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

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1NCHRP Project 15-29, “Design Specifications for Live Load Distribution to Buried Struc- tures,” investigated how surface live loads distribute through the soil and load various culvert structures. AASHTO Standard and LRFD Specifications differ in how live loads are spread through fill onto culvert structures. AASHTO Standard Specifications apply surface point loads and spread loads at the rate of 1.75 times the culvert depth. The LRFD Specifications 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. This research investigated how live loads spread with depth, as a function of soil and cul- vert type, using three-dimensional (3D) numerical modeling. The numerical investigation included selection of appropriate software and soil models, verification of model predic- tions, and 3D analysis of 830 buried culverts. Modeling was conducted for the following six culvert types: • Concrete arch, • Concrete pipe, • Concrete box, • Corrugated metal pipe, • Corrugated metal arch, and • High-density polyethylene (HDPE) profile wall pipe. This modeling provided a basis for developing simplified design equations (SDEs) for structural response. Numerical modeling conducted to evaluate model characteristics, software, and soil constitutive models indicated that a linearly elastic, perfectly plastic model with a Mohr- Coulomb failure criterion provided the best mix of capturing (1) the important aspects of soil behavior in transmitting live loads to structures and (2) offering simplicity in modeling. In implementing this soil model, the elastic soil properties were based on depth of fill. Parameters for the soil model were based on the Selig (1988 and 1990) properties. The proposed properties are conservative relative to field data. Culverts composed of solid material and regular geometry may be represented by isotropic structural elements, meaning that bending and membrane properties are the same in all directions. This category includes concrete boxes, concrete pipe, smooth steel pipe, and smooth thermoplastic pipe. Both thermoplastic and metal culvert products use cross-sectional shapes that are orthotropic, meaning the structural properties vary by direction. These cul- vert shapes typically have much higher circumferential bending stiffness than longitudinal bending stiffness. In addition, the circumferential membrane stiffness is higher than the lon- gitudinal membrane stiffness. In order to model these culverts accurately, 3D orthotropic S U M M A R Y Recommended Design Specifications for Live Load Distribution to Buried Structures

structural elements that permit specification of different stiffnesses for bending and mem- brane behavior are required. Modeling results show that live load spread depends on depth, soil characteristics, and cul- vert characteristics. Pavements substantially reduce soil stress and structure forces, so the unpaved case controls. The distribution of vertical stresses on the plane at the crown of buried culverts varies substantially depending on the soil properties, culvert characteristics and depth. A spreading constant of 1.75 does not adequately represent the modeling results; a spreading constant of 1.15 is slightly unconservative at shallow depths, is adequate for 24-in culverts at most depths, and conservative for larger culverts. Regarding bending moments in the structures, the crown bending moment has the great- est absolute magnitude in response to live loads. The peak negative bending moment is typ- ically at the springline or above, as high as 60 degrees above the springline for large-diameter culverts near the surface. Peak thrusts may occur anywhere from the culvert crown to the springline. Shallow burial tends to produce peak thrusts near the crown and deeper burial tends to shift the peak thrust closer to the springline. Invert thrusts typically are small and may be either slightly negative or slightly positive. Proposed revisions to the 4th edition of the AASHTO Design Specifications were devel- oped using the following methodology. First, the limit states and current design methodolo- gies were evaluated and compared for all culvert types included in the AASHTO specifica- tions. Next, numerical values of the limit states from the numerical modeling were compared with the values resulting from the Standard and LRFD Specifications. Finally, proposed SDEs were developed that provided better correlation with modeling results. For all culvert types, the proposed SDEs included a culvert span-related term in the cal- culation of the load spread parallel to the culvert axis (perpendicular to the direction of vehicle travel). The following proposed SDE for concrete box culverts illustrates the change. The first equation determines the depth at which adjacent wheels on an axle, or wheels on adjacent axles, interact: 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, typically 1.15 Di is the inside span of the culvert, in. The area loaded by the wheel load may be estimated by where H is the culvert depth, ft lt is the tire patch length, 10 in. ForH H A w s LLDF H DLL t w l i≥ = + + + ⎛⎝⎜ ⎞int • •.12 0 06 12⎠⎟ + ⎛⎝⎜ ⎞⎠⎟• • ( ) l LLDF Ht l 12 3 ForH H A w LLDF H DLL t l i< = + + ⎛⎝⎜ ⎞⎠⎟int • • •.12 0 06 12 l LLDF Ht l 12 2+ ⎛⎝⎜ ⎞⎠⎟• ( ) H s w D LLDF w t i l int . ( )= − − 12 0 06 12 1 2

