平面S波在饱和多孔热弹性介质边界的反射问题研究

Reflection of Plane S Waves at the Boundary of Saturated Porous Thermo-Elastic Media

摘要:

针对饱和多孔介质中热弹性波的传播特性问题，基于多孔介质理论和广义的热弹性模型，研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发，建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件，经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算，分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明：各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大，同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。

Abstract:

To solve the problem of propagation characteristics of thermo-elastic waves in saturated porous media, based on the theory of porous media and the generalized thermo-elasticity model, the reflection problem of plane S waves at the boundary of saturated porous thermo-elastic media is studied in this paper. The thermal-fluid-solid coupling model of elastic waves in saturated porous media is established, based on the wave equations for saturated porous media considering fluid-solid coupling and the generalized thermo-elastic basic equations considering thermal-elastic coupling. By introducing the potential function and considering the adiabatic boundary conditions of free-water permeability, the theoretical expressions of amplitude reflectivity of four reflection waves on the boundary of saturated porous thermo-elastic media are given by theoretical derivation. The effects of some parameters, i.e., the incident frequency of plane S waves, the incident angle, and the thermal expansion coefficient, on amplitude reflectivity of the four reflection waves are analyzed by numerical calculation. Results showed that the amplitude reflectivity of each reflected wave increases with increasing frequency and thermal expansion coefficient, and is also affected by the change of incident angle of the plane S-wave. These conclusions are significant for theoretical research into soil dynamics and related exploratory projects.