Geoscience Reference
In-Depth Information
3 SPATIAL DISCRETIZATION OF SOIL
Mixed formulations complicate finite-element analyses in that the particular
elements used to discretize the problem must be chosen judiciously—not all
elements will yield meaningful results (Hughes, 1987). To date, very few coupled
deformation-flow analyses of geosynthetically reinforced soil structures have
been performed.
Irreducible finite-element analyses of reinforced soil structures have
employed various continuum elements to discretize the backfill soil. Constant
strain triangles (Banerjee, 1975), four-node quadrilaterals (Herrmann and Al-
Yassin, 1978; Al-Yassin and Herrmann, 1979; Seed and Duncan, 1986; Ling
et al., 2000), nonconforming five-node quadrilaterals (Romstad et al., 1976;
Shen et al., 1976; Chang and Forsyth, 1977; Al-Hussaini and Johnson, 1978;
Ebeling et al., 1992), and six-node quadrilaterals (Naylor, 1978; Naylor and
Richards, 1978) have all been used in such analyses.
For the most part, the above analyses were confined to “working stress”
(nonfailure) conditions. If the analysis is to be continued to failure, the choice of
element type and their spatial distribution is more critical. Past work (Nagtegaal
et al., 1974; Sloan and Randolph, 1982) indicates that constant, linear, quadratic,
and cubic strain triangles are capable of accurately simulating failure conditions,
particularly for soft soils under undrained conditions. Eight-node quadrilateral
elements employing reduced integration do not appear to give as accurate results
(Sloan, 1984).
In developing finite-element models of reinforced soil structures, one
important aspect that is sometimes overlooked is the extent of the boundaries of
the solution domain. If a specific structure has fixed boundaries due to the manner
in which it was constructed (e.g., if it is built in the laboratory in a frame and
resting on a rigid floor), then the boundaries of the solution domain are directly
known. However, if a field structure is analyzed, the boundaries of the domain are
not explicitly known. There are two approaches for modeling domain boundaries
for the latter case.
In the first approach, the exterior boundary of the solution domain is fixed
at a large but finite distance. Using standard finite elements, the domain is then
discretized only up to this exterior boundary. The extent of this boundary is fixed
by performing mesh sensitivity studies in which the boundary is progressively
extended outward until further increases in the boundary have no appreciable
effect on the solution. This approach has the potential disadvantage of possibly
introducing new error sources. In particular, in quasi-static analyses, the stiffness
of an infinite domain differs from that for a finite domain; in dynamic analyses,
infinite domains do not include boundaries that reflect waves, whereas finite
domains do.
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