Unified Symmetric BEM‐FEM for Site Effects on Ground Motion—SH Waves

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Abstract
This paper is concerned with the numerical solution of time‐harmonic transition problems in elasticity, in general, and with soil amplification in inhomogeneous alluvial valleys, in particular. A mixed variational formulation based on Hamilton's principle, involving field equations only within the valley and an integral representation for the surrounding medium, is developed and used to derive a symmetric finite element‐boundary‐element method for this problem. This method, valid for all frequencies, incorporates automatically the displacement and traction interface continuity conditions; therefore, it imposes no boundary constraints on the approximating functions. The BEM‐FEM is applied to the response of semicircular inhomogeneous valleys with linearly increasing shear modulus with depth, due to oblique incident SH waves. Numerical results emphasize the importance of two‐dimensional resonant effects in deep valleys, and the strong effects of varying stiffness on surface motion, including a rapid spatial variation, especially near valley edges. This can have practical implications in design as it suggests that it is possible for two similar structures located near each other to experience different levels of shaking and, thus, different damage levels during the same earthquake.