Extended stiffness matrix method for horizontal vibration of a rigid disk embedded in stratified soils

Abstract

• Horizontal vibration of a rigid disk embedded in stratified soils is studied. • Potential function method is applied to obtained the general solutions of a poroleastic medium and an elastic medium. • An extended stiffness matrix method is proposed for solution of the stratified soils. • The mixed boundary value problem of soils–disk interaction is represented as four coupled integral equations. • Examples are carried out to illustrate the influences of groundwater, embedment position of the disk. In this paper, an extended stiffness matrix method is proposed for horizontal vibration of a rigid disk embedded in stratified soils. Considering the influence of groundwater level, the soils are modeled as a layered system composed of elastic and poroelastic media. The potential functions, Fourier series and Hankel transform are applied to obtain the displacement and stress solutions of the elastic medium and poroelastic medium. Conventional stiffness matrix method is generally used to solve a single-medium layered system with high efficiency and computational stability, but cannot be directly applied to the present layered model. The principle of the extended stiffness matrix method is to make the displacement and stress and stiffness matrix dimensions of the poroelastic layer match those of adjacent elastic layers, allowing the assembly of a global equation. the problem of imcompatibility between an elastic medium and a poroelastic medium at interface is addressed by the extended stiffness matrix method which also provides a new idea for solution of layered systems consisting of different media. Subsquently, the mixed boundary value problem of the soils–disk interaction is represented as four coupled integral equations which can be reduced to a pair of Fredholm integral equations of the second kind to solve. The accuracy of the present method is verified by the existing solutions, and then several numerical examples are presented to illustrate the effects of groundwater level and permeability of saturated soil layer as well as the embedded depth of the rigid disk on the dynamic interaction between the disk and the stratified soils.