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

doi:10.1007/s11709-022-0904-3

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (1) : 10-24 https://doi.org/10.1007/s11709-022-0904-3

RESEARCH ARTICLE

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

Yusheng YANG^1,², Haitao YU^3,⁴(

), Yong YUAN⁴, Dechun LU⁵, Qiangbing HUANG³

¹. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
². Shanghai Construction No.4 (Group) Co., Ltd., Shanghai 201103, China
³. Key Laboratory of Western China’s Mineral Resources and Geological Engineering of Ministry of Education, Chang’an University, Xi’an 710054, China
⁴. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China
⁵. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

Download: PDF(15030 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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.

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

Corresponding Author(s): Haitao YU

About author:

Changjian Wang and Zhiying Yang contributed equally to this work.

Just Accepted Date: 24 November 2022 Online First Date: 16 January 2023 Issue Date: 02 March 2023

Cite this article:

Yusheng YANG,Haitao YU,Yong YUAN, et al. A numerical framework for underground structures in layered ground under inclined P-SV waves using stiffness matrix and domain reduction methods[J]. Front. Struct. Civ. Eng., 2023, 17(1): 10-24.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-022-0904-3
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I1/10

Fig.1 Analysis models: (a) global model and (b) local model with plane wave assumption.

Fig.2 Layered ground under inclined P-SV waves.

Fig.3 Scheme of the DRM.

Fig.4 Ricker wavelet: (a) time history; (b) frequency spectrum.

Fig.5 Seismograms in the homogeneous ground: (a) horizontal displacement and (b) vertical displacement.

Fig.6 Displacements at positions: (a) (0,–40) and (b) (0,–140).

Fig.7 Displacement contours at different moments (unit: m).

Fig.8 Seismograms in the two-layer ground: (a) horizontal displacement and (b) vertical displacement.

Fig.9 Displacements at positions: (a) (0,–60) and (b) (0,–120).

Fig.10 Seismogram in the pressure-dependent homogeneous ground: (a) horizontal displacement and (b) vertical displacement.

Fig.11 Displacement contours at different moments in the pressure-dependent ground (unit: m).

Fig.12 Extended model.

Fig.13 Comparison of maximum displacements of the tunnel: (a) maximum horizontal displacement; (b) maximum vertical displacement.

Fig.14 One-dimensional models using: (a) the proposed method; (b) viscous-spring boundary; (c) viscous boundary.

Fig.15 Displacement comparison in the homogeneous ground among different methods at depths of: (a) 190 m; (b) 0 m.

Fig.16 Displacement comparison in the two-layer ground among different methods at depths of: (a) 190 m; (b) 0 m.

parameter	value	description
$ρ$ (kg/m³)	2000	density
$P r e f$ (kPa)	101	reference effective confining pressure
$G r$ (kPa)	$1 × 105$	reference shear modulus
$B r$ (kPa)	$1.67 × 105$	reference bulk modulus
d	0.5	pressure dependency coefficient
$γ m a x, r$	0.1	maximum shear strain
$?$ (° )	33.5	friction angle
$? P T$ (° )	25.5	phase transformation angle
c (kPa)	0.1	cohesion
e	0.7	void ratio
c₁	0.045	control the shear-induced volumetric change, contraction tendency based on the dilation history, and overburden stress effect
c₂	5
c₃	0.15
d₁	0.06	reflect dilation tendency, stress history, and overburden stress effect
d₂	3
d₃	0.15
liq₁	1	define accumulated permanent shear strain
liq₂	0	define accumulated permanent shear strain
NYS	20	number of yield surface

Tab.1 PDMY02 model parameters

Fig.17 Geometry of the numerical model (unit: m). (a) The whole soil?structure model; (b) the detail structure model.

Fig.18 Deformation of the structure: (a) horizontal drift ratio (

Δ H / H

) and (b) vertical drift ratio (

Δ V / W

Fig.19 Internal forces of the central column at the top: (a) axial force, (b) shear force and (c) moment.

Fig.20 Deformation of the structure: (a) horizontal drift ratio (

Δ H / H

) and (b) vertical drift ratio (

Δ V / W

) under different incident angles.

