Formulation and Performance of Multi-Transmitting Formula with Spectral Element Method in 2D Ground Motion Simulations Under Plane-Wave Incidence: SV Wave Problem

To simulate the ground motions of 2D arbitrary sites subjected to plane SV waves, we put forward a numerical method combining the multi-transmitting formula (MTF) and spectral element method (SEM). The investigation results demonstrate a high simulation accuracy of the presented method. Most importantly, the MTF exhibits a notably superior stability performance in the SEM than in traditional finite-element method (FEM). Without any additional treatment, high-frequency instability does not occur when controlling the Courant number value C and the ratio between the MTF parameter S and C; the upper limit value of this ratio is significantly smaller than that of the SH-wave problem. In addition, a preliminary stability criterion for the MTF in SEM is given based on the homogeneous half-space model. For low-frequency stability, the occurrence time of instability is considerably lagged when no interventions are adopted. Moreover, the low-frequency instability can be readily eliminated by using smaller modification parameter in the SEM compared with the FEM.