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 —α at the layer–rock interface is no longer equal to −1. The modified value of α can be determined straightforwardly by considering one‐dimensional wave propagation along the cone. The low‐ and high‐frequency limits lead to a frequency‐independent α, 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.