Fig.21 Internal forces of the central column at the top: (a) axial force, (b) shear force and (c) moment under different incident angles.

1	D McCallen, A Petersson, A Rodgers, A Pitarka, M Miah, F Petrone, B Sjogreen, N Abrahamson, H Tang. 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 https://doi.org/10.1177/8755293020970982
2	E Bilotta, G Lanzano, S P G Madabhushi, F Silvestri. A numerical Round Robin on tunnels under seismic actions. Acta Geotechnica, 2014, 9(4): 563–579 https://doi.org/10.1007/s11440-014-0330-3
3	Y Yuan, Y S Yang, S H Zhang, H T Yu, J Sun. A benchmark 1 g shaking table test of shallow segmental mini-tunnel in sand. Bulletin of Earthquake Engineering, 2020, 18(11): 5383–5412 https://doi.org/10.1007/s10518-020-00909-w
4	J Régnier, L F Bonilla, P Y Bard, E Bertrand, F Hollender, H Kawase, D Sicilia, P Arduino, A Amorosi, D Asimaki, D Boldini, L Chen, A Chiaradonna, F DeMartin, M Ebrille, A Elgamal, G Falcone, E Foerster, S Foti, E Garini, G Gazetas, C Gélis, A Ghofrani, A Giannakou, J R Gingery, N Glinsky, J Harmon, Y Hashash, S Iai, B Jeremić, S Kramer, S Kontoe, J Kristek, G Lanzo, A Lernia, F Lopez-Caballero, M Marot, G McAllister, Mercerat E Diego, P Moczo, S Montoya-Noguera, M Musgrove, A Nieto-Ferro, A Pagliaroli, F Pisanò, A Richterova, S Sajana, d’Avila M P Santisi, J Shi, F Silvestri, M Taiebat, G Tropeano, L Verrucci, K Watanabe. 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 https://doi.org/10.1785/0120150284
5	J A Abell, N Orbović, D B McCallen, B Jeremic. 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 https://doi.org/10.1002/eqe.3026
6	A Løkke, A K Chopra. 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 https://doi.org/10.1002/eqe.3150
7	J Lysmer, R L Kuhlemeyer. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 1969, 95(4): 859–877 https://doi.org/10.1061/JMCEA3.0001144
8	W S Zhao, W Z Chen, D S Yang, X J Tan, H Gao, C Li. 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 https://doi.org/10.1016/j.engstruct.2018.12.050
9	P Li, E X Song. Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input. Computers and Geotechnics, 2015, 63: 229–243 https://doi.org/10.1016/j.compgeo.2014.10.003
10	J Q Huang, M Zhao, X Du. Non-linear seismic responses of tunnels within normal fault ground under obliquely incident P waves. Tunnelling and Underground Space Technology, 2017, 61: 26–39 https://doi.org/10.1016/j.tust.2016.09.006
11	B B Sun, S R Zhang, W Cui, M J Deng, C Wang. Nonlinear dynamic response and damage analysis of hydraulic arched tunnels subjected to P waves with arbitrary incoming angles. Computers and Geotechnics, 2020, 118: 103358 https://doi.org/10.1016/j.compgeo.2019.103358
12	D Baffet, J Bielak, D Givoli, T Hagstrom, D Rabinovich. Long-time stable high-order absorbing boundary conditions for elastodynamics. Computer Methods in Applied Mechanics and Engineering, 2012, 241-244: 20–37 https://doi.org/10.1016/j.cma.2012.05.007
13	N A Haskell. The dispersion of surface waves on multilayered media. Bulletin of the Seismological Society of America, 1953, 43(1): 17–34 https://doi.org/10.1785/BSSA0430010017
14	W T Thomson. Transmission of elastic waves through a stratified soil medium. Journal of Applied Physics, 1950, 21(2): 89–93 https://doi.org/10.1063/1.1699629
15	E Kausel. Thin-layer method: Formulation in the time domain. International Journal for Numerical Methods in Engineering, 1994, 37(6): 927–941 https://doi.org/10.1002/nme.1620370604
16	E Kausel, J M Roësset. Stiffness matrices for layered soils. Bulletin of the Seismological Society of America, 1981, 71(6): 1743–1761 https://doi.org/10.1785/BSSA0710061743
17	J Bielak, K Loukakis, Y Hisada, C Yoshimura. 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 https://doi.org/10.1785/0120010251
18	W Zhang, E E Seylabi, E Taciroglu. An ABAQUS toolbox for soil-structure interaction analysis. Computers and Geotechnics, 2019, 114: 103143 https://doi.org/10.1016/j.compgeo.2019.103143
19	W Zhang, E Taciroglu. 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 https://doi.org/10.1002/eqe.3443
20	J F Semblat, L Lenti, A Gandomzadeh. 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 https://doi.org/10.1002/nme.3035
21	Abaqus. Version 6.11. Paris: Dassault Systemes Simulia Corporation. 2011
22	S MazzoniF McKennaM H ScottG L Fenves. OpenSees Command Language Manual. 2006
23	Y Miao, H J He, H B Liu, S Y Wang. Reproducing ground response using in-situ soil dynamic parameters. Earthquake Engineering & Structural Dynamics, 2022, 51(10): 2449–2465 https://doi.org/10.1002/eqe.3671
24	S Y Wang, H Y Zhuang, H Zhang, H J He, W P Jiang, E L Yao, B Ruan, Y X Wu, Y Miao. Near-surface softening and healing in eastern Honshu associated with the 2011 magnitude-9 Tohoku-Oki Earthquake. Nature Communications, 2021, 12(1): 1215 https://doi.org/10.1038/s41467-021-21418-7
25	A Elgamal, Z H Yang, E Parra, A Ragheb. Modeling of cyclic mobility in saturated cohesionless soils. International Journal of Plasticity, 2003, 19(6): 883–905 https://doi.org/10.1016/S0749-6419(02)00010-4
26	N M Newmark. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division, 1959, 85(3): 67–94 https://doi.org/10.1061/JMCEA3.0000098

