Abstract Analytical methods based on linear elasticity have been used to model the dynamic response of foundations. These solutions commonly assume that soils are isotropic and elastic. Incorporation of anisotropy and the two-phased nature of soils (solid skeleton with pores filled with water) is important in the study of dynamic response of foundations. This paper presents the explicit analytical solutions for a transversely isotropic poroelastic soil half-space under a buried time-harmonic vertical load and a time-harmonic pore pressure discontinuity. These versatile fundamental solutions are derived by using Hankel integral transforms. They can be used to analyze a variety of dynamic problems in geomechanics. The fundamental solutions are then applied to solve the time-harmonic vertical vibration of a flexible circular foundation by using variational methods. Selected numerical results are presented to demonstrate the influence of soil anisotropy, poroelasticity, foundation flexibility, depth of embedment and frequency of excitation on the vertical dynamic response of foundation and the force transmitted to soil.

中文翻译：

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横向各向同性多孔弹性土中圆形地基的竖向振动

摘要 基于线弹性的分析方法已被用于模拟地基的动力响应。这些解决方案通常假设土壤是各向同性和弹性的。结合各向异性和土壤的两相性质（具有充满水的孔隙的固体骨架）在地基动力响应研究中很重要。本文提出了在埋地时谐垂直载荷和时谐孔隙压力不连续性下横向各向同性多孔弹性土壤半空间的显式解析解。这些通用的基本解决方案是通过使用 Hankel 积分变换推导出来的。它们可用于分析地质力学中的各种动态问题。然后应用基本解通过变分方法求解柔性圆形基础的时谐竖向振动。选定的数值结果展示了土壤各向异性、孔隙弹性、地基柔性、嵌入深度和激励频率对地基垂直动力响应和传递到土壤的力的影响。