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92 C H A P T E R 4 Conclusions and Suggested Research Following are the conclusions and recommendations that can be drawn based on the review of the analysis results shown in this report and in the appendices: Recommendations â AASHTO LRFD Bridge Design Specifications ï· Depth of live load, Article 220.127.116.11a 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 (design tandem) 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 resulting in a factored live load of 26% of the factored earth load and a net load factor of 1.14. 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. ï· Live load distribution, Articles 18.104.22.168a, Article 22.214.171.124.2 â The current specifications for live load distribution through earth fill are discontinuous at a depth of 2 feet of fill due to change from a slab bridge distribution procedure (Article 126.96.36.199) to a distribution through earth fill procedure (Article 188.8.131.52.6). The suggested revision is based on an investigation of this research of 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 184.108.40.206 and 220.127.116.11 are both expressed in terms of wheel loads. The new equations in 18.104.22.168.3 provide the expressions necessary to address the interaction of adjacent axles for multi-axle configurations such as tandems and tridems. ï· Lateral Pressure Coefficient, Article 22.214.171.124 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 MBE. 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. ï· Approaching wheel load, Article 126.96.36.199.1 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. Figure 71 (previous chapter) 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 pressures, are the peak pressures and decrease away from the wheel location.
93 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. Recommendations â AASHTO Manual for Bridge Evaluation (MBE) ï· LRFR Culverts, New Article 6A.10 A new section for rating of culverts in LRFR has been added. This touches on rating issues such as use of spring constants, finite element modeling, use of pavements, shear capacity, and approaching wheel load (live load surcharge). It also includes sections on metal, thermoplastic and fiberglass culverts. ï· ASD/LFD Culverts, New Article 6B.10 This section provides guidance for rating culverts that were designed using ASD or LFD. These recommend changes are presented in the following section. The changes in ballot item format are provided in Appendix H. Proposed Revisions to the LRFD Specifications and the MBE Based on the conclusions and proposals presented, the following revisions to the LRFD Specifications and to the MBE are suggested. Deletions and additions are noted. The full background of each proposed revision (in ballot item format) is provided in Appendix H of this report. The proposed revisions on the following pages are modified from the AASHTO Manual for Bridge Evaluation, 3rd Edition and the AASHTO LRFD Bridge Design Specifications, 8th Edition, by the American Association of State Highway and Transportation Officials, Washington, DC. Used by permission.
94 Article 188.8.131.52.6a Revise the first paragraph of Article 184.108.40.206.6a-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. Article 220.127.116.11.6a 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 18.104.22.168. 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 22.214.171.124. 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 Revise Article 126.96.36.199.2 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 (188.8.131.52.2-1) Parallel to the span: Espan = td2 + LLDF(H) (184.108.40.206.2-2) Add to notation td1 = tire dimension (lt or wt, see 220.127.116.11.6) perpendicular to the span td2 = tire dimension (lt or wt, see 18.104.22.168.6) parallel to the span Revise Article C22.214.171.124.2 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 C126.96.36.199.2-1.
95 Figure C188.8.131.52.2-1 â Single-Axle Transverse Distribution Through Fill Revise Article 184.108.40.206.3 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 (220.127.116.11.2-3) Parallel to the span: Espan = td2 + LLDF(H) (18.104.22.168.2-4) where: Ax = No. of axles in axle group Axxp = Spacing of axles in axle group
96 Revise Article C22.214.171.124.3 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. Article 126.96.36.199 Addition to Article 188.8.131.52 184.108.40.206-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: C220.127.116.11 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. Article 18.104.22.168.1 Add new title to Article 22.214.171.124.1 Article 126.96.36.199.1 Walls (Section otherwise unchanged) Add new article: Article 188.8.131.52.2 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. 184.108.40.206.2-1: âp(hd) = 700/hd â¤ 800 psf Eq. 220.127.116.11.2-1 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.
