Duality system-based derivation of the modified scaled boundary finite element method in the time domain and its application to anisotropic soil

• A duality system-based derivation of the modified SBFEM in time domain is firstly obtained.
• It is suitable for the solution of anisotropic soil model.
• Efficient precise time-integration method is firstly employed to solve the global motion equation of SBFEM.
• The governing equations and solutions of SBFEM are derived in details.
• The solution is semi-analytical, very high accuracy.

In this study, an efficient method is proposed for the dynamic analysis of a two-dimensional semi-infinite soil with rigid bedrock, which is applicable to the cross-isotropic and anisotropic soil models. The original scaling center is replaced by a scaling line, so the modified scaled boundary finite element method (SBFEM) is more suitable for analyzing the horizontal layered soil. For the first time, the dual system is employed to derive the displacement equation for the modified SBFEM. By introducing the dual variables, the governing equations are derived in the framework of a Hamilton system. Next, the dynamic stiffness equation is obtained according to the weighted residuals method. The displacement equation of motion for the far field is built by applying the continued fraction method and introducing auxiliary variables. Based on the sub-structure method, the far field can be seamlessly coupled with the near field. Importantly, the efficient and precise time-integration method is first employed to solve the global equation of motion. High computational precision can be achieved using the proposed method. An extremely efficient and accurate solution can be obtained by applying this method to solve the equation of motion for the modified SBFEM. Finally, the accuracy and high efficiency of the proposed method is demonstrated for the anisotropic soil model based on numerical examples.