashed lines represent fieldâcollected data while the solid lines represent the results obtained from the 3D model. The stress comparisons in Figure 61 show similar behavior between the 3D model and the experimental results. Â
Appendix K â Calibration Information Kâ49 Figure 58 â Location of Marks (Location of Axles for each Load Case) (M6C2) Figure 59 â Location of Strain Gages and String Potentiometers (M6C2) Figure 60 â Load Truck Configuration (M6C2)Â
Appendix K â Calibration Information Kâ50 Figure 61 â Load Case 1: Rear Wheel Placed Over Each Loading (Quarter) Point (M6C2) â120 â100 â80 â60 â40 â20 0 20 40 60 80 0 0.25 0.5 L Gauge 4 Test 1 Test 2 Test 3 Model â80 â60 â40 â20 0 20 0 0.25 0.5 L Gauge 6 Test 1 Test 2 Test 3 Model â60 â40 â20 0 20 40 60 0 0.25 0.5 L Gauge 7 Test 1 Test 2 Test 3 Model
Appendix K â Calibration Information Kâ51 1.7 Calibration Summary â Model 7, Candidate 1 Model 7, Candidate 1 consists of a corrugated aluminum arch culvert in Attleboro, Massachusetts.  Additional details of the field testing plan and instrumentation can be in Appendix F of this document.  Multiple approaches were taken to determine the best course of modeling the structure in LUSAS and then using the selected approach to carry out the calibration effort.  This effort and the lessons learned were then used to shape the approach used to model and calibrate the remaining corrugated metal culverts.  A detailed overview of the modeling approach used in the 3D modeling of this culvert is provided following the results along with comparisons between the before and after paving conditions. Experimental Data is recorded and presented in forms of stresses and displacements. The location of the strain gages and the string potentiometers are depicted in Figure 62.  The load configuration of the experimental truck is shown in Figure 63.  Phase 1 is the truck configuration for the loading prior to paving and Phase 2 is the configuration for the loading after paving was completed. The calibration summary herein, presents the LUSAS results (3âD finite element analysis) of Model 7, Candidate 1 under the truck load that was used in the experimental program. The wheel line of the truck was run over the line of gauges below.  Because the culvert is composed of corrugated metal rib sections, the gauges were mounted in clusters to capture both the crest and the valley strains in the corrugations.  Adjacent ribs were instrumented for redundancy. Figure 62 â Location of Strain Gages and String Potentiometers (M7C1)Â
Appendix K â Calibration Information Kâ52 1.8 Truck Wheel Load and Spacing Data Phase 1  Phase 2 Figure 63 â Truck Loading Configurations for Phases 1 and 2Â
Appendix K â Calibration Information Kâ53 Figure 64 â Culvert Plan View Schematic with Gauge Cluster Locations  (M7C1) Load Set 1 thru 7.Â
Appendix K â Calibration Information Kâ54 Load Set 8 thru 15.  Figure 65 â M7C1 Schematics of Loading for Each Load CaseÂ
Appendix K â Calibration Information Kâ55 1.8.1 3D LUSAS Model An isometric view of the 3D LUSAS model is shown in Figure 57 below.  In general, the 3D models were developed using the parameters described in Appendix B of this document.  Figure 66 â Isometric View of 3D LUSAS Model (M7C1) Calibration Results Comparisons between the field data stresses and displacements as compared to the 3D model predicted values are shown in Figure 67 through Figure 81.  A comparison between the Phase 1 and Phase 2 results follows in the next section. In each of the graphs, the vertical axis represents the stress at strain gauge locations.  The horizontal axis represents the load locations for each of the load positions shown in Figure 65. For all gauge locations, see Figure 64in the graphs, the dashed lines represent fieldâcollected data while the solid lines represent the results obtained from the 3D model.Â
Appendix K â Calibration Information Kâ56 Figure 67 â Results of Test 1âN1 Culvert 7 (15 loadâcases) for Gages 1 thru 4 (Gage Cluster 5) Figure 68 â Results of Test 1âN1 Culvert 7 (15 loadâcases) for Gages 5 thru 8 (Gage Cluster 4) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Gage 1â Field Gage 2â Field Gage 3â Field Gage 4â Field Gage 1â Lusas Gage 2â Lusas Gage 3â Lusas Gage 4â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Gage 5â Field Gage 6â Field Gage 7â Field Gage 8â Field Gage 5â Lusas Gage 6â Lusas Gage 7â Lusas Gage 8â Lusas
Appendix K â Calibration Information Kâ57 Figure 69 â Results of Test 1âN1 Culvert 7 (15 loadâcases) for Gages 9 thru 12 (Gage Cluster 3) Figure 70 â Results of Test 1âN1 Culvert 7 (15 loadâcases) for Gages 13 thru 16 (Gage Cluster 2) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Gage 9â Field Gage 10â Field Gage 11â Field Gage 12â Field Gage 9â Lusas Gage 10â Lusas Gage 11â Lusas Gage 12â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Gage 13â Field Gage 14â Field Gage 15â Field Gage 16â Field Gage 13â Lusas Gage 14â Lusas Gage 15â Lusas Gage 16â Lusas
Appendix K â Calibration Information Kâ58 Figure 71 â Results of Test 1âN1 Culvert 7 (15 loadâcases) for Gages 17 thru 20 (Gage Cluster 1) Figure 72 â Results of Test 1âN2 Culvert 7 (15 loadâcases) for Gages 1 thru 4 (Gage Cluster 5) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Gage 17â Field Gage 18â Field Gage 19â Field Gage 20â Field Gage 17â Lusas Gage 18â Lusas Gage 19â Lusas Gage 20â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Gage 1â Field Gage 2â Field Gage 3â Field Gage 4â Field Gage 1â Lusas Gage 2â Lusas Gage 3â Lusas Gage 4â Lusas
Appendix K â Calibration Information Kâ59 Figure 73 â Results of Test 1âN2 Culvert 7 (15 loadâcases) for Gages 5 thru 8 (Gage Cluster 4) Figure 74 â Results of Test 1âN2 Culvert 7 (15 loadâcases) for Gages 9 thru 12 (Gage Cluster 3) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Gage 5â Field Gage 6â Field Gage 7â Field Gage 8â Field Gage â5 Lusas Gage 6â Lusas Gage 7â Lusas Gage 8â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Gage 9â Field Gage 10â Field Gage 11â Field Gage 12â Field Gage 9â Lusas Gage 10â Lusas
Appendix K â Calibration Information Kâ60 Figure 75 â Results of Test 1âN2 Culvert 7 (15 loadâcases) for Gages 13 thru 16 (Gage Cluster 2) Figure 76 â Results of Test 1âN2 Culvert 7 (15 loadâcases) for Gages 17 thru 20 (Gage Cluster 1) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Gage 13â Field Gage 14â Field Gage 15â Field Gage 16â Field Gage 13â Lusas Gage 14â Lusas Gage 15â Lusas Gage 16â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Gage 17â Field Gage 18â Field Gage 19â Field Gage 20â Field Gage 17â Lusas Gage 18â Lusas Gage 19â Lusas Gage 20â Lusas
Appendix K â Calibration Information Kâ61 Figure 77 â Results of Test 1âN3 Culvert 7 (15 loadâcases) for Gages 1 thru 4 (Gage Cluster 5) Figure 78 â Results of Test 1âN3 Culvert 7 (15 loadâcases) for Gages 5 thru 8 (Gage Cluster 4) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Gage 1â Field Gage 2â Field Gage 3â Field Gage 4â Field Gage 1â Lusas Gage 2â Lusas Gage 3â Lusas Gage 4â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Gage 5â Field Gage 6â Field Gage 7â Field Gage 8â Field Gage 5â Lusas Gage 6â Lusas Gage 7â Lusas Gage 8â Lusas
Appendix K â Calibration Information Kâ62 Figure 79 â Results of Test 1âN3 Culvert 7 (15 loadâcases) for Gages 9 thru 12 (Gage Cluster 3) Figure 80 â Results of Test 1âN3 Culvert 7 (15 loadâcases) for Gages 13 thru 16 (Gage Cluster 2) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Gage 9â Field Gage 10â Field Gage 11â Field Gage 12â Field Gage 9â Lusas Gage 10â Lusas Gage 11â Lusas Gage 12â Lusas â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Gage 13â Field Gage 14â Field Gage 15â Field Gage 16â Field Gage 13â Lusas Gage 14â Lusas Gage 15â Lusas Gage 16â Lusas
Appendix K â Calibration Information Kâ63 Figure 81 â Results of Test 1âN3 Culvert 7 (15 loadâcases) for Gages 17 thru 20 (Gage Cluster 1) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Gage 17â Field Gage 18â Field Gage 19â Field Gage 20â Field Gage 17â Lusas Gage 18â Lusas Gage 19â Lusas Gage 20â Lusas
Appendix K â Calibration Information Kâ64 1.9 Details on Model 7 Calibration  This section documents the process used to model and calibrate Model 7, the long span corrugated metal culvert located in Attleboro, MA.  Multiple approaches were taken to determine the best course of modeling the structure in LUSAS and then using the selected approach to carry out the calibration effort.  This effort and the lessons learned were then used to shape the approach used to model and calibrate the remaining corrugated metal culverts.  These modeling methods can also serve as a guide for further research in the 3D modeling of culverts using FEA. The experimental program for Culvert 7 consists of two main phases: Phase 1 loading the culvert prior to placement of the pavement; and Phase 2, loading the culvert after the pavement is placed. Each phase included three main sets of loading (Figure 82): N1, with the center of truck over the center of culvert (and gages); N2, with the left wheel line of the truck centered over the centerline of the culvert; and N3, with the right wheel line of the truck centered over the centerline of the culvert.  Five clusters of four gages (20 gages total) are mounted on the lower face of the culvert as shown in Figure 62. For each test, one of the axles of the truck (3 axles) is placed over one of the gage clusters, producing 15 loading configurations for each set of loading Figure 82 â M7C1 Plan View: Showing Location of Gages and Truck Positioning for Each Set of Test Model 7 intends to capture the behavior of deep corrugated metal arches. Several approaches are considered to accurately capture the behavior of corrugations including shell elements with orthotropic material properties, shell elements with stiffeners in the direction of corrugations, and double thin shell elements with orthotropic material properties.  Table 1 summarizes each approach with assigned material properties. The following is a summary of each model:Â ï· Model 1 is the actual corrugation of Culvert 7. ï· Model 2 presents the approach where a stiffener is added to the shell to represent the corrugation. ï· Model 3 presents an approach where the thickness and modulus of elasticity in strong axis (E x) is defined so that both axial rigidity and flexural rigidity in the strong axis match those of the actual corrugation. Modulus of elasticity in weak axis (E y) is defined based on new thickness to capture the flexural behavior in the weak axis and E xy is defined based on axial adjustment.
