A MIXED METHOD FOR TRANSIENT ANALYSIS OF STRUCTURES INCLUDING SOIL-STRUCTURE INTERACTION

Equations describing single and multi-scattering of anti-plane and in-plane waves by elastic structures situated on or embedded in the half space were developed. These structures may have material damping and specified tractions or displacements or any combination thereof on portions of their boundaries not common with the soil. The semi-infinite homogeneous linearly elastic isotropic medium was modeled by the Boundary Element method. A finite element/boundary element (FE-BE) mixed method for the steady-state as well as the transient two-dimensional analysis of soil-structure interaction was developed. The solution procedure for the transient problem consisted of three steps. In the first step the problem is mapped into the Fourier Transform space. The transformed equations were solved in the second step using the FE-BE combined model. In this step, single or multiple structures can be included in a single or in several disconnected finite element regions. Use of a continuous line source to describe the scattered wave was introduce instead of a set of discrete sources used by many investigators. The discrete line sources were found to give solutions sensitive to the locations and the number of these sources. For problems with known solutions it may be possible to design an arrangement which would give adequate accuracy. However, these methods would in general be unreliable. The continuous line source representation was found to be much more stable and accurate. In the last step, the time domain solution was recovered using the inverse transform. A fast Fourier transform algorithm was employed.; The procedures developed were applied to the anti-plane problem for both the steady-state and the transient analysis. In the frequency domain, application to the problem for which solutions are available in the literature showed the method to be quite accurate. Parametric studies were carried out to study the influence of various variables upon the results. Examples studied included diffraction of SH-wave by a semi-cylindrical canyon and by a surface structure. In the transient analysis, a shear wall and an underground tunnel were subjected to a time-dependent SH-wave. Effect of refinement of the time step on the accuracy of the transient solutions was studied.