A time domain solution for complex multilayered soil model with circular inhomogeneity by the SBFEM

The scaled boundary finite method (SBFEM) is developed for analyzing wave propagation problem in the two-dimensional unbounded domain with rigid bedrock. It combines the advantages of the finite element method and boundary element boundary method. Moreover, the original scaling center is replaced by a scaling line which is more suitable for analyzing the multilayered soil model. Therefore, the modified SBFEM develops the original SBFEM. A new derivation of the modified SBFEM equation is built in the frame of Hamilton system. A continued fraction solution of the dynamic stiffness of the soil model with bedrock is obtained for the first time. Then, by introducing the continued fraction solution and auxiliary variables, it leads to the model resting on bedrock can be solved in time domain. The global equation of motion is solved by the efficient precise time-integration method. This integral method is firstly employed in the modified SBFEM. The precision of the proposed method can achieve computer precision. Therefore, an extremely efficient and accurate solution of the modified SBFEM in time domain is obtained. The results of the complex soil model with circular inhomogeneity show that the proposed method yields excellent results, and high accuracy is observed.