Appendix K â Calibration Information Kâ65Â ï· Model 4 is similar to Model 3, except that E y is adjusted based on axial properties and E xy is adjusted based on flexural (warping) properties. ï· Model 5 is also similar to Model 3, except that both E y and E xy are adjusted based on flexural properties. ï· Model 6 presents the approach where two overlapping shell elements are defined to capture the behavior of the corrugation. The thickness and moduli of elasticity of each shell element is defined so that the superâimposition of both elements would capture all of the rigidity components of the corrugated metal sheets. Table 1 â Material and Section Properties of Models for Modeling the Corrugation (M7C1)Â
Appendix K â Calibration Information Kâ66 The proposed approaches are used to create six culverts (without surrounding soil). Each culvert is loaded with an axial and lateral force and the deformation and stresses at each culvert is compared (Figure 83). Table 2 summarizes the results of each culvert. The green values show close match to actual corrugation, while red or grey values show mismatches.  Results of this study suggest that any of the Model 3, 4, or 5 can adequately capture the behavior of the corrugation. For calibration, Model 3 was selected as the best approach.  Figure 83 â Deformation Comparison of Six Proposed Models (M7C1) Calibration and PostâProcessing Using the approach of Model 3, the culvert is modeled using orthotropic material properties. Calibration of the model is carried out by changing the overlay material properties. Given that for Test 1, the culvert was loaded prior to casting the pavement, the loads where transferred to the culvert through compacted overlay. The modulus of elasticity of 7500 ksf is adopted for the overlay material (for well graded coarse material and crushed stone).  In order to make sure that the plastic strains of the soil are not carried to the next load case, each load case is run separately where for each load case, the gravity is applied to model and then the live load is applied to model. Then, the results of the gravity are subtracted from the final results to capture the effect of live load.  Given that shell elements do not have the same section properties as the actual corrugated metal sheet, for postâprocessing the Force/Moment output is abstracted from the associated nodes and the following equation is used to derive the actual stresses at the location of the strain gages:Â
Appendix K â Calibration Information Kâ67 ð ð ð´ ðð¥ ð¼ where:  ð  stress along the direction of strain gages (strong axis);  ð  Axial force transferred in the direction of the strong axis (kip/in);  ð´  area of the cross section per unit length = ð /ð ð¡ ; ð  carried moment in the direction of strong axis (kâin/in);  ð¦  half of the depth of corrugation; ð¼  moment of inertia of a unit length of corrugated metal sheet= ;  ð  pitch of the corrugation;  ð  length of the arch along the corrugation. Â
Appendix K â Calibration Information Kâ68 Model 7 Results Before and After Paving Introduction Model 7 is a corrugated metal box culvert located in Attleboro, Massachusetts. The Research Team was able to coordinate with MASSDOT and the culvert contractor to instrument and test this culvert under construction with the intent that the effects of paving on the response of the culvert could be captured. This memorandum presents the LUSAS results (3-D finite element analysis) of Model 7, Candidate 1 under the truck load that was used in the experimental program. For this culvert, the experimental program consisted of two main phases: Phase 1 loading the culvert prior to placement of the pavement; and Phase 2, loading the culvert after the pavement is placed. The results herein show the force effects obtained both prior to and after paving. The calibration and approach to the 3-D modeling of this culvert in LUSAS is documented in detail in Interim Report No. 3. Culvert Loading and Instrumentation Each phase included three main sets of loading (Figure 1): N1, with the center of truck over the center of culvert (and gages); N2, with the left wheel line of the truck centered over the centerline of the culvert; and N3, with the right wheel line of the truck centered over the centerline of the culvert. Five clusters of four gages (20 gages total) are mounted on the lower face of the culvert as shown in Figure 3. For each test, one of the axles of the truck (3 axles) is placed over one of the gage clusters, producing 15 loading configurations for each set of loading. Figure 84 â M7C1 Plan View: Showing Location of Gages and Truck Positioning for Each Set of Test Figure 85 â Truck Dimensions for each Phase of TestingÂ
Appendix K â Calibration Information Kâ69 Figure 86 â Instrumentation LocationsÂ
Appendix K â Calibration Information Kâ70 (a) Load Set 1 thru 7. (b) Load Set 8 thru 15. Figure 87 â Schematics of Loading for Each Load Case for Culvert 7 Results Before and After Paving While the results presented in Interim Report Number 3 document the selection of a 3âD modeling scheme and the corresponding results from Test 1 (prior to paving), the results herein illustrate the differences in the stresses at each of the strain gauge locations as measured in the field.  Similar comparisons were made between the stresses at each location as obtained in the 3âD LUSAS models. In the figures below, Test 1 results are shown in dashed lines and represent the condition without pavement and Test 2 results are shown in solid lines and represent the culvert after paving. The results show a significant reduction in measured strains.  Gage Cluster 3 at midspan shows a 33% reduction in peak stress under the live load.  Gage Cluster 4 at the shoulder, the other critical location, shows a 50% reduction.  These reductions are also notable as the pavement was placed on high quality, highly compacted fill being prepared for interstate traffic.  Pavements over softer soils will show a more significant benefit with the same paving.  We conclude that live load ratings can be improved by including the effects of pavement.  A 3âD model is not required to analyze live load response associated with a paved surface. The 2âD CANDE software has been modified to allow the user to specify a paved surface (See Interim Report Number 3, Section 5.1.2.2 Updates to the CANDE Toolbox).  A parametric study and recommendations on the inclusion of pavement was documented as part of Interim Report Number 2, Section 4.1.2.4.1.Â
Appendix K â Calibration Information Kâ71 Figure 88 â Model 7 Before and After Paving: Test N1, Gauges 1â4 (Cluster 5) Figure 89 â Model 7 Before and After Paving: Test N1, Gauges 5â8 (Cluster 4) â7.000 â5.000 â3.000 â1.000 1.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 5) Gage 1â Test 1 Gage 2â Test 1 Gage 3â Test 1 Gage 4â Test 1 Gage 1â Test 2 Gage 2â Test 2 Gage 3â Test 2 Gage 4â Test 2 â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 4) Gage 5â Test 1 Gage 6â Test 1 Gage 7â Test 1 Gage 8â Test 1 Gage 5â Test 2 Gage 6â Test 2 Gage 7â Test 2 Gage 8â Test 2
Appendix K â Calibration Information Kâ72 Figure 90 â Model 7 Before and After Paving: Test N1, Gauges 9â12 (Cluster 3) Figure 91 â Model 7 Before and After Paving: Test N1, Gauges 13â16 (Cluster 2) â7.000 â5.000 â3.000 â1.000 1.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 3) Gage 9â Test 1 Gage 10â Test 1 Gage 11â Test 1 Gage 12â Test 1 Gage 9â Test 2 Gage 10â Test 2 Gage 11â Test 2 Gage 12â Test 2 â7.000 â5.000 â3.000 â1.000 1.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 2) Gage 13â Test 1 Gage 14â Test 1 Gage 15â Test 1 Gage 16â Test 1 Gage 13â Test 2 Gage 14â Test 2 Gage 15â Test 2 Gage 16â Test 2
Appendix K â Calibration Information Kâ73 Figure 92 â Model 7 Before and After Paving: Test N1, Gauges 17â20 (Cluster 1) Figure 93 â Model 7 Before and After Paving: Test N2, Gauges 1â4 (Cluster 5) â7.000 â5.000 â3.000 â1.000 1.000 3.000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 1) Gage 17â Test 1 Gage 18â Test 1 Gage 19â Test 1 Gage 20â Test 1 Gage 17â Test 2 Gage 18â Test 2 Gage 19â Test 2 Gage 20â Test 2 â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 5) Gage 1â Test 1 Gage 2â Test 1 Gage 3â Test 1 Gage 4â Test 1 Gage 1â Test 2 Gage 2â Test 2 Gage 3â Test 2 Gage 4â Test 2
Appendix K â Calibration Information Kâ74 Figure 94 â Model 7 Before and After Paving: Test N2, Gauges 5â8 (Cluster 4) Figure 95 â Model 7 Before and After Paving: Test N2, Gauges 9â2 (Cluster 3) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 4) Gage 5â Test 1 Gage 6â Test 1 Gage 7â Test 1 Gage 8â Test 1 Gage 5â Test 2 Gage 6â Test 2 Gage 7â Test 2 Gage 8â Test 2 â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 3) Gage 9â Test 1 Gage 10â Test 1 Gage 11â Test 1 Gage 12â Test 1 Gage 9â Test 2 Gage 10â Test 2 Gage 11â Test 2 Gage 12â Test 2
