Infinite boundary elements for dynamic problems of 3‐D half space

In this paper, a new procedure for solving 3‐D dynamic problems of unbounded foundations in the frequency domain by using BEM is studied. For simulations of wave propagations due to far field effects, a type of infinite boundary element (IBEM) is presented for modelling a 3‐D regular or irregular half space. The wave type considered could be compressional, shear or a combination of the two. Through the analysis of the asymptotic behaviour of 3‐D fundamental solutions for elasto dynamics, a rather feasible technique for obtaining singular integral coefficients for dynamic problems has been developed. Through the analysis of the dynamic response for a 3‐D square foundation under a uniform load distribution, excellent accuracy has been achieved in agreement with previous numerical solutions. Another example–analysis of the dynamic compliance of a rigid square plate on a half space–has also shown very good results. The development of this infinite boundary element provides a powerful tool for dealing with 3‐D structure foundation interaction or wave propagation problems for irregular foundations such as arch dam canyons.