Semianalytical Solution for the Transient Response of One-Dimensional Saturated Multilayered Soil Column

Abstract

A semianalytical solution was obtained in the time domain directly for the one-dimensional transient response of a saturated multilayered soil column under typical boundary conditions based on Biot theory, which could take into account the inertial, viscous, and mechanical couplings of saturated porous soil media. First, one-dimensional wave equations were established by using the nondimensionless method. Then, by decomposing the displacement solution into dynamic and static components, the boundary conditions of the soil column were homogenized. The transfer matrix method was used to obtain the eigenvalue and eigenfunction of homogenized boundary conditions. With the help of undetermined coefficients and orthogonality of eigenfunctions methods, the solution to the problem of nonhomogeneous boundary conditions could be converted to solve the initial value problem of a series of ordinary differential equations. The semianalytical solutions were approached by the precise time-integration method. The proposed method can be used for a soil column under various boundary conditions. Several numerical simulations were carried out to validate this method. Finally, the one-dimensional transient responses of hard–soft double-layered saturated soil under step load was analyzed. The results demonstrate that the rigidity of substratum and different rigidity ratio of hard–soft layers mainly affect the responses over a long period of time.