Appendix K â Calibration Information Kâ75 Figure 96 â Model 7 Before and After Paving: Test N2, Gauges 13â16 (Cluster 1) Figure 97 â Model 7 Before and After Paving: Test N2, Gauges 17â20 (Cluster 1) â7.000 â5.000 â3.000 â1.000 1.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 2) Gage 13â Test 1 Gage 14â Test 1 Gage 15â Test 1 Gage 16â Test 1 Gage 13â Test 2 Gage 14â Test 2 Gage 15â Test 2 Gage 16â Test 2 â7.000 â5.000 â3.000 â1.000 1.000 3.000 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 1) Gage 17â Test 1 Gage 18â Test 1 Gage 19â Test 1 Gage 20â Test 1 Gage 17â Test 2 Gage 18â Test 2 Gage 19â Test 2 Gage 20â Test 2
Appendix K â Calibration Information Kâ76 Figure 98 â Model 7 Before and After Paving: Test N3, Gauges 1â4 (Cluster 5) Figure 99 â Model 7 Before and After Paving: Test N3, Gauges 5â8 (Cluster 4) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 5) Gage 1â Test 1 Gage 2â Test 1 Gage 3â Test 1 Gage 4â Test 1 Gage 1â Test 2 Gage 2â Test 2 Gage 3â Test 2 Gage 4â Test 2 â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 4) Gage 5â Test 1 Gage 6â Test 1 Gage 7â Test 1 Gage 8â Test 1 Gage 5â Test 2 Gage 6â Test 2 Gage 7â Test 2 Gage 8â Test 2
Appendix K â Calibration Information Kâ77 Figure 100 â Model 7 Before and After Paving: Test N3, Gauges 9â12 (Cluster 3) Figure 101 â Model 7 Before and After Paving: Test N3, Gauges 13â16 (Cluster 2) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 3) Gage 9â Test 1 Gage 10â Test 1 Gage 11â Test 1 Gage 12â Test 1 Gage 9â Test 2 Gage 10â Test 2 Gage 11â Test 2 Gage 12â Test 2 â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 2) Gage 13â Test 1 Gage 14â Test 1 Gage 15â Test 1 Gage 16â Test 1 Gage 13â Test 2 Gage 14â Test 2 Gage 15â Test 2 Gage 16â Test 2
Appendix K â Calibration Information Kâ78 Figure 102 â Model 7 Before and After Paving: Test N3, Gauges 17â20 (Cluster 1) â7.000 â6.000 â5.000 â4.000 â3.000 â2.000 â1.000 0.000 1.000 2.000 3.000 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 St re ss  (k si) Test No. Stress Comparison (Gage Cluster 1) Gage 17â Test 1 Gage 18â Test 1 Gage 19â Test 1 Gage 20â Test 1 Gage 17â Test 2 Gage 18â Test 2 Gage 19â Test 2 Gage 20â Test 2
Lâ1 Appendix L â Caltrans ModelsâLRFRâLFR Comparisons Appendix L â LRFR/LFR Rating Comparisons in BrDR Using Caltrans Models This appendix provides a comparison of a select set of culverts provided by Caltrans in the software package AASHTOWare BrDR. The runs were made in Version 6.8.2 of the software.Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ2  Naming convention for âCulvert Nameâ CX WWxHH; XX DDDD CS â single cell culvert CD â double cell culvert WW â cell width HH â Cell height XX â maximum fill height DDDD â culvert year   For Example The culvert name âCS10x8;10 2002â Is a single cell culvert with a 10â cell width, 8â cell height; a maximum fill of 10â and was designed in 2002.  Notes: â In the tables on the following pages, the ratio represents the ratio of the LFR rating to the LRFR rating. In cases where the ratio is less than one (i.e. the LFR rating is less than the LRFR rating) the column is highlighted in red. â The LFR ratings were performed with the HS20â44 vehicle with a scale factor of 1.25  Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ3  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR 42 CS10x8;10 2002 HLâ93 (US) 0 0.609 0.789 HS 20â44 0.544 0.908 0.89 1.15  CS10x8;10 2002 HLâ93 (US) 0.5 0.597 0.774 HS 20â44 0.513 0.856 0.86 1.11  CS10x8;10 2002 HLâ93 (US) 1 0.579 0.75 HS 20â44 0.481 0.804 0.83 1.07  CS10x8;10 2002 HLâ93 (US) 1.5 0.558 0.723 HS 20â44 0.487 0.813 0.87 1.12  CS10x8;10 2002 HLâ93 (US) 1.9 0.539 0.699 HS 20â44 0.459 0.767 0.85 1.10  CS10x8;10 2002 HLâ93 (US) 2 1.002 1.298 HS 20â44 1.023 1.708 1.02 1.32  CS10x8;10 2002 HLâ93 (US) 4 1.472 1.908 HS 20â44 2.109 3.523 1.43 1.85  CS10x8;10 2002 HLâ93 (US) 7 1.752 2.271 HS 20â44 3.188 5.323 1.82 2.34  CS10x8;10 2002 HLâ93 (US) 9 1.615 2.094 HS 20â44 3.421 5.713 2.12 2.73  CS10x8;10 2002 HLâ93 (US) 10 1.413 1.832 HS 20â44 3.297 5.506 2.33 3.01 43 CS10x8;5 1933 HLâ93 (US) 0 0.878 1.139 HS 20â44 0.778 1.299 0.89 1.14  CS10x8;5 1933 HLâ93 (US) 0.5 0.847 1.098 HS 20â44 0.743 1.24 0.88 1.13  CS10x8;5 1933 HLâ93 (US) 1 0.813 1.054 HS 20â44 0.707 1.181 0.87 1.12  CS10x8;5 1933 HLâ93 (US) 1.5 0.776 1.006 HS 20â44 0.727 1.213 0.94 1.21  CS10x8;5 1933 HLâ93 (US) 1.9 0.745 0.965 HS 20â44 0.695 1.16 0.93 1.20  CS10x8;5 1933 HLâ93 (US) 2 0.587 0.761 HS 20â44 0.735 1.228 1.25 1.61  CS10x8;5 1933 HLâ93 (US) 3 0.641 0.831 HS 20â44 1.081 1.805 1.69 2.17  CS10x8;5 1933 HLâ93 (US) 4 0.631 0.818 HS 20â44 1.288 2.152 2.04 2.63  CS10x8;5 1933 HLâ93 (US) 5 0.522 0.676 HS 20â44 1.382 2.308 2.65 3.41 44 CS10x8;8 1966 HLâ93 (US) 0 0.642 0.833 HS 20â44 0.635 1.06 0.99 1.27  CS10x8;8 1966 HLâ93 (US) 0.5 0.641 0.831 HS 20â44 0.604 1.009 0.94 1.21  CS10x8;8 1966 HLâ93 (US) 1 0.655 0.849 HS 20â44 0.573 0.957 0.87 1.13  CS10x8;8 1966 HLâ93 (US) 1.5 0.653 0.847 HS 20â44 0.587 0.98 0.90 1.16  CS10x8;8 1966 HLâ93 (US) 1.9 0.649 0.842 HS 20â44 0.559 0.934 0.86 1.11  CS10x8;8 1966 HLâ93 (US) 2 0.688 0.892 HS 20â44 0.701 1.17 1.02 1.31  CS10x8;8 1966 HLâ93 (US) 4 0.925 1.199 HS 20â44 1.308 2.185 1.41 1.82  CS10x8;8 1966 HLâ93 (US) 6 0.921 1.194 HS 20â44 1.495 2.496 1.62 2.09  CS10x8;8 1966 HLâ93 (US) 7 0.837 1.085 HS 20â44 1.455 2.43 1.74 2.24Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ4  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS10x8;8 1966 HLâ93 (US) 8 0.654 0.848 HS 20â44 1.214 2.028 1.86 2.39 45 CS10x8;10 2010 HLâ93 (US) 0 0.737 0.955 HS 20â44 0.708 1.182 0.96 1.24  CS10x8;10 2010 HLâ93 (US) 0.5 0.741 0.96 HS 20â44 0.677 1.131 0.91 1.18  CS10x8;10 2010 HLâ93 (US) 1 0.744 0.965 HS 20â44 0.646 1.079 0.87 1.12  CS10x8;10 2010 HLâ93 (US) 1.5 0.746 0.968 HS 20â44 0.666 1.112 0.89 1.15  CS10x8;10 2010 HLâ93 (US) 1.9 0.747 0.969 HS 20â44 0.638 1.065 0.85 1.10  CS10x8;10 2010 HLâ93 (US) 2 1.306 1.693 HS 20â44 1.331 2.222 1.02 1.31  CS10x8;10 2010 HLâ93 (US) 4 2.023 2.623 HS 20â44 2.845 4.751 1.41 1.81  CS10x8;10 2010 HLâ93 (US) 7 2.862 3.709 HS 20â44 4.754 7.94 1.66 2.14  CS10x8;10 2010 HLâ93 (US) 9 3.151 4.085 HS 20â44 5.816 9.713 1.85 2.38  CS10x8;10 2010 HLâ93 (US) 10 3.162 4.099 HS 20â44 6.174 10.31 1.95 2.52 46 CS10x8;10 1933 HLâ93 (US) 0 1.358 1.76 HS 20â44 1.108 1.851 0.82 1.05  CS10x8;10 1933 HLâ93 (US) 0.5 1.346 1.745 HS 20â44 1.073 1.791 0.80 1.03  CS10x8;10 1933 HLâ93 (US) 1 1.346 1.745 HS 20â44 1.036 1.731 0.77 0.99  CS10x8;10 1933 HLâ93 (US) 1.9 1.297 1.681 HS 20â44 1.05 1.754 0.81 1.04  CS10x8;10 1933 HLâ93 (US) 2 1.029 1.334 HS 20â44 1.113 1.858 1.08 1.39  CS10x8;10 1933 HLâ93 (US) 3 1.247 1.616 HS 20â44 1.702 2.842 1.36 1.76  CS10x8;10 1933 HLâ93 (US) 5 1.522 1.973 HS 20â44 2.474 4.131 1.63 2.09  CS10x8;10 1933 HLâ93 (US) 7 1.452 1.882 HS 20â44 3.142 5.247 2.16 2.79  CS10x8;10 1933 HLâ93 (US) 9 1.14 1.478 HS 20â44 3.255 5.436 2.86 3.68  CS10x8;10 1933 HLâ93 (US) 10 0.848 1.1 HS 20â44 3.059 5.108 3.61 4.64 47 CS10x8;5 1952 HLâ93 (US) 0 0.593 0.768 HS 20â44 0.547 0.914 0.92 1.19  CS10x8;5 1952 HLâ93 (US) 0.5 0.575 0.746 HS 20â44 0.517 0.864 0.90 1.16  CS10x8;5 1952 HLâ93 (US) 1 0.556 0.72 HS 20â44 0.487 0.813 0.88 1.13  CS10x8;5 1952 HLâ93 (US) 1.5 0.533 0.691 HS 20â44 0.494 0.825 0.93 1.19  CS10x8;5 1952 HLâ93 (US) 1.9 0.513 0.665 HS 20â44 0.466 0.779 0.91 1.17  CS10x8;5 1952 HLâ93 (US) 2 0.511 0.662 HS 20â44 0.52 0.868 1.02 1.31  CS10x8;5 1952 HLâ93 (US) 3 0.564 0.732 HS 20â44 0.758 1.266 1.34 1.73Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ5  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS10x8;5 1952 HLâ93 (US) 4 0.612 0.793 HS 20â44 0.869 1.451 1.42 1.83  CS10x8;5 1952 HLâ93 (US) 5 0.581 0.753 HS 20â44 0.861 1.437 1.48 1.91 48 CS10x8;12 1952 HLâ93 (US) 0 0.794 1.03 HS 20â44 0.772 1.289 0.97 1.25  CS10x8;12 1952 HLâ93 (US) 0.5 0.806 1.044 HS 20â44 0.744 1.242 0.92 1.19  CS10x8;12 1952 HLâ93 (US) 1 0.817 1.059 HS 20â44 0.715 1.194 0.88 1.13  CS10x8;12 1952 HLâ93 (US) 1.9 0.836 1.084 HS 20â44 0.717 1.198 0.86 1.11  CS10x8;12 1952 HLâ93 (US) 2 0.86 1.115 HS 20â44 0.859 1.434 1.00 1.29  CS10x8;12 1952 HLâ93 (US) 4 1.225 1.588 HS 20â44 1.717 2.867 1.40 1.81  CS10x8;12 1952 HLâ93 (US) 7 1.428 1.851 HS 20â44 2.344 3.914 1.64 2.11  CS10x8;12 1952 HLâ93 (US) 9 1.143 1.482 HS 20â44 2.11 3.523 1.85 2.38  CS10x8;12 1952 HLâ93 (US) 11 12.88 16.696 HS 20â44 13.613 22.734 1.06 1.36 CS10x8;12 1952 HLâ93 (US) 12 13.546 17.56 HS 20â44 0 0 0.00 0.00 49 CS10x8;6 1948 HLâ93 (US) 0 0.696 0.902 HS 20â44 0.706 1.178 1.01 1.31  CS10x8;6 1948 HLâ93 (US) 0.5 0.681 0.883 HS 20â44 0.675 1.128 0.99 1.28  CS10x8;6 1948 HLâ93 (US) 1 0.664 0.861 HS 20â44 0.644 1.076 0.97 1.25  CS10x8;6 1948 HLâ93 (US) 1.5 0.645 0.836 HS 20â44 0.664 1.108 1.03 1.33  CS10x8;6 1948 HLâ93 (US) 1.9 0.627 0.813 HS 20â44 0.636 1.062 