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SUMMARYWhile the study of kinematic interaction (i.e. the dynamic response of massless foundations to seismic loads) calls, in general, for advanced analytical and numerical techniques, an excellent approximation was proposed recently by Iguchi.1.2 This approximation was used by the authors to analyse embedded foundations subjected to spatially random SH-wave fields, i.e. motions that exhibit some degree of incoherence. The wave fields considered ranged from perfectly coherent motions (resulting from seismic waves arriving from a single direction) to chaotic motions, resulting from waves arriving simultaneously from all directions. Additional parameters considered were the shape of the foundation (cylindrical or rectangular) and the degree of embedment. It was found that kinematic interaction usually reduces the severity of the motions transmitted to the structure, and that incoherent motions do not exhibit the frequency selectivity (i.e. narrow valleys in the foundation response spectra) that coherent motions do.

The numerical solution of problems in elastodynamics involving infinite media calls for the use of discrete techniques such as the boundary element method and the finite element method. These techniques can, in turn, be formulated in the time or frequency domains, and have each relative merits and drawbacks. This paper presents a comparative study of the accuracy and limitations of three different implementations of these methods.The problem studied is that of transient loads on the surface of homogeneous elastic halfspaces, and of finite depth strata. In each case, the response is computed first for an uninterrupted (continuous) medium, and then for a medium that includes a trench (or cavity).Three independent computer programs were used that incorporated the followiiig methods: (i) frequency domain boundary element method (FD-BEM), using a discrete fundamental solution; (ii) time domain boundary element method (TD-BEM) using an analytical fundamental solution; and (iii) a coupled time domain boundary element-finite element model (BEM/FEM).It is found that for convex domains (halfspace or stratum without a trench) the three independent implementations are in excellent agreement, while for non-convex domains (trench in the path of the waves), numerical errors associated with non-causal behaviour become evident in some cases.

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SUMMARYIn the analysis of structural foundations for seismic loads, it is customary to distinguish two types of soil-structure interaction effect: kinematic interaction (or wave passage), and inertial interaction. The former refers to the phenomenon of wave scattering, which occurs because the foundation is much stiffer than the surrounding soil and cannot accommodate to its distortions. Inertial interaction, on the other hand, is caused by feedback of kinetic energy of the structure into the soil. This paper is concerned only with the first phenomenon.The rigorous analysis of rigid, embedded foundations subjected to seismic disturbances requires, in general, substantial computational effort. Indeed, a typical analysis would normally require models with finite elements and/or boundary elements. Although such methods may be used to find an accurate solution to the problem of kinematic interaction, their use is not always warranted, given the many uncertainties involved and the multitude of assumptions that must be considered. Hence, approximate solutions are attractive for this problem. One such approximate method is the remarkably simple algorithm proposed by 1guchi.j This paper presents first an appraisal of this method by way of a comparison with accurate numerical solutions for cylindrical foundations; next the algorithm is applied to rectangular (prismatic) foundations. It is found that Iguchi's method gives results that are adequate for engineering purposes, even if not entirely accurate.