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Response spectrum method for seismic soil–structure interaction analysis of underground structure

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Abstract

The response spectrum method (RSM) has been incorporated into many codes for seismic design of aboveground structures since 1950s. However, no RSM is presented in details for the seismic design of underground structures due to the complexity of seismic soil–structure interaction (SSI). In this paper, the RSM is developed for the seismic analysis of the underground structures including SSI. First, the underground design response spectrum is derived using two different procedures from the ground design response spectrum that is commonly available in most seismic design codes. Second, the SSI analysis model consisting of the underground structure and its adjacent soil is established with the roller side boundaries and the bottom boundary subjected to the underground response spectrum. Third, the RSM is applied to the SSI analysis model to estimate the structural response under the underground response spectrum. Finally, the numerical examples are presented to demonstrate the feasibility of the RSM for the SSI analysis model of underground structure.

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References

  • ABAQUS (2012) ABAQUS/standard user’s manual version 5.8. Karlsson Sorensen Inc, Hibbit

    Google Scholar 

  • Abuhajar O, El Naggar H, Newson T (2015) Experimental and numerical investigations of the effect of buried box culverts on earthquake excitation. Soil Dyn Earthq Eng 79:130–148

    Article  Google Scholar 

  • Afra H, Pecker A (2002) Calculation of free field response spectrum of a non-homogeneous soil deposit from bed rock response spectrum. Soil Dyn Earthq Eng 22(2):157–165

    Article  Google Scholar 

  • AIJ (2004) Recommendations for loads on buildings. Architectural Institute of Japan, Tokyo (in Japanese)

    Google Scholar 

  • Amorosi A, Boldini D (2009) Numerical modeling of the transverse dynamic behavior of circular tunnels in clayey soils. Soil Dyn Earthq Eng 59(6):1059–1072

    Article  Google Scholar 

  • Asthana AK, Datta TK (1990) A simplified response spectrum method for random vibration analysis of flexible base buildings. Eng Struct 12(3):185–194

    Article  Google Scholar 

  • Ates S, Constantinou MC (2011) Example of application of response spectrum analysis for seismically isolated curved bridges including soil-foundation effects. Soil Dyn Earthq Eng 31(4):648–661

    Article  Google Scholar 

  • Berrah M, Kausel E (2010) Response spectrum analysis of structures subjected to spatially varying motions. Earthq Eng Struct Dyn 21(6):461–470

    Article  Google Scholar 

  • Bhavikatti Q, Cholekar SB (2017) Soil structure interaction effect for a building resting on sloping ground including infiill subjected to seismic analysis. Int J Res Eng Appl Sci 4(7):1547–1551

    Google Scholar 

  • BSL (2000) The building standard law of Japan. The Ministry of Construction, Tokyo

    Google Scholar 

  • Butt UA, Ishihara T (2012) Seismic load evaluation of wind turbine support structures considering low structural damping and soil structure interaction. In: European wind energy association annual event, Copenhagen

  • Chen Y (2014) Effect of pile–soil–structure interaction on the cable-stayed bridge in response to the earthquake. Appl Mech Mater 539:731–735

    Article  Google Scholar 

  • Chen HT, Tan P, Zhou FL (2017) An improved response spectrum method for non-classically damped systems. Bull Earthq Eng 15(10):4375–4397

    Article  Google Scholar 

  • Chopra AK (2001) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Chopra AK (2010) Elastic response spectrum: a historical note. Earthq Eng Struct Dyn 36(1):3–12

    Article  Google Scholar 

  • Cilingir U, Madabhushi SPG (2011) A model study on the effects of input motion on the seismic behavior of tunnels. Soil Dyn Earthq Eng 31(3):452–462

    Article  Google Scholar 

  • CJJ (2012) Urban bridge seismic specification (CJJ 166-2011). Architecture and Building Press, Beijng (in Chinese)

    Google Scholar 

  • Clough RW, Penzien J (1993) Dynamics of structures, 2nd edn. McGraw-Hill Inc, New York

    Google Scholar 

  • Der Kiureghian A, Neuenhofer A (1992) Response spectrum method for multi-support seismic excitations. Earthq Eng Struct Dyn 21(8):713–740

    Article  Google Scholar 

  • Du XL, Zhao M (2010a) Stability and identification for rational approximation of frequency response function of unbounded soil. Earthq Eng Struct Dyn 39(2):165–186

    Google Scholar 

  • Du XL, Zhao M (2010b) A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media. Soil Dyn Earthq Eng 30(10):937–946

    Article  Google Scholar 

  • Eurocode 8 (2003) Design of structures for earthquake resistance. European Committee for Standardization, Brussels

    Google Scholar 

  • Gasparini, DA, Vanmarcke EH (1976) Simulated earthquake motions compatible with prescribed response spectra. Department of Civil Engineering, Research Report R76-4, Massachusetts Institute of Technology, Cambridge