1.01 1.31  CS10x8;6 1948 HLâ93 (US) 2 0.688 0.892 HS 20â44 0.707 1.181 1.03 1.32  CS10x8;6 1948 HLâ93 (US) 3 0.8 1.037 HS 20â44 1.077 1.798 1.35 1.73  CS10x8;6 1948 HLâ93 (US) 4 0.903 1.17 HS 20â44 1.313 2.192 1.45 1.87  CS10x8;6 1948 HLâ93 (US) 5 0.861 1.115 HS 20â44 1.431 2.39 1.66 2.14  CS10x8;6 1948 HLâ93 (US) 6 0.751 0.973 HS 20â44 1.482 2.474 1.97 2.54 50 CS10x8;5 1922 HLâ93 (US) 0 1.018 1.32 HS 20â44 0.765 1.278 0.75 0.97  CS10x8;5 1922 HLâ93 (US) 0.5 1.026 1.33 HS 20â44 0.735 1.228 0.72 0.92  CS10x8;5 1922 HLâ93 (US) 1 1.001 1.298 HS 20â44 0.705 1.177 0.70 0.91  CS10x8;5 1922 HLâ93 (US) 1.5 0.963 1.248 HS 20â44 0.73 1.219 0.76 0.98  CS10x8;5 1922 HLâ93 (US) 1.9 0.931 1.207 HS 20â44 0.702 1.173 0.75 0.97  CS10x8;5 1922 HLâ93 (US) 2 0.735 0.953 HS 20â44 0.791 1.321 1.08 1.39Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ6  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS10x8;5 1922 HLâ93 (US) 3 0.848 1.099 HS 20â44 1.225 2.046 1.44 1.86  CS10x8;5 1922 HLâ93 (US) 4 0.912 1.182 HS 20â44 1.529 2.553 1.68 2.16  CS10x8;5 1922 HLâ93 (US) 5 0.871 1.129 HS 20â44 1.717 2.867 1.97 2.54 51 CS10x8;10 1981 HLâ93 (US) 0 0.574 0.744 HS 20â44 0.514 0.858 0.90 1.15  CS10x8;10 1981 HLâ93 (US) 0.5 0.556 0.721 HS 20â44 0.483 0.807 0.87 1.12  CS10x8;10 1981 HLâ93 (US) 1 0.537 0.696 HS 20â44 0.452 0.754 0.84 1.08  CS10x8;10 1981 HLâ93 (US) 1.5 0.514 0.666 HS 20â44 0.455 0.76 0.89 1.14  CS10x8;10 1981 HLâ93 (US) 1.9 0.494 0.64 HS 20â44 0.427 0.713 0.86 1.11  CS10x8;10 1981 HLâ93 (US) 2 0.955 1.239 HS 20â44 0.988 1.651 1.03 1.33  CS10x8;10 1981 HLâ93 (US) 4 1.391 1.803 HS 20â44 2.026 3.383 1.46 1.88  CS10x8;10 1981 HLâ93 (US) 7 1.6 2.074 HS 20â44 3.006 5.02 1.88 2.42  CS10x8;10 1981 HLâ93 (US) 9 1.405 1.821 HS 20â44 3.143 5.249 2.24 2.88  CS10x8;10 1981 HLâ93 (US) 10 1.174 1.522 HS 20â44 2.963 4.948 2.52 3.25 52 CS8x8;10 2010 HLâ93 (US) 0 0.733 0.95 HS 20â44 0.619 1.034 0.84 1.09  CS8x8;10 2010 HLâ93 (US) 0.5 0.751 0.973 HS 20â44 0.594 0.993 0.79 1.02  CS8x8;10 2010 HLâ93 (US) 1 0.763 0.989 HS 20â44 0.569 0.951 0.75 0.96  CS8x8;10 2010 HLâ93 (US) 1.5 0.756 0.98 HS 20â44 0.589 0.984 0.78 1.00  CS8x8;10 2010 HLâ93 (US) 1.9 0.749 0.97 HS 20â44 0.567 0.946 0.76 0.98  CS8x8;10 2010 HLâ93 (US) 2 0.988 1.28 HS 20â44 1.056 1.761 1.07 1.38  CS8x8;10 2010 HLâ93 (US) 4 1.559 2.021 HS 20â44 2.406 4.004 1.54 1.98  CS8x8;10 2010 HLâ93 (US) 7 2.109 2.733 HS 20â44 4.329 7.23 2.05 2.65  CS8x8;10 2010 HLâ93 (US) 9 12.57 16.294 HS 20â44 10.559 17.634 0.84 1.08  CS8x8;10 2010 HLâ93 (US) 10 12.184 15.794 HS 20â44 10.264 17.141 0.84 1.09 53 CS7x7;10 2010 HLâ93 (US) 0 0.793 1.028 HS 20â44 0.625 1.044 0.79 1.02  CS7x7;10 2010 HLâ93 (US) 0.5 0.827 1.072 HS 20â44 0.604 1.009 0.73 0.94  CS7x7;10 2010 HLâ93 (US) 1 0.864 1.12 HS 20â44 0.583 0.973 0.67 0.87  CS7x7;10 2010 HLâ93 (US) 1.5 0.871 1.129 HS 20â44 0.608 1.015 0.70 0.90  CS7x7;10 2010 HLâ93 (US) 1.9 0.872 1.131 HS 20â44 0.588 0.982 0.67 0.87Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ7  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS7x7;10 2010 HLâ93 (US) 2 1.11 1.439 HS 20â44 1.145 1.909 1.03 1.33  CS7x7;10 2010 HLâ93 (US) 4 1.953 2.531 HS 20â44 2.845 4.734 1.46 1.87  CS7x7;10 2010 HLâ93 (US) 7 2.879 3.731 HS 20â44 5.489 9.101 1.91 2.44  CS7x7;10 2010 HLâ93 (US) 9 14.511 18.81 HS 20â44 11.776 19.666 0.81 1.05  CS7x7;10 2010 HLâ93 (US) 10 14.125 18.31 HS 20â44 11.481 19.173 0.81 1.05 54 CS6x6;10 2010 HLâ93 (US) 0 0.815 1.057 HS 20â44 0.577 0.963 0.71 0.91  CS6x6;10 2010 HLâ93 (US) 0.5 0.844 1.094 HS 20â44 0.559 0.934 0.66 0.85  CS6x6;10 2010 HLâ93 (US) 1 0.874 1.133 HS 20â44 0.541 0.903 0.62 0.80  CS6x6;10 2010 HLâ93 (US) 1.5 0.906 1.174 HS 20â44 0.566 0.945 0.62 0.80  CS6x6;10 2010 HLâ93 (US) 1.9 0.933 1.209 HS 20â44 0.549 0.917 0.59 0.76  CS6x6;10 2010 HLâ93 (US) 2 1.099 1.425 HS 20â44 1.128 1.882 1.03 1.32  CS6x6;10 2010 HLâ93 (US) 4 2.084 2.701 HS 20â44 3.029 5.042 1.45 1.87  CS6x6;10 2010 HLâ93 (US) 7 3.202 4.151 HS 20â44 5.973 9.91 1.87 2.39  CS6x6;10 2010 HLâ93 (US) 9 17.095 22.161 HS 20â44 13.385 22.354 0.78 1.01  CS6x6;10 2010 HLâ93 (US) 10 16.71 21.661 HS 20â44 13.09 21.86 0.78 1.01  CS5x5;10 2010 HLâ93 (US) 0 0.783 1.014 HS 20â44 0.526 0.879 0.67 0.87 Single CS5x5;10 2010 HLâ93 (US) 0.5 0.823 1.066 HS 20â44 0.512 0.855 0.62 0.80  CS5x5;10 2010 HLâ93 (US) 1 0.867 1.124 HS 20â44 0.497 0.83 0.57 0.74  CS5x5;10 2010 HLâ93 (US) 1.5 0.916 1.188 HS 20â44 0.522 0.872 0.57 0.73  CS5x5;10 2010 HLâ93 (US) 1.9 0.96 1.244 HS 20â44 0.508 0.849 0.53 0.68  CS5x5;10 2010 HLâ93 (US) 2 1.065 1.381 HS 20â44 1.13 1.885 1.06 1.36  CS5x5;10 2010 HLâ93 (US) 4 2.189 2.838 HS 20â44 3.299 5.494 1.51 1.94  CS5x5;10 2010 HLâ93 (US) 7 3.724 4.827 HS 20â44 6.679 11.094 1.79 2.30  CS5x5;10 2010 HLâ93 (US) 9 16.684 21.628 HS 20â44 11.593 19.361 0.69 0.90  CS5x5;10 2010 HLâ93 (US) 10 16.299 21.128 HS 20â44 11.298 18.867 0.69 0.89 56 CS4x4;10 2010 HLâ93 (US) 0 0.769 0.997 HS 20â44 0.492 0.822 0.64 0.82  CS4x4;10 2010 HLâ93 (US) 0.5 0.826 1.071 HS 20â44 0.481 0.803 0.58 0.75  CS4x4;10 2010 HLâ93 (US) 1 0.893 1.157 HS 20â44 0.469 0.783 0.53 0.68Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ8  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS4x4;10 2010 HLâ93 (US) 1.5 0.97 1.258 HS 20â44 0.495 0.827 0.51 0.66  CS4x4;10 2010 HLâ93 (US) 1.9 1.044 1.353 HS 20â44 0.484 0.809 0.46 0.60  CS4x4;10 2010 HLâ93 (US) 2 1.144 1.483 HS 20â44 1.311 2.187 1.15 1.47  CS4x4;10 2010 HLâ93 (US) 4 2.5 3.24 HS 20â44 3.995 6.652 1.60 2.05  CS4x4;10 2010 HLâ93 (US) 7 4.816 6.244 HS 20â44 8.418 13.976 1.75 2.24  CS4x4;10 2010 HLâ93 (US) 9 26.405 34.229 HS 20â44 19.738 32.963 0.75 0.96  CS4x4;10 2010 HLâ93 (US) 10 26.019 33.729 HS 20â44 19.443 32.47 0.75 0.96 57 CD10x8;10 2002 HLâ93 (US) 0 0.634 0.822 HS 20â44 0.438 0.731 0.69 0.89  CD10x8;10 2002 HLâ93 (US) 0.5 0.639 0.828 HS 20â44 0.479 0.8 0.75 0.97  CD10x8;10 2002 HLâ93 (US) 1 0.631 0.818 HS 20â44 0.521 0.87 0.83 1.06  CD10x8;10 2002 HLâ93 (US) 1.5 0.621 0.805 HS 20â44 0.567 0.947 0.91 1.18  CD10x8;10 2002 HLâ93 (US) 1.9 0.612 0.793 HS 20â44 0.536 0.895 0.88 1.13  CD10x8;10 2002 HLâ93 (US) 2 0.892 1.156 HS 20â44 1.071 1.733 1.20 1.50  CD10x8;10 2002 HLâ93 (US) 4 1.267 1.643 HS 20â44 1.618 2.664 1.28 1.62  CD10x8;10 2002 HLâ93 (US) 7 1.183 1.534 HS 20â44 1.787 2.979 1.51 1.94  CD10x8;10 2002 HLâ93 (US) 9 0.547 0.709 HS 20â44 1.436 2.369 2.63 3.34  CD10x8;10 2002 HLâ93 (US) 10 0.077 0.1 HS 20â44 0 0 0.00 0.00 58 CD10x8;10 2010 HLâ93 (US) 0 0.763 0.99 HS 20â44 0.8 1.336 1.05 1.35  CD10x8;10 2010 HLâ93 (US) 0.5 0.762 0.988 HS 20â44 0.766 1.279 1.01 1.29  CD10x8;10 2010 HLâ93 (US) 1 0.76 0.986 HS 20â44 0.731 1.22 0.96 1.24  CD10x8;10 2010 HLâ93 (US) 1.5 0.757 0.982 HS 20â44 0.753 1.258 0.99 1.28  CD10x8;10 2010 HLâ93 (US) 1.9 0.754 0.978 HS 20â44 0.701 1.171 0.93 1.20  CD10x8;10 2010 HLâ93 (US) 2 1.217 1.577 HS 20â44 1.335 2.229 1.10 1.41  CD10x8;10 2010 HLâ93 (US) 4 1.902 2.465 HS 20â44 2.378 3.898 1.25 1.58  CD10x8;10 2010 HLâ93 (US) 7 2.279 2.954 HS 20â44 3.16 5.27 1.39 1.78  CD10x8;10 2010 HLâ93 (US) 9 1.893 2.454 HS 20â44 3.611 5.987 1.91 2.44  CD10x8;10 2010 HLâ93 (US) 10 1.537 1.993 HS 20â44 3.417 5.669 2.22 2.84 59 CD10x8;2 1966 HLâ93 (US) 0 0.257 0.333 HS 20â44 0.532 0.888 2.07 2.67Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ9  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD10x8;2 1966 HLâ93 (US) 0.5 0.323 0.418 HS 20â44 0.592 0.988 1.83 2.36  CD10x8;2 1966 HLâ93 (US) 1 0.395 0.512 HS 20â44 0.553 0.923 1.40 1.80  CD10x8;2 1966 HLâ93 (US) 1.5 0.473 0.613 HS 20â44 0.556 0.929 1.18 1.52  CD10x8;2 1966 HLâ93 (US) 1.9 0.509 0.66 HS 20â44 0.522 0.871 1.03 1.32  CD10x8;2 1966 HLâ93 (US) 2 0.436 0.566 HS 20â44 0.689 1.15 1.58 2.03 60 CD10x8;16 1966 HLâ93 (US) 0 0.365 0.473 HS 20â44 0.697 1.164 1.91 2.46  CD10x8;16 1966 HLâ93 (US) 1.9 0.751 0.974 HS 20â44 0.79 1.319 1.05 1.35  CD10x8;16 1966 HLâ93 (US) 2 0.556 0.721 HS 20â44 1.039 1.735 1.87 2.41  CD10x8;16 1966 HLâ93 (US) 4 1.83 2.372 HS 20â44 2 3.34 1.09 1.41  CD10x8;16 1966 HLâ93 (US) 7 1.491 1.932 HS 20â44 1.413 2.36 0.95 1.22  CD10x8;16 1966 HLâ93 (US) 9 0.955 1.238 HS 20â44 0.984 1.643 1.03 1.33  CD10x8;16 1966 HLâ93 (US) 11 0.4 0.519 HS 20â44 0.535 0.894 1.34 1.72  CD10x8;16 1966 HLâ93 (US) 13 0 0 HS 20â44 0.087 0.145 #DIV/0! #DIV/0!  CD10x8;16 1966 HLâ93 (US) 15 0 0 HS 20â44 0 0 #DIV/0! #DIV/0!  CD10x8;16 1966 HLâ93 (US) 16 0 0 HS 20â44 0 0 #DIV/0! #DIV/0! 