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Simulations of ground motions under plane wave incidence in 2D complex site based on the spectral element method (SEM) and multi-transmitting formula (MTF): SH problem

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Abstract

Recent ground motion simulations based on the spectral element method have mainly focused on source-internal problems. Reports on seismic responses due to plane wave incidence are rare, even though these are frequently encountered in site effect analysis and soil-structure interaction simulations. In this study, a seismic motion simulation method for 2D complex sites under plane SH wave incidence is proposed based on high-precision spectral element method (SEM) and multi-transmitting formula (MTF). The accuracy and stability of this method are validated through numerous numerical examples. Comparisons with analytical solutions and extended results demonstrate the high simulation accuracies for the ground motions in 2D complex site models when SH plane waves are vertically incident from the bottom. Compared with MTF in the traditional finite-element method (FEM), MTF integrated into SEM demonstrates better performance for both high- and low-frequency stabilities. First, until to the third-order MTF, this method shows a fairly good ability to eliminate high-frequency instability. This instability only occurs when the artificial wavespeed, ca, adopted in the MTF is larger than about five times the physical velocity, cs. For the most common case of ca = cs, long-term stable results can be achieved without any special treatments. In addition, under the condition of no interventions, the low-frequency drift instability for MTF in SEM is considerably lessened compared with that of MTF in FEM, and the drift instability can also be eliminated by a smaller perturbation parameter than in the latter. The method presented in this study combines the advantages of SEM and MTF, and exhibits better stability performance, indicating good application prospects for wave motion simulations of plane wave incidence problems.

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Acknowledgements

The authors would like to appreciate the constructive comments and suggestions of two anonymous reviewers for improving the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China under Grant No. 51808371.

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Authors and Affiliations

  1. Key Laboratory of Structure Engineering of Jiangsu Province, Suzhou University of Science and Technology, Suzhou, 215011, China

    Yanyan Yu & Haiping Ding

  2. Institute of Engineering Mechanics, China Earthquake Administration, Harbin, 150080, China

    Xubin Zhang

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  1. Yanyan Yu
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  2. Haiping Ding
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  3. Xubin Zhang
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Correspondence to Haiping Ding.

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Yu, Y., Ding, H. & Zhang, X. Simulations of ground motions under plane wave incidence in 2D complex site based on the spectral element method (SEM) and multi-transmitting formula (MTF): SH problem. J Seismol 25, 967–985 (2021). https://doi.org/10.1007/s10950-021-09995-y

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