平面S波在非饱和土自由边界上的反射问题研究

运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性，分析了平面S波在非饱和土层自由边界上的反射问题。根据边界条件，分别导出了在非饱和土自由边界上的四种反射波：反射P1波、反射P2波、反射P3波及反射S波的振幅反射率及能量反射率的理论表达式，并在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关，也受到饱和度变化的影响，这些结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。

Reflection of plane-S-waves at a free boundary of unsaturated soil

The unsaturated poroelasticity theory is used to describe the propagation characteristics of elastic waves in unsaturated soil, and the reflection problem of plane-S-waves at the free boundary of unsaturated soil is analyzed. According to the boundary conditions, the theoretical expressions of the amplitude reflection ratios and energy reflection ratios for the four reflected waves at the boundary, i.e., reflected P1 wave, reflected P2 wave, reflected P3wave and reflected S wave, are respectively derived and the numerical calculations are then carried out. The effects of the incident angle of plane-S-waves and saturation degree of the soil layer on the amplitude reflection ratios and energy reflection ratios of the four reflected waves are discussed in the numerical example. It is shown that the amplitude reflection ratios and energy reflection ratios of the various waves are influenced by not only the incident angle but also the saturation degree. These conclusions are useful for the theoretical researches of soil dynamics and related seismic exploration projects.