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J.C.SMALL and J.R.BOOKER
The University of Sydney, Sydney, Australia

ABSTRACT

For certain classes of problems, the use of the finite layer method can
dramatically reduce the computational and data preparation time as
compared to that required for obtaining a solution using conventional
numerical techniques such as finite element or finite difference methods.
This saving is especially evident for problems which are three
dimensional in nature, as such problems can be reduced so that they
involve only one spatial dimension.
The method relies upon being able to represent the field quantities,
such as the displacements, stresses etc., by an orthogonal series or on
being able to transform them by the use of integral transforms. The only
restriction to doing this is that the material properties do not vary in one or
two spatial directions. One of the simplest forms of orthogonal series is
the Fourier series, and this is commonly used in the solution of problems
using the finite layer method.

In this chapter, the basic theory of the finite layer method is presented
for both series and integral transforms. The application of the method to
many different types of problems in geomechanics is then demonstrated
with examples of problems involving stress analysis, settlement of
foundations, and soil-structure interaction, as well as time dependent
problems involving settlement, viscoelasticity and thermoelasticity.

Spatially periodic loading on a  horizontally layered deposit.There are many other problems to which the finite layer method may
be applied beside those which have been presented here, and it is hoped
that this chapter may serve as an introduction to the method which
engineers and researchers working in the field of geomechanics may wish
to adapt or use for solving new or complex problems in their own field of
interest.