Diffraction of plane P waves by a circular-arc canyon in an unsaturated poroelastic half-space

Abstract

Based on the theory of unsaturated porous elastic medium, the diffraction around the circular-arc canyon in unsaturated half-space under the incidence of plane P wave is studied by using the Fourier-Bessel series expansion method of wave function. Through numerical examples, the influence of parameters such as incident wave frequency, incident angle, arc depth-width ratio and saturation on the surface displacement amplitude in unsaturated half-space circular-arc canyon is analyzed. The results show that the saturation has a significant effect on the variation of surface displacement amplitude, and the influence law of saturated and unsaturated site soils on the variation of surface displacement amplitude is very different under different depth-to-width ratio and incident frequency. In the case of different depth-width ratios of unsaturated half-space circular-arc canyon, the displacement amplitude change of semi-circular canyon (h/a = 1) is more sensitive to the change of saturation than that of shallow circular canyon (h/a = 0.5). When the incident frequency is low, the maximum displacement amplitude of the half-space circular-arc-canyon in both saturated and unsaturated cases increases with the increase of the incident angle. It is worth noting that when the saturation Sr = 0.99, i.e., when the soil is close to saturation, the maximum surface displacement amplitude caused by unsaturated depressed terrain (Sr = 0.8) is greater than that caused by the saturated soil case as the incidence angle increases.