61 CD10x8;3 1952 HLâ93 (US) 0 0.259 0.336 HS 20â44 0.504 0.842 1.95 2.51  CD10x8;3 1952 HLâ93 (US) 0.5 0.325 0.422 HS 20â44 0.566 0.945 1.74 2.24  CD10x8;3 1952 HLâ93 (US) 1 0.407 0.528 HS 20â44 0.542 0.905 1.33 1.71  CD10x8;3 1952 HLâ93 (US) 1.5 0.495 0.642 HS 20â44 0.561 0.938 1.13 1.46  CD10x8;3 1952 HLâ93 (US) 1.9 0.573 0.743 HS 20â44 0.541 0.903 0.94 1.22  CD10x8;3 1952 HLâ93 (US) 2 0.439 0.57 HS 20â44 0.596 0.996 1.36 1.75  CD10x8;3 1952 HLâ93 (US) 3 0.678 0.878 HS 20â44 0.752 1.255 1.11 1.43 62 CD10x8;9 1952 HLâ93 (US) 0 0.295 0.383 HS 20â44 0.555 0.926 1.88 2.42  CD10x8;9 1952 HLâ93 (US) 0.5 0.373 0.483 HS 20â44 0.646 1.079 1.73 2.23  CD10x8;9 1952 HLâ93 (US) 1 0.461 0.598 HS 20â44 0.739 1.234 1.60 2.06  CD10x8;9 1952 HLâ93 (US) 1.5 0.554 0.719 HS 20â44 0.894 1.494 1.61 2.08  CD10x8;9 1952 HLâ93 (US) 1.9 0.638 0.827 HS 20â44 0.874 1.459 1.37 1.76  CD10x8;9 1952 HLâ93 (US) 2 0.485 0.629 HS 20â44 0.936 1.563 1.93 2.48Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ10  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD10x8;9 1952 HLâ93 (US) 4 1.459 1.891 HS 20â44 1.878 3.136 1.29 1.66  CD10x8;9 1952 HLâ93 (US) 6 1.59 2.06 HS 20â44 1.563 2.61 0.98 1.27  CD10x8;9 1952 HLâ93 (US) 8 1.126 1.46 HS 20â44 1.22 2.038 1.08 1.40  CD10x8;9 1952 HLâ93 (US) 9 0.879 1.139 HS 20â44 1.042 1.74 1.19 1.53 63 CD10x8;5 1948 HLâ93 (US) 0 0.21 0.272 HS 20â44 0.44 0.734 2.10 2.70  CD10x8;5 1948 HLâ93 (US) 0.5 0.275 0.357 HS 20â44 0.521 0.87 1.89 2.44  CD10x8;5 1948 HLâ93 (US) 1 0.346 0.449 HS 20â44 0.498 0.831 1.44 1.85  CD10x8;5 1948 HLâ93 (US) 1.5 0.425 0.551 HS 20â44 0.514 0.858 1.21 1.56  CD10x8;5 1948 HLâ93 (US) 1.9 0.494 0.641 HS 20â44 0.493 0.823 1.00 1.28  CD10x8;5 1948 HLâ93 (US) 2 0.396 0.513 HS 20â44 0.544 0.908 1.37 1.77  CD10x8;5 1948 HLâ93 (US) 3 0.398 0.516 HS 20â44 0.485 0.811 1.22 1.57  CD10x8;5 1948 HLâ93 (US) 4 0.171 0.221 HS 20â44 0.317 0.53 1.85 2.40 CD10x8;5 1948 HLâ93 (US) 5 0 0 HS 20â44 0.141 0.235 #DIV/0! #DIV/0! 64 CD10x8;9 1948 HLâ93 (US) 0 0.216 0.28 HS 20â44 0.456 0.762 2.11 2.72  CD10x8;9 1948 HLâ93 (US) 0.5 0.281 0.364 HS 20â44 0.547 0.913 1.95 2.51  CD10x8;9 1948 HLâ93 (US) 1 0.358 0.464 HS 20â44 0.633 1.058 1.77 2.28  CD10x8;9 1948 HLâ93 (US) 1.5 0.439 0.569 HS 20â44 0.661 1.103 1.51 1.94  CD10x8;9 1948 HLâ93 (US) 1.9 0.509 0.66 HS 20â44 0.64 1.069 1.26 1.62  CD10x8;9 1948 HLâ93 (US) 2 0.402 0.521 HS 20â44 0.708 1.182 1.76 2.27  CD10x8;9 1948 HLâ93 (US) 4 1.022 1.325 HS 20â44 1.269 2.118 1.24 1.60  CD10x8;9 1948 HLâ93 (US) 6 0.842 1.092 HS 20â44 0.91 1.519 1.08 1.39  CD10x8;9 1948 HLâ93 (US) 8 0.33 0.427 HS 20â44 0.531 0.887 1.61 2.08  CD10x8;9 1948 HLâ93 (US) 9 0.064 0.082 HS 20â44 0.325 0.542 5.08 6.61 65 CD8x8;5 1933 HLâ93 (US) 0 0.227 0.294 HS 20â44 0.476 0.796 2.10 2.71  CD8x8;5 1933 HLâ93 (US) 0.5 0.293 0.379 HS 20â44 0.551 0.92 1.88 2.43  CD8x8;5 1933 HLâ93 (US) 1 0.365 0.473 HS 20â44 0.626 1.046 1.72 2.21  CD8x8;5 1933 HLâ93 (US) 1.5 0.447 0.579 HS 20â44 0.756 1.262 1.69 2.18  CD8x8;5 1933 HLâ93 (US) 1.9 0.518 0.672 HS 20â44 0.729 1.218 1.41 1.81Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ11  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD8x8;5 1933 HLâ93 (US) 2 0.414 0.537 HS 20â44 0.823 1.374 1.99 2.56  CD8x8;5 1933 HLâ93 (US) 3 0.824 1.068 HS 20â44 1.465 2.447 1.78 2.29  CD8x8;5 1933 HLâ93 (US) 4 1.315 1.705 HS 20â44 1.91 3.19 1.45 1.87  CD8x8;5 1933 HLâ93 (US) 5 1.485 1.925 HS 20â44 1.804 3.013 1.21 1.57 66 CD8x8;10 1933 HLâ93 (US) 0 0.318 0.413 HS 20â44 0.615 1.027 1.93 2.49  CD8x8;10 1933 HLâ93 (US) 0.5 0.394 0.511 HS 20â44 0.691 1.154 1.75 2.26  CD8x8;10 1933 HLâ93 (US) 1 0.478 0.62 HS 20â44 0.768 1.283 1.61 2.07  CD8x8;10 1933 HLâ93 (US) 1.9 0.663 0.859 HS 20â44 0.928 1.55 1.40 1.80  CD8x8;10 1933 HLâ93 (US) 2 0.512 0.664 HS 20â44 0.976 1.63 1.91 2.45  CD8x8;10 1933 HLâ93 (US) 3 1.079 1.398 HS 20â44 2.225 3.715 2.06 2.66  CD8x8;10 1933 HLâ93 (US) 5 2.895 3.753 HS 20â44 3.762 6.283 1.30 1.67  CD8x8;10 1933 HLâ93 (US) 7 3.852 4.994 HS 20â44 3.51 5.862 0.91 1.17  CD8x8;10 1933 HLâ93 (US) 9 3.443 4.463 HS 20â44 3.203 5.35 0.93 1.20  CD8x8;10 1933 HLâ93 (US) 10 3.219 4.173 HS 20â44 3.043 5.081 0.95 1.22 67 CD8x8;5 1924 HLâ93 (US) 0 0.226 0.293 HS 20â44 0.476 0.795 2.11 2.71  CD8x8;5 1924 HLâ93 (US) 0.5 0.292 0.379 HS 20â44 0.551 0.92 1.89 2.43  CD8x8;5 1924 HLâ93 (US) 1 0.365 0.473 HS 20â44 0.624 1.042 1.71 2.20  CD8x8;5 1924 HLâ93 (US) 1.5 0.447 0.579 HS 20â44 0.655 1.094 1.47 1.89  CD8x8;5 1924 HLâ93 (US) 1.9 0.518 0.671 HS 20â44 0.638 1.066 1.23 1.59  CD8x8;5 1924 HLâ93 (US) 2 0.414 0.536 HS 20â44 0.768 1.282 1.86 2.39  CD8x8;5 1924 HLâ93 (US) 3 0.823 1.067 HS 20â44 1.236 2.064 1.50 1.93  CD8x8;5 1924 HLâ93 (US) 4 1.063 1.378 HS 20â44 1.674 2.795 1.57 2.03  CD8x8;5 1924 HLâ93 (US) 5 1.152 1.494 HS 20â44 2.099 3.506 1.82 2.35 68 CD8x8;10 1924 HLâ93 (US) 0 0.269 0.349 HS 20â44 0.526 0.879 1.96 2.52  CD8x8;10 1924 HLâ93 (US) 0.5 0.339 0.439 HS 20â44 0.603 1.006 1.78 2.29  CD8x8;10 1924 HLâ93 (US) 1 0.416 0.539 HS 20â44 0.68 1.135 1.63 2.11  CD8x8;10 1924 HLâ93 (US) 1.9 0.579 0.75 HS 20â44 0.889 1.485 1.54 1.98  CD8x8;10 1924 HLâ93 (US) 2 0.46 0.596 HS 20â44 0.883 1.474 1.92 2.47Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ12  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD8x8;10 1924 HLâ93 (US) 3 0.918 1.19 HS 20â44 1.97 3.29 2.15 2.76  CD8x8;10 1924 HLâ93 (US) 5 2.534 3.285 HS 20â44 3.358 5.607 1.33 1.71  CD8x8;10 1924 HLâ93 (US) 7 3.354 4.348 HS 20â44 3.104 5.184 0.93 1.19  CD8x8;10 1924 HLâ93 (US) 9 2.938 3.809 HS 20â44 2.801 4.678 0.95 1.23  CD8x8;10 1924 HLâ93 (US) 10 2.713 3.517 HS 20â44 2.642 4.413 0.97 1.25 69 CS12x8;10 2010 HLâ93 (US) 0 0.767 0.995 HS 20â44 0.81 1.353 1.06 1.36  CS12x8;10 2010 HLâ93 (US) 0.5 0.761 0.987 HS 20â44 0.772 1.29 1.01 1.31  CS12x8;10 2010 HLâ93 (US) 1 0.754 0.977 HS 20â44 0.734 1.226 0.97 1.25  CS12x8;10 2010 HLâ93 (US) 1.5 0.744 0.965 HS 20â44 0.754 1.259 1.01 1.30  CS12x8;10 2010 HLâ93 (US) 1.9 0.735 0.953 HS 20â44 0.72 1.202 0.98 1.26  CS12x8;10 2010 HLâ93 (US) 2 1.233 1.598 HS 20â44 1.315 2.197 1.07 1.37  CS12x8;10 2010 HLâ93 (US) 4 1.841 2.386 HS 20â44 2.651 4.427 1.44 1.86  CS12x8;10 2010 HLâ93 (US) 7 2.403 3.115 HS 20â44 3.891 6.498 1.62 2.09  CS12x8;10 2010 HLâ93 (US) 9 2.356 3.054 HS 20â44 4.457 7.444 1.89 2.44  CS12x8;10 2010 HLâ93 (US) 10 2.199 2.85 HS 20â44 4.437 7.41 2.02 2.60 70 CS14x9;10 2010 HLâ93 (US) 0 0.849 1.101 HS 20â44 0.958 1.599 1.13 1.45  CS14x9;10 2010 HLâ93 (US) 0.5 0.837 1.085 HS 20â44 0.913 1.525 1.09 1.41  CS14x9;10 2010 HLâ93 (US) 1 0.822 1.066 HS 20â44 0.868 1.45 1.06 1.36  CS14x9;10 2010 HLâ93 (US) 1.5 0.804 1.042 HS 20â44 0.891 1.488 1.11 1.43  CS14x9;10 2010 HLâ93 (US) 1.9 0.789 1.022 HS 20â44 0.851 1.421 1.08 1.39  CS14x9;10 2010 HLâ93 (US) 2 1.167 1.513 HS 20â44 1.489 2.487 1.28 1.64  CS14x9;10 2010 HLâ93 (US) 4 1.842 2.388 HS 20â44 2.684 4.482 1.46 1.88  CS14x9;10 2010 HLâ93 (US) 7 2.357 3.056 HS 20â44 3.772 6.3 1.60 2.06  CS14x9;10 2010 HLâ93 (US) 9 2.236 2.899 HS 20â44 4.25 7.098 1.90 2.45  CS14x9;10 2010 HLâ93 (US) 10 2.001 2.594 HS 20â44 4.192 7 2.09 2.70 71 CS4x3;10 2010 HLâ93 (US) 0 0.767 0.994 HS 20â44 0.49 0.819 0.64 0.82  CS4x3;10 2010 HLâ93 (US) 0.5 0.824 1.068 HS 20â44 0.479 0.8 0.58 0.75  CS4x3;10 2010 HLâ93 (US) 1 0.891 1.155 HS 20â44 0.467 0.781 0.52 0.68Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ13  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS4x3;10 2010 HLâ93 (US) 1.5 0.969 1.256 HS 20â44 0.493 0.824 0.51 0.66  CS4x3;10 2010 HLâ93 (US) 1.9 1.043 1.352 HS 20â44 0.482 0.806 0.46 0.60  CS4x3;10 2010 HLâ93 (US) 2 1.145 1.484 HS 20â44 1.308 2.182 1.14 1.47  CS4x3;10 2010 HLâ93 (US) 4 2.533 3.283 HS 20â44 3.99 6.644 1.58 2.02  CS4x3;10 2010 HLâ93 (US) 7 4.892 6.342 HS 20â44 8.406 13.959 1.72 2.20  CS4x3;10 2010 HLâ93 (US) 9 36.622 47.472 HS 20â44 26.24 43.821 0.72 0.92  CS4x3;10 2010 HLâ93 (US) 10 36.236 46.972 HS 20â44 25.945 43.327 0.72 0.92 72 CS6x4;10 2010 HLâ93 (US) 0 0.812 1.052 HS 20â44 0.574 0.958 0.71 0.91  CS6x4;10 2010 HLâ93 (US) 0.5 0.84 1.089 HS 20â44 0.556 0.929 0.66 0.85  CS6x4;10 2010 HLâ93 (US) 1 0.87 1.128 HS 20â44 0.538 0.899 0.62 0.80  CS6x4;10 2010 HLâ93 (US) 1.5 0.902 1.17 HS 20â44 0.563 0.94 0.62 0.80  CS6x4;10 2010 HLâ93 (US) 1.9 0.93 1.205 HS 20â44 0.547 0.913 0.59 0.76  CS6x4;10 2010 HLâ93 (US) 2 1.075 1.394 HS 20â44 1.096 1.829 1.02 1.31  CS6x4;10 2010 HLâ93 (US) 4 2.037 2.64 HS 20â44 2.952 4.915 1.45 1.86  CS6x4;10 2010 HLâ93 (US) 7 3.239 4.198 HS 20â44 5.791 9.615 1.79 2.29  CS6x4;10 2010 HLâ93 (US) 9 26.381 34.197 HS 20â44 19.409 32.414 0.74 0.95  CS6x4;10 2010 HLâ93 (US) 10 25.995 33.697 HS 20â44 19.114 31.92 0.74 0.95 73 CS8x6;10 2010 HLâ93 (US) 0 0.731 0.947 HS 20â44 0.616 1.028 0.84 1.09  CS8x6;10 2010 HLâ93 (US) 0.5 0.749 0.971 HS 20â44 0.591 0.988 0.79 1.02  CS8x6;10 2010 HLâ93 (US) 1 0.768 0.995 HS 20â44 0.567 0.946 0.74 0.95  CS8x6;10 2010 HLâ93 (US) 1.5 0.787 1.02 HS 20â44 0.586 0.979 0.74 0.96  CS8x6;10 2010 HLâ93 (US) 1.9 0.789 1.023 HS 20â44 0.564 0.942 0.71 0.92  CS8x6;10 2010 HLâ93 (US) 2 1 1.296 HS 20â44 1.042 1.738 1.04 1.34  CS8x6;10 2010 HLâ93 (US) 4 1.593 2.066 HS 20â44 2.32 3.875 1.46 1.88  CS8x6;10 2010 HLâ93 (US) 7 2.173 2.817 HS 20â44 4.01 6.697 1.85 2.38  CS8x6;10 2010 HLâ93 (US) 9 15.442 20.017 HS 20â44 11.628 19.419 0.75 0.97  CS8x6;10 2010 HLâ93 (US) 10 15.056 19.517 HS 20â44 11.333 18.925 0.75 0.97 74 CD4x3;10 2010 HLâ93 (US) 0 0.685 0.888 HS 20â44 0.45 