A new analysis of the complex two-dimensional multilayered anisotropic soil in time domain

Abstract

The dynamic analysis of two-dimensionalmultilayered anisotropic soilwith rigid bedrock is studied. An efficient numerical approach named the modified scaled boundary finite element method (SBFEM) is proposed in the time domain. Based on introducing the continued fraction method and auxiliary variables, the time domain solution is obtained. This solution can be applied to the transversely isotropic medium without any difficulty. For the modified SBFEM, the original scaling center is replaced by a scaling line. These characteristics enable the modified SBFEM to model the horizontal layered medium. Three significant technologies have been introduced in the formula derivation and solving process. First, the dual system is used to derive the displacement equation of the modified SBFEM, which is built on a Hamilton system. According to the principle of virtual work, the displacement equation is transformed to the dynamic stiffness equation. Second, the new continued fraction method for the unbounded domain resting on rigid bedrock is proposed. By introducing auxiliary variables, the displacement equation of motion of an unbounded domain is built. Third, it is an extremely important point that the accurate precise time-integration method is first employed to solve the global equation of motion of the modified SBFEM. This numerical integral method can achieve the machine precision. By using this method in solving the equation of motion of the modified SBFEM, an extremely accurate solution can be achieved. Finally, numerical examples validate the accuracy of the new proposed method, especially for the complex inclined model with anisotropic soil.