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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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Suggested Citation:"Chapter 3." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Modifications to AASHTO Culvert Load Rating Specifications. Washington, DC: The National Academies Press. doi: 10.17226/25673.
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43 C H A P T E R 3 Findings and Applications This chapter summarizes the findings from the literature review, field testing, analysis, and the experiences of the research team and discusses application to practice. The summary of the outcomes of this chapter (specification recommendations) are provided in Chapter 4. Calibration of the 3D Models The field testing and portions of the analytical program are closely linked in that the FEA models are an analytical representation of what is being tested in the field. The models create during phase II were constructed using available information from the contract plans of the structures with consideration of the type of installation and backfill material specified in the contract documents. The initial models developed in phase II were used as a starting point. Any other pertinent information available in the field was included where possible in the modeling effort including pavement type and condition, actual test loading and installed sensor positions, environmental conditions, etc., with the objective of matching the analytical model as closely as possible to the field test conditions. Summaries of each of the seven field tests are presented in Appendix K. Additional details on the modeling approach taken in the development of Model 7 are also provided in that appendix due to the complexities involved in the modeling of the corrugations of a metal culvert. Model 7 is also unique in that this was the only culvert where the RT was able to model the culvert both before and after paving as this model was under construction during these tests. In reviewing the results presented in Appendix K, it should be noted that deflection measurements capture the total response of the soil-structure system, while strains measurements capture thrusts and moments. Deflection and strain measurements were compared to computer model predictions to assess the accuracy of the model. The research team adjusted the models based on this comparison. A complete match of model to field data is often difficult with buried structures as many material properties cannot be as accurately characterized as in the case of above ground bridges. As such, the research team looked for significant deviations from expected results that indicate unanticipated behavior. The calibration effort involved the development of the 3D models in LUSAS and applying loading conditions to match the applied experimental loads used in the field testing of each of the culverts. The strains and deflection data obtained in the field is offloaded from the data acquisition system and imported into spreadsheet form for further processing. This processing involves a review of the data, averaging raw strain and deflection values to remove “noise” and formatting the data to appear in a more readily understood form (labeling, etc.) This data is then combined with the recorded time data taken in the field that represents the time window for each loading condition. Stresses and deflections within each of those time windows are then averaged to generate values to be compared to analytical results from the 3D models. The first step of the calibration consists of an initial review of the output to see that the deflected shape of the culvert conforms to the expected shape under the applied loading and is also in line with the field- obtained data. If good agreement between the field and analytical data is not observed at the onset, adjustments are made to the models to attempt to achieve better agreement. This includes adjustments to the geometric stiffness which must be approximated in particular for the corrugated metal structures,

44 material stiffness for concrete structures where the compressive strength may differ from the target design strength and can also be impacted by cracking. Soil properties are also considered in the adjustments to the model as necessary to complete the calibration. The modeling effort and the calibration methods used for Model 7 (the long span corrugated steel culvert) was documented and details of that calibration are provided in Appendix K. The RT documented notable aspects of the calibration effort for each of the models included in the summary reports of these calibrations. Summary of Areas of Specification to Review This section provides a summary and background for the proposed specifications and any background data for the expected effect that those revisions will have. Chapter 4 of the report contains the recommended specification changes based on this research. Appendix H contains the draft specification agenda items –

45 Effects of Subgrade on Rating The effects of using the modulus of subgrade reaction to model the foundation support under box culverts are discussed in this section. Three different subgrade soils will be used for comparison purpose. The culverts were analyzed using AASHTOWare BrDR using a variety of fill depths. The models used were the field tested RC box models and a couple of the models provided by Caltrans. Each model was analyzed in BrDR; once without considering spring support and additional runs considering spring supports with different subgrade moduli (see Figure 39). Figure 39 – BrDR Input Window for Spring Constants Design of box culverts in BrDR typically applies vertical loads as uniform pressures. This approach ignores the effects of soil-culvert interaction which produces a beneficial redistribution of load with pressure peak over the sidewalls and reduced pressure at midspan. This is demonstrated in Figure 40 taken from the CANDE program. The higher soil strains near midspan produce shear stresses in the soil that transfer load toward the corners of the box section. This reduces the moments. BrDR can reproduce this effect by the use of springs under the bottom slab that simulate soil-culvert interaction. The effect is significant in the bottom slab at all depths of fill and in the top slab at deep fills. The moments in the top slab of shallow culverts is dominated by moving vehicle loads and load redistribution cannot be modeled with BrDR. This redistribution suggests areas for improvement in culvert rating: • Providing guidance for spring stiffnesses when rating with BrDR or other box culvert programs that support spring stiffeners. Stiffer foundation soils will result in greater redistribution of soil pressure and a more significant reduction in moments and shears. • For deep culverts, where the top and bottom slabs are subject to the same vertical forces, the bottom slab shear and moment forces, which benefit from the load redistribution, can be considered as governing the top slab as well if the geometry and reinforcement are the same in the top and bottom of the culvert.

46 Figure 40 – Vertical Soil Strain (in./in.) on Concrete Box Section The benefits of using springs is demonstrated in the form of rating factors from BrDR based on the analyses listed in Table 3. Table 3 – Description of Models Analyzed in BrDR Along with Soil Models for Spring Constants Model Description Modulus of Subgrade Re Model 1 – NCHRP 15-54 field tested model Single Cell Culvert: 25’ span 7.5’ height Various Fill Depths 100 kcf (Clayey soil qu<4 ksf) 200 kcf (Medium Dense Sand) 400 kcf (Clayey Soil, qu>8 ksf) Model 2 – NCHRP 15-54 field tested model Twin Cell Culvert 2-10’ spans 7’ height Various fill depts 100 kcf (Clayey soil qu<4 ksf) 200 kcf (Medium Dense Sand) 400 kcf (Clayey Soil, qu>8 ksf) Model 3 – NCHRP 15-54 field tested model Single Cell Culvert 12’ span 6’ height 100 kcf (Clayey soil qu<4 ksf) 200 kcf (Medium Dense Sand) 400 kcf (Clayey Soil, qu>8 ksf) CS16x12;0 1922 EAE-200kcf Caltrans Model (y. 1922) Single Cell Culvert 16’ span 12’ height 200 kcf (Medium Dense Sand) CS12x8;10 1952-Rev-200KCF Caltrans Model (y. 1952) Single Cell Culvert 12’ span 8’ height 200 kcf (Medium Dense Sand) The rating factors for varying fill depths are provided in the following tables and figures. Table 4 provides an inventory/operating rating factor comparison for LRFR with an HL93 vehicle in a model with no foundation springs and a model with a 100 kcf subgrade modulus. Table 5 provides a similar comparison for 200 kcf subgrade modulus and Table 6 with a 400 kcf subgrade modulus. Figure 42 through Figure 46

47 provide comparative plots of the HL93 inventory ratings for 200 kcf springs/no-springs. As expected, the benefit of the springs is minimal for depths of cover less than 2 ft and increasingly more significant as the depth increases and is greater with stiffer subgrade soils. The benefit due to the use of springs is not as evident in Model 2, a two-cell culvert, due to the presence of the center wall which reduces deflection of the slab and the subsequent redistribution of load. The recommendations for the agenda item related to this are provided in Chapter 4 of this report. The agenda item is provided in Appendix H. It should be noted that a decrease in the rating factor occurs as the fill depth increases for some of the culvert models. An example is the Model 1 RF in Table 4 (highlighted) which for inventory (with 100 kcf springs) decreases from 1.376 to 0.816 when the fill depth changes from 5 feet to 7 feet. The operating rating factor also decreases in the same range from 1.793 to 1.058. Looking closely at the rating differences between the 5’ and 7’ layer for the 100 kcf springs indicates that the DL is increasing at a faster rate than the LL is decreasing. The plot in Figure 41 below shows the plot of the regression data produced by BrDR where the DL, LL, and Capacity changes as the fill increases for the Model 1 culvert with springs. A similar plot occurs (not pictured) for the case without springs. The rating factor (RF) is also plotted. From this graph, the rating factors are calculated as follows (all units in kip-feet). At 5’ fill RF = (56.593 -35.31)/15.472 = 1.376 At 7’ fill RF = (56.855 – 47.037)/12.029 = 0.816 As the graph illustrates, the dead load is about 62% of the capacity at 5 feet of fill and about 84% of the capacity at 7 feet of fill. At the same time the live load is about 27% of the capacity at 5 feet of fill and only decreases to 21% at 7 feet of fill. It should also be noted that for Model 2, the springs will have little effect. This is a shallow culvert where live load effects dominate the rating factor in the upper half of the culvert. Figure 41 – Rating Results Moment (left vertical axis), Rating (right vertical axis) vs. Fill Depth