0.752 0.66 0.85Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ14  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD4x3;10 2010 HLâ93 (US) 0.5 0.72 0.933 HS 20â44 0.436 0.728 0.61 0.78  CD4x3;10 2010 HLâ93 (US) 1 0.763 0.989 HS 20â44 0.422 0.704 0.55 0.71  CD4x3;10 2010 HLâ93 (US) 1.5 0.816 1.058 HS 20â44 0.441 0.736 0.54 0.70  CD4x3;10 2010 HLâ93 (US) 1.9 0.867 1.124 HS 20â44 0.428 0.714 0.49 0.64  CD4x3;10 2010 HLâ93 (US) 2 1.282 1.662 HS 20â44 1.457 2.433 1.14 1.46  CD4x3;10 2010 HLâ93 (US) 4 2.994 3.881 HS 20â44 4.089 6.829 1.37 1.76  CD4x3;10 2010 HLâ93 (US) 7 4.798 6.219 HS 20â44 7.743 12.993 1.61 2.09  CD4x3;10 2010 HLâ93 (US) 9 32.975 42.745 HS 20â44 26.682 44.558 0.81 1.04  CD4x3;10 2010 HLâ93 (US) 10 32.806 42.527 HS 20â44 26.386 44.065 0.80 1.04 75 CD6x4;10 2010 HLâ93 (US) 0 0.63 0.817 HS 20â44 0.429 0.716 0.68 0.88  CD6x4;10 2010 HLâ93 (US) 0.5 0.641 0.831 HS 20â44 0.407 0.679 0.63 0.82  CD6x4;10 2010 HLâ93 (US) 1 0.644 0.835 HS 20â44 0.384 0.641 0.60 0.77  CD6x4;10 2010 HLâ93 (US) 1.5 0.648 0.84 HS 20â44 0.391 0.653 0.60 0.78  CD6x4;10 2010 HLâ93 (US) 1.9 0.652 0.845 HS 20â44 0.371 0.619 0.57 0.73  CD6x4;10 2010 HLâ93 (US) 2 1.046 1.356 HS 20â44 1.089 1.817 1.04 1.34  CD6x4;10 2010 HLâ93 (US) 4 2.141 2.775 HS 20â44 2.973 4.965 1.39 1.79  CD6x4;10 2010 HLâ93 (US) 7 2.118 2.745 HS 20â44 3 5.013 1.42 1.83  CD6x4;10 2010 HLâ93 (US) 9 2.044 2.649 HS 20â44 3.044 5.098 1.49 1.92  CD6x4;10 2010 HLâ93 (US) 10 1.831 2.374 HS 20â44 2.718 4.557 1.48 1.92 76 CD8x6;10 2010 HLâ93 (US) 0 0.64 0.829 HS 20â44 0.58 0.968 0.91 1.17  CD8x6;10 2010 HLâ93 (US) 0.5 0.642 0.832 HS 20â44 0.548 0.915 0.85 1.10  CD8x6;10 2010 HLâ93 (US) 1 0.643 0.834 HS 20â44 0.517 0.864 0.80 1.04  CD8x6;10 2010 HLâ93 (US) 1.5 0.645 0.836 HS 20â44 0.526 0.879 0.82 1.05  CD8x6;10 2010 HLâ93 (US) 1.9 0.646 0.837 HS 20â44 0.499 0.833 0.77 1.00  CD8x6;10 2010 HLâ93 (US) 2 1.253 1.624 HS 20â44 1.29 2.15 1.03 1.32  CD8x6;10 2010 HLâ93 (US) 4 2.09 2.71 HS 20â44 2.655 4.223 1.27 1.56  CD8x6;10 2010 HLâ93 (US) 7 2.124 2.754 HS 20â44 2.765 4.613 1.30 1.68  CD8x6;10 2010 HLâ93 (US) 9 1.807 2.342 HS 20â44 2.749 4.59 1.52 1.96Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ15  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD8x6;10 2010 HLâ93 (US) 10 1.52 1.97 HS 20â44 2.361 3.954 1.55 2.01 77 CD12x8;10 2010 HLâ93 (US) 0 0.784 1.016 HS 20â44 0.886 1.479 1.13 1.46  CD12x8;10 2010 HLâ93 (US) 0.5 0.771 0.999 HS 20â44 0.823 1.374 1.07 1.38  CD12x8;10 2010 HLâ93 (US) 1 0.756 0.98 HS 20â44 0.78 1.302 1.03 1.33  CD12x8;10 2010 HLâ93 (US) 1.5 0.74 0.959 HS 20â44 0.798 1.333 1.08 1.39  CD12x8;10 2010 HLâ93 (US) 1.9 0.725 0.94 HS 20â44 0.76 1.269 1.05 1.35  CD12x8;10 2010 HLâ93 (US) 2 1.263 1.637 HS 20â44 1.43 2.327 1.13 1.42  CD12x8;10 2010 HLâ93 (US) 4 1.732 2.245 HS 20â44 2.178 3.584 1.26 1.60  CD12x8;10 2010 HLâ93 (US) 7 2.022 2.621 HS 20â44 2.622 4.374 1.30 1.67  CD12x8;10 2010 HLâ93 (US) 9 1.82 2.359 HS 20â44 2.887 4.755 1.59 2.02  CD12x8;10 2010 HLâ93 (US) 10 1.521 1.971 HS 20â44 2.542 4.184 1.67 2.12 78 CD14x9;10 2010 HLâ93 (US) 0 0.866 1.123 HS 20â44 0.991 1.655 1.14 1.47  CD14x9;10 2010 HLâ93 (US) 0.5 0.845 1.096 HS 20â44 0.941 1.571 1.11 1.43  CD14x9;10 2010 HLâ93 (US) 1 0.823 1.066 HS 20â44 0.891 1.487 1.08 1.39  CD14x9;10 2010 HLâ93 (US) 1.5 0.798 1.034 HS 20â44 0.91 1.519 1.14 1.47  CD14x9;10 2010 HLâ93 (US) 1.9 0.776 1.006 HS 20â44 0.865 1.445 1.11 1.44  CD14x9;10 2010 HLâ93 (US) 2 1.327 1.72 HS 20â44 1.393 2.322 1.05 1.35  CD14x9;10 2010 HLâ93 (US) 4 1.757 2.278 HS 20â44 2.204 3.631 1.25 1.59  CD14x9;10 2010 HLâ93 (US) 7 1.895 2.456 HS 20â44 2.486 4.144 1.31 1.69  CD14x9;10 2010 HLâ93 (US) 9 1.649 2.138 HS 20â44 2.666 4.37 1.62 2.04  CD14x9;10 2010 HLâ93 (US) 10 1.278 1.656 HS 20â44 2.293 3.751 1.79 2.27 79 CS4x3;10 2002 HLâ93 (US) 0 0.764 0.991 HS 20â44 0.488 0.816 0.64 0.82  CS4x3;10 2002 HLâ93 (US) 0.5 0.822 1.066 HS 20â44 0.477 0.797 0.58 0.75  CS4x3;10 2002 HLâ93 (US) 1 0.889 1.153 HS 20â44 0.466 0.778 0.52 0.67  CS4x3;10 2002 HLâ93 (US) 1.5 0.968 1.255 HS 20â44 0.491 0.821 0.51 0.65  CS4x3;10 2002 HLâ93 (US) 1.9 1.033 1.339 HS 20â44 0.481 0.803 0.47 0.60  CS4x3;10 2002 HLâ93 (US) 2 0.974 1.262 HS 20â44 1.304 2.176 1.34 1.72  CS4x3;10 2002 HLâ93 (US) 4 1.761 2.282 HS 20â44 3.984 6.635 2.26 2.91Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ16  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS4x3;10 2002 HLâ93 (US) 7 3.14 4.071 HS 20â44 8.391 13.938 2.67 3.42  CS4x3;10 2002 HLâ93 (US) 9 25.714 33.334 HS 20â44 21.136 35.297 0.82 1.06  CS4x3;10 2002 HLâ93 (US) 10 25.603 33.19 HS 20â44 21.095 35.229 0.82 1.06 80 CS6x4;10 2002 HLâ93 (US) 0 0.754 0.977 HS 20â44 0.571 0.953 0.76 0.98  CS6x4;10 2002 HLâ93 (US) 0.5 0.767 0.994 HS 20â44 0.553 0.924 0.72 0.93  CS6x4;10 2002 HLâ93 (US) 1 0.779 1.01 HS 20â44 0.535 0.894 0.69 0.89  CS6x4;10 2002 HLâ93 (US) 1.5 0.792 1.026 HS 20â44 0.56 0.935 0.71 0.91  CS6x4;10 2002 HLâ93 (US) 1.9 0.815 1.057 HS 20â44 0.544 0.908 0.67 0.86  CS6x4;10 2002 HLâ93 (US) 2 0.874 1.133 HS 20â44 1.084 1.809 1.24 1.60  CS6x4;10 2002 HLâ93 (US) 4 1.566 2.03 HS 20â44 2.932 4.884 1.87 2.41  CS6x4;10 2002 HLâ93 (US) 7 2.143 2.777 HS 20â44 5.749 9.548 2.68 3.44  CS6x4;10 2002 HLâ93 (US) 9 19.44 25.2 HS 20â44 13.853 23.134 0.71 0.92  CS6x4;10 2002 HLâ93 (US) 10 19.262 24.969 HS 20â44 13.557 22.64 0.70 0.91 81 CS8x6;10 2002 HLâ93 (US) 0 0.73 0.946 HS 20â44 0.614 1.026 0.84 1.08  CS8x6;10 2002 HLâ93 (US) 0.5 0.73 0.946 HS 20â44 0.59 0.985 0.81 1.04  CS8x6;10 2002 HLâ93 (US) 1 0.727 0.942 HS 20â44 0.565 0.944 0.78 1.00  CS8x6;10 2002 HLâ93 (US) 1.5 0.721 0.935 HS 20â44 0.585 0.977 0.81 1.04  CS8x6;10 2002 HLâ93 (US) 1.9 0.715 0.927 HS 20â44 0.563 0.94 0.79 1.01  CS8x6;10 2002 HLâ93 (US) 2 0.882 1.144 HS 20â44 1.045 1.743 1.18 1.52  CS8x6;10 2002 HLâ93 (US) 4 1.339 1.736 HS 20â44 2.347 3.92 1.75 2.26  CS8x6;10 2002 HLâ93 (US) 7 1.681 2.179 HS 20â44 4.084 6.821 2.43 3.13  CS8x6;10 2002 HLâ93 (US) 9 13.761 17.839 HS 20â44 10.054 16.79 0.73 0.94  CS8x6;10 2002 HLâ93 (US) 10 13.376 17.339 HS 20â44 9.758 16.296 0.73 0.94 82 CS12x8;10 2002 HLâ93 (US) 0 0.608 0.788 HS 20â44 0.592 0.989 0.97 1.26  CS12x8;10 2002 HLâ93 (US) 0.5 0.595 0.771 HS 20â44 0.554 0.925 0.93 1.20  CS12x8;10 2002 HLâ93 (US) 1 0.579 0.751 HS 20â44 0.516 0.861 0.89 1.15  CS12x8;10 2002 HLâ93 (US) 1.5 0.561 0.728 HS 20â44 0.515 0.86 0.92 1.18  CS12x8;10 2002 HLâ93 (US) 1.9 0.545 0.707 HS 20â44 0.481 0.803 0.88 1.14Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ17  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS12x8;10 2002 HLâ93 (US) 2 0.93 1.206 HS 20â44 0.982 1.64 1.06 1.36  CS12x8;10 2002 HLâ93 (US) 4 1.318 1.709 HS 20â44 1.897 3.168 1.44 1.85  CS12x8;10 2002 HLâ93 (US) 7 1.493 1.935 HS 20â44 2.44 4.074 1.63 2.11  CS12x8;10 2002 HLâ93 (US) 9 1.191 1.544 HS 20â44 2.245 3.748 1.88 2.43  CS12x8;10 2002 HLâ93 (US) 10 0.872 1.13 HS 20â44 1.776 2.966 2.04 2.62 83 CS14x9;10 2002 HLâ93 (US) 0 0.655 0.849 HS 20â44 0.684 1.143 1.04 1.35  CS14x9;10 2002 HLâ93 (US) 0.5 0.635 0.823 HS 20â44 0.639 1.067 1.01 1.30  CS14x9;10 2002 HLâ93 (US) 1 0.612 0.793 HS 20â44 0.594 0.991 0.97 1.25  CS14x9;10 2002 HLâ93 (US) 1.5 0.582 0.755 HS 20â44 0.591 0.986 1.02 1.31  CS14x9;10 2002 HLâ93 (US) 1.9 0.549 0.712 HS 20â44 0.55 0.918 1.00 1.29  CS14x9;10 2002 HLâ93 (US) 2 0.917 1.189 HS 20â44 1.096 1.83 1.20 1.54  CS14x9;10 2002 HLâ93 (US) 4 1.231 1.595 HS 20â44 2.006 3.349 1.63 2.10  CS14x9;10 2002 HLâ93 (US) 7 1.153 1.495 HS 20â44 2.222 3.982 1.93 2.66  CS14x9;10 2002 HLâ93 (US) 9 0.742 0.961 HS 20â44 2.091 3.771 2.82 3.92  CS14x9;10 2002 HLâ93 (US) 10 0.339 0.44 HS 20â44 1.531 2.321 4.52 5.28 84 CD4x3;10 2002 HLâ93 (US) 0 0.686 0.889 HS 20â44 0.451 0.753 0.66 0.85  CD4x3;10 2002 HLâ93 (US) 0.5 0.722 0.935 HS 20â44 0.437 0.73 0.61 0.78  CD4x3;10 2002 HLâ93 (US) 1 0.765 0.992 HS 20â44 0.423 0.706 0.55 0.71  CD4x3;10 2002 HLâ93 (US) 1.5 0.819 1.062 HS 20â44 0.442 0.738 0.54 0.69  CD4x3;10 2002 HLâ93 (US) 1.9 0.871 1.13 HS 20â44 0.429 0.716 0.49 0.63  CD4x3;10 2002 HLâ93 (US) 2 1.155 1.497 HS 20â44 1.319 2.202 1.14 1.47  CD4x3;10 2002 HLâ93 (US) 4 2.675 3.468 HS 20â44 3.662 6.115 1.37 1.76  CD4x3;10 2002 HLâ93 (US) 7 4.214 5.462 HS 20â44 6.905 11.582 1.64 2.12  CD4x3;10 2002 HLâ93 (US) 9 21.358 27.686 HS 20â44 17.621 29.427 0.83 1.06  CD4x3;10 2002 HLâ93 (US) 10 21.181 27.457 HS 20â44 17.525 29.267 0.83 1.07 85 CD6x4;10 2002 HLâ93 (US) 0 0.634 0.822 HS 20â44 0.429 0.717 0.68 0.87  CD6x4;10 2002 HLâ93 (US) 0.5 0.642 0.832 HS 20â44 0.407 0.68 0.63 0.82  CD6x4;10 2002 HLâ93 (US) 1 0.646 0.837 HS 20â44 0.384 0.642 0.59 0.77Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ18  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD6x4;10 2002 HLâ93 (US) 1.5 0.651 0.843 HS 20â44 0.392 0.654 0.60 0.78  CD6x4;10 2002 HLâ93 (US) 1.9 0.655 0.849 HS 20â44 0.372 0.621 0.57 0.73  CD6x4;10 2002 HLâ93 (US) 2 1.026 1.329 HS 20â44 1.068 1.781 1.04 