CONE MODELS FOR A SOIL LAYER ON A FLEXIBLE ROCK HALF-SPACE

A modified truncated cone model is used to calculate approximately the dynamic response of a disk on the surface of a soil layer resting on flexible rock. The procedure is analogous to that for a layer on rigid rock, the only modification being that the reflection coefficient -alpha at the layer-rock interface is no longer equal to -1. The modified value of alpha can be determined straightforwardly by considering one-dimensional wave propagation along the cone. The low- and high-frequency limits lead to a frequency-independent alpha, which allows the dynamic analysis to be performed directly in the familiar time domain. This cone represents a wave pattern with amplitude decay and also incorporates the reflection at the free surface and the reflection-refraction at the layer-rock interface. The results for the static stiffness of the disk are highly accurate for a wide range of geometrical and material properties of the layer and the rock. For the dynamic stiffness the agreement with the exact solution is satisfactory.