3D Lamb's problem in transversely isotropic saturated soils subjected to internal excitation

Based on the Biot's theory for fluid-saturated porous media, the 3D wave equations for transversely isotropic saturated soils in cylindrical coordinate are transformed into the two uncoupling governing differential equations by introducing displacement functions, and the general solutions are presented by the operator theory. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform methods. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for saturated soils are obtained. Furthermore, the systematic study on Lamb's problems in the transversely isotropic saturated soils subjected to the internal excitation is performed. The calculated results indicate the rapid vibration attenuation of vertical surface displacement of the saturated soils subjected to a low-frequency interior excitation in small depth.