Amplification Of Rayleigh Waves By Cavities In A Layered Half-space

The analysis of wave propagation in layered soil is important both in theory and engineering. Wolf derived dynamic-stiffness matrix of elastic layered soil and Green's functions for distributed loads acting on inclined line in his book"Dynamic Soil-Structure Interaction", which formed a complete theory for wave propagation in layered site and dynamic soil-structure interaction. All of those formed the foundation for calculating the wave scattering by cavities of arbitrary shape in half-space using the indirect boundary-element method (IBEM). Liang Jianwen and You Hongbing extended this theory to calculating the amplification of body waves by cavities in a layered half-space. How to extend Wolf's theory to the case of Rayleigh waves will be mainly resolved in this paper.Free-filed response of layered site is systematically researched by direct stiffness method. The dispersion and damping identity of Rayleigh waves and the amplification of P, SV and Rayleigh waves are given in this paper. The half-space, a homogeneous layer resting on a half-space and multi-layers resting on a half-space are calculated.Green's functions are re-derived for distributed loads acting on inclined line in a layered site, which resolved the key problems in wave scattering by local soil conditions and dynamic soil-structure interaction by using the IBEM.The differences of amplification of Rayleigh waves by a cavity or two in single-phase layered and in homogeneous half-space are studied by using the indirect boundary-element method. The reasons for these differences are also discussed. This method can be used in the dynamic analysis of underground structure such as cavities.