Three-dimensional Responses Of A Canyon And A Hill In A Layered Transversely Isotropic Half Space

The seismic effect due to topographies is important in earthquake engineering,seismology and geophysics,which has been extensively studied in isotropic medium.However,the natural soil shows obvious anisotropy because of the sedimentation and weathering.The research results show that the vertical material parameters are different with those in transversal direction,so the transversely isotropic(TI)medium can be used to simulate the natural soil.However,there are a few researches on the seismic effect of topography in TI media.Adopting a TI model to study earthquake response of topography is vital for theoretical research and practical application.Utilizing the indirect boundary element methods(IBEM),the scattering problem of elastic wave due to 2.5D topography(canyon and hill)in a layered TI half space is studied in this paper.And the main contents are displayed as follows.Based on the 3D precise dynamic matrix of layered TI half space,the dynamic Green's functions for moving distributed loads acting on an inclined line in a multi-layered TI half space was derived.And then the accuracy of Green's functions was verified.In addition,parametric calculations were performed to discuss the influencing factors of the Green's function.Using the dynamic Green's functions,the scattering problems of qP-,qSV-and SH-waves for canyon and hill topographies in TI medium can be solved by the IBEM.The accuracy of the method is verified by comparing with the results of isotropic half space.And then,the numerical calculations were executed in a homogeneous TI half space and a single layered soil TI half space,to study the effects of the incident angle,the incident frequency and the modulus of the TI medium on the amplitude of displacement near the topography.The results show that,the 3D responses of a canyon and a hill in a TI half space are significantly different from an isotropic one,which is highly dependent on the incident frequency,the incident angles and the dynamic natures of the TI medium.And,the modulus ratio of the TI medium has a vital influence on the dynamic characteristics in a single layered soil TI half space,resulting in the difference of displacement amplitudes between those in a single layered soil TI half space and in an isotropic half space.