48 Table 4 – Rating Factors – Models 1,2,3 – No Springs vs. 100 kcf Fill Depth (ft) Vehicle HL93-Inv- NoSprings HL93-Op- NoSprings HL93-Inv- 100 kcf Springs HL93-Op- 100kcf Springs Inv- Ratio* Op- Ratio* Model 1 1.5 HL-93 (US) 0.8 1.038 0.802 1.04 0.998 0.998 1.99 HL-93 (US) 0.733 0.95 0.739 0.957 0.992 0.993 2 HL-93 (US) 1.47 1.905 1.541 1.998 0.954 0.953 2.1 HL-93 (US) 1.486 1.927 1.56 2.022 0.953 0.953 2.2 HL-93 (US) 1.502 1.947 1.577 2.045 0.952 0.952 2.4 HL-93 (US) 1.531 1.984 1.611 2.088 0.950 0.950 2.5 HL-93 (US) 1.538 1.994 1.621 2.101 0.949 0.949 3 HL-93 (US) 1.509 1.956 1.61 2.087 0.937 0.937 5 HL-93 (US) 1.147 1.487 1.376 1.783 0.834 0.834 7 HL-93 (US) 0.395 0.512 0.816 1.058 0.484 0.484 Model 2 1.5 HL-93 (US) 0.791 1.026 0.782 1.014 1.012 1.012 1.9 HL-93 (US) 0.8 1.037 0.783 1.015 1.022 1.022 2 HL-93 (US) 1.524 1.976 1.541 1.998 0.989 0.989 2.5 HL-93 (US) 1.712 2.22 1.717 2.225 0.997 0.998 3 HL-93 (US) 1.92 2.489 1.925 2.495 0.997 0.998 3.5 HL-93 (US) 2.148 2.784 2.152 2.789 0.998 0.998 4 HL-93 (US) 2.335 3.027 2.339 3.032 0.998 0.998 7 HL-93 (US) 3.271 4.24 3.19 4.136 1.025 1.025 10 HL-93 (US) 2.738 3.55 2.671 3.462 1.025 1.025 Model 3 1.5 HL-93 (US) 1.452 1.882 1.461 1.894 0.994 0.994 1.9 HL-93 (US) 1.452 1.882 1.461 1.894 0.994 0.994 2 HL-93 (US) 1.414 1.833 1.423 1.845 0.994 0.993 2.5 HL-93 (US) 1.547 2.006 1.558 2.019 0.993 0.994 3 HL-93 (US) 1.7 2.204 1.713 2.22 0.992 0.993 3.5 HL-93 (US) 1.811 2.347 1.841 2.386 0.984 0.984 4 HL-93 (US) 1.823 2.363 1.943 2.519 0.938 0.938 7 HL-93 (US) 1.627 2.11 1.859 2.41 0.875 0.876 10 HL-93 (US) 0.841 1.09 1.206 1.564 0.697 0.697 *the ratios indicate the no spring model RF divided by the spring model rating factor. A value less than 1.0 indicates a higher RF for the spring model.

49 Table 5 – Rating Factors – Models 1,2,3 – Caltrans Models – No Springs vs. 200 kcf Fill Depth (ft) Vehicle HL93-Inv- NoSprings HL93-Op- NoSprings HL93- Inv- 200 kcf Springs HL93- Op- 200 kcf Springs Inv-Ratio* Op-Ratio* Model 1 1.5 HL-93 (US) 0.8 1.038 0.803 1.041 0.996 0.997 1.99 HL-93 (US) 0.733 0.95 0.739 0.958 0.992 0.992 2 HL-93 (US) 1.47 1.905 1.573 2.039 0.935 0.934 2.1 HL-93 (US) 1.486 1.927 1.593 2.064 0.933 0.934 2.2 HL-93 (US) 1.502 1.947 1.611 2.089 0.932 0.932 2.4 HL-93 (US) 1.531 1.984 1.646 2.134 0.930 0.930 2.5 HL-93 (US) 1.538 1.994 1.657 2.148 0.928 0.928 3 HL-93 (US) 1.509 1.956 1.655 2.146 0.912 0.911 5 HL-93 (US) 1.147 1.487 1.438 1.864 0.798 0.798 7 HL-93 (US) 0.395 0.512 0.9 1.167 0.439 0.439 Model 2 1.5 HL-93 (US) 0.791 1.026 0.783 1.015 1.010 1.011 1.9 HL-93 (US) 0.8 1.037 0.785 1.017 1.019 1.020 2 HL-93 (US) 1.524 1.976 1.54 1.996 0.990 0.990 2.5 HL-93 (US) 1.712 2.22 1.729 2.241 0.990 0.991 3 HL-93 (US) 1.92 2.489 1.939 2.514 0.990 0.990 3.5 HL-93 (US) 2.148 2.784 2.169 2.811 0.990 0.990 4 HL-93 (US) 2.335 3.027 2.357 3.055 0.991 0.991 7 HL-93 (US) 3.271 4.24 3.288 4.263 0.995 0.995 10 HL-93 (US) 2.738 3.55 2.861 3.708 0.957 0.957 Model 3 1.5 HL-93 (US) 1.452 1.882 1.469 1.904 0.988 0.988 1.9 HL-93 (US) 1.452 1.882 1.469 1.904 0.988 0.988 2 HL-93 (US) 1.414 1.833 1.431 1.855 0.988 0.988 2.5 HL-93 (US) 1.547 2.006 1.567 2.031 0.987 0.987 3 HL-93 (US) 1.7 2.204 1.723 2.233 0.986 0.987 3.5 HL-93 (US) 1.811 2.347 1.852 2.401 0.977 0.977 4 HL-93 (US) 1.823 2.363 1.956 2.535 0.932 0.932 7 HL-93 (US) 1.627 2.11 2.128 2.758 0.764 0.765 10 HL-93 (US) 0.841 1.09 1.631 2.114 0.515 0.515 CS16x12;0 1922 EAE-200kcf 1.5 HL-93 (US) 0.559 0.725 0.695 0.901 0.804 0.805 1.9 HL-93 (US) 0.512 0.664 0.662 0.858 0.773 0.774 2 HL-93 (US) 0.496 0.643 0.649 0.841 0.764 0.765 2.5 HL-93 (US) 0.52 0.674 0.675 0.874 0.770 0.771

50 Fill Depth (ft) Vehicle HL93-Inv- NoSprings HL93-Op- NoSprings HL93- Inv- 200 kcf Springs HL93- Op- 200 kcf Springs Inv-Ratio* Op-Ratio* 3 HL-93 (US) 0.514 0.666 0.693 0.898 0.742 0.742 3.5 HL-93 (US) 0.439 0.569 0.682 0.884 0.644 0.644 4 HL-93 (US) 0.35 0.454 0.661 0.857 0.529 0.529 CS12x8;10 1952-Rev-200KCF 1.5 HL-93 (US) 0.923 1.197 0.911 1.18 1.013 1.014 1.9 HL-93 (US) 0.905 1.173 0.899 1.165 1.006 1.007 2 HL-93 (US) 1.027 1.332 1.08 1.401 0.951 0.951 3 HL-93 (US) 1.243 1.611 1.267 1.643 0.981 0.981 4 HL-93 (US) 1.315 1.705 1.396 1.809 0.942 0.942 7 HL-93 (US) 1.204 1.56 1.481 1.92 0.813 0.813 10 HL-93 (US) 0.363 0.471 0.609 0.789 0.596 0.597 *the ratios indicate the no spring model RF divided by the spring model rating factor. A value less than 1.0 indicates a higher RF for the spring model.