  • GB (2010) Code for seismic design of buildings (GB 50011-2010). China Architecture and Building Press, Beijing (in Chinese)

    Google Scholar 

  • GB (2014) Code for seismic design of urban rail transit structures (GB 50909-2014). China Planning Press, Beijing (in Chinese)

    Google Scholar 

  • Gupta VK, Trifunac MD (1991) Seismic response of multistoried buildings including the effects of soil–structure interaction. Soil Dyn Earthq Eng 10(8):414–422

    Article  Google Scholar 

  • Hashash YMA, Hook JJ, Schmidt B, Yao IC (2001) Seismic design and analysis of underground structures. Tunn Undergr Space Technol 16(4):247–293

    Article  Google Scholar 

  • Hatzigeorgiou GD, Beskos DE (2010) Soil–structure interaction effects on seismic inelastic analysis of 3-D tunnels. Soil Dyn Earthq Eng 30(9):851–861

    Article  Google Scholar 

  • Hu YX (2006) Earthquake engineering. Seismological Press, Beijing (in Chinese)

    Google Scholar 

  • Huang JQ, Zhao M, Du XL (2017) Non-linear seismic responses of tunnels within normal fault ground under obliquely incident P waves. Tunn Undergr Space Technol 61:26–39

    Article  Google Scholar 

  • ICC (2003) International building code (IBC). International Code Council, Falls Church

    Google Scholar 

  • Kaul MK (1978) Stochastic characterization of earthquakes through their response spectrum. Earthq Eng Struct Dyn 6(5):497–509

    Article  Google Scholar 

  • Kishida A, Takewaki I (2010) Response spectrum method for kinematic soil–pile interaction analysis. Adv Struct Eng 13(1):181–198

    Article  Google Scholar 

  • Kojima K, Fujita K, Takewaki I (2014) Unified analysis of kinematic and inertial earthquake pile responses via the single-input response spectrum method. Soil Dyn Earthq Eng 63(1):36–55

    Article  Google Scholar 

  • Li Y, Zhao M, Xu CS, Du XL, Li Z (2018) Earthquake input for finite element analysis of soil–structure interaction on rigid bedrock. Tunn Undergr Space Technol 79:250–262

    Article  Google Scholar 

  • Liu GH, Lian JJ, Liang C, Li G, Hu JJ (2016) An improved complex multiple-support response spectrum method for the non-classically damped linear system with coupled damping. Bull Earthq Eng 14(1):161–184

    Article  Google Scholar 

  • Liu GH, Lian JJ, Liang CL, Zhao M (2017) An effective approach for simulating multi-support earthquake underground motions. Bull Earthq Eng 15(11):4635–4659

    Article  Google Scholar 

  • Lou M, Wang H, Chen X, Zhai Y (2011) Structure–soil–structure interaction: literature review. Soil Dyn Earthq Eng 31(12):1724–1731

    Article  Google Scholar 

  • Luco JE, Contesse L (1973) Dynamic structure–soil–structure interaction. Bull Seismol Soc Am 63(4):1289–1303

    Google Scholar 

  • Maldonad GO, Singh MP (1991) An improved response spectrum method for calculating seismic design response. Part 2: non-classically damped structures. Earthq Eng Struct Dyn 20(7):637–649

    Article  Google Scholar 

  • Pitilakis K, Tsinidis G (2014) Performance and seismic design of underground structures. In: Maugeri M, Soccodato C (eds) Earthquake geotechnical engineering design. Geotechnical, geological and earthquake engineering, vol 28. Springer, Basel, pp 279–340

    Chapter  Google Scholar 

  • Raheem SEA, Ahmed MM, Alazrek TMA (2014) Soil–structure interaction effects on seismic response of multi-story buildings on raft foundation. J Eng Sci 42(4):05–930

    Google Scholar 

  • Schnabel PB, Lysmer J, Seed HB (1972) SHAKE: a computer program for earthquake response analysis of horizontally layered sites. Report No. UCB/EERC-72/12, University of California, Berkeley

  • Singh V, Mala K (2017) Effect on seismic response of building with underground storey considering soil structure interaction. Int J Res Eng Appl Sci 4(6):96–102

    Google Scholar 

  • Singh MP, Singh S, Matheu EE (2000) A response spectrum approach for seismic performance evaluation of actively controlled structures. Earthq Eng Struct Dyn 29(7):1029–1051

    Article  Google Scholar 

  • Suman D, Tengali SK (2017) Soil structure interaction of RC building with different foundations and soil types. Int J Res Eng Appl Sci 4(7):732–736

    Google Scholar 

  • Sutharshana S, Mcguire W (1988) Non-linear response spectrum method for three-dimensional structures. Earthq Eng Struct Dyn 16(6):885–900

    Article  Google Scholar 

  • Thakkar SK, Dubey RN, Singh JP (2002) Effect of Inertia of embedded portion of well foundation on seismic response of bridge substructure. In: 12th symposium on earthquake engineering, I.I.T. Roorkee, India