Figure S-1 compares the variation of live load with depth for concrete boxes, for the Standard, LRFD, and proposed SDE. The SDE distribution starts out wider than LRFD, but increases width with depth at the same rate. Recommended changes to the AASHTO LRFD Design Specifications are presented in Chapter 3 and Appendix C. The recommended changes are limited to Specification Section 3, where the live load magnitude is specified, and Section 12, where structural responses are cal- culated. Table 3-1 in Chapter 3 summarizes the changes to each section for the six culvert types. In order to understand the effect of the proposed SDEs on culvert designs, the critical struc- tural responses were calculated and compared (for Standard, LRFD and proposed design equations) for the following 248 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; and • Concrete arch—8 cases. The findings of the parametric study are discussed below in the context of the overall design and reliability margin. The research team conducted extensive 3D modeling of the transfer of surface live loads to buried culverts. From the results, the research team has proposed SDEs that permit culvert design without modeling. However, many design situations are not addressed by the SDEs. In these situations, two-dimensional (2D) and 3D modeling may be necessary for design. Guidelines were developed for conducting 2D and 3D modeling. The 2D guidelines pro- vide a means for selecting the surface load intensity to be applied to a 2D elastic model, the most commonly used modeling technique. 2D computer models have an inherent limitation 3 Figure S-1. Live load variation with depth for concrete box culverts (SDE refers to the proposed simplified design equations).

when computing the effect of surface live loads. Because the models are 2D, the load spread- ing that occurs in the longitudinal direction, parallel to the axis of the culvert, cannot be cor- rectly computed. The model represents a vertical slice through the real-world, 3D geometry. Parameters for peak thrust and crown moment are sufficiently different that separate analy- ses should be conducted for each. 2D response ratios for concrete boxes, concrete arches, and corrugated metal arches were too variable to be captured adequately by these guidelines. The 3D guidelines address software, live load application, representing the pavement, representing the soil, model dimensions, element size, symmetry and boundary condi- tions, representing culvert structures, and the soil-culvert interface. Details may be found in Section 2.5.2. The overall design and reliability margin of the proposed SDEs was assessed by computing statistics about the ratio of SDE design force to Standard design force, and the ratio of SDE to LRFD design forces. The maximum, minimum, and average design force ratios are shown in Figure S-2. In the figure, the square represents the average ratio, and the ends of the vertical bars represent the minimum and maximum ratios. For most design forces, the average ratio of SDE to LRFD is between about 0.9 and 1.1. Exceptions to these limits are the reinforced concrete pipe (RCP) crown moment at 0.888, the corrugated metal arch (CMA) peak thrust at 1.460, and the reinforced concrete arch (RCA) peak moment at 0.882. The range of design force ratios is generally larger for the SDE/Standard ratio. This reflects that the SDEs, like the LRFD design methods, spread the loads from a finite-size wheel patch (typically 20 in. by 10 in.), rather than a point load. Figure S-2 illustrates that, except for a few structure forces, the proposed SDEs do not sig- nificantly affect the design margin or reliability on average. However, the relatively large spread in the ratios does mean that for some combinations of soil type, diameter, and depth the SDEs are significantly different than the LRFD design forces. Where there is a significant variation between the proposed SDEs and current practice, the differences are not random—the SDEs model behavior not captured in the current standards. 4 Figure S-2. Maximum, minimum and average design force ratio.

For example, in corrugated metal pipe, the ratio gets larger as depth of fill decreases. As noted earlier, this is the result of the high thrust occurring in the crown of these culverts, which occurs because of the low bending stiffness and high axial stiffness. Based on this research, the current AASHTO load spreading method provides a neutral or conservative approach for all culvert types, except corrugated metal arches. The pro- posed SDEs are a better fit to the modeling results produced in this study and are generally less conservative than the current AASHTO load-spreading method. For most reinforced concrete pipe diameters and depths considered, the SDEs generally predict much lower crown moments than the Standard method and moderately lower crown moments that the LRFD method. However, the SDEs are still quite conservative rel- ative to the American Concrete Pipe Association (ACPA) Handbook methods that have been used without issue for a substantial number of years. The research team believes that the proposed SDEs reflect an improvement in the distri- bution of live load with depth and better culvert designs. 5