Recommended Design Specifications for Live Load Distribution to Buried Structures (2010) / Chapter Skim
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From page 9... ...
. 2.1.2 Model Verification with Field Tests Initial investigation of culvert responses to live loads from 2D analyses with linear-elastic, Mohr-Coulomb, and hardeningsoil models showed that responses from the Mohr-Coulomb and hardening-soil models were very close to each other whereas responses from the linear-elastic model were significantly different from other models (see Appendix A for the detailed treatment)
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From page 10... ...
The interface strength was assumed to be 50% of the strength of surrounding soil. Structures, finite-element models, live load tests, and material properties were described in detail in the literature (McGrath et al., 2002, and McGrath et al., 2005)
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For the HDPE pipe study, evaluating the Plaxis model predictions for the Mohr-Coulomb and hardening-soil models against the field data was accomplished by comparing deflections, and evaluating the force predictions. Figures 2-3 and 2-4 compare vertical crown displacements horizontal diameter extensions along the culvert for the two cases of HDPE pipe analysis: the case with the Mohr-Coulomb model and the case with the hardening-soil model.
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2.1.3 Discussion During development and testing of computer models, soil models, and modeling methodology (described in Appendix A) the research team learned that soil-structure interaction analysis of buried culverts subjected to live loads with the linearelastic soil model could produce significantly different structural response than those with the Mohr-Coulomb soil model 12 (a)
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The analyses presented here indicate some of the difficulties in predicting structural response of buried culverts subjected to live loads. The soil parameters currently used in design appear to yield soil behavior that is softer than achieved in the field tests.
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This selection offered the best mix of capturing the important aspects of soil behavior in transmitting live loads to structures and simplicity in modeling to allow the research team to complete the greatest number of analyses in the least amount of time. In implementing this soil model, the research team recommended that the elastic soil properties be selected based on depth of fill.
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. All culvert structures modeled here used shell structural elements -- isotropic shell elements were used for concrete, PVC, FRP and smooth metal culverts, and orthotropic shell elements were used for corrugated metal and profile wall culverts.
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2.2.4 Culvert Structures Nine culvert structures were modeled: • Concrete arch, • Concrete pipe • Concrete box, • Corrugated metal pipe, • Corrugated metal arch, • Fiberglass-reinforced plastic pipe, • HDPE profile wall pipe, • PVC pipe, and • Smooth metal pipe. The solid cross-section culverts were all modeled as isotropic structures; the corrugated metal pipe, corrugated metal arch, and HDPE profile wall pipe were modeled as orthotropic structures.
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Summary of isotropic structural properties for concrete pipe.
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were not factored. Live loads were applied and factored as follows: where mmpf is the multiple presence factor (1.2)
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Figure 2-8. Location and intensity of live load, before factoring.
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. in this section illustrate the soil zone meshes, culvert structural meshes, and live load application.
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For example, simplified design of concrete culverts is based on the indirect method where a three-edge bearing load that produces an equivalent bending moment to the in-ground loads is determined, while corrugated metal pipe is evaluated solely on the basis of compressive thrust due to earth load. The proposed SDEs presented in this section were
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From page 22... ...
A further benefit of this term is that the proposed distribution equations produce the same result at 2-ft depth, whether computed using the strip equations for depths of 2 feet or less or the proposed equations for depths of 2 feet or greater. 2.3.1.1 Standard Versus LRFD Specifications In developing the proposed design equations, the research team compared the proposed calculation procedures and the methods in the current AASHTO LRFD and Standard Specifications.
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The approach taken was to consider concrete box culverts first, because box sections have flat top slabs which afford an opportunity to evaluate not only the design forces but the vertical soil stresses on the top slab. Normal pressures on round or elliptical culverts are more difficult to interpret.
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Span Box Sections 12 3251 3.0% -1003 1.9% 24 2060 3.6% -884 3.7% 48 997 1.6% -600 1.6% 96 422 4.2% -301 4.1% Table 2-20. Computer model bending moments.
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For the time being, the research team is reluctant to increase the distribution for live loads to box sections significantly greater than allowed by the current LRFD specifications. Thus, the research team proposes the following live load distribution equation for box sections: where LLpres is the live load pressure at depth H, psi LL is the total live load applied at surface, lb wt is the width of tire (or axle length plus tire width at depths where wheels interact)
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In evaluating live load distribution onto concrete pipe, the research team first looked at the peak and springline thrusts. Figures 2-19 through 2-21 compare the model values of springline and peak thrusts with the thrusts based on Equation 6.
