P1波在非饱和土地基表面的反射特性

REFLECTION CHARACTERISTICS OF P1 WAVES AT THE FREE BOUNDARY OF UNSATURATED SOIL

非饱和土是地表天然土体中最常见的一种形式。与饱和土不同,非饱和土内可传播四种体波:一种剪切波(S波)和三种压缩波(P1波、P2波、P3波)。其中P1传播特性与饱和土中的快压缩波相似:传播速度最快,且衰减系数最低。因此,该文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P1波在非饱和土介质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波的振幅反射系数及能量反射系数的理论表达式,并且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系数及能量反射系数受P1波入射角及地基土体饱和度变化的影响情况。结果表明:各反射波的振幅反射系数及能量反射系数不仅与入射角有关,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工程地震勘探具有一定指导意义。

The unsaturated soil is the most common nature soil form on the earth＇s surface, unlike the fully saturated soil, four bulk waves exist in this soil： one shear wave （i.e., S wave） and three compressional waves （i.e., P1 wave, P2 wave, P3 wave）. Among these four type waves, P1 wave is the wave with fastest wave velocity and lowest attenuation coefficient, which is similar to the fast compressional wave in fully saturated soil. Hence the unsaturated poroelasticity theory is used to describe the propagation characteristics of elastic waves in unsaturated fluid-saturated soils, and the reflection problem of plane-Pl-waves at the free boundary of unsaturated soils is analyzed. Based on the boundary conditions, the theoretical expressions of the amplitude reflection coefficients and energy reflection coefficients for the four reflected waves at the boundary, i.e., reflected P1 wave, reflected P2 wave, reflected P3 wave and reflected S wave, are respectively derived and the numerical calculations are then carried out. The effects of the incident angle and saturation degree of the soils on the amplitude reflection coefficients and energy reflection coefficients of the four reflected waves are discussed in the numerical example. It is shown that the amplitude reflection coefficients and energy reflection coefficients of the waves is effected by not only the incident but also the saturation degree. These conclusions are useful for the theoretical research and seismic exploration projects.