1.34  CD6x4;10 2002 HLâ93 (US) 4 1.773 2.298 HS 20â44 3 5.01 1.69 2.18  CD6x4;10 2002 HLâ93 (US) 7 1.884 2.443 HS 20â44 3.056 5.107 1.62 2.09  CD6x4;10 2002 HLâ93 (US) 9 1.648 2.136 HS 20â44 3.132 5.244 1.90 2.46  CD6x4;10 2002 HLâ93 (US) 10 1.374 1.781 HS 20â44 2.821 4.729 2.05 2.66 86 CD8x6;10 2002 HLâ93 (US) 0 0.602 0.78 HS 20â44 0.529 0.883 0.88 1.13  CD8x6;10 2002 HLâ93 (US) 0.5 0.602 0.78 HS 20â44 0.498 0.831 0.83 1.07  CD8x6;10 2002 HLâ93 (US) 1 0.601 0.779 HS 20â44 0.467 0.78 0.78 1.00  CD8x6;10 2002 HLâ93 (US) 1.5 0.6 0.778 HS 20â44 0.472 0.788 0.79 1.01  CD8x6;10 2002 HLâ93 (US) 1.9 0.599 0.777 HS 20â44 0.445 0.742 0.74 0.95  CD8x6;10 2002 HLâ93 (US) 2 1.158 1.501 HS 20â44 1.165 1.943 1.01 1.29  CD8x6;10 2002 HLâ93 (US) 4 1.627 2.109 HS 20â44 2.331 3.715 1.43 1.76  CD8x6;10 2002 HLâ93 (US) 7 1.473 1.91 HS 20â44 2.249 3.75 1.53 1.96  CD8x6;10 2002 HLâ93 (US) 9 0.963 1.249 HS 20â44 1.948 3.252 2.02 2.60  CD8x6;10 2002 HLâ93 (US) 10 0.553 0.717 HS 20â44 1.183 1.975 2.14 2.75 87 CD12x8;10 2002 HLâ93 (US) 0 0.669 0.867 HS 20â44 0.471 0.786 0.70 0.91  CD12x8;10 2002 HLâ93 (US) 0.5 0.659 0.854 HS 20â44 0.516 0.861 0.78 1.01  CD12x8;10 2002 HLâ93 (US) 1 0.64 0.829 HS 20â44 0.561 0.937 0.88 1.13  CD12x8;10 2002 HLâ93 (US) 1.5 0.618 0.802 HS 20â44 0.636 1.062 1.03 1.32  CD12x8;10 2002 HLâ93 (US) 1.9 0.6 0.777 HS 20â44 0.598 0.998 1.00 1.28  CD12x8;10 2002 HLâ93 (US) 2 0.918 1.19 HS 20â44 1.04 1.715 1.13 1.44  CD12x8;10 2002 HLâ93 (US) 4 1.211 1.569 HS 20â44 1.55 2.555 1.28 1.63  CD12x8;10 2002 HLâ93 (US) 7 1.095 1.42 HS 20â44 1.507 2.512 1.38 1.77  CD12x8;10 2002 HLâ93 (US) 9 0.368 0.477 HS 20â44 0.938 1.572 2.55 3.30  CD12x8;10 2002 HLâ93 (US) 10 0 0 HS 20â44 0 0 #DIV/0! #DIV/0! 88 CD14x9;10 2002 HLâ93 (US) 0 0.747 0.969 HS 20â44 0.627 1.047 0.84 1.08Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ19  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD14x9;10 2002 HLâ93 (US) 0.5 0.722 0.936 HS 20â44 0.679 1.134 0.94 1.21  CD14x9;10 2002 HLâ93 (US) 1 0.694 0.9 HS 20â44 0.731 1.22 1.05 1.36  CD14x9;10 2002 HLâ93 (US) 1.5 0.664 0.861 HS 20â44 0.748 1.249 1.13 1.45  CD14x9;10 2002 HLâ93 (US) 1.9 0.638 0.827 HS 20â44 0.703 1.174 1.10 1.42  CD14x9;10 2002 HLâ93 (US) 2 0.951 1.233 HS 20â44 1.05 1.754 1.10 1.42  CD14x9;10 2002 HLâ93 (US) 4 1.278 1.656 HS 20â44 1.635 2.697 1.28 1.63  CD14x9;10 2002 HLâ93 (US) 7 1.115 1.445 HS 20â44 1.506 2.51 1.35 1.74  CD14x9;10 2002 HLâ93 (US) 9 0.304 0.394 HS 20â44 0.967 1.619 3.18 4.11  CD14x9;10 2002 HLâ93 (US) 10 0 0 HS 20â44 0 0 #DIV/0! #DIV/0! 89 CS2x1_;66 1966 HLâ93 (US) 0 0.779 1.01 HS 20â44 0.53 0.884 0.68 0.88  CS2x1_;66 1966 HLâ93 (US) 1.9 1.833 2.376 HS 20â44 0.553 0.923 0.30 0.39  CS2x1_;66 1966 HLâ93 (US) 2 2.521 3.268 HS 20â44 3.255 5.425 1.29 1.66  CS2x1_;66 1966 HLâ93 (US) 4 6.838 8.865 HS 20â44 10.538 17.495 1.54 1.97  CS2x1_;66 1966 HLâ93 (US) 10 33.031 42.818 HS 20â44 28.849 48.178 0.87 1.13  CS2x1_;66 1966 HLâ93 (US) 25 37.175 48.19 HS 20â44 34.455 57.539 0.93 1.19  CS2x1_;66 1966 HLâ93 (US) 40 40.402 52.374 HS 20â44 38.91 64.979 0.96 1.24  CS2x1_;66 1966 HLâ93 (US) 50 42.24 54.756 HS 20â44 41.137 68.698 0.97 1.25  CS2x1_;66 1966 HLâ93 (US) 60 0 0 HS 20â44 0 0 #DIV/0! #DIV/0!  CS2x1_;66 1966 HLâ93 (US) 66 0 0 HS 20â44 0 0 #DIV/0! #DIV/0! 90 CS4x3;28 1966 HLâ93 (US) 0 0.723 0.937 HS 20â44 0.562 0.939 0.78 1.00  CS4x3;28 1966 HLâ93 (US) 1.9 0.984 1.275 HS 20â44 0.562 0.938 0.57 0.74  CS4x3;28 1966 HLâ93 (US) 2 1.188 1.54 HS 20â44 1.302 2.174 1.10 1.41  CS4x3;28 1966 HLâ93 (US) 4 2.522 3.27 HS 20â44 3.93 6.562 1.56 2.01  CS4x3;28 1966 HLâ93 (US) 7 4.868 6.311 HS 20â44 8.268 13.808 1.70 2.19  CS4x3;28 1966 HLâ93 (US) 10 12.768 16.552 HS 20â44 11.111 18.556 0.87 1.12  CS4x3;28 1966 HLâ93 (US) 15 12.351 16.011 HS 20â44 11.089 18.519 0.90 1.16  CS4x3;28 1966 HLâ93 (US) 20 11.911 15.44 HS 20â44 10.991 18.355 0.92 1.19  CS4x3;28 1966 HLâ93 (US) 25 0 0 HS 20â44 0 0 #DIV/0! #DIV/0!Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ20  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS4x3;28 1966 HLâ93 (US) 28 0 0 HS 20â44 0 0 #DIV/0! #DIV/0! 91 CS6x4;10 1966 HLâ93 (US) 0 0.654 0.848 HS 20â44 0.665 1.11 1.02 1.31  CS6x4;10 1966 HLâ93 (US) 0.5 0.661 0.857 HS 20â44 0.648 1.082 0.98 1.26  CS6x4;10 1966 HLâ93 (US) 1 0.668 0.866 HS 20â44 0.63 1.052 0.94 1.21  CS6x4;10 1966 HLâ93 (US) 1.5 0.674 0.873 HS 20â44 0.663 1.108 0.98 1.27  CS6x4;10 1966 HLâ93 (US) 1.9 0.689 0.894 HS 20â44 0.647 1.081 0.94 1.21  CS6x4;10 1966 HLâ93 (US) 2 0.758 0.982 HS 20â44 1.049 1.752 1.38 1.78  CS6x4;10 1966 HLâ93 (US) 4 1.304 1.691 HS 20â44 2.635 4.4 2.02 2.60  CS6x4;10 1966 HLâ93 (US) 7 1.641 2.127 HS 20â44 5.03 8.4 3.07 3.95  CS6x4;10 1966 HLâ93 (US) 9 6.654 8.626 HS 20â44 5.997 10.015 0.90 1.16  CS6x4;10 1966 HLâ93 (US) 10 6.531 8.466 HS 20â44 5.94 9.92 0.91 1.17 92 CS8x6;13 1966 HLâ93 (US) 0 0.59 0.764 HS 20â44 0.536 0.894 0.91 1.17  CS8x6;13 1966 HLâ93 (US) 0.5 0.599 0.777 HS 20â44 0.512 0.855 0.85 1.10  CS8x6;13 1966 HLâ93 (US) 1 0.607 0.787 HS 20â44 0.488 0.815 0.80 1.04  CS8x6;13 1966 HLâ93 (US) 1.5 0.577 0.748 HS 20â44 0.502 0.838 0.87 1.12  CS8x6;13 1966 HLâ93 (US) 1.9 0.568 0.736 HS 20â44 0.48 0.802 0.85 1.09  CS8x6;13 1966 HLâ93 (US) 2 0.757 0.981 HS 20â44 0.738 1.232 0.97 1.26  CS8x6;13 1966 HLâ93 (US) 4 1.103 1.43 HS 20â44 1.541 2.574 1.40 1.80  CS8x6;13 1966 HLâ93 (US) 6 1.286 1.668 HS 20â44 2.081 3.475 1.62 2.08  CS8x6;13 1966 HLâ93 (US) 7 1.272 1.649 HS 20â44 2.201 3.675 1.73 2.23  CS8x6;13 1966 HLâ93 (US) 8 1.21 1.569 HS 20â44 2.204 3.68 1.82 2.35 93 CS12x8;5 1966 HLâ93 (US) 0 0.567 0.734 HS 20â44 0.615 1.027 1.08 1.40  CS12x8;5 1966 HLâ93 (US) 0.5 0.54 0.701 HS 20â44 0.578 0.966 1.07 1.38  CS12x8;5 1966 HLâ93 (US) 1 0.511 0.663 HS 20â44 0.541 0.903 1.06 1.36  CS12x8;5 1966 HLâ93 (US) 1.5 0.479 0.621 HS 20â44 0.545 0.91 1.14 1.47  CS12x8;5 1966 HLâ93 (US) 1.9 0.451 0.584 HS 20â44 0.512 0.854 1.14 1.46  CS12x8;5 1966 HLâ93 (US) 2 0.496 0.642 HS 20â44 0.531 0.887 1.07 1.38  CS12x8;5 1966 HLâ93 (US) 3 0.538 0.698 HS 20â44 0.748 1.249 1.39 1.79Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ21  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CS12x8;5 1966 HLâ93 (US) 4 0.561 0.727 HS 20â44 0.813 1.358 1.45 1.87  CS12x8;5 1966 HLâ93 (US) 5 0.485 0.628 HS 20â44 0.748 1.249 1.54 1.99 94 CD4x3;11 1966 HLâ93 (US) 0 0.405 0.525 HS 20â44 0 0 0.00 0.00  CD4x3;11 1966 HLâ93 (US) 0.5 0.48 0.622 HS 20â44 0 0 0.00 0.00  CD4x3;11 1966 HLâ93 (US) 1 0.576 0.747 HS 20â44 0 0 0.00 0.00  CD4x3;11 1966 HLâ93 (US) 1.9 0.725 0.939 HS 20â44 0 0 0.00 0.00  CD4x3;11 1966 HLâ93 (US) 2 0.666 0.863 HS 20â44 0 0 0.00 0.00  CD4x3;11 1966 HLâ93 (US) 4 1.822 2.361 HS 20â44 4.163 6.952 2.28 2.94  CD4x3;11 1966 HLâ93 (US) 6 2.37 3.072 HS 20â44 6.623 11.061 2.79 3.60  CD4x3;11 1966 HLâ93 (US) 8 2.754 3.57 HS 20â44 6.995 11.682 2.54 3.27  CD4x3;11 1966 HLâ93 (US) 10 13.535 17.546 HS 20â44 11.551 19.291 0.85 1.10  CD4x3;11 1966 HLâ93 (US) 11 13.385 17.351 HS 20â44 11.494 19.195 0.86 1.11 95 CD6x4;4 1966 HLâ93 (US) 0 0.28 0.363 HS 20â44 0 0 0.00 0.00  CD6x4;4 1966 HLâ93 (US) 0.5 0.351 0.455 HS 20â44 0 0 0.00 0.00  CD6x4;4 1966 HLâ93 (US) 1 0.432 0.56 HS 20â44 0 0 0.00 0.00  CD6x4;4 1966 HLâ93 (US) 1.5 0.527 0.683 HS 20â44 0.496 0.828 0.94 1.21  CD6x4;4 1966 HLâ93 (US) 1.9 0.618 0.801 HS 20â44 0.476 0.796 0.77 0.99  CD6x4;4 1966 HLâ93 (US) 2 0.484 0.628 HS 20â44 0.847 1.415 1.75 2.25  CD6x4;4 1966 HLâ93 (US) 3 1.118 1.449 HS 20â44 1.653 2.761 1.48 1.91  CD6x4;4 1966 HLâ93 (US) 4 1.362 1.765 HS 20â44 2.564 4.282 1.88 2.43 96 CD8x6;3 1966 HLâ93 (US) 0 0.274 0.355 HS 20â44 0 0 0.00 0.00  CD8x6;3 1966 HLâ93 (US) 0.5 0.337 0.437 HS 20â44 0.583 0.974 1.73 2.23  CD8x6;3 1966 HLâ93 (US) 1 0.418 0.542 HS 20â44 0.553 0.924 1.32 1.70  CD8x6;3 1966 HLâ93 (US) 1.5 0.51 0.661 HS 20â44 0.567 0.946 1.11 1.43  CD8x6;3 1966 HLâ93 (US) 1.9 0.572 0.742 HS 20â44 0.54 0.902 0.94 1.22  CD8x6;3 1966 HLâ93 (US) 2 0.457 0.592 HS 20â44 0.691 1.155 1.51 1.95  CD8x6;3 1966 HLâ93 (US) 3 0.521 0.675 HS 20â44 0.609 1.017 1.17 1.51 97 CD12x8;2 1966 HLâ93 (US) 0 0.29 0.376 HS 20â44 0.554 0.926 1.91 2.46Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons  Lâ22  ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR  CD12x8;2 1966 HLâ93 (US) 0.5 0.367 0.475 HS 20â44 0.665 1.11 1.81 2.34  CD12x8;2 1966 HLâ93 (US) 1 0.455 0.59 HS 20â44 0.677 1.131 1.49 1.92  CD12x8;2 1966 HLâ93 (US) 1.5 0.555 0.72 HS 20â44 0.682 1.138 1.23 1.58  CD12x8;2 1966 HLâ93 (US) 1.9 0.578 0.749 HS 20â44 0.64 1.068 1.11 1.43  CD12x8;2 1966 HLâ93 (US) 2 0.481 0.624 HS 20â44 0.655 1.094 1.36 1.75 98 CD12x8;14 1966 HLâ93 (US) 0 0.515 0.668 HS 20â44 0.684 1.143 1.33 1.71  CD12x8;14 1966 HLâ93 (US) 1 0.752 0.975 HS 20â44 0.702 1.172 0.93 1.20  CD12x8;14 1966 HLâ93 (US) 1.9 0.924 1.198 HS 20â44 0.777 1.298 0.84 1.08  CD12x8;14 1966 HLâ93 (US) 2 0.666 0.863 HS 20â44 0.932 1.556 1.40 1.80  CD12x8;14 1966 HLâ93 (US) 4 1.625 2.106 HS 