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The spectral cell method in nonlinear earthquake modeling

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Abstract

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr–Coulomb and Drucker–Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (\(p \ge 3\)) require mesh resolutions above of \(PPW \ge \)10 to ensure displacement errors below 10%.

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Acknowledgements

The authors are thankful to Universidad EAFIT for the institutional and financial support given to this project. Some of the computations were performed on Apolo in the Center of Computer Science at Universidad EAFIT, and on Blue Waters at the National Center for Supercomputing Applications (NCSA). Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and is supported by the state of Illinois and the U.S. National Science Foundation (NSF) (awards OCI-0725070 and ACI-1238993). This work was also part of NSF PRAC awards: Extending the Spatiotemporal Scales of Physics-Based Seismic Hazard Analysis (ACI-1440085), and Improving Earthquake Forecasting and Seismic Hazard Analysis Through Extreme-Scale Simulations (ACI-1713792). The SCEC contribution number for this paper is 7283. We also thank two anonymous reviewers, and Assistant Professor Ricardo Taborda from the Center for Earthquake Research and Information (CERI) at the University of Memphis, for their helpful comments, suggestions, and careful reading of our work.

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  1. Civil Engineering Department, Universidad EAFIT, Medellín, Colombia

    Daniel Giraldo & Doriam Restrepo

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  1. Daniel Giraldo
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Correspondence to Daniel Giraldo.

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Giraldo, D., Restrepo, D. The spectral cell method in nonlinear earthquake modeling. Comput Mech 60, 883–903 (2017). https://doi.org/10.1007/s00466-017-1454-8

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