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6.0 NUMERICAL MODELING
The database of well characterized and instrumented case studies on the seismic performance of
bridge abutments on sloping embankments is very limited. Such cases require pre- and postearthquake
geotechnical and survey data, recorded earthquake motions in vicinity of the site (or a
reasonable estimate of the ground motions from a site response investigation), structural “asbuilt”
drawings of the bridge and abutments affected by the ground motions, and the extraction
of piles to inspect for possible subsurface damage. To supplement the case study data, a
numerical modeling study was conducted. A numerical model is advantageous because
numerous scenarios can be analyzed, and various design parameters can easily be adjusted to
determine their influence on an embankment’s seismic performance. The major concern with
applying a model to soil-structure interaction problems is the numerical uncertainty. This
concern is limited in this study because a series of validation studies were performed using the
available case study data on the seismic performance of various earth and retaining structures at
sites where liquefaction was observed.
The numerical modeling was accomplished utilizing a commercial finite difference computer
program entitled Fast Lagrangian Analysis of Continua (FLAC) version 3.34 (Itasca Consulting
Group 1997). The FLAC model is a non-linear, two-dimensional finite difference program
capable of modeling both static and dynamic situations. Elements or zones represent the
materials (soil and structural), with all the elements and zones constituting the grid (mesh). The
FLAC model utilizes a time-marching scheme, where during each timestep, the following
procedures take place (Figure 6.1): (1) nodal velocities and displacements are calculated from
stresses and forces using the equations of motion, then (2) the basic explicit calculation sequence
uses the velocities to computes strain rates, which are derived from the nodal velocities, which
are used to update the stresses used in the following time step are computed from the strain rates.
.These two procedures are then repeated until the computed unbalanced forces within the mesh
are within a user-specified limit.
Equilibrium Equation
(Equation of Motion)
new velocities
and
displacements
new
stresses or
forces
Stress/Strain Relationship
(Constitutive Model)
Figure 6.1: Basic Explicit Calculation Cycle
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