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.

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.