Dynamic Green’s functions of saturated soils subjected to the internal excitation

Based on the modified theory of elastic wave in saturated soils, Lamb’s problem for saturated soils is studied in this paper. First, the governing differential equations for saturated soils are solved by means of Hankel transform. Then, under the consideration of the boundary value condition, the solutions for the displacement and stress components of the saturated soils are expressed in term of integral forms which can be evaluated by numerical quadrature. Finally, the vertical surface displacement is numerically presented and the influence of the permeability and the frequency of the excitation on the vertical displacement is investigated. This study is reasonable for engineering practice and provides an effective method to analyze the similar problem about dynamic response of underground structure.