Recommended Design Specifications for Live Load Distribution to Buried Structures (2010)

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6Much analytical and experimental work has been con- ducted to investigate the distribution of surface loads through earth fills. The classical Boussinesq (1885) solution and sim- ple assumptions such as spreading a surface load over an area that is a linear function of depth are perhaps the most widely used calculation procedures. Poulos and Davis (1974) sum- marize several elastic solutions for this problem, mostly con- sidering different configurations of surface loads. However, little definitive work has been completed regarding the dis- tribution of live loads through fills when a structure is embedded in the ground, because the problem remains too complex to complete closed form solutions for the wide range of the variables that must be considered. Experimen- tal work (McGrath, et al., 2002, and other studies) has shown that the presence of a structure increases the effective spread of a live load substantially. Probably two key mechanisms are involved in distributing live loads to buried structures: • The stiffness of buried structures allows distribution of the live load within the structure. For example, live load in a box culvert slab can be distributed over a width of about 4 ft due solely to the structural stiffness of the slab (McGrath, et al., 2005). This behavior is well documented. • The shear stiffness of soil spreads load over greater areas when flexible structures deform under live loads. Although not quantified through research, this mechanism is believed to explain why live load distribution on flexible structures is similar in width to that in rigid culverts, even though flex- ible culverts often do not have sufficient internal stiffness to accomplish the spreading. For design, the AASHTO Standard and LRFD Specifications have two major differences relative to the treatment of live loads spreading through fills: • The Standard Specifications apply live loads as a point load at the surface, increasing with depth to a square with sides equal to 1.75 times the depth of cover. The LRFD speci- fications apply live load through a tire footprint of 10 in. by 20 in. at the surface but attenuate with a lower coefficient (1.00 or 1.15 as a function of soil type) as the depth of fill increases. • The Standard Specifications increase loads for impact effects by 30% for zero depth of cover, decaying to 0% for 3 ft of cover; the LRFD specifications increase loads for impact effects by 33% for zero depth of cover, but the effect does not drop to 0% until the depth of cover is 8 ft. At depths of about 2 to 4 ft, the LRFD Specifications re- sult in loads about 15 to 20% higher than the Standard Specifications. Because of the two key mechanisms described above, investigating the differences between the Standard and LRFD Specifications required a comprehensive program of three-dimensional (3D) numerical analyses of buried cul- verts. In order to be reliable, the analyses had to be con- ducted using an appropriate soil model and structural analysis software capable of incorporating several types of soil, several types of structures, and appropriate soil struc- ture interfaces. The research approach adopted for the project involved several sequential steps of literature re- view, model development, model testing, extensive model- ing, analysis and synthesis of model results, and develop- ment of simplified design equations (SDEs). The resulting SDEs were exercised to demonstrate their effect on culvert forces. Included in the research was development of guide- lines for two-dimensional (2D) and 3D modeling for those designers interested in more refined analysis. The research results were incorporated into the recommended AASHTO LRFD design specifications. The specifics of the research approach are described in the following paragraphs. C H A P T E R 1 Introduction and Research Approach

