Transient analysis of wave propagation in layered soil by using the scaled boundary finite element method

An efficient method for modelling the propagation of elastic waves in layered media is developed. It is applicable to scalar and vector wave soil–structure interaction problems involving semi-infinite layers. The scaled boundary finite element method is employed to derive an equation for the displacement unit-impulse response matrix on the near field/far field interface. An accurate and efficient time discretization method is proposed for that equation. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. In addition, a reasonable viscous damping model is proposed for this problem. The existence of damping will cause the displacement unit-impulse response matrix to decay faster. Therefore, an earlier truncation time can be adopted, thus further reducing the computational effort. Numerical examples demonstrate the accuracy and high efficiency of the new method.