A BIEM approach to a time-harmonic analysis of saturated soil–structure interaction with elastic-type contact conditions

This study presents a solution for the dynamic response of a porous saturated medium to a harmonic motion of a rigid inclusion where an elastic type intermediate layer is located at the interface. The problem has been solved using the Neumann series which terms are obtained by means of recurrence relationships of simple iteration type. To perform regularization we consider every singular integral as an integral in sense of finite part by Hadamard. A modified Shanks transform was used to accelerate the series convergence. The method allows avoid the solution of large system of the linear algebraic equations with densely filled matrix. However, for problems with complicate boundary, which includes segments with large curvature, the requested number of series members sharply increases. The approach is valid for problems which potential satisfied to the Hölder-Lipschitz condition of the first order.Using the proposed approach the problem of a linear harmonic motion of the circular inclusion was investigated and the effect of the frequency on the contact stresses has been studied. It was found that for this specific example, when the vibration frequency increases the maxima of both contact normal stress and porous pressure decrease, while the maximum of the contact shear stress remains almost unchanged.