Cone Models for Embedded Foundation

Abstract

The dynamic analysis of surface footings may be performed approximately, but quite accurately, by idealizing the soil as a truncated cone instead of an elastic half‐space. In this paper, cone models are extended to represent embedded foundations. To this end, a double‐cone model is introduced to represent a disk in the interior of a homogeneous full space. Symmetry considerations applied to a pair of double cones enable the simulation of a free surface midway between the two disks. By using a stack of such disk pairs, an embedded foundation is modeled. The subsequent calculation is conducted by conventional matrix methods familiar from elementary finite element analysis. The accuracy of both frequency‐domain and time‐domain formulations is just as good as for surface footings. This is confirmed by comparing the dynamic‐stiffness coefficients for cone models with rigorous solutions. In addition, cone models enable simple determination of the effective foundation input motion imposed by earthquakes upon structures with embedded foundations.