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