51 Table 6 – Rating Factors – Models 1,2,3 – No Springs vs. 400 kcf Fill Depth (ft) Vehicle HL93- Inv No Springs HL93- Op-No Springs HL93- Inv 400 kcf Springs HL93- Op 400 kcf Springs Inv- Ratio* Op- Ratio* Model 1 1.5 HL-93 (US) 0.8 1.038 0.804 1.042 0.995025 0.996161 1.99 HL-93 (US) 0.733 0.95 0.74 0.959 0.990541 0.990615 2 HL-93 (US) 1.47 1.905 1.604 2.08 0.916459 0.915865 2.1 HL-93 (US) 1.486 1.927 1.625 2.106 0.914462 0.915005 2.2 HL-93 (US) 1.502 1.947 1.644 2.131 0.913625 0.913656 2.4 HL-93 (US) 1.531 1.984 1.681 2.179 0.910767 0.910509 2.5 HL-93 (US) 1.538 1.994 1.693 2.194 0.908447 0.908842 3 HL-93 (US) 1.509 1.956 1.701 2.205 0.887125 0.887075 5 HL-93 (US) 1.147 1.487 1.5 1.944 0.764667 0.764918 7 HL-93 (US) 0.395 0.512 0.983 1.274 0.401831 0.401884 Model 2 1.5 HL-93 (US) 0.791 1.026 0.784 1.016 1.008929 1.009843 1.9 HL-93 (US) 0.8 1.037 0.787 1.021 1.016518 1.015671 2 HL-93 (US) 1.524 1.976 1.551 2.011 0.982592 0.982596 2.5 HL-93 (US) 1.712 2.22 1.745 2.262 0.981089 0.981432 3 HL-93 (US) 1.92 2.489 1.958 2.538 0.980592 0.980693 3.5 HL-93 (US) 2.148 2.784 2.19 2.839 0.980822 0.980627 4 HL-93 (US) 2.335 3.027 2.384 3.09 0.979446 0.979612 7 HL-93 (US) 3.271 4.24 3.419 4.433 0.956712 0.956463 10 HL-93 (US) 2.738 3.55 3.241 4.201 0.844801 0.845037 Model 3 1.5 HL-93 (US) 1.452 1.882 1.482 1.921 0.979757 0.979698 1.9 HL-93 (US) 1.452 1.882 1.482 1.921 0.979757 0.979698 2 HL-93 (US) 1.414 1.833 1.444 1.872 0.979224 0.979167 2.5 HL-93 (US) 1.547 2.006 1.582 2.05 0.977876 0.978537 3 HL-93 (US) 1.7 2.204 1.74 2.256 0.977011 0.97695 3.5 HL-93 (US) 1.811 2.347 1.872 2.427 0.967415 0.967037 4 HL-93 (US) 1.823 2.363 1.979 2.565 0.921172 0.921248 7 HL-93 (US) 1.627 2.11 2.51 3.254 0.648207 0.648433 10 HL-93 (US) 0.841 1.09 2.254 2.922 0.373114 0.373032 *the ratios indicate the no spring model RF divided by the spring model rating factor. A value less than 1.0 indicates a higher RF for the spring model.

52 Figure 42 – Model 1 – HL93-Inventory Rating Factors vs. Fill Depth – No Spring vs. 200 kcf Figure 43 – Model 2 – HL93-Inventory Rating Factors vs. Fill Depth – No Spring vs. 200 kcf

53 Figure 44 – Model 3 – HL93-Inventory Rating Factors vs. Fill Depth – No Spring vs. 200 kcf Figure 45–Caltrans-CS16x12-1922 – HL93-Inventory Rating Factors vs. Fill Depth – No Spring vs. 200 kcf

54 Figure 46 –Caltrans CS12x8-1952– HL93-Inventory Rating Factors vs. Fill Depth – No Spring vs. 200 kcf

55 Design-Analysis Much of the Design-Analysis guidance was based on results presented in the following paragraphs. The conclusion from that study are presented as an agenda item in Appendix H of this report. In the RT’s experience, box culvert computer design programs often make different assumptions in modeling and designing box sections. This can result in unnecessarily conservative designs/ratings if the assumptions do not address actual behavior and in varying rating strengths relative to design strengths if different programs are used for design and rating. If a less conservative program is used for rating, the capacity will be underestimated and could result in rating factors less than one for good culverts. Analysis/Design decisions that can affect load rating include:  the stiffness effect of haunches,  the change in critical design locations resulting from haunches,  reduction of reinforcement tension by compressive thrust, and  load redistribution due to culvert and soil stiffness. This review evaluates design and analysis options in three computer programs and how those options can affect box culvert load ratings.  BOXCAR – BOXCAR V3.2 designs box sections in accordance with current AASHTO LRFD Specifications. BOXCAR, or its predecessors has been used to develop all of the standard designs for precast concrete box sections in ASTM and AASHTO product specifications. Analysis in BOXCAR is completed with an elastic frame model. BOXCAR does not rate culverts but produces output that is sufficient for rating.  CANDE – CANDE is a finite element program developed to analyze and design all types of culverts. CANDE was developed by FHWA for the purpose of completing soil-structure interaction models of culverts. CANDE incorporates non-linear models for steel, reinforced concrete and embedment soils.  BrDR – BrDR is the AASHTO software for designing and rating bridges. BrDR includes a module for the design and analysis of buried culverts. An analysis was performed on a 10 ft span by 10 ft rise culvert with geometry based on a 1962 Caltrans design, as presented in Table 7. This geometry demonstrates the features of concern in comparing programs. Table 7 - Box Study Culvert Geometry Parameter Cover over reinforcement Span (ft) 10 All inside reinforcement (in) 1.5 Rise (ft) 10 Top outside (in) 2.0 Top slab thickness (in) 9.5 Side outside (in) 1.5 Bottom slab thickness (in) 10 Bottom outside ((in) 3.0 Wall thickness (in) 11 Material strengths Vertical haunch (in) 0, 10 Reinforcement yield stress (ksi) 60.0 Horizontal haunch (in) 0, 10 Concrete design strength (ksi) 4.0 Some evaluations were conducted in design mode to generate required reinforcing areas (BOXCAR) while others were conducted in evaluation mode to determine design forces and/or ratings. In all cases, the

56 reinforcing layouts consisted of u-shaped outside reinforcement extending into and lapping at the center of the top and bottom slabs and straight bars for inside reinforcement. The culvert was subjected to earth loads using a soil density of 120 pcf. Live load was HL-93 for BOXCAR and BrDr, but just the design tandem for CANDE (i.e. 2-25kip axles spaced at 4’). Figure 47 shown below is taken from ASTM C1433 for precast reinforced concrete box sections. The diagram for Fill Height 2 ft and Greater shows the reinforcement layout, except for our modeling we extended the U bars to the center of the slab to avoid numerical issues in CANDE. Figure 47 – Figure from ASTM C1433 for Precast Reinforced Concrete Box Sections BOXCAR - The culvert was analyzed at depths of 0.0, 2.0, 8.0, and 12.0 feet. Reinforcement and shear capacities are presented in Table 8 and Table 9.

57 Table 8 – BOXCAR Reinforcement (in^2/ft) Depth (ft) 0.0 2.00 8.0 8.0 No LL 12.0 12.0 No LL 12.0 No Thrust With Haunches Outside 0.264 0.264 0.264 0.264 0.280 0.264 0.420 Top inside 0.427 0.411 0.352 0.253 0.450 0.389 0.493 Bottom inside 0.355 0.389 0.379 0.278 0.478 0.416 0.538 Without Haunches Outside 0.323 0.486 0.637 - - - - Top inside 0.459 0.450 0.389 - - - - Bottom inside 0.397 0.440 0.447 - - - - Notes:  Outside reinforcement in the section with haunches is always controlled in the sidewall and is minimum required reinforcement to depths through 8 ft.  Outside reinforcement in the box without haunches is always controlled in the top slab.  At a depth of 8.0 ft the outside reinforcement in the section without haunches is controlled by cracking which is not a required check for rating. Table 9 – BOXCAR Shear Loads (Fraction of capacity) Depth (ft) 0.0 2.00 8.0 8.0 No LL 12.0 12.0 No LL With Haunches Top slab 1.01 0.91 0.52 0.40 0.66 0.60 Bottom slab 0.77 0.84 0.66 0.54 0.82 0.75 Without Haunches Top slab 1.13 0.99 0.63 0.49 Bottom slab 1.04 0.94 0.80 0.66 Effect of Haunches - The inclusion of haunches results in significantly reduced reinforcement due to the following effects:  The stiffness effect of haunches increases the negative corner moments and decreases the positive moments.  Haunches reduce inside and outside reinforcement. The outside reinforcement decreases even though the corner moments increase since the critical design location moves from top slab face of wall to sidewall tip of haunch.

