A numerical framework for underground structures in layered ground under inclined P-SV waves using stiffness matrix and domain reduction methods

Abstract

A numerical framework was proposed for the seismic analysis of underground structures in layered ground under inclined P-SV waves. The free-field responses are first obtained using the stiffness matrix method based on plane-wave assumptions. Then, the domain reduction method was employed to reproduce the wavefield in the numerical model of the soil–structure system. The proposed numerical framework was verified by providing comparisons with analytical solutions for cases involving free-field responses of homogeneous ground, layered ground, and pressure-dependent heterogeneous ground, as well as for an example of a soil–structure interaction simulation. Compared with the viscous and viscous-spring boundary methods adopted in previous studies, the proposed framework exhibits the advantage of incorporating oblique incident waves in a nonlinear heterogeneous ground. Numerical results show that SV-waves are more destructive to underground structures than P-waves, and the responses of underground structures are significantly affected by the incident angles.

Graphical abstract

Keywords

underground structures / seismic response / stiffness matrix method / domain reduction method / P-SV waves

References

[1] McCallen D, Petersson A, Rodgers A, Pitarka A, Miah M, Petrone F, Sjogreen B, Abrahamson N, Tang H. EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow. Earthquake Spectra, 2021, 37(2): 707–735

[2] Bilotta E, Lanzano G, Madabhushi S P G, Silvestri F. A numerical Round Robin on tunnels under seismic actions. Acta Geotechnica, 2014, 9(4): 563–579

[3] Yuan Y, Yang Y S, Zhang S H, Yu H T, Sun J. A benchmark 1 g shaking table test of shallow segmental mini-tunnel in sand. Bulletin of Earthquake Engineering, 2020, 18(11): 5383–5412

[4] Régnier J, Bonilla L F, Bard P Y, Bertrand E, Hollender F, Kawase H, Sicilia D, Arduino P, Amorosi A, Asimaki D, Boldini D, Chen L, Chiaradonna A, DeMartin F, Ebrille M, Elgamal A, Falcone G, Foerster E, Foti S, Garini E, Gazetas G, Gélis C, Ghofrani A, Giannakou A, Gingery J R, Glinsky N, Harmon J, Hashash Y, Iai S, Jeremić B, Kramer S, Kontoe S, Kristek J, Lanzo G, Lernia A, Lopez-Caballero F, Marot M, McAllister G, Diego Mercerat E, Moczo P, Montoya-Noguera S, Musgrove M, Nieto-Ferro A, Pagliaroli A, Pisanò F, Richterova A, Sajana S, Santisi d’Avila M P, Shi J, Silvestri F, Taiebat M, Tropeano G, Verrucci L, Watanabe K. International benchmark on numerical simulations for 1D, nonlinear site response (PRENOLIN): Verification phase based on canonical cases. Bulletin of the Seismological Society of America, 2016, 106(5): 2112–2135

[5] Abell J A, Orbović N, McCallen D B, Jeremic B. Earthquake soil-structure interaction of nuclear power plants, differences in response to 3-D, 3×1-D, and 1-D excitations. Earthquake Engineering & Structural Dynamics, 2018, 47(6): 1478–1495

[6] Løkke A, Chopra A K. Direct finite element method for nonlinear earthquake analysis of concrete dams: Simplification, modeling, and practical application. Earthquake Engineering & Structural Dynamics, 2019, 48(7): 818–842

[7] Lysmer J, Kuhlemeyer R L. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 1969, 95(4): 859–877

[8] Zhao W S, Chen W Z, Yang D S, Tan X J, Gao H, Li C. Earthquake input mechanism for time-domain analysis of tunnels in layered ground subjected to obliquely incident P- and SV-waves. Engineering Structures, 2019, 181: 374–386

[9] Li P, Song E X. Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input. Computers and Geotechnics, 2015, 63: 229–243

[10] Huang J Q, Zhao M, Du X. Non-linear seismic responses of tunnels within normal fault ground under obliquely incident P waves. Tunnelling and Underground Space Technology, 2017, 61: 26–39

[11] Sun B B, Zhang S R, Cui W, Deng M J, Wang C. Nonlinear dynamic response and damage analysis of hydraulic arched tunnels subjected to P waves with arbitrary incoming angles. Computers and Geotechnics, 2020, 118: 103358

[12] Baffet D, Bielak J, Givoli D, Hagstrom T, Rabinovich D. Long-time stable high-order absorbing boundary conditions for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 2012, 241-244: 20–37

[13] Haskell N A. The dispersion of surface waves on multilayered media. Bulletin of the Seismological Society of America, 1953, 43(1): 17–34

[14] Thomson W T. Transmission of elastic waves through a stratified soil medium. Journal of Applied Physics, 1950, 21(2): 89–93

[15] Kausel E. Thin-layer method: Formulation in the time domain. International Journal for Numerical Methods in Engineering, 1994, 37(6): 927–941

[16] Kausel E, Roësset J M. Stiffness matrices for layered soils. Bulletin of the Seismological Society of America, 1981, 71(6): 1743–1761

[17] Bielak J, Loukakis K, Hisada Y, Yoshimura C. Domain reduction method for three-dimensional earthquake modeling in localized regions, part I: Theory. Bulletin of the Seismological Society of America, 2003, 93(2): 817–824

[18] Zhang W, Seylabi E E, Taciroglu E. An ABAQUS toolbox for soil-structure interaction analysis. Computers and Geotechnics, 2019, 114: 103143

[19] Zhang W, Taciroglu E. 3D time-domain nonlinear analysis of soil-structure systems subjected to obliquely incident SV waves in layered soil media. Earthquake Engineering & Structural Dynamics, 2021, 50(8): 2156–2173

[20] Semblat J F, Lenti L, Gandomzadeh A. A simple multi-directional absorbing layer method to simulate elastic wave propagation in unbounded domains. International Journal for Numerical Methods in Engineering, 2011, 85(12): 1543–1563

[21] Abaqus. Version 6.11. Paris: Dassault Systemes Simulia Corporation. 2011

[22] MazzoniSMcKennaFScottM HFenvesG L. OpenSees Command Language Manual. 2006

[23] Miao Y, He H J, Liu H B, Wang S Y. Reproducing ground response using in-situ soil dynamic parameters. Earthquake Engineering & Structural Dynamics, 2022, 51(10): 2449–2465

[24] Wang S Y, Zhuang H Y, Zhang H, He H J, Jiang W P, Yao E L, Ruan B, Wu Y X, Miao Y. Near-surface softening and healing in eastern Honshu associated with the 2011 magnitude-9 Tohoku-Oki Earthquake. Nature Communications, 2021, 12(1): 1215

[25] Elgamal A, Yang Z H, Parra E, Ragheb A. Modeling of cyclic mobility in saturated cohesionless soils. International Journal of Plasticity, 2003, 19(6): 883–905

[26] Newmark N M. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division, 1959, 85(3): 67–94

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 41922059, 42177134, and 51778487), Fundamental Research Funds for the Central Universities, CHD (300102262506), and Top Discipline Plan of Shanghai Universities-Class I.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11709-022-0904-3 and is accessible for authorized users.

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

RIGHTS & PERMISSIONS

2023 The Author(s). This article is published with open access at link.springer.com and journal.hep.com.cn