theory (18,19,20) and the visco-elastic layer analysis (7) are all based

on these three properties of material behavior. As previously noted,

the type of theory most widely used at the present time is the

multilayered linear elastic theory. The development of multilayered

elastic solutions is presented below.

2.2.2 One-Layer System

 The mathematical solution of the elastic problem for a concentrated

load on a boundary of a semi-infinite body was given by Boussinesq in

1885 (13). His solution was based on the assumption that the material

is elastic, homogeneous, and isotropic. Boussinesq's equation (133;

p. 28) indicates that the vertical stress is dependent on the depth and

radial distance and is independent of the properties of the transmitting

medium. There are several limitations of this solution when applied to

pavements. For example, the type of surface loading usually encountered

in flexible pavements is not a point load but a load which is distri-

buted over an elliptical area (133).

 Further work with the Boussinesq equation expanded the solutions

for a uniformly distributed circular load by integration. Newmark (85)

developed influence charts for determination of stresses in elastic soil

masses. The charts are widely used in foundation work. Love (60) used

the principle of superposition to extend Boussinesq's solution to solve

for a distributed load on a circular area. Foster and Ahlvin (36)

presented charts for computing vertical stress, horizontal stress, and

vertical elastic strains due to circular loaded plates, for a Poisson's

ratio of 0.5. This work was subsequently refined by Ahlvin and Ulery

(4) to allow for an extensive solution of the complete pattern of