Design and Construction Guidelines for Geosynthetic-Reinforced Soil Bridge Abutments with a Flexible Facing (2006)

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B-1 APPENDIX B A Brief Description of DYNA3D and LS-DYNA [Note:This appendix has not been edited by TRB.] The computer codes DYNA3D (Hallquist and Whirley 1989) and LS-DYNA, a PC-version of DYNA3D, are employed for the analysis of GRS bridge abutments. The rea- sons for choosing DYNA3D/LS-DYNA are twofold. Firstly, the code has soil models (two- and three-invariant models) with large deformation formulation that are capable of ana- lyzing the behavior of compacted fill in a bridge abutment and the approach fill, under both service-state and ultimate- state loading conditions (hence capable of predicting failure conditions). Secondly, the reliability of the code has been well documented and the code has been accepted by the Cal- ifornia Department of Transportation as well as other DOTs. Description of DYNA3D DYNA3D is a finite element code for analyzing the dynamic response of three-dimensional solids and structures. DYNA3D is based on a finite element discretization of the three spatial dimensions and a finite difference discretization of time. The explicit central difference method is used to integrate the equations of motion in time. The element for- mulations available include one-dimensional truss and beam elements, two-dimensional quadrilateral and triangular shell elements, and three-dimensional continuum elements. Many material models are available to represent a wide range of material behavior, including elasticity, plasticity, thermal effects, and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including fric- tional sliding and single surface contact, to handle a range of mechanical interactions between independent bodies. This capability is essential for the analyses of segmental walls. DYNA3D has been used extensively at Lawrence Livermore National Laboratory and in industry. It has been applied to a wide spectrum of problems, many involving large inelastic deformations and contact. The following models, suitable for simulation of soil and concrete, are available in DYNA3D: • An elastic-plastic model with the Mohr-Coulomb yield surface and a Tresca limit: a simple model suitable for soil. • An extended two invariant geologic cap model suited for soils: In this model, volumetric response is elastic until the stress point hits the cap surface. Thereafter, plastic volumetric strain (compaction) is generated at a rate controlled by the hardening law. Thus, in addition to controlling the amount of dilatancy, the introduction of the cap surface adds more experimentally observed response characteristic of geological materials into the model. • A three-invariant viscoplastic cap model: The model is similar to the extended two invariant geologic cap model, briefly described above, but is more suited for soils exhibiting time-dependent behavior. • Elastic-plastic with damage and failure: a simple model for plain concrete. • Isotropic elastic-plastic with oriented cracks model: suited for porous brittle materials such as the concrete used for segmental facings where pressure-hardening effects are not significant. The Elasto-Plastic Soil Model The cap plasticity model has been widely used in finite ele- ment analysis programs for a variety of geotechnical engi- neering applications (Nelson and Baladi 1977, Baladi and Rohani 1979, Chen and McCarron 1983, Minuzo and Chen 1984, Daddazio et al. 1987, McCarron and Chen 1987). The cap model is very appropriate to soil behavior because it is capable of considering the effect of stress history, stress path, dilatancy, and the effect of the intermediate principal stress (Huang and Chen 1990). The failure function used in the cap model (see Figure B-1) is of the Drucker-Prager type (Drucker and Prager 1952) Equation B-1 where J1 is the first invariant of the effective stress tensor; J2D is the second invariant of the deviatoric stress tensor; and  and  are material constants related to the friction and cohe- sion of the soil through Equation B-2 Equation B-3 where φ is the internal friction angle of the soil and c is the cohesion intercept of the soil. Both φ and c are determined from conventional triaxial compression test results. The strain-hardening elliptic cap function (see Figure B-1) is of the form Equation B-4f J L R J X LD2 1 2 2 2 2 0= − + − − =( ) ( ) α φ φ = −( ) 6 3 3 c cos sin θ φ φ = −( ) 2 3 3 sin sin f J J2D1 1= − +θ α

Initial cap J1 2DJ f 1 2 f Elliptic cap Xo L X Figure B-1. The cap model. B-2 where R is the ratio of the major to minor axis of the elliptic cap, X and L define the J1 value at the intersections of the ellipse cap with the J1 axis and the failure function, respectively. The cap model uses the hardening function proposed by Dimaggio and Sandler (1971) Equation B-5 where D, W and X0 are material constants, and pv is the plas- tic volumetric strain. The results of one hydrostatic compression test can be used to evaluate the parameters D and W. A plastic volu- metric strain versus pressure curve can be obtained from the total volumetric strain curve by subtracting the elastic strains X D W Xv p = − − +1 1 0ln( )  from the latter. The parameter W represents the asymptote value of the plastic volumetric strain curve. The parameter D can be obtained by trial-and-error until a best fit of the plas- tic volumetric strain versus pressure curve is achieved. The parameter X0 is the first invariant of the effective stress tensor corresponding to the initial yield cap (see Figure B-1). This parameter can be used to account for backfill pre-stress caused by compaction. The calculated vertical stress, σv, due to the compaction machine can be used to estimate the at-rest lateral stress of the soil. The parameter X0 is then calculated by adding the three principal stresses, i.e., the vertical stress and the two at-rest lateral stresses [X0 = v(1 + 2K0), where v is the vertical stress and K0 is the coefficient of lateral earth pres- sure at rest].