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OCR for page 141
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 response characteristic of geological materials into the
1989) and LS-DYNA, a PC-version of DYNA3D, are model.
employed for the analysis of GRS bridge abutments. The rea- · A three-invariant viscoplastic cap model: The model is
sons for choosing DYNA3D/LS-DYNA are twofold. Firstly, similar to the extended two invariant geologic cap
the code has soil models (two- and three-invariant models) model, briefly described above, but is more suited for
with large deformation formulation that are capable of ana- soils exhibiting time-dependent behavior.
lyzing the behavior of compacted fill in a bridge abutment · Elastic-plastic with damage and failure: a simple model
and the approach fill, under both service-state and ultimate- for plain concrete.
state loading conditions (hence capable of predicting failure · Isotropic elastic-plastic with oriented cracks model:
conditions). Secondly, the reliability of the code has been suited for porous brittle materials such as the concrete
well documented and the code has been accepted by the Cal- used for segmental facings where pressure-hardening
ifornia Department of Transportation as well as other DOTs. effects are not significant.
Description of DYNA3D
The Elasto-Plastic Soil Model
DYNA3D is a finite element code for analyzing the
The cap plasticity model has been widely used in finite ele-
dynamic response of three-dimensional solids and structures.
ment analysis programs for a variety of geotechnical engi-
DYNA3D is based on a finite element discretization of the
neering applications (Nelson and Baladi 1977, Baladi and
three spatial dimensions and a finite difference discretization
Rohani 1979, Chen and McCarron 1983, Minuzo and Chen
of time. The explicit central difference method is used to
1984, Daddazio et al. 1987, McCarron and Chen 1987). The
integrate the equations of motion in time. The element for-
cap model is very appropriate to soil behavior because it is
mulations available include one-dimensional truss and beam
capable of considering the effect of stress history, stress path,
elements, two-dimensional quadrilateral and triangular shell
dilatancy, and the effect of the intermediate principal stress
elements, and three-dimensional continuum elements. Many
(Huang and Chen 1990).
material models are available to represent a wide range of
The failure function used in the cap model (see Figure B-1)
material behavior, including elasticity, plasticity, thermal
is of the Drucker-Prager type (Drucker and Prager 1952)
effects, and rate dependence. In addition, DYNA3D has a
sophisticated contact interface capability, including fric-
f1 = J1 - J2D + Equation B-1
tional sliding and single surface contact, to handle a range of
mechanical interactions between independent bodies. This
where J1 is the first invariant of the effective stress tensor; J2D
capability is essential for the analyses of segmental walls.
is the second invariant of the deviatoric stress tensor; and
DYNA3D has been used extensively at Lawrence Livermore
and are material constants related to the friction and cohe-
National Laboratory and in industry. It has been applied to a
sion of the soil through
wide spectrum of problems, many involving large inelastic
deformations and contact.
2 sin
The following models, suitable for simulation of soil and = Equation B-2
concrete, are available in DYNA3D: 3( 3 - sin )
· An elastic-plastic model with the Mohr-Coulomb yield 6 c cos
= Equation B-3
surface and a Tresca limit: a simple model suitable for 3( 3 - sin )
soil.
· An extended two invariant geologic cap model suited where is the internal friction angle of the soil and c is the
for soils: In this model, volumetric response is elastic cohesion intercept of the soil. Both and c are determined
until the stress point hits the cap surface. Thereafter, from conventional triaxial compression test results.
plastic volumetric strain (compaction) is generated at a The strain-hardening elliptic cap function (see Figure B-1)
rate controlled by the hardening law. Thus, in addition is of the form
to controlling the amount of dilatancy, the introduction
of the cap surface adds more experimentally observed f2 = ( J1 - L)2 + R 2 J 2 D - (X - L )2 = 0 Equation B-4
OCR for page 142
B-2
J 2D
f1 f2
Elliptic
cap
Initial
cap
J1
Xo L X
Figure B-1. The cap model.
where R is the ratio of the major to minor axis of the elliptic from the latter. The parameter W represents the asymptote
cap, X and L define the J1 value at the intersections of the ellipse value of the plastic volumetric strain curve. The parameter D
cap with the J1 axis and the failure function, respectively. can be obtained by trial-and-error until a best fit of the plas-
The cap model uses the hardening function proposed by tic volumetric strain versus pressure curve is achieved.
Dimaggio and Sandler (1971) The parameter X0 is the first invariant of the effective stress
tensor corresponding to the initial yield cap (see Figure B-1).
1 p
X = - ln(1 - v ) + X 0 Equation B-5 This parameter can be used to account for backfill pre-stress
D W caused by compaction. The calculated vertical stress, v, due
where D, W and X0 are material constants, and p v is the plas- to the compaction machine can be used to estimate the at-rest
tic volumetric strain. lateral stress of the soil. The parameter X0 is then calculated by
The results of one hydrostatic compression test can be adding the three principal stresses, i.e., the vertical stress and
used to evaluate the parameters D and W. A plastic volu- the two at-rest lateral stresses [X0 = v(1 + 2K0), where v is
metric strain versus pressure curve can be obtained from the the vertical stress and K0 is the coefficient of lateral earth pres-
total volumetric strain curve by subtracting the elastic strains sure at rest].