58  Design shear forces are reduced as the location of the critical sections moves to a distance “d” from the tip of the haunch. Design for Shear Capacity -  Exceeding the shear capacity at zero cover was expected based on the culvert geometry and the concrete strength. At the time this culvert was designed the code allowed slabs that met flexural design requirements to be assumed adequate in shear.  The change in shear design criteria in the LRFD Specifications results in a significant increase in shear capacity as the fill depth becomes greater than 2.0 ft. At depths less than 2 ft shear is evaluated using the general design method in LRFD Article 5.7.3 while at depths greater than 2 ft the shear strength need is evaluated according to LRFD Article 5.7.12.3, where the β factor need not be taken less than 3. Live Load Attenuation with Depth It is common among designers to read the LRFD Specifications as not requiring consideration of live loads for depths greater than 8 ft, although the specifications state “Live load may be neglected when the depth of fill is more than the span length and exceeds the span length; for multiple span culverts the effects may be neglected where the depth of fill exceeds the distance between the inside faces of the end walls.” This requires that as the span increases above 8 ft the depth of fill for live load design increases at the same rate.  At a depth of 8 ft earth load reinforcement accounts for about 70% of the total reinforcement.  At a depth of 12 ft earth load reinforcement accounts for about 86% of total reinforcement. For the box culvert considered above, with 12 ft of cover, the live load would not be considered in design according to the current LRFD Specifications (Depth greater than 8 ft and greater than the span). If considered, the factored live load moment is 15% of the total factored earth moment under typical frame analysis assumptions (i.e. BOXCAR type analysis). The factored dead load moment is 20% greater than the service earth plus live load moments, suggesting a net load factor of about 1.2. While this is less than commonly assumed target values, the project team is unaware of performance issues related to the current design specifications. This is in part due to the small overall live load relative to earth load, but there is additional safety due to the assumption of uniform pressure distribution, as shown elsewhere in this report. Consideration of Thrust -  At a depth of 8 ft, required outside reinforcement increases about 10% if the calculation does not include the effect of compressive thrust. The project team recommends that thrust always be considered in design and rating. This produces economy in design without reducing overall safety. We included the analysis with and without thrust as we have seen some computer programs in the past that did not include thrust. We wished to demonstrate the shortcomings of that approach.  At a depth of 12 ft required outside reinforcement increases about 50% if the calculation does not include the effect of compressive thrust. CANDE CANDE is a culvert-soil interaction program. As such, it does not apply loads directly to the culvert, rather it allows the soil and culvert to interact as governed by the material properties and calculates the internal structural forces that result. There are many levels of sophistication in how finite element analyses are conducted. CANDE incorporates non-linear soil and non-linear culvert behavior to allow matching actual in situ behavior as closely as possible.

59 In this study, CANDE was operated in an analysis mode where reinforcement areas are provided, and the output is the culvert response. For this comparison, the CANDE model incorporated reinforcement that approximated the BOXCAR analysis for 8 ft of fill without live load (see Table 10). Table 10 – Reinforcement Areas in CANDE Models (in2/ft) Outside Top inside Bottom inside 0.26 0.35 0.35 In situ soil was modeled as a linear elastic soil with a modulus of 5,000 psi while the bedding and backfill were modeled as with non-linear properties representing a sandy gravel without fines compacted to 90% of maximum standard Proctor density. A key feature of culvert-soil interaction analysis is that the soil pressures on the culvert are not uniform. The culvert slabs deflect at midspan which results in a shift of load toward the corners. This is demonstrated in Figure 48 which shows the soil vertical strains at a depth of 8 ft. The deflection at midspan allows more vertical strain and thus the transfer of load to the corners. This effect varies with the stiffness (soil type and compaction level) of the materials around the culvert and is generally more pronounced in the bottom slab as in situ soils are often quite stiff. Figure 48 – CANDE Typical Vertical Strain Around Box Section A first comparison is the design forces calculated in CANDE versus those calculated in BOXCAR (see Table 11).

60 Table 11 – Comparison of Factored Moments – CANDE vs BOXCAR, 8 Ft Fill (ft-k/ft) No Haunch – No LL No Haunch – LL Haunch CANDE BOXCAR CANDE BOXCAR CANDE BOXCAR Negative -12.9 -11.8 -13.9 -14.8 -7.6 -11.9 Top positive 10.0 11.6 12.7 14.0 9.2 10.5 Bottom positive 10.9 14.9 10.8 16.6 10.6 12.8 Note: The controlling moment for negative reinforcement occurs in the slabs for sections without haunches and in the walls for sections with haunches For the section without haunches, Table 11 shows comparable moments for the negative and top positive moments and substantially lower moment for the bottom positive moment which is a result of the load redistribution discussed above. The positive moments are lower when haunches are added, particularly the negative moments in CANDE due to the load redistribution. BOXCAR shows about the same negative moment with and without haunches; however, the shift of the critical section from the top slab to the sidewall means more compressive thrust and more favorable geometry as the wall is thicker than the top slab and the reinforcing cover is reduced in the sidewall, hence the reduction in reinforcement with haunches shown in Table 7 for BOXCAR. CANDE shows the bottom slab moments to be relatively unchanged with or without haunches and live loading. This is because the soil-structure interaction results in high vertical pressures under the culvert walls and low vertical pressure at midspan. We recommend that rectangular box section continue to be designed using frame models and uniform pressure assumptions. This offers simplicity of design and has a long history of successful application. For special cases, where rating proves difficult with this approach, finite element analysis offers more accurate modeling of soil-culvert interaction and can reduce the moment and shear forces with the resulting pressure redistributions. Structures designed with finite element analysis should be rated with finite element modeling. CANDE is only one such finite element program but it was developed specifically for culverts and has a load rating function in the latest version developed under this project. BrDr AASHTOWare BrDR was used to rate the culvert at depths of 0 ft, 2 ft, and 8 ft. At 0 and 2 ft the standard distributed load assumption was used while at 8 ft the standard distribution was compared to spring supports with stiffnesses of 100 and 400 pci. In all cases the reinforcement provided was based on the BOXCAR evaluations at 8 ft of fill. Results are presented in Table 12.

61 Table 12 – BrDr Inventory Rating Factors Depth (ft) Load application No Haunch Loc./Limit With Haunch Loc./Limit 0 Distributed 0.93 Top/shear 1.14 Top/shear 2 Distributed 1.10 Top/flexure 1.19 Top/flexure 8 Distributed 1.81 Top/flexure 1.88 Bot/flexure 8 Bedding springs, 100 pci 1.86 Top/flexure 2.10 Bot/flexure 8 Bedding springs, 400 pci 1.99 Top/flexure 2.42 Top/flexure Review of Table 12 in light of the BOXCAR analyses and reinforcement level indicates the following:  The rating factor at 0.0 ft cover and no haunches of less than 1.0 was expected.  The rating factors at 2.0 ft cover of just over 1.0 were expected given the reinforcement was based on BOXCAR analysis at 8 ft.  Introducing haunches improves the rating factor.  The introduction of spring support for the bedding reaction increases the rating factor as a function of the spring stiffness. At 400 pci in the section with haunches the limiting location shifts back to the top slab. This is consistent with the low forces in the bottom slab in CANDE. Discussion and Findings The results presented above confirm some prior knowledge about box section capacity and demonstrates several areas where changes to current design and rating procedures may be made. Known analysis/design features that should be clearly delineated in the MBE include:  Haunches should be included in the analysis if present in the actual box section. This includes the stiffness effect of haunches and the change in design locations.  The effect of compressive thrust in reducing reinforcing requirements can be significant, especially for deeper culverts. This should be considered in design and rating. A change in live load distribution at 2 ft of fill is a long-standing feature of the AASHTO design specifications related to the change in treatment of the top slab from a bridge deck to a buried slab. While this was mitigated with revisions to the AASHTO Design Specifications in 2000, there is still a slight change. The bridge deck treatment takes advantage of the longitudinal stiffness of the top slab to increase the load distribution provided by the soil. The research team looked at two options for providing a uniform change in load:   The simple approach of using the deck strip width at depths greater than 2 ft until the distribution width calculated using the soil distribution width is greater.  Dr. Katona developed another approach based on engineering mechanics (See Appendix I). While the research team found this approach to offer little benefit for new design which requires design only for a single loaded lane with multiple presence factor of 1.2. This approach provides adequate designs for multiple lane conditions. The method proposed by Dr. Katona provides greater distribution widths for single lane loadings but would not result in significant savings or increased ratings as the multiple lane conditions would limit the width that could be used. The method has applications for low volume roads where a rating engineer might consider only a single lane loading as appropriate. The consideration of culvert-soil interaction in CANDE or spring supports in BrDr improves culvert design and rating. Based on this limited study the effect is greater in CANDE where load redistribution

62 occurs in both the top and bottom slab. The difficulty in this approach for design is uncertainty about the foundation and backfill stiffness that will be achieved in the field. However, for rating culverts, where construction records and inspection findings can provide guidance on the stiffness of the bedding and backfill, this should be a good tool to help improve ratings. The BOXCAR models show that the factored live load is about 36% of the total factored load (factored vertical earth plus live load) at a depth of 8 feet, controlled by the design tandem. This percentage continues to decrease with increasing depth of cover. This raises the question of whether rating should be required for culverts under deep fills and if not, at what depths it could be dispensed with. Again, there are two possibilities:  AASHTO LRFD Specifications do not require consideration of live load if the depth is greater than 8 ft and greater than the span of the culvert. One approach is to accept the current limit not require rating for live load if consideration in design was not required. However, this approach would require longer span culverts to be designed for live load at considerable depths, such as the model 1 culvert in this program, with a 25 ft span.  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. Shear strength of slabs in concrete box culverts is problematic in that many culverts were designed at a time when slabs were assumed adequate in shear if properly designed for flexure yet do not meet current standards for shear strength capacity. In general, these culverts are providing good service. We recommend that rating engineers investigate these culverts and how they are analyzed to determine if a refined approach such as discussed here will show that these culverts can be rated. If that is not possible, we will include a provision in the MBE recommendations that the culvert may be rated at 1.0 for shear strength if inspections show it to be in good condition.