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These figures also show that the soil type has very little influence on the load distribution for concrete pipe, as was the case with box sections. The research team investigated the effect of improving the quality of prediction for peak thrust by modifying the LLDF based on diameter and developed the following equations: where LLDFcp is the live load distribution factor for concrete pipe Di is the inside span of the culvert, in.
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t is the pipe wall thickness, in. Using this approach, the research team computed the bedding factors shown in Figure 2-22 using the peak thrusts and peak positive bending moments from the computer study.
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2.3.2.4 Corrugated Metal Pipe Thrust. Initial calculations for evaluating peak thrust in corrugated metal pipe were completed using the live load pressure computed from Equation 6, multiplied by one-half the smaller of the load spread parallel to the span direction or the pipe diameter.
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Standard and ACPA modified to match impact and multiple presence of LRFD Table 2-25. Comparison of proposed live load D-load on 12-ft diameter concrete pipe with past practice.
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2.3.2.5 Corrugated Metal Arches Predicted thrusts computed using the live load pressure of Equation 6 are compared with the model thrusts in Figure 2-25. Similar to metal pipe, the thrusts show a high maximum thrust at shallow depths relative to that predicted by Equation 6.
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Figure 2-25. Comparison of SDE and computer model thrusts for corrugated metal arches.
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Comparison of SDE and computer model thrusts for thermoplastic pipe. Ratio of Calculated to Computer Model Thrust Ca lc ul at ed /M od el Figure 2-28.
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Thermoplastic pipe -- ratio of calculated to model thrust for earth load plus peak live load thrust.
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Analysis of the data shows that the 35 Soil Type 4.thF SW95 1.00 SW90, ML95 0.75 SW85, ML90, CL95 0.50 ML85, CL90 0.38 CL85 0.25 Table 2-28. Soil correction factor, F4.th, for bending moment in thermoplastic pipe.
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From page 36... ...
2.4 Effect of SDEs on Culvert Forces The research team calculated and compared the critical structural responses for the following culvert types and depthspan combinations: • Concrete box -- 6 combinations • Concrete pipe -- 100 combinations • Corrugated metal pipe -- 42 combinations • Thermoplastic (profile wall) -- 80 combinations • Metal arch -- 6 combinations • Concrete arch -- 8 combinations The research team provides direct comparison of the structural responses generated under the AASHTO Standard Specification, AASHTO LRFD Specification, and the proposed SDEs.
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From page 37... ...
The service live load is computed from where Di is the inside diameter or span of the culvert, inches 2.4.1.2 AASHTO LRFD The live load equations for the AASHTO LRFD Specification are where LHS20 is the wheel load from the HS20 load case, 16,000 lb LL is the live load force, lb Determine the wheel interaction depth where Hint is the wheel interaction depth, ft sw is the wheel spacing, 6 ft wt is the tire patch width, 20 in. LLDFl is the live load distribution factor, 1.15 Determine the live load area and pressure where H is the culvert depth, ft lt is the tire patch length, 10 in.
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From page 38... ...
2.4.2 Proposed SDEs 2.4.2.1 Live Loads The proposed live load equations differ for each culvert type, so they are presented in sections 2.4.3.1 through 2.4.8.1. 2.4.2.2 Dead Loads Dead loads vary according to the culvert type, so they are presented in sections 2.4.3.2 through 2.4.8.2.
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From page 39... ...
Live load variation with depth for concrete box culverts. Parameter Value Soil density 120 pcf Minimum lateral pressure coefficient 0.25 Maximum lateral pressure coefficient 0.5 Installation type Embankment/ Compacted Soil-structure interaction factor 1.083 Fluid density 62.5 pcf Table 2-32.
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The research team expects similar results for larger-span concrete box culverts. 40 Figure 2-35.
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Figure 2-37. Top slab shear comparison for concrete boxes.
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. 2.4.4.1 Live Load Equations The proposed live load equations used for concrete pipe design calculations are similar to the AASHTO LRFD equations presented in Section 2.4.1.2, except as follows: where LLDFcp is the live load distribution factor for concrete pipe Determine the wheel interaction depth Determine the live load area and pressure H s w D LLDF w t i cp int .
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This data is for a 48-in.-diameter RCP at 1-ft depth of burial and compares the AASHTO standard to proposed SDE. The moment or shear values plot so far off the 1:1 because the Standard Specifications treat the live load as a point load for burial depths of 1 foot.
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44 Figure 2-40. Crown moment comparison for RCP.
