Scattering Of SH-Wave By Triangular Hill And Subsurface Cavity

Influence of a hill or dike structure on ground motion is always an important problem in earthquake engineering. Antiplane responses of a scalene triangular hill or structure, an isosceles triangular hill or structure, an isosceles triangular hill with a subsurface cavity to incident SH waves are studied in this paper based on methods of wave function expanding, complex function, moving coordinates and by employing idea of assistant function. At first the model is divided into two domains, domain I involves a triangular hill or structure with a hemi-circular bottom, the rest is domain Ⅱ. A wave function, which satisfies the zero-stress condition at the triangular wedges, is constructed in domain Ⅰ , a scattered wave function which satisfies the zero-stress condition at the horizontal surface is constructed in domain Ⅱ. Then displacement continuity and stress equilibrium as well as other boundary condition is used to establish the algebraic equations, which is solved by Fourier expanding. Finally, numerical examples and relative results are provided to discuss influences of wave number, incident angle, hill's or structure's shape and material, subsurface cavity's radius and depth on the ground motion. Base on the analysis and discussion, some conclusions are arrived at as follows:1. Solving antiplane response of triangular hill or structure to incident SH waves by using the idea of assistant functions and division, the standing-wave equation constructed in domain Ⅰ must satisfy the governing equation and the zero-stress condition on the wedges. Or else right theory and results can not be arrived at.2. As for antiplane response of triangular hill or structure, increasing the height of hill can be regarded as the increase of wave number η. In this case, the stiffness of the hill or structure will decrease, which leads to easier influence of incident wave on the displacement amplitudes.