63 Culvert Load Distribution The proposed culvert load distribution modifications are shown in Appendix H Agenda Item (Subject: Live Load Distribution for Culverts). The changes are to Article 3.6.1.2.6a and various parts of Article 4.6.2.10. The changes were incorporated into a debug version of BrDR and regression test to determine the overall effects of the change. Since the tire dimensions used for the test were 20” x 10”, the primary effects occur at the 2’ fill mark where there was a slight increase in the rating factor for the revised change. The results using several of the Caltrans culverts (modified) are shown in Table 13. Culverts with 2 foot of cover show a slight improvement in rating factor and no change at other depths. Table 13 – Effects on Rating Factors for Changes to LRFR Live Load Distribution in BrDR Caltrans Culvert Name, Year Built Fill Depth Vehicle Inv Rating Before Change Op Rating Before Change Inv Rating After Change Op Rating After Change Inv Ratio Before/ After* Op Ratio Before/ After CD8x8;10 1924-Rev 1.9 ft Cover HL-93 (US) 0.579 0.751 0.579 0.751 1 1 CD8x8;10 1924-Rev 2 ft Cover HL-93 (US) 0.596 0.773 0.602 0.781 0.990 0.990 CD8x8;10 1924-Rev 3 ft Cover HL-93 (US) 1.27 1.646 1.27 1.646 1 1 CD8x8;10 1933-Rev 1.9 ft Cover HL-93 (US) 0.657 0.851 0.657 0.851 1 1 CD8x8;10 1933-Rev 2 ft Cover HL-93 (US) 0.676 0.876 0.684 0.886 0.988 0.989 CD8x8;10 1933-Rev 3 ft Cover HL-93 (US) 1.388 1.8 1.388 1.8 1 1 CD10x8;3 1952-Rev 1.9 ft Cover HL-93 (US) 0.578 0.75 0.578 0.75 1 1 CD10x8;3 1952-Rev 2 ft Cover HL-93 (US) 0.594 0.77 0.6 0.778 0.990 0.990 CD10x8;3 1952-Rev 3 ft Cover HL-93 (US) 0.706 0.915 0.706 0.915 1 1 CD10x8;16 1966-Rev 1.9 ft Cover HL-93 (US) 0.736 0.954 0.736 0.954 1 1 CD10x8;16 1966-Rev 2 ft Cover HL-93 (US) 0.753 0.976 0.762 0.987 0.988 0.989 CD10x8;16 1966-Rev 2.5 ft Cover HL-93 (US) 1.125 1.459 1.125 1.459 1 1 CD10x8;16 1966-Rev 3 ft Cover HL-93 (US) 1.449 1.879 1.449 1.879 1 1 CS10x8;5 1922-Rev 1.9 ft Cover HL-93 (US) 0.932 1.208 0.932 1.208 1 1 CS10x8;5 1922-Rev 2 ft Cover HL-93 (US) 0.917 1.189 0.924 1.197 0.992 0.993 CS10x8;5 1922-Rev 2.5 ft Cover HL-93 (US) 0.985 1.277 0.985 1.277 1 1 CS10x8;5 1922-Rev 3 ft Cover HL-93 (US) 1.041 1.35 1.041 1.35 1 1 CS10x8;5 1933-Rev 1.9 ft Cover HL-93 (US) 0.748 0.97 0.748 0.97 1 1 CS10x8;5 1933-Rev 2 ft Cover HL-93 (US) 0.735 0.952 0.74 0.959 0.993 0.993 CS10x8;5 1933-Rev 2.5 ft Cover HL-93 (US) 0.768 0.996 0.768 0.996 1 1 CS10x8;5 1933-Rev 3 ft Cover HL-93 (US) 0.786 1.018 0.786 1.018 1 1

64 Caltrans Culvert Name, Year Built Fill Depth Vehicle Inv Rating Before Change Op Rating Before Change Inv Rating After Change Op Rating After Change Inv Ratio Before/ After* Op Ratio Before/ After CS10x8;10 1933-Rev 1.9 ft Cover HL-93 (US) 1.297 1.681 1.297 1.681 1 1 CS10x8;10 1933-Rev 2 ft Cover HL-93 (US) 1.282 1.661 1.291 1.674 0.993 0.992 CS10x8;10 1933-Rev 2.5 ft Cover HL-93 (US) 1.409 1.827 1.409 1.827 1 1 CS10x8;10 1933-Rev 3 ft Cover HL-93 (US) 1.559 2.021 1.559 2.021 1 1 CD12x8;9 1948-Rev 1.9 ft Cover HL-93 (US) 0.569 0.737 0.569 0.737 1 1 CD12x8;9 1948-Rev 2 ft Cover HL-93 (US) 0.553 0.717 0.606 0.785 0.912 0.913 CD12x8;9 1948-Rev 4 ft Cover HL-93 (US) 0.811 1.052 0.811 1.052 1 1 CD12x8;9 1952-Rev 1.9 ft Cover HL-93 (US) 0.834 1.081 0.834 1.081 1 1 CD12x8;9 1952-Rev 2 ft Cover HL-93 (US) 0.855 1.108 0.865 1.121 0.988 0.988 CD12x8;9 1952-Rev 3 ft Cover HL-93 (US) 1.501 1.945 1.501 1.945 1 1 CD12x12;2 1966-Rev 1.9 ft Cover HL-93 (US) 0.545 0.706 0.545 0.706 1 1 CD12x12;2 1966-Rev 2 ft Cover HL-93 (US) 0.516 0.67 0.517 0.67 0.998 1 CD12x12;2 1966-Rev 2.5 ft Cover HL-93 (US) 0.383 0.496 0.383 0.496 1 1 CD12x12;2 1966-Rev 3 ft Cover HL-93 (US) 0.244 0.316 0.244 0.316 1 1 CD12x12;20 2010- Rev 1.9 ft Cover HL-93 (US) 1.553 2.013 1.553 2.013 1 1 CD12x12;20 2010- Rev 2 ft Cover HL-93 (US) 2.435 3.157 2.452 3.179 0.993 0.993 CD12x12;20 2010- Rev 2.5 ft Cover HL-93 (US) 2.435 3.157 2.452 3.179 0.993 0.993 CD12x12;20 2010- Rev 3 ft Cover HL-93 (US) 3.359 4.355 3.359 4.355 1 1 CS12x8;5 1922-Rev 1.9 ft Cover HL-93 (US) 0.98 1.27 0.98 1.27 1 1 CS12x8;5 1922-Rev 2 ft Cover HL-93 (US) 0.965 1.251 0.972 1.26 0.993 0.993 CS12x8;5 1922-Rev 3 ft Cover HL-93 (US) 1.098 1.423 1.098 1.423 1 1 CS12x8;10 1952-Rev 1.9 ft Cover HL-93 (US) 0.905 1.173 0.905 1.173 1 1 CS12x8;10 1952-Rev 2 ft Cover HL-93 (US) 1.027 1.332 1.035 1.341 0.992 0.993 CS12x8;10 1952-Rev 3 ft Cover HL-93 (US) 1.243 1.611 1.243 1.611 1 1 CS12x8;10 2010-Rev 1.9 ft Cover HL-93 (US) 0.748 0.97 0.748 0.97 1 1 CS12x8;10 2010-Rev 2 ft Cover HL-93 (US) 1.576 2.043 1.587 2.058 0.993 0.992 CS12x8;10 2010-Rev 2.5 ft Cover HL-93 (US) 1.733 2.246 1.733 2.246 1 1 CS12x8;10 2010-Rev 3 ft Cover HL-93 (US) 1.913 2.48 1.913 2.48 1 1

65 Caltrans Culvert Name, Year Built Fill Depth Vehicle Inv Rating Before Change Op Rating Before Change Inv Rating After Change Op Rating After Change Inv Ratio Before/ After* Op Ratio Before/ After CS12x12;10 2002- Rev 1.9 ft Cover HL-93 (US) 0.569 0.738 0.569 0.738 1 1 CS12x12;10 2002- Rev 2 ft Cover HL-93 (US) 1.339 1.736 1.349 1.749 0.992 0.992 CS12x12;10 2002- Rev 2.5 ft Cover HL-93 (US) 1.465 1.899 1.465 1.899 1 1 CS12x12;10 2002- Rev 3 ft Cover HL-93 (US) 1.584 2.053 1.584 2.053 1 1 *Ratios are of the Before Rating Factor / After Rating Factor. If this ratio is less than 1.0 the rating factor improved.

