Response of a rigid foundation to a spatially random ground motion

Abstract

Abstract A method to obtain the dynamic response of an extended rigid foundation supported on an elastic half‐space when subjected to a spatially varying ground motion including both random and deterministic effects is presented. The method relies on an integral representation of the response of the foundation in terms of the free‐field ground motion. Numerical results for a rigid square foundation and for a ground motion characterized by a particular spatial coherence function are described. The results obtained indicate that the spatial randomness of the ground motion produces effects similar to the deterministic effects of wave passage including reduction of the translational components of the response at high frequencies and creation of rocking and torsional response components. The possibility of defining an effective apparent horizontal velocity which produces effects equivalent to those from a given spatial randomness is explored.