不同饱和度土层分界面上剪切波的反射与透射

基于多相孔隙介质弹性理论，给出了非饱和土中不同弹性波的传播方程。根据分界面上的边界条件，建立了各势函数波幅值之间的关系式，讨论了入射剪切波在不同饱和度土层分界面上的反射与透射问题。在无限空间非饱和土体中存在3种压缩波和1种剪切波，因此，当剪切波传播到不同饱和度的非饱和土层分界面上将分别在上、下土层激发产生4种反射波和4种透射波。推导出不同反射波和透射波的振幅比例系数和能量比例系数的理论表达式，并且在此基础上进行数值分析。在数值算例中分别研究了各反射波与透射波的能量比例系数（即能量反射率和能量透射率）受入射频率、入射角度以及上、下土层土体饱和度变化的影响情况。计算结果表明：各能量反射率和能量透射率不仅与入射角和入射频率有关，而且其受上、下土层饱和度变化的影响也同样不能忽视。

Reflection and transmission of shear wave at interface between soil layers with different saturation degrees

Based on the multiphase pore elasticity theory, the propagation equations for the various elastic waves in unsaturated soils are derived. According to the boundary conditions at the interface, the relationships between different wave amplitudes of various potential functions are established; and then the reflection and transmission problems of incident shear wave at the interface between unsaturated soil layers with different saturation degrees are discussed. Three compressional waves and one shear wave exist in the infinite unsaturated soils, therefore four reflected waves and four transmitted waves are generated when the shear wave propagates at the interface between different unsaturated soil layers. The theoretical expressions for the amplitude ratios and energy ratios for the various waves are derived; and the numerical analysis is then performed. In the numerical examples, the influences of incident frequency, incident angle and saturation degrees of the upper and lower soil layers on the proportionality coefficients of the reflected wave energy and transmitted wave energy (namely energy reflection ratios and energy transmission ratios) are discussed respectively. It is shown that the energy reflection ratios and energy transmission ratios are affected by both the incident angle and the incident frequency. Additionally, the influence of the saturation degrees of the upper and lower soil layers on the reflected and transmitted waves should not be ignored.