66 Non-Rectangular Culverts Culverts other than box sections incorporate a range of shapes and sizes and are designed by a variety of methods, most developed by manufacturer’s trade associations and then adopted by AASHTO. While design procedures for concrete box culverts have evolved, procedures for other types of culverts have remained largely unchanged since first added to the AASHTO Specifications. Thus, providing methods to deal with changes, e.g. early box sections were assumed adequate in shear if designed properly to meet flexure requirements, is not necessary for these other types of culverts. Culverts carry loads through their own structure and through soil support. This is particularly true for the non-rectangular shapes. The nature of soil support is a key factor in rating the non-rectangular shapes and this must be evaluated through inspections. Inspections should document culvert shape, cracks in culvert walls, and any other field conditions that indicate potential distress. Design methods for flexible pipe in particular must consider the effect of shape change in the rating calculation. Concrete pipes have long been designed with an indirect design procedure based on the three-edge bearing test. In the 1980’s the concrete pipe industry developed a direct design method based on finite element analyses. Both methods are incorporated into the LRFD Specifications. Concrete pipes can be rated by either method, but should be completed by the same method used for design as the methods produce different results. In the experience of the research team, the direct design method is quite conservative when applied to small diameter pipes. There are a number of different corrugated metal structures and each has its own design method – empirical (pipe and long-span structures), semi-empirical (box culverts) and rigorous (deep corrugated). These structures must be rated by the same method by which they were designed. The National Corrugated Steel Pipe Association (NCSPA) issued Design Data No. 19 Load Rating and Structural Evaluation of In- Service Corrugated Steel Structures (NCSPA DD 19) in 1995 which provides useful guidance that is still applicable to most metal culvert types today. Deep corrugated structures were added to AASHTO Specifications after the publication of NCSPA DD 19. These structures are designed and should be rated by finite element analysis. The Ohio DOT has developed a series of spreadsheets to conduct rating calculations for metal culverts based on NCSPA DD 19. They have also developed a procedure to rate metal pipe installed at less than the AASHTO prescribed minimum depth of fill. Other states are using these methods and are satisfied with the findings. Thermoplastic pipe design procedures have evolved some since first incorporated in the LRFD Specifications, but the current procedure is applicable to all thermoplastic pipes. The method is semi- empirical in nature but addresses all key limit states. Fiberglass pipe, the most recent addition to the LRFD Specifications, are designed and should be rated in accordance with the procedures in American Water Works Association Manual of Practice 54 (AWWA M54). This method was developed in the 1980’s by the AWWA and has served as a national and international standard for fiberglass pipe design since that time. Pavement This section provides the background for the effects of pavement on the ratings of culverts. The first section provides a review of the Model 7 culvert that was load tested with and without pavement. The next section provides a review of the CANDE models created using the CANDE Tool Box developed for this project and reviewed/rated for pavement and no pavement.

67 Model 7 3D Analysis Review 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. The following sections present 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 the approach to the 3-D modeling of this culvert in LUSAS is documented in detail in Appendix K and Appendix M. Culvert Loading and Instrumentation Each phase included three main sets of loading (Figure 49): N1, with the center of truck over the center of the 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. The truck dimensions for each phase is provided in Figure 50. Five clusters of four gages (20 gages total) were mounted on the lower face of the culvert as shown in Figure 51. 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 (see Figure 52). Figure 49 M7C1 Plan View: Showing Location of Gages and Truck Positioning for Each Set of Test Figure 50 - Truck Dimensions for Each Phase of Testing

68 Figure 51 - Instrumentation Locations

69 Load Set 1 thru 7. Load Set 8 thru 15. Figure 52 - Schematics of Loading for Each Load Case for Culvert 7

70 Results Before and After Paving While the results presented in Appendix K and Appendix M document the selection of a 3-D 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 3-D LUSAS models. In the figures below (Figure 53 to Figure 67), 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. Figure 53 - Model 7 Before and After Paving: Test N1, Gauges 1-4 (Cluster 5) Figure 54 - Model 7 Before and After Paving: Test N1, Gauges 5-8 (Cluster 4) ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 1‐ Test 1 Gage 2‐ Test 1 Gage 3‐ Test 1 Gage 4‐ Test 1 Gage 1‐ Test 2 Gage 2‐ Test 2 Gage 3‐ Test 2 Gage 4‐ Test 2 ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 5‐ Test 1 Gage 6‐ Test 1 Gage 7‐ Test 1 Gage 8‐ Test 1 Gage 5‐ Test 2 Gage 6‐ Test 2 Gage 7‐ Test 2 Gage 8‐ Test 2

71 Figure 55 - Model 7 Before and After Paving: Test N1, Gauges 9-12 (Cluster 3) Figure 56 - Model 7 Before and After Paving: Test N1, Gauges 13-16 (Cluster 2) ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 9‐ Test 1 Gage 10‐ Test 1 Gage 11‐ Test 1 Gage 12‐ Test 1 Gage 9‐ Test 2 Gage 10‐ Test 2 Gage 11‐ Test 2 Gage 12‐ Test 2 ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 13‐ Test 1 Gage 14‐ Test 1 Gage 15‐ Test 1 Gage 16‐ Test 1 Gage 13‐ Test 2 Gage 14‐ Test 2 Gage 15‐ Test 2 Gage 16‐ Test 2

72 Figure 57 - Model 7 Before and After Paving: Test N1, Gauges 17-20 (Cluster 1) Figure 58 - Model 7 Before and After Paving: Test N2, Gauges 1-4 (Cluster 5) ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 17‐ Test 1 Gage 18‐ Test 1 Gage 19‐ Test 1 Gage 20‐ Test 1 Gage 17‐ Test 2 Gage 18‐ Test 2 Gage 19‐ Test 2 Gage 20‐ Test 2 ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 1‐ Test 1 Gage 2‐ Test 1 Gage 3‐ Test 1 Gage 4‐ Test 1 Gage 1‐ Test 2 Gage 2‐ Test 2 Gage 3‐ Test 2 Gage 4‐ Test 2

73 Figure 59 - Model 7 Before and After Paving: Test N2, Gauges 5-8 (Cluster 4) Figure 60 - Model 7 Before and After Paving: Test N2, Gauges 9-2 (Cluster 3) ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 5‐ Test 1 Gage 6‐ Test 1 Gage 7‐ Test 1 Gage 8‐ Test 1 Gage 5‐ Test 2 Gage 6‐ Test 2 Gage 7‐ Test 2 Gage 8‐ Test 2 ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 9‐ Test 1 Gage 10‐ Test 1 Gage 11‐ Test 1 Gage 12‐ Test 1 Gage 9‐ Test 2 Gage 10‐ Test 2 Gage 11‐ Test 2 Gage 12‐ Test 2

74 Figure 61 - Model 7 Before and After Paving: Test N2, Gauges 13-16 (Cluster 1) Figure 62 – Model 7 Before and After Paving: Test N2, Gauges 17-20 (Cluster 1) ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 13‐ Test 1 Gage 14‐ Test 1 Gage 15‐ Test 1 Gage 16‐ Test 1 Gage 13‐ Test 2 Gage 14‐ Test 2 Gage 15‐ Test 2 Gage 16‐ Test 2 ‐7.000 ‐5.000 ‐3.000 ‐1.000 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 17‐ Test 1 Gage 18‐ Test 1 Gage 19‐ Test 1 Gage 20‐ Test 1 Gage 17‐ Test 2 Gage 18‐ Test 2 Gage 19‐ Test 2 Gage 20‐ Test 2

