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

ABSTRACT

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.

KEYWORDS:

• Multi-transmitting formula
• spectral element method
• SV wave
• stability

Acknowledgments

The authors would like to thank two anonymous reviewers for their constructive comments on improving the manuscript.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under [Grant No. 51808371], and the Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration [Grant No. 2021EEEVL0001].