Abstract The traveling wave responses in an unsaturated medium induced by a solid force and fluid mass sources are derived in 3D Green's functions using the Dirac Delta function decompositions. The wave behaviors are described in pore fluid pressures and solid frame displacement along with fluctuations of capillary pressure in response to time variant fluid injections and solid force loadings. These solutions are numerically calculated and analyzed for unconsolidated sands as a function of water saturation as representative examples. Our results reveal and validate four wave modes, a fast compressional wave (P1), two slow compressional waves (P2 and P3), and a shear wave. The P1 wave and shear wave can be effectively observed. The slow waves with diffusive characters bear low amplitudes and low velocities. The traveling waves in the pore fluid pressures and solid displacement are sensitive to the different sources and the water saturation. The solid force induces the total stress perturbation while the fluid mass sources directly make the volume strains in the fluid phases. This fluid-solid coupling difference causes the distinct traveling wave signature contrasts in the pore-fluid and solid-frame response amplitudes and tendencies with water retention. For the variation of water saturation, the traveling wave shows a nonmonotonic feature. The fluctuation of capillary pressure exhibits a concave upward relationship, which can further interpret the changes of wave amplitude with water saturation. A solid force may enhance the fluctuation. However, for high water saturation, the interactive fluid-solid effect by the solid force may break the fluid contact due to the extremely compressible air.

中文翻译：

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固体力和流体质量源在不饱和介质中引起的非单调行波

摘要 在不饱和介质中由固体力和流体质量源引起的行波响应是使用 Dirac Delta 函数分解在 3D Green 函数中导出的。波浪行为在孔隙流体压力和固体框架位移以及毛细管压力波动中描述，以响应时变流体注入和固体力载荷。作为代表性示例，对于松散砂土作为水饱和度的函数，对这些解进行数值计算和分析。我们的结果揭示并验证了四种波模式，一个快速压缩波 (P1)、两个慢压缩波（P2 和 P3）和一个剪切波。可以有效地观测到 P1 波和横波。具有扩散特性的慢波具有低振幅和低速度。孔隙流体压力和固体位移中的行波对不同来源和含水饱和度敏感。固体力引起总应力扰动，而流体质量源直接在流体相中产生体积应变。这种流固耦合差异导致孔隙-流体和固体框架响应幅度和持水趋势的明显行波特征对比。对于含水饱和度的变化，行波表现出非单调特征。毛细管压力的波动呈凹向上的关系，可以进一步解释波幅随含水饱和度的变化。坚实的力量可能会增强波动。然而，对于高含水饱和度，