97 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 C18.104.22.168.1 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, Figure C22.214.171.124.1-1, replaces the live load surcharge as more appropriate for culverts. Figure C126.96.36.199.1-1 â Approaching Wheel Load Pressure Condition for Culverts Delete Article 6A.5.12 As noted, portions of this Article are incorporated into the proposed new Article 6A.10 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. These include culvert dimensions, materials and material properties, and â¤Â 2Â ft ApproachingÂ wheelÂ loadÂ â appliedÂ toÂ bothÂ sidesÂ ofÂ culvert
98 installation methods. The data from construction documents, including culvert dimensions, materials and 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.
99 Table 6A.10.3.1-1 Modulus of Subgrade Reaction for Bedding Support of Rectangular Concrete Culverts Soil Range2 (pci) Rating Values3 (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 â¤ 4 ksf 40-85 60 8 ksf â¤ qu â¤ 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 midspan, 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 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
100 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. 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:
101 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.1-.4-1) In which, for the strength limit states: ð¶ ð ð ðð (6A.1-.4-2) Where: 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 Î³DC = LRFD load factor for structural components and attachments Î³DW = LRFD load factor for wearing surfaces and utilities Î³EV = LRFD load factor for vertical earth pressure Î³EH = LRFD load factor for horizontal earth pressure Î³ES = LRFD load factor for earth surcharge Î³LL = evaluation live load factor Î³AW = Live 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.
102 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.
103 Table 6A.10.5-1 Limit States and Load Factors for Culvert Load Rating (Modified from current MBE Table 6A.5.12.5-1)
104 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.188.8.131.52-Dead Loads No change from current Article 6A.5.12.9 6A.184.108.40.206- Earth Pressure 6A.220.127.116.11a-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.18.104.22.168b-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 22.214.171.124. 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.126.96.36.199c-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. 6A.10.10.3-Live Loads No change from current Article 6A.188.8.131.52 C6A.184.108.40.206 No change from current Article C6A.220.127.116.11
105 C6A.18.104.22.168a-Live Load Distribution Current specification Article 6A.22.214.171.124a 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 126.96.36.199.6a do not require rating for live loads. Change 2 â Deleted sentence. No replacement. Change 3 â Replace deleted sentence with: 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 188.8.131.52. 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.184.108.40.206b
106 C6A.220.127.116.11b No change from current Article C6A.18.104.22.168b 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 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 22.214.171.124. 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.
107 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: 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.
108 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 126.96.36.199.2, 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 188.8.131.52.2-1) Use the unmodified Mu if the controlling factored 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. 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.
109 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. 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. 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.
110 Suggested Research In addition to the results of the research and recommendations provided in the previous section, the following are recommended follow-ups to the research of this project: â Updates to CANDE â The CANDE software was updated for this project and is included as part of the deliverable. While in some cases the analysis engine was updated, time and budget constraints prevented the CANDE graphical user interface from being updated. The software is not unusable in its current form but should be updated so that the GUI input matches the formatted text input of the analysis engine. â Updates to the CANDE Tool Box â while this was not a software development project, the CANDE Tool Box was developed for this research to facilitate the investigation. Currently the CANDE Tool Box runs as a separate pre-processor and post-processor to the CANDE software. While the software worked well for this research and can continued to be used, the integration of these tools into the CANDE software would be beneficial to future users. â CANDE import â An export file from BrR to CANDE could be developed to allow for box culverts developed in BrR be exported to CANDE input files for further analysis. Conversely, an export file from CANDE to a BrDR could also be created so that CANDE models could be imported into BrDR. This would need to be discussed under the AASHTOWare contract. â LFRD-LFD comparison â and initial comparison of the LRFD/LFD ratings for a set of reinforced concrete box culverts were made for this project using BrR. A full review of these results was not completed for this project and perhaps this comparison could be made with the culverts gathered for this research. (See Appendix L). Data Archiving Upon completion of the analysis and testing program phases, many data are available that could aid future researchers. This section provides a description of the data that is delivered this project These include but are not necessarily limited to:Â â Any changes in the CANDE software that are used for this project â CANDE input files used for this research project â AASHTOWare BrDR export files (XML) of all culverts analyzed for this project â AASHTOWare regression data with newly created report IDâs defined â 3D FEM model files used during the analysis phase â Field testing data The files described above are documented and included as a final delivery for the research project. The full documentation of the files is provided on the media on which it is delivered. The following sections provide a brief description of the anticipated data included for each item. Changes to the CANDE Software The revised CANDE software, both program source code and compiled installation versions of the software is provided. This code is documented and new features of the software are documented within the programs User Manuals. A new manual is provided for the CANDE Tool Box software is provided on the media (see Appendix C of this report as well). A revised installation of the software is also provided. CANDE Input Files The CANDE input files used for this project are documented and included on the media delivered with the final report. The documentation includes descriptions of each file or groups of files along with a summary description of the contents.
