Cone Models for Soil Layer on Rigid Rock. II

It is quite difficult to compute rigorously the dynamic response of a footing or base mat on a soil layer resting on rigid rock. As an alternative to the rigorous approach, the semi‐finite truncated cone models appropriate for footings on unlayered soil may be employed in modified form. The physically motivated concept of echoes converts the response of the footing on unlayered soil to that of the footing on the layer. The calculations, performed exclusively in the familiar time domain, are in remarkable agreement with rigorous solutions, both for static and dynamic excitation. The necessary echo constants are evaluated for translational and rotational motions in either the flexibility or stiffness formulation of the response. The concept of echoes captures the important effect of the cutoff frequency. The computational procedures, which may be implemented by hand for excitations of short duration, are illustrated by a practical example.