A unified approach for the formulation of interaction problems by the boundary element method

A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid–solid and soil–structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods. It eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. To explain the formulation, it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input, where both the inclusion and surrounding medium are treated as viscoelastic. It is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation. Then, the formulation is extended to other types of interaction problems: a multiinclusion problem and an interaction problem involving a foundation embedded in a viscoelastic halfspace. It is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis, but also in the analysis involving diffraction of waves in a medium containing holes