[1]

Download

[1]	Yeong-Bin Yang, Zeyang Zhou, Xiongfei Zhang, Xiaoli Wang. Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method[J]. Front. Struct. Civ. Eng., 2022, 16(12): 1530-1551.
[2]	Zhenning BA, Jisai FU, Zhihui ZHU, Hao ZHONG. An end-to-end 3D seismic simulation of underground structures due to point dislocation source by using an FK-FEM hybrid approach[J]. Front. Struct. Civ. Eng., 2022, 16(12): 1515-1529.
[3]	Yujie YU, Zhihua CHEN, Renzhang YAN. Finite element modeling of cable sliding and its effect on dynamic response of cable-supported truss[J]. Front. Struct. Civ. Eng., 2019, 13(5): 1227-1242.
[4]	Guobo WANG, Mingzhi YUAN, Xianfeng MA, Jun WU. Numerical study on the seismic response of the underground subway station- surrounding soil mass-ground adjacent building system[J]. Front. Struct. Civ. Eng., 2017, 11(4): 424-435.
[5]	Baiping DONG, James M. RICLES, Richard SAUSE. Seismic performance of steel MRF building with nonlinear viscous dampers[J]. Front. Struct. Civ. Eng., 2016, 10(3): 254-271.
[6]	Dejian YANG,Meiling DUAN. Seismic responses of subway station with different distributions of soft soil in Tianjin[J]. Front. Struct. Civ. Eng., 2014, 8(2): 187-193.
[7]	YANG Menggang, HU Jianhua. Investigations concerning seismic response control of self-anchored suspension bridge with MR dampers[J]. Front. Struct. Civ. Eng., 2008, 2(1): 43-48.
[8]	LI Peizhen, REN Hongmei, LU Xilin, SONG Heping, CHEN Yueqing. Shaking table testing of hard layered soil-pile-structure interaction system[J]. Front. Struct. Civ. Eng., 2007, 1(3): 346-352.
[9]	LOU Menglin, LI Yuchun, LI Nansheng. Analyses of the seismic responses of soil layers with deep deposits[J]. Front. Struct. Civ. Eng., 2007, 1(2): 188-193.

Viewed

Full text

Abstract

Cited

Shared

Discussed