111 AASHTOWare BrDR Export Files (XML) The AASHTOWare BrDR software has the intrinsic capability to export bridge files (in this case culvert files) to an XML format that can then be reimported into future versions of the software. The BrDR export files for each culvert used in this research are included on the media delivered with this project. This includes the test suite provided by Caltrans and revised for this project along with additional BrDR culvert files created for this project. The files are documented in a summary form and are included with the delivered research data. AASHTOWare BrDR Regression Data/Report ID Descriptions AASHTOWare BrDR has the ability to produce output data in a format similar to that developed for NCHRP 12-50. The data for each of the culverts run in the current version of BrDR will be saved for use in comparison with BrDR data after specification changes have been implemented. This type of comparison is referred to as regression testing. The regression testing data for culverts in AASHTOWare BrDR was recently updated and can be useful for this type of testing. The regression test files from both original version of BrDR with unchanged specs along with the regression data from the revised specs are included in the data delivery. The data includes a summary document of each file or groups of files. In addition, a document providing a description of the report IDs is provided. For a description of âreport IDs, see NCHRP Report 485: Bridge SoftwareâValidation Guidelines and Examples. 3D FEM Files The research team used the LUSAS finite element modeling software to perform all of the 3D analyses required as part of the analytical work performed for NCHRP 15-54. In an effort to preserve the data for future use, the archival of the native LUSAS command (data input) files will be supplemented by also saving the model data in one of the various neutral and/or third party formats available as export options within the current version of LUSAS. Below is a summary of the various file formats supported in LUSAS for importing and exporting model data. Interface file name and extension Import file into LUSAS? Export file from LUSAS? CMD (.cmd) YES YES SOLVER Data File (.dat) YES NO DXF (.dxf) YES YES IGES (.igs) YES YES LMS CADA-X (.nf) YES YES NASTRAN Bulk Data Files (.bdf, .dat) YES NO ANSYS (cdb) YES NO ABAQUS (.input) YES NO PATRAN (.def) YES NO STEP (.step, .stp) YES YES STL (.stl) YES YES Interface files are used to transfer external modeling or material data into and out of LUSAS Modeller. The full model or a selected portion of a model can, dependent upon the file format chosen, be exported to a chosen interface file. The currently supported list of interface file formats is:
112 â CMD (.cmd) Format for import of LUSAS Modeller model files saved as command (CMD) files in previous versions of LUSAS. Â â Solver Data Files (.dat) LUSAS Solver data files (used to import or node and element data). â DXF (.dxf) AutoCAD Drawing eXchange Format. â IGES (.igs) Initial Graphics Exchange Specification. Format for import and export of geometry data. â LMS CADA-X (.nf) Model description and modal data exported to a file that can be read by the LMS software. â NASTRAN Bulk Data files (.bdf, .dat) (used to import node and element data). â ANSYS cdb files (.cdb) (used to import node and element data). â Abaqus input files (.inp) (used to import node and element data). â PATRAN (.def) Neutral file format for inputting phase I geometry information and outputting phase II mesh information. â STEP (.stp) Standard for the Exchange of Product data. â STL (.stl) Stereolithography data files. Field Testing Data The raw data files arising out of the field testing effort is include along with the post-processed data that is also be archived in a readily accessible format, e.g., Microsoft Excel spreadsheets or ASCII text files. The content of the files is documented for content and format.