71.1 Review and Evaluation of Relevant Experience The foundation of the research was a review and evaluation of relevant field and modeling experience. The research team reviewed and evaluated relevant practice, performance data, research findings, and other information from domestic and international research, on the basis of applicability, conclu- siveness of findings, and usefulness for the development of LRFD specifications for live load distribution to buried struc- tures. Specific areas of interest were as follows: • Data from tests required to validate the computer model- ing conducted later in the project. Of greatest interest were reports and papers where the structure, the backfill, and the load vehicle and loading procedures were well documented. • Candidate soil models were investigated to identify those models suitable for analysis of the live load problem. • Appropriate software for conducting the 3D analyses neces- sary to investigate the transfer of live loads from the surface to the buried structures was identified. 1.2 Soil Constitutive Models and Software Next, the research team selected and tested soil models hav- ing the following characteristics: • Stress-dependent stiffness. The model must stiffen as con- fining stresses increase and soften as the deviator stress increases. • Strength. Under many live load conditions, soil failure can occur under the vehicle wheels and at the structure-soil interface; this failure probably affects the load transferred into the structure. • 3D behavior. Live load distribution through fills is a 3D problem. The research team next developed the following criteria for assessing the suitability of specific modeling software: • Soil-structure interaction. This capability was essential, because it is the principal focus of this project. • Sequential model development. This capability, to “build” models in a manner compatible with real-world construc- tion sequences, was essential. • Structure/soil interface modeling. The software had to have a general capability to model the contact between the buried structure and the soil. • 2D and 3D—A single source for both 2D and 3D software was important, but not essential. • Structural analysis capabilities. Most candidate software could not model culverts with orthotropic structural response (i.e., corrugated metal pipe and profile wall ther- moplastic culverts). The ability to do so was essential. • Built-in soil models with non-linear material capabilities. This was essential because prior experience indicated that linear soil material behavior is inadequate to model buried structure problems. • User-friendliness/learning curve. This was moderately important for software not currently in use at the organiza- tions performing the research. • Efficiency of computations. This criterion was important, but slow software can be overcome with additional com- puter hardware and software. • Output capabilities. This criterion was moderately im- portant. After considering these initial criteria, the research team selected FLAC3D (Itasca, 2005). FLAC3D has a graphical user interface and a command-line or datafile-driven interface. The command-line/datafile-driven interface is readily amenable to parametric studies. In addition, much pre- and post-processing can be further automated using the built-in programming language. Using the built-in language, the research team auto- mated all major model development steps, based on relatively few input parameters (e.g., depth, diameter, structure type, and soil type). 1.3 2D and 3D Modeling After selecting and testing both soil constitutive models and software, the research team conducted more than 800 3D analy- ses of buried culverts. Nine culvert structures were modeled: • Concrete arch, • Concrete pipe, • Concrete box, • Corrugated metal pipe (CMP), • Corrugated metal arch (CMA), • Fiberglass-reinforced plastic pipe, • High-density polyethylene (HDPE) profile wall pipe, • Polyvinyl chloride (PVC) pipe, and • Smooth metal pipe. The solid cross-section culverts were all modeled as isotropic structures, and the corrugated metal pipe, corrugated metal arch, and HDPE profile wall pipe were modeled as orthotropic structures. Depths ranged from 1 to 12 ft, spans ranged from 1 to 30 ft, and four soil types were considered. Three model states were saved for each analysis conducted: State 1 was the soil mass in equilibrium, with no culvert or live

8load; State 2 (dead load) was the soil mass plus the culvert, in equilibrium; State 3 (dead load plus live load) was State 2 plus application of the live load pressure. Unless noted other- wise, all numerical results presented in tables and graphs in this report are for State 3 minus State 2 (i.e., dead plus live load minus dead load). All graphical output from FLAC3D is for States 1, 2, or 3 (but not, for example, State 3 minus State 2). The built-in programming language of FLAC3D was used to extract selected results, typically thrust and moment in the structure, and normal and shear forces on the structure, on a plane under the live load. The results for all structure/depth/ span/soil combinations were imported into a spreadsheet for quality control review, analysis, and presentation. 1.4 Development of SDEs The existing Standard and LRFD methods for simplified design were reviewed and summarized. Then, proposed SDEs were developed based on the culvert structure forces predicted by the structural analyses. Box section forces were evaluated first, because box sec- tions have flat top slabs which afford an opportunity to eval- uate not only the design forces but the vertical soil stresses on the top slab. Normal pressures on round or elliptical culverts are typically more difficult to interpret. The findings from box sections were then used to investigate the other culverts. For all culvert types, design equation development focused on modifications to how the surface live loads spread with depth in the direction parallel to the culvert (perpendicular to the direction of vehicle travel). 1.5 Investigation of Effect of SDEs on Culvert Forces A critical metric in assessing the SDEs was the effect on critical culvert forces (and hence the culvert design). Know- ing if the proposed design equations affect culvert forces sig- nificantly was important. The research team calculated and compared the critical structural responses (for Standard, LRFD, and proposed design equations) for the following 242 culvert, depth, span, and soil combinations: • Concrete box—6 cases • Concrete pipe—100 cases • Corrugated metal pipe—42 cases • Thermoplastic (profile wall)—80 cases • Metal arch—6 cases • Concrete arch—8 cases Graphs directly comparing the structural responses gener- ated under the AASHTO Standard Specification, the AASHTO LRFD Specification, and the proposed SDEs were prepared. (Appendix D.1 contains MathCAD templates illustrating Stan- dard, LRFD, and Proposed calculations for all structure types; Appendix D.2 lists the results.) 1.6 Refined Analysis Guidelines In cases where the SDEs are not applicable, refined analy- sis methods (e.g., 2D and 3D structural analysis) will be nec- essary. This research provided significant insight into the 3D modeling of buried culverts. The experience gained from this research may be helpful in selecting soil constitutive models, software, loading conditions, model sizes, element sizes, soil- structure interfaces, and other features. Although the spread of live load with depth is inherently a 3D problem, many designers do not have access to 3D mod- eling software or expertise. In these situations, it may be use- ful to have guidelines for the pseudo live loads to apply to 2D models to achieve appropriate results. A series of 2D-3D com- panion models were run for the same physical problem. The results were used to develop empirical equations for estimat- ing the 2D live load to apply.