This paper establishes an efficient model for simulating wave propagation in a multi-layered transversely isotropic (TI) saturated medium. The complex frequency shifted perfectly matched layer (CFSPML) is integrated into the thin layer method (TLM) framework to address instability issues associated with the classical PML in TI media. The three-dimensional closed-form fundamental solution for dynamic sources acting on a layered TI half-space is derived in the frequency-space domain. By eliminating the necessity of double discrete Fourier transform of spatial coordinates, this approach provides an efficient and accurate tool for exploring wave propagation in saturated soils. Numerical examples are conducted to determine the parameters involved in CFSPML for an unbounded TI saturated medium across various material anisotropy ratios, including the total thickness of CFSPML domain H, the parameter Δ related to the number of CFSPML elements, and the reflection coefficient within the discrete CFSPML domain . A comprehensive investigation systematically analyses the effect of material anisotropy on dynamic responses. Numerical studies highlight that the anisotropy in the shear modulus exerts the most substantial influence on the dynamic response, followed by Young's modulus and the permeability coefficient. The effect of permeability coefficient anisotropy cannot be disregarded, particularly in the context of fluid sources.

中文翻译：

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使用耦合薄层和复频移完美匹配层方法求解层状横观各向同性饱和半空间动态响应的三维基本解


本文建立了一个有效的模型来模拟多层横观各向同性（TI）饱和介质中的波传播。将复杂频移完美匹配层 (CFSPML) 集成到薄层方法 (TLM) 框架中，以解决 TI 介质中与经典 PML 相关的不稳定问题。在频空间域中推导了作用于分层 TI 半空间的动态源的三维封闭形式基本解。通过消除空间坐标的双离散傅立叶变换的必要性，该方法为探索饱和土壤中的波传播提供了有效且准确的工具。通过数值算例确定了各种材料各向异性比下无界 TI 饱和介质的 CFSPML 涉及的参数，包括 CFSPML 域 H 的总厚度、与 CFSPML 单元数量相关的参数 Δ 以及离散区域内的反射系数。 CFSPML 域。一项全面的研究系统地分析了材料各向异性对动态响应的影响。数值研究强调，剪切模量的各向异性对动态响应影响最大，其次是杨氏模量和渗透系数。渗透系数各向异性的影响不容忽视，特别是在流体源的情况下。