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The model uses an explicit method, where the calculation timestep is very short compared with
the time necessary for information (acceleration, velocity, displacement) to physically pass from
one element to another. It also utilizes a Lagrangian formulation, where the incremental
displacements are added to the coordinates at each timestep so that the grid moves and deforms
with the material it represents.
There are several advantages and disadvantages in using FLAC as compared to implicit finite
element programs (Table 6.1). Because of the explicit Lagrangian methodology and the explicit
use of the equations of motion, FLAC is advantageous in modeling non-linear, large strain,
physically unstable situations (Itasca Consulting Group 1997).
Table 6.1: Comparison of FLAC and Finite Element Numerical Programs
FLAC (Explicit)
Timestep must be smaller than a critical value for
stability.
Small amount of computation effort per timestep.
No significant numerical damping introduced for
dynamic solution.
No iterations necessary to follow nonlinear
constitutive law.
Provided that the timestep criterion is always
satisfied, nonlinear laws are always followed in a
valid physical way.
Matrices are never formed. Memory requirements
are always at a minimum. No band-width
limitations.
Since matrices are never formed, large
displacements and strains are accommodated
without additional computing effort.
Finite Element (Implicit)
Timestep can be arbitrarily large, with
unconditionally stable schemes.
Large amount of computational effort per timestep.
Numerical damping dependent on timestep present
with unconditionally stable schemes.
Iterative procedure necessary to follow nonlinear
constitutive law.
Always necessary to demonstrate that the above
mentioned procedure is a) stable, and b) follows the
physically correct path (for path-sensitive problems).
Stiffness matrices must be stored. Ways must be
found to overcome associated problems such as bandwidth.
Memory requirements tend to be large.
Additional computing effort needed to follow large
displacements and strains.
6.1 CONSTITUTIVE SOIL MODEL
An effective stress Mohr-Coulomb constitutive model was used for this study. It is able to model
plastic deformations utilizing a plastic flow rule. The elastic behavior of the soil is defined by the
bulk and shear modulus, and the strength is defined by the angle of friction and cohesion. This
significantly simplifies the dynamic soil behavior; however, it is not capable of accounting for
the strain dependent dynamic properties such as damping and shear modulus. This model has
been demonstrated to yield satisfactory displacement results for a variety of applications
involving seismically-induced deformations of earth structures and retaining walls (Roth et al.
1993; Roth and Inel 1993; Dickenson and Yang 1998; McCullough and Dickenson 1998). The
elastic and strength properties of the soil were estimated from established correlations with
normalized SPT values ((N 1 ) 60 ), unless otherwise noted.
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