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45 Figure 2-42. Crown shear comparison for RCP.
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2.4.5.2 Dead Load Equations Corrugated metal pipe dead loads were computed from where We is the earth dead load, lb/ft we is the earth unit weight, lb/cubic ft Fe is the soil-structure interaction factor, 1.0 The total dead load is 2.4.5.3 Thrust Calculations For AASHTO Standard Specifications, the total factored thrust is where Tt is the factored thrust per unit length (lb/ft)
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. 2.4.6.1 Live Load Equations The proposed live load equations used for profile wall thermoplastic pipe are as presented in Section 2.4.1.2, except the live load area is as follows: Determine the wheel interaction depth H s w D LLDF w t i l int .
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From page 48... ...
LLDFl is the AASHTO LRFD live load distribution factor, 1.15 Di is the inside span of the culvert, in. sw is the wheel spacing, 6 ft Figure 2-46 compares the variation of live load with depth for thermoplastic pipe, for Standard, LRFD, and the proposed SDE.
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AASHTO tables with modulus coefficients for thermoplastic pipe (profile wall)
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Peak thrust comparison for thermoplastic pipe (profile wall)
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From page 51... ...
2.4.7.2 Dead Load Equations Corrugated metal arch dead loads are calculated from where we is the earth unit weight, pcf We is the earth dead load, lb/ft H is the culvert depth, ft S is the outside span of the culvert, ft The total dead load is DL We= ( )
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Comparisons were made for peak thrust, peak shear, peak positive moment, and peak negative moment. Structural responses to the applied dead and live loads were computed using the 2D structural analysis program (SAP, 2000)
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From page 53... ...
S is the culvert span, ft LLDFl is the AASHTO LRFD live load distribution factor, 1.15 sw is the wheel spacing, 6 ft The service live loads were determined from For AASHTO Standard W I W S LLDF L LL s = +( )
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The peak thrusts are not significantly influenced by the footing boundary conditions. Figure 2-54 illustrates the peak shear values calculated using the three methods.
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Figure 2-54. Peak shear values for concrete arches.
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the same as from the Standard and LRFD loads, although there is a lot of scatter. 2.5 Guidelines for Use of Refined Analysis Methods This project has conducted extensive 3D modeling of the transfer of surface live loads to buried culverts.
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This section refers to the left-right direction as the transverse direction and the up-down direction as the longitudinal direction. The fundamental equation in all live load spread calculations is that the total force at depth H is equal to the total force at the surface: The surface pressure is For 3D spreading, the live load pressure at depth is the force divided by the area: where PH is the vertical pressure at depth H LL is the live load force at the surface, 16,000 lb unfactored wt is the transverse dimension of the tire patch, typically 10 in.
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Each figure includes the curve resulting from 58 Figure 2-57. Peak thrust TDRR for concrete pipe (AASHTO refers to Eqn (113)
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Peak thrust TDRR for corrugated metal pipe (AASHTO refers to Eqn (113)
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Crown moment TDRR for corrugated metal pipe (AASHTO refers to Equation 113)
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. Culvert Type Structural Response Constant a Constant b Peak Thrust 1.387 1.595 Concrete Pipe Crown Moment 0.509 0.411 Peak Thrust 1.303 0.757 Profile Wall Crown Moment 1.195 0.787 Peak Thrust 2.132 2.379 Corrugated Metal Pipe Crown Moment 0.794 0.511 Table 2-36.
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Because of the significant affect of this load spreading and shielding and given that live loads are possible prior to 62 Figure 2-64. Composite graph for crown moment two-dimensional response ratio (AASHTO refers to Equation 113)
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From page 63... ...
This selection offers the best mix of capturing the important aspects of soil behavior in transmitting live loads to structures. The Mohr-Coulomb constitutive model does not offer all of the benefits of the Duncan-Selig/ hardening-soil models in capturing stress-dependent stiffness behavior of soil, but for a live load study, the Mohr-Coulomb model appears to provide sufficient accuracy.
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. This category of culverts includes concrete boxes and concrete pipe, smooth steel pipe, and smooth thermoplastic pipe.
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Concrete pipes have a joint shear test, but drainage pipes are not typically subjected to it. Metal pipes do not currently have a joint shear test.
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Structural responses to live loads did not change significantly when the interface strength was changed from 50% of the soil shear strength to 100%, although the cases with the 100% strength showed slightly larger peak responses than those with the 50% strength, except for moments of the thermoplastic pipe with 2-ft cover. A change in the interface strength affected thrusts more than moments.
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