Free-field response of a transversely isotropic saturated half-space subjected to incident plane qP1- and qSV-waves

摘要

Many natural soils and rocks are not only saturated but are also anisotropic. Due to the fundamental importance of having an understanding of the free-field response of an anisotropic half-space subjected to incident seismic waves, the surface displacements, surface strain, rocking, and pore pressure due to reflection of plane waves in a transversely isotropic (TI) saturated half-space are discussed. The governing equations in u-w formulation are first derived and the plane harmonic wave solution of these equations is then proposed. The free-field response is finally determined by specifying the stress free and surface drainage conditions at the boundary. The half-space surface can be either completely permeable or impermeable, and the excitation includes incident plane qPl- and qSV-waves. The proposed formulations are verified by comparing our results with those for the isotropic half-space. A parametric study is performed to illustrate the influences of the material anisotropy, surface drainage condition and permeability on the surface motions. Numerical results show that the surface motions of the TI half-space are significantly different from those of the isotropic case. The surface motions of the TI half-space are much more dependent on the TI parameters when the incident waves are qSV-waves than when they are qP1-waves because the dynamic responses change sharply as the incident angles approach the critical angles. In contrast with the isotropic case, with an identical angle of 45, the total reflection angle of the TI half-space varies with the TI parameters. In general, the surface motions of the permeable surface are smaller than those of the impermeable surface, particularly in response to incident qSV-waves.