Abstract
The effect of sediment-filled valley on seismic ground motion has become of major interest recently. In this paper the boundary element method (BEM) is used for the response analyses of axisymmetric valleys subjected to incident waves, and the vibration characteristics of the valleys are investigated in detail. The errors resulting from using the full-space fundamental solutions and the finite model simulation are theoretically clarified. The axisymmetric problems are solved by considering the cyclic symmetry of the coefficient matrix and introducing a transformation. The case studies are performed for examining the effects of the shape ratio, the impedance contrast, the oblique incidence of body waves, the Rayleigh wave incidence and the valley damping on the resonance characteristics. The main conclusions are as follows. The specific resonance patterns of valleys exhibit two modes, namely the shear modes and bulk modes. The frequency of resonance modes is shown to depend only on two parameters : the one-dimensional resonance frequency at the valley center and the shape ratio, regardless of the incident wave field and impedance contrast. The fundamental resonance amplitudes depend on the shape ratio and the impedance contrast. The proposed empirical formulas for estimating the fundamental resonance frequencies and the maximum fundamental resonance amplitudes at the valley center are verified by numerical examples for valleys with different shapes and extensive impedance contrast.
