Analytical Analysis of the Scattering Problem of Plane SV Waves Caused by a Circular Arc Canyon in an Unsaturated Half-Space

Abstract

Because the porous multiphase nature of circular arc canyon media has an essential influence on the scattering of seismic waves, elastic media, as well as saturated porous media, do not fully respond to the actual properties of the soil body. Therefore, in this paper, an analytical model of seismic response of a circular arc canyon in a homogeneous unsaturated soil half-space under the action of SV waves is developed. The scattering pattern of plane SV waves resulting from a circular arc canyon in a homogeneous unsaturated soil half-space is investigated based on the large circle assumption and the wave function expansion method. The research results show that there is a significant difference in the characteristics of the space allocation of the surface displacement amplitude between the saturated and the unsaturated cases of the site soil. It is essential to consider the porous heterogeneity of the medium reasonably to evaluate the seismic response of the site correctly. The variation of the displacement amplitude of a semicircular arc canyon (h/a = 1) shows a certain regularity with the increase of saturation, and its surface displacement amplitude shows a decreasing trend with the increase of saturation. Also, the change in the surface displacement amplitude of the semicircular arc canyon is more sensitive to the change in saturation relative to the change in the surface displacement amplitude of a shallow circular arc canyon. With the increase in saturation, the displacement response characteristics of the spatial points inside the canyon vary significantly, and the surface displacement amplitude peaks when the saturation increases to a specific range (Sr = 0.4–0.6). Notably, when the saturation increases to a specific limit value (Sr = 0.9), the displacement amplitude gradually shows a tendency to get stabilized.