  • Tongaonkar NP, Jangid RS (2003) Seismic response of isolated bridges with soil–structure interaction. Soil Dyn Earthq Eng 23(4):287–302

    Article  Google Scholar 

  • Tsinidis G (2017) Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking. Tunn Undergr Space Technol 62:1–22

    Article  Google Scholar 

  • Tsinidis G, Pitilakis K, Anagnostopoulos C (2016a) Circular tunnels in sand: dynamic response and efficiency of seismic analysis methods at extreme lining flexibilities. Bull Earthq Eng 14(10):2903–2929

    Article  Google Scholar 

  • Tsinidis G, Pitilakis K, Madabhushi G (2016b) On the dynamic response of square tunnels in sand. Eng Struct 125:419–437

    Article  Google Scholar 

  • Tsinidis G, Rovithis E, Pitilakis K, Chazelas JL (2016c) Seismic response of box-type tunnels in soft soil: experimental and numerical investigation. Tunn Undergr Space Technol 59:199–214

    Article  Google Scholar 

  • Vidya V, Raghuprasad BK, Amarnath K (2015) Seismic response of high rise structure due to the interaction between soil and structure. Int J Res Eng Appl Sci 5(5):207–218

    Google Scholar 

  • Wang Z, Der Kiureghian A (2015) Multiple-support response spectrum analysis using load-dependent Ritz vectors. Earthq Eng Struct Dyn 43(15):2283–2297

    Article  Google Scholar 

  • Wilson EL, Der Kiureghian A, Bayo EP (1981) Short communications: a replacement for the SRSS method in seismic analysis. Earthq Eng Struct Dyn 9(2):187–192

    Article  Google Scholar 

  • Wolf JP (1985) Dynamic soil–structure interaction. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Wolf JP (1988) Soil–structure-interaction analysis in time domain. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Wolf JP (1994) Foundation vibrational analysis using simple physical models. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Yu RF, Zhou XY (2007) Simplifications of CQC method and CCQC method. Earthq Eng Eng Vib 6(1):65–76

    Article  Google Scholar 

  • Yu RF, Zhou XY (2008) Response spectrum analysis for non-classically damped linear system with multiple-support excitations. Bull Earthq Eng 6(2):261–284

    Article  Google Scholar 

  • Yu HT, Cai C, Guan XF, Yuan Y (2016) Analytical solution for long lined tunnels subjected to travelling loads. Tunn Undergr Space Technol 58:209–215

    Article  Google Scholar 

  • Yu H, Yuan Y, Bobet A (2017) Seismic analysis of long tunnels: a review of simplified and unified methods. Undergr Space 2:73–87

    Article  Google Scholar 

  • Zhao M, Du XL, Liu JB, Liu H (2011) Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide. Int J Numer Methods Eng 87(11):1074–1104

    Article  Google Scholar 

  • Zhao M, Gao ZD, Wang LT, Du XL, Huang JQ, Li Y (2017) Obliquely incident earthquake for soil–structure interaction in layered half space. Earthq Struct 13(6):573–588

    Google Scholar 

  • Zhao M, Li HF, Du XL, Wang PG (2018a) Time-domain stability of artificial boundary condition coupled with finite element for dynamic and wave problems in unbounded media. Int J Comput Methods Singap 15(3):1850099

    Google Scholar 

  • Zhao M, Wu LH, Du XL, Zhong ZL, Xu CS, Li L (2018b) Stable high-order absorbing boundary condition based on new continued fraction for scalar wave propagation in unbounded multilayer media. Comput Method Appl Mech Eng 334:111–137

    Article  Google Scholar 

  • Zienkiewicz OC, Bianic N, Shen FQ (1988) Earthquake input definition and the transmitting boundary condition. In: Conference on advances in computational non-linear mechanics, pp 109–138

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Acknowledgements

This work described in this paper is supported by National Key R&D Program of China (2018YFC1504305), National Basic Research Program of China (973 Program) (2015CB057902) and National Natural Science Foundation of China (NSFC) (U1839201, 51678015 and 51421005). Opinions and positions expressed in this paper are those of the authors only and do not reflect those of the National Key R&D Program, 973 Program and NSFC.

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Authors and Affiliations

  1. Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, 100124, China

    Mi Zhao, Zhidong Gao, Xiuli Du & Zilan Zhong

  2. Beijing Collaborative Innovation Center for Metropolitan Transportation, Beijing University of Technology, Beijing, 100124, China

    Mi Zhao, Zhidong Gao, Xiuli Du & Zilan Zhong

  3. College of Civil Engineering, Tongji University, Shanghai, 200092, China

    Junjie Wang

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  1. Mi Zhao
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Correspondence to Mi Zhao.

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Zhao, M., Gao, Z., Du, X. et al. Response spectrum method for seismic soil–structure interaction analysis of underground structure. Bull Earthquake Eng 17, 5339–5363 (2019). https://doi.org/10.1007/s10518-019-00673-6

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