20â44 2.324 3.881 1.43 1.84  CD12x8;14 1966 HLâ93 (US) 7 2.31 2.994 HS 20â44 2.312 3.861 1.00 1.29  CD12x8;14 1966 HLâ93 (US) 9 2.052 2.66 HS 20â44 1.954 3.263 0.95 1.23  CD12x8;14 1966 HLâ93 (US) 11 1.583 2.052 HS 20â44 1.57 2.622 0.99 1.28  CD12x8;14 1966 HLâ93 (US) 13 1.085 1.406 HS 20â44 1.183 1.976 1.09 1.41  CD12x8;14 1966 HLâ93 (US) 14 0.604 0.783 HS 20â44 0.99 1.653 1.64 2.11 99 CS2x1_;32 1952 HLâ93 (US) 0 0.995 1.29 HS 20â44 0.641 1.07 0.64 0.83  CS2x1_;32 1952 HLâ93 (US) 1.9 2.341 3.035 HS 20â44 0.677 1.131 0.29 0.37  CS2x1_;32 1952 HLâ93 (US) 2 2.335 3.027 HS 20â44 2.983 4.982 1.28 1.65  CS2x1_;32 1952 HLâ93 (US) 4 6.337 8.215 HS 20â44 9.647 16.111 1.52 1.96  CS2x1_;32 1952 HLâ93 (US) 7 13.523 17.53 HS 20â44 22.315 37.266 1.65 2.13  CS2x1_;32 1952 HLâ93 (US) 12 30.496 39.531 HS 20â44 26.513 44.276 0.87 1.12  CS2x1_;32 1952 HLâ93 (US) 18 31.4 40.703 HS 20â44 28.209 47.108 0.90 1.16  CS2x1_;32 1952 HLâ93 (US) 24 32.303 41.875 HS 20â44 29.822 49.803 0.92 1.19  CS2x1_;32 1952 HLâ93 (US) 30 33.207 43.047 HS 20â44 31.186 52.081 0.94 1.21  CS2x1_;32 1952 HLâ93 (US) 32 33.509 43.437 HS 20â44 31.641 52.84 0.94 1.22 100 CS4x3;13 1952 HLâ93 (US) 0 0.773 1.002 HS 20â44 0.587 0.981 0.76 0.98  CS4x3;13 1952 HLâ93 (US) 1 0.908 1.177 HS 20â44 0.566 0.946 0.62 0.80  CS4x3;13 1952 HLâ93 (US) 1.9 1.077 1.396 HS 20â44 0.591 0.988 0.55 0.71Â
Appendix L â Caltrans ModelsâLRFRâLFR comparisons Lâ23 ID Culvert Name LRFD Vehicle Fill Height (ft) LRFR Inv LRFR Oper LFR Vehicle HS20â44 with a 1.25 factor LFR Inve LFR Opera Ratio Inventory LFR/LRFR Ratio Operating LFR/LRFR CS4x3;13 1952 HLâ93 (US) 2 0.966 1.253 HS 20â44 1.059 1.768 1.10 1.41 CS4x3;13 1952 HLâ93 (US) 4 1.983 2.57 HS 20â44 3.122 5.213 1.57 2.03 CS4x3;13 1952 HLâ93 (US) 7 3.644 4.724 HS 20â44 6.283 10.493 1.72 2.22 CS4x3;13 1952 HLâ93 (US) 9 8.235 10.675 HS 20â44 7.542 12.595 0.92 1.18 CS4x3;13 1952 HLâ93 (US) 11 8.091 10.488 HS 20â44 7.623 12.731 0.94 1.21 CS4x3;13 1952 HLâ93 (US) 12 8.018 10.394 HS 20â44 7.664 12.799 0.96 1.23 CS4x3;13 1952 HLâ93 (US) 13 7.946 10.301 HS 20â44 7.673 12.814 0.97 1.24Â
Appendix M â 3D Culvert Approach Mâ1 Appendix M â 3D Culvert Analysis Approach MEMORANDUM DATE: January 4, 2017 TO: Mark Mlynarski FROM: Thomas Murphy RE: NCHRP 15â54 â 3D Culvert Analysis PN3471 This memo documents M&Mâs planned approach to modeling the 6 test culverts using three dimensional FEA.  The intent is to communicate to the research team our approach, and resolve any concerns prior to beginning model development. Soil Constitutive Model: linearlyâelastic, perfectlyâplastic model with a MohrâCoulomb failure criterion for backfill soils and a linearâelastic model for inâsitu soils o LUSAS MohrâCoulomb material model will be used for backfill soils.  (See attached description) It is applicable where there is no volumetric strain during shear but allows volumetric plastic strain. ï§ MohrâCoulomb models require the following information: ï· Initial Cohesion ï· Initial Friction Angle ï· Final Friction Angle ï· Dilation Angle o We were not planning on getting into two phase material modeling, but rather adjusting the properties as appropriate when below the ground water table. o Modulus will vary depending on depth; use values shown in table below from Selig (1990) for backfill soil.  Use initial Maximum Principal Stress Level to determine which values to use based on compaction level.  Likely will bound the modulus. o For inâsitu soils, use a linear elastic material with an elastic modulus in the range of 6â20 ksi.  Modulus should be high enough to limit settlement of inâsitu soil in model.
Appendix M â 3D Culvert Approach   Mâ2   Pavement Constitutive Model: assume pavement behaves in linearâelastic fashion.Â ï· elastic pavement properties based on material (concrete or asphalt) o Asphalt pavement modulus varies based on temperature and individual materials; values increase with decreased temperaturesÂ ï§ Range from 70 ksi to 434 ksi in (Little, Crockford, & Gaddam 1992).Â ï§ Report provides the following equation for modulus based on temperature but is may only be useful for that particular combination of materials: E=e12.211195+0.056374Fâ0.000619F*F where F is in degrees Fahrenheit (note that this equation is only valid for a range of temperatures).  May be able to use other data in report to develop other equations. o Asphalt pavement Poissonâs ratio varies based on temperature and individual materials; values decrease with decreased temperature o Deteriorated pavement will be modeled using either reduced thickness or reduced modulus.  Upper and lower limits will be bounded in the analyses.  3D FEA Element UsageÂ ï· Culvert Structure Elements â use shell elements with linear elastic material propertiesÂ
Appendix M â 3D Culvert Approach   Mâ3  o Use isotropic material properties/elements for concrete and smooth metal culverts.  For concrete, an effective moment of inertia will be utilized in those areas where preliminary analysis indicates cracking is likely. o Use orthotropic material properties/elements for corrugated metal and profile wall culverts.    With orthotropic material properties, the bending stiffness in both directions will be correct, and the axial stiffness in one direction will be correct, but not in the other.  This approach will be validated with a more detailed model.Â ï· CulvertâSoil Interface â The interface will not be explicitly modeled.Â ï· Soil â use hexahedra solid elements to represent soil, using material properties from Selig.  We will define different materials to be used throughout the depth of the trench to account for the variation in principal stress.Â ï· Pavement â use solid elements to represent pavement  o select reasonable values for required material properties o Use of solid elements will allow modeling of the load spreading through the pavement in both horizontal directions.Â ï· Refine mesh based on initial results; increase density in areas of large strains.Â ï· Choice of linear or quadratic elements (midâside nodes) left to designer based on speed and accuracy of results.  MODELING TECHNIQUES:Â ï· Extents of soil to be included in analysis o The width of the model will be approximately 3 times the culvert span o Model full length of culvert o Include 2Ãculvert rise of soil under bottom of trench surface where culvert is placed, may reduce to 1Ãculvert rise due to load spreading through the pavement and soil above the culvert.Â ï· Do not model stages of construction and backâfill, but assume a soil density and inâsitu stress state.Â ï· Inâsitu stresses o Assumed based on depth of culvert and type of soils o Vertical pressure will depend on the material â take as γÃh where γ is the unit weight of the overburden soil and h is the depth to the location of interest. o Horizontal pressure will depend on the vertical pressure and Ko as well as the amount of water present.Â ï§ Ko can range from 0.3 to 1.1 depending on the type of soil.  Will use one of the common equations for concrete culverts.  Use of equations for metal culverts will have to be evaluated. A panel member asked how Ko is computed. In finite element analysis the lateral pressures develop as soil is placed in increments. The lateral pressures are variable as a function of the soil properties input by the user. This can result in some discrepancies from frame analysis results where specific lateral pressures are input. We will assess whether these discrepancies are acceptable or need to be addressed.Â ï§ Î³Â ranges from 70â150 lb/ft3 o accounted for using initial stress loadingsÂ ï· Live loads o Wheel loads and areas need to be measured during field testing to be used in LUSASÂ
Appendix M â 3D Culvert Approach   Mâ4  o Wheel loads will be modeled using patch loads o Wheel loads will be marched across the structure in each analysis â use nonâlinear analysisÂ ï· Nonlinear & Transient Analysis o We will not consider consolidation, or other timeârelated effects.Â ï· Support conditions o RestraintsÂ ï§ Horizontal restraint provided on vertical faces of soilÂ ï§ Provide vertical restraint at bottom surface of modelÂ ï§ Restrain rotation about the Xâ (along direction of travel) and Yâ (vertical) axes at the culvert edges at the extents of the model. o Rigid restraints or springsÂ ï§ Will use rigid restraints with the model boundaries a relatively large distance away from the culvert such that their effect is minimized.   REFERENCES Selig, E.T. (1990), âSoil Properties for Plastic Pipe Installations,â Buried Plastic Pipe Technology, STP1093, G.S. Buczala and M.J. Cassady, Eds., ASTM, Philadelphia, PA, pp. 141â158.  Little, D.N., W.W. Crockford, and V.K.R. Gaddam. (1992), âResilient Modulus of Asphalt Concrete.â Texas Transportation Institute, The Texas A&M University System, College Station, TX, 168 pp, Report No. FHWA/TXâ93â1177â1F. Â