75 Figure 63 – Model 7 Before and After Paving: Test N3, Gauges 1-4 (Cluster 5) Figure 64 – Model 7 Before and After Paving: Test N3, Gauges 5-8 (Cluster 4) ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 1‐ Test 1 Gage 2‐ Test 1 Gage 3‐ Test 1 Gage 4‐ Test 1 Gage 1‐ Test 2 Gage 2‐ Test 2 Gage 3‐ Test 2 Gage 4‐ Test 2 ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 5‐ Test 1 Gage 6‐ Test 1 Gage 7‐ Test 1 Gage 8‐ Test 1 Gage 5‐ Test 2 Gage 6‐ Test 2 Gage 7‐ Test 2 Gage 8‐ Test 2

76 Figure 65 – Model 7 Before and After Paving: Test N3, Gauges 9-12 (Cluster 3) Figure 66 – Model 7 Before and After Paving: Test N3, Gauges 13-16 (Cluster 2) ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 9‐ Test 1 Gage 10‐ Test 1 Gage 11‐ Test 1 Gage 12‐ Test 1 Gage 9‐ Test 2 Gage 10‐ Test 2 Gage 11‐ Test 2 Gage 12‐ Test 2 ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 13‐ Test 1 Gage 14‐ Test 1 Gage 15‐ Test 1 Gage 16‐ Test 1 Gage 13‐ Test 2 Gage 14‐ Test 2 Gage 15‐ Test 2 Gage 16‐ Test 2

77 Figure 67 – Model 7 Before and After Paving: Test N3, Gauges 17-20 (Cluster 1) ‐7.000 ‐6.000 ‐5.000 ‐4.000 ‐3.000 ‐2.000 ‐1.000 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 17‐ Test 1 Gage 18‐ Test 1 Gage 19‐ Test 1 Gage 20‐ Test 1 Gage 17‐ Test 2 Gage 18‐ Test 2 Gage 19‐ Test 2 Gage 20‐ Test 2

78 CANDE Models with and Without Pavement Several of the models in this study were analyzed in CANDE with varying fill heights and with and without pavement elements. These were analyzed using CANDE and the new features provided in the CANDE Tool Box. Each of the models were reviewed and the rating results compared. For discussion purposes, Model 7 results are shown here while the analysis for the remaining models are provided in Appendix D of this report. Model 7 The original CANDE mesh for this model was provided by CONTECH. The general process for modifying the model is described in an earlier section of this report. A sample mesh of the model is provided in Figure 68 below. The model was modified to include the moving tandem load and was analyzed with and without pavement. Figure 68 – M7C1 Sample CANDE Mesh Without Pavement The rating analysis for the culvert with and without pavement using a two axle tandem load and excluding lane load is provided in Table 14. A schematic showing the beam nodes referenced in the table are provided in Figure 69. The results for this model and those presented in Appendix D for the other models indicate that the pavement provides a benefit for increasing the rating factor. Table 14 – M7C1 Rating Results Rating No pavement E = 200,000 psi  = 0.33 Pavement (6”) 1.5 ft fill Material Thrust 14.64 (Node 16) 15.61 (Node 14) Buckling Thrust 8.56 (Node 16) 4.57 (Node 9) Seam Thrust 14.64 (Node 16) 15.61 (Node 14) Plastic-Penatrate 10000 (Node 1) 10000 (Node 1) Combined T&M Ratio 2.13 (Node 23) 3.75 (Node 23)

79 Figure 69 – Node Numbering for M7C1 Recommendations We conclude that live load ratings can be improved by including the effects of pavement. A 3-D model is not required to analyze live load response associated with a paved surface. As discussed and detailed in the previous section, the 2-D CANDE software has been modified to allow the user to specify a paved surface (See Chapter 2 of this report and Appendix C-CANDE Tool Box Manual for Load Rating).Recommendations for using pavement for rating is provided in the form of recommend specification changes and are provided in Chapter 4 and in Appendix H. A parametric study of the 2D models tested for this project using CANDE and the CANDE Tool Box is provided in Appendix D. The recommendations for reducing loads on culverts from the effects of pavement are provided in Chapter 4 and in the Appendix H ballot items (Subject: Rating and Condition Evaluation of Culverts).

80 Shear Capacity The shear capacity of reinforced concrete culverts was reviewed as part of this research. The following sections provide the reasoning for the changes recommend in Chapter 4 of this report related to the AASHTO MBE Article 6A.5.13.1. The final agenda item for Shear Capacity is provided in Appendix H (Ballot MBE-1) and is also highlighted in Chapter 4 The culvert set described in this section was analyzed and ratings were saved for the existing 3rd Edition MBE using the AASHTOWare BrR program (version 6.8.3). The Inventory HL93 shear ratings were compared with the same ratings after the proposed modifications were made for BrDR. The comparative results for the shear rating are provided in a table later in this section. The PennDOT study (modified from McGrath et al., 2004, 2005) investigated longitudinal live load distribution (i.e., distribution perpendicular to the span) for the purpose of investigating the suitability of the distribution incorporated into the 2nd Edition of the LRFD Specifications relative to the provision from the AASHTO Standard Specifications. Figure 70 presents the distribution of forces at critical design sections from that study. Figure 70 – Distribution Width vs. Span (PennDOT Study, McGrath et al, 2004, 2005)

81 The PennDOT study concluded that the distribution from the AASHTO Standard Specifications (red dotted line) matched the distribution width for shear forces and was the most conservative. Based on this, the provisions of the AASHTO Standard Specification were adopted into the LRFD Specifications. However, the positive and negative moments distribute over broader widths. The proposed fix to the shear equation is to reduce the negative moments at dv from the tip of the haunch to take advantage of that broader distribution. The solid blue line represents a curve proposed to reduce negative moments at critical shear design locations as discussed below. Reducing the negative moments increases the shear strength as described here. In the LRFD general procedure, the reinforcement strain is computed as: The term Mu/dv is significant in this equation and reducing the moment to reflect the PennDOT report figure effectively reduces the reinforcement strain. However, the LRFD definitions state that Mu shall not be taken less than Vu * d, a limitation that prevents a significant increase in capacity. Therefore, two steps are required to improve ratings based on shear. 1. Reduce the negative moments at the controlling shear design sections (not at all locations). 2. Eliminate the requirement that Mu> Vu*d. This change is suggested only for the rating top slabs of box culverts under less than 2 ft of fill and showing good performance in the field. Box culverts with more than two feet of fill are designed by Article 5.12.7.3 which allows using a minimum β factor of 3.0. The modification is based on relating the LRFD Load distribution width Equation 4.6.2.10-1: Axle Distribution = 96 + 1.44 * Span to the solid blue line shown in Figure 70: Modified Axle Distribution = 96 + 5.47 * Span Assuming the greater distribution width produces a proportional reduction in the live load moment at critical shear sections, we can compute a reduction factor for the live load moments to be used in Eq. 5.7.3.4.2-4): Moment Modification Factor = Axle Distribution/Modified Axle Distribution Economic Impact Overall the change provided an improvement in shear rating factors for many culverts with a fill depth below 2’. Cases where no improvement was shown are when the value for Mu is greater than zero at the dcritical location. Table 15 provides a comparison of differences in the shear rating factor with the revised specification vs. the existing specification. The values displayed are for covers below 2 feet. As expected, no changes were detected above 2 feet of cover. The full table showing all of the culvert runs for the shear capacity changes

82 is provided in Appendix G. These were run using AASHTOWare BrR using a revision to 6.8.3 of the software. The ratio in the final column is of the existing shear capacity calculation to the revised shear capacity calculation. A value below 1.0 indicates an improvement in the rating factor for HL93. Many of the culverts were obtained from Caltrans and show a variety of culvert sizes and years built. The Models 1, 2, and 3 were culverts that were load tested for the NCHRP 15-54 project. Improvements for this change were shown below 2’ of fill. The average shear rating factor improvement for fills below 2’ is about 8.5% with a maximum improvement of about 20% (Culvert Model1 with 1.5 foot of fill -1.8193 vs a previous value of 1.4574).

