High performance of the scaled boundary finite element method applied to the inclined soil field in time domain

An efficient method for modelling the wave propagation in semi-infinite domain is proposed. It is applicable to soil–structure interaction problems for complex inclined soil field. The scaled boundary finite element method is modified through the original scaling center substituting by a scaling line. Based on this scaling line, the dynamic stiffness equation is derived. Then, an accurate and efficient continued fraction method is firstly introduced for solving equation for the model with rigid bedrock. By using the continued fraction solution and introducing auxiliary variables, the equation of motion of unbounded domain is built. Coupling the far field modelling by modified scaled boundary finite element method with the near field modelling by the finite element method, the global time-domain equation is obtained, which is a standard equation of motion for the whole domain. As a key point, the precise time-integration method is firstly employed to solve global equation of motion. The advantages of this integration method are that the integral interval is divided into quite small piece. It makes sure the precision achieve to computer precision. Owning to adopting five terms Taylor expansion for each small integral interval, the computational precision is increased greatly. Applying precise time-integration method in this paper, it greatly improves the accuracy and computing speed of proposed method. By using the sub-structure method, the inclined soil field is modelled. Numerical examples demonstrate accuracy and high efficiency of the new method, especially for complex dip mediums.