Vertical vibration of a circular foundation in a transversely isotropic poroelastic soil

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.