83 Table 15 – Comparisons of Shear Rating Factors for Change in the Shear Capacity Calculation Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Inv 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 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;16 1966-Rev 1.9 Top Slab 1 9.0893 Top Slab 1 9.0893 1.601 1.8908 0.8467 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;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;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;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 CD12x12;20 2010-Rev 1.9 Top Slab 2 1.227 Top Slab 2 1.227 3.1552 3.5462 0.8897 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 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 CD12x8;9 1948-Rev 1.9 Top Slab 1 10.79 Top Slab 1 10.79 1.2148 1.364 0.8906 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 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 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 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 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 1933-Rev 1 Top Slab 1 7.0937 Top Slab 1 7.0937 2.0784 2.3505 0.8842

84 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Inv Rating Factor HL93 (After) Ratio (Before/ After) CD8x8;10 1933-Rev 1.9 Top Slab 1 7.0937 Top Slab 1 7.0937 2.3552 2.7004 0.8722 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 CS10x8;10 1933-Rev 1.9 Top Slab 1 1.1503 Top Slab 1 1.1503 2.4883 2.4883 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 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 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;12 1952-Rev 1.9 Top Slab 1 1.116 Top Slab 1 1.116 1.6469 1.8724 0.8796 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 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 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;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;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 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 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 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;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 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 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 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

85 Bridge ID Fill Depth Critical Element (Before) Location (Before) Critical Element (After) Location (After) Shear Inv Rating Factor HL93 (Before) Shear Inv Rating Factor HL93 (After) Ratio (Before/ After) 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 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 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 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 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 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 3- Candidate 1- Rev 1.5 Top Slab 1 1.4337 Top Slab 1 1.4337 3.1686 3.4535 0.9175 Model 3- Candidate 1- Rev 1.9 Top Slab 1 1.4337 Top Slab 1 1.4337 3.1686 3.4535 0.9175 References: McGrath, T.J., Liepins, A.A., and Beaver, J.L., (2005), Live Load Distribution Widths for Reinforced Concrete Box Sections, Transportation Research Record: Journal of the Transportation Research Board, CD 11-S, Transportation Research Board of the National Academies, Washington, DC, pp 99-108. McGrath, T.J., Liepins, A.A., Beaver, J.L., Strohman, B.P., (2004), Live Load Distributions for Design of Box Culverts, A Study for the Pennsylvania Department of Transportation.

86 Live Load Surcharge vs. Approaching Wheel Load This section summarizes the change related to the proposed culvert section in the LRFD 3.11.6.4. The culvert set described in this section was run and ratings were saved for the existing 8th Edition LRFD. The overall HL93 inventory and operating ratings were compared with the same ratings after the proposed modifications were made for BrDR. The comparative results for the LL surcharge rating are provided in a table later in this section. Background/Spec Change Proposal The current LRFD Specifications and the MBE define a live load surcharge (LS) in Article 3.11.6.4 to account for vehicles located adjacent to retaining walls. The loading is also applied to culverts to represent the effect of a vehicle approaching a culvert. This is not an appropriate representation of an approaching wheel load (AW) because:  Unlike retaining walls where a vehicle load near the 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.  The lateral pressure on a culvert produced by an approaching wheel reduces rapidly with increasing depth of fill.  The point of highest lateral pressure from an approaching vehicle on a culvert is near the top. This pressure is transmitted directly through the top slab and does not create bending moments. ASTM standards for precast reinforced concrete box sections with depths of fill less than two feet have always been designed for a lateral pressure resulting from an approaching vehicle using the formula: p-lat(H) = 700/H < 800 psf where: p-lat = lateral soil pressure resulting from an approaching wheel load at depth H, psf H = depth of fill to depth where pressure is calculated, ft The basis for this change is shown in Figure 71 below. In the figure, the culvert is shown schematically in green. The other plotted lines show the lateral pressures based on the AASHTO LRFD Specifications with a 2 ft surcharge and lateral pressure coefficient of 0.5, ASTM box section specifications, and FEM calculated pressures for three axle positions approaching the culvert from Model 1 of this project.

87 Figure 71 – Approaching Vehicle Lateral Pressure on Culvert Wall vs. Depth The FEM models show high pressure near the surface that reduces quickly with increasing depth of fill. The ASTM design pressure shows a similar trend, while the LRFD 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 likely not a design issue for several reasons.  The pressure, shown in the figure are the peak pressures and decrease away from the wheel location.  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. Also, the compression load spreads longitudinally through the slab and the reaction pressure is much smaller than the applied pressure.  The research team is unaware of any structural issues in a box culvert due to lateral load. 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. For the BrDR runs described in the following section, the distributed vertical load was applied at all depths (i.e. even at depths below 2’ of top fill), based on the 700/H calculation. ‐18 ‐16 ‐14 ‐12 ‐10 ‐8 ‐6 ‐4 ‐2 0 ‐1200 ‐1000 ‐800 ‐600 ‐400 ‐200 0 200 400 600 De pt h  (ft ) Lateral Pressure Distribution on Wall, psf Axle @  3'‐1" from CL wall Axle @  2'‐0" from CL wall Axle @  1'‐3" from CL wall ASTM Wall Pressure AASHTO LL Surcharge Culvert

88 For the existing specifications, the following values were input that are used in the calculation of the LS load in BrDR  Lateral Earth Pressure Coefficient = 0.5  Surcharge Height = 2.0’  Unit weight of Soil = 120.0 Pcf Note: The change made in BrDR was applying a revised LS (now referred to as AW) at all fill depths. The change was applied as shown in Table 16 and Figure 72. Table 16 – Proposed Lateral Pressure p-lat(H) vs. Current Lateral Pressure qls Fill Depth (ft) Proposed- p-lat(H) (ksf) Current- qls (ksf) 0 0.8000 0.120 0.5 0.8000 0.120 1 0.7000 0.120 1.5 0.4667 0.120 2 0.3500 0.120 2.5 0.2800 0.120 3 0.2333 0.120 3.5 0.2000 0.120 4 0.1750 0.120 4.5 0.1556 0.120 5 0.1400 0.120 5.5 0.1273 0.120 6 0.1167 0.120 6.5 0.1077 0.120 7 0.1000 0.120 7.5 0.0933 0.120 8 0.0875 0.120 8.5 0.0824 0.120 9 0.0778 0.120 9.5 0.0737 0.120 10 0.0700 0.120 10.5 0.0667 0.120 11 0.0636 0.120 11.5 0.0609 0.120

89 Figure 72 – Lateral Pressure vs. Fill Depth (Proposed/Current) Economic Impact Overall the change provided an improvement in the controlling rating factors for many culverts. In many cases, improvement is shown for both less than 2’ of fill and for greater than 2’ of fill. A few cases show a very slight decrease in the overall rating factor (3rd decimal place of the RF). These are all for fill depths less than 2 feet. Table 17 below represents the culverts that had changes in the controlling HL93 inventory ratings for a randomly selected set of culverts from the Caltrans set and the 3 RC box culverts field tested for this research. A full table showing all of the culverts run and the depths of cover are provided in Appendix G. For the table below, the average increase in rating factor is about 6.5%, while the maximum increase in rating factor is about 36% - Culvert LS-CD8x8;10 1924-Rev at 5 feet of cover (Inventory 1.453 vs. 0.919).

90 Table 17 – HL93 Inventory Controlling Rating Comparisons for the Change in LL Surcharge Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (Before) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio 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 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 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 7 ft Cover 1.525 1.977 1.758 2.279 0.867463 0.867486 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;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-CS12x12;10 2002-Rev 1.5 ft Cover 1.191 1.544 1.192 1.545 0.999161 0.999353

91 Culvert Cover Inv Rating HL93 (Before) Oper Rating Factor HL93 (Before) Inv Rating HL93 (After) Oper Rating Factor HL93 (After) Inventory Ratio Operating Ratio 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-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 2.5 ft Cover 1.5 1.944 1.504 1.95 0.99734 0.996923 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 2- Candidate 1-R 1.5 ft cover 1.475 1.912 1.471 1.907 1.002719 1.002622 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-CS7x7;10 2010-Rev 1.5 ft Cover 1.528 1.981 1.529 1.982 0.999346 0.999495 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 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 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-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

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Proposed Modifications to AASHTO Culvert Load Rating Specifications Get This Book
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Over the past decade, significant state and federal resources have been expended to develop a state‐of-the-art set of reliability‐based bridge design and load rating specifications, including Load and Resistance Factor Design (LRFD) and Load and Resistance Factor Rating (LRFR). However, these design and rating methods were developed for larger bridge structures, and may result in overly conservative ratings when applied to buried culverts. Of the more than 600,000 records in the National Bridge Inventory, over 130,000 represent culverts, thus constituting a significant proportion of the nation’s bridge infrastructure.

The TRB National Cooperative Highway Research Program's Web-Only Document 268: Proposed Modifications to AASHTO Culvert Load Rating Specifications proposes modifications to the culvert load rating specifications in the Manual for Bridge Evaluation and revises the AASHTO LRFD Bridge Design Specifications accordingly.

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