Bulletin of Earthquake Engineering

, Volume 17, Issue 9, pp 5339–5363 | Cite as

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

  • Mi ZhaoEmail author
  • Zhidong Gao
  • Xiuli Du
  • Junjie Wang
  • Zilan Zhong
Original Research


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.


Seismic design Underground structure Dynamic soil–structure interaction Response spectrum method Design response spectrum 



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.


  1. ABAQUS (2012) ABAQUS/standard user’s manual version 5.8. Karlsson Sorensen Inc, HibbitGoogle Scholar
  2. 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 79:130–148Google Scholar
  3. 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):157–165Google Scholar
  4. AIJ (2004) Recommendations for loads on buildings. Architectural Institute of Japan, Tokyo (in Japanese) Google Scholar
  5. Amorosi A, Boldini D (2009) Numerical modeling of the transverse dynamic behavior of circular tunnels in clayey soils. Soil Dyn Earthq Eng 59(6):1059–1072Google Scholar
  6. Asthana AK, Datta TK (1990) A simplified response spectrum method for random vibration analysis of flexible base buildings. Eng Struct 12(3):185–194Google Scholar
  7. 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):648–661Google Scholar
  8. Berrah M, Kausel E (2010) Response spectrum analysis of structures subjected to spatially varying motions. Earthq Eng Struct Dyn 21(6):461–470Google Scholar
  9. 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):1547–1551Google Scholar
  10. BSL (2000) The building standard law of Japan. The Ministry of Construction, TokyoGoogle Scholar
  11. 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, CopenhagenGoogle Scholar
  12. Chen Y (2014) Effect of pile–soil–structure interaction on the cable-stayed bridge in response to the earthquake. Appl Mech Mater 539:731–735Google Scholar
  13. Chen HT, Tan P, Zhou FL (2017) An improved response spectrum method for non-classically damped systems. Bull Earthq Eng 15(10):4375–4397Google Scholar
  14. Chopra AK (2001) Dynamics of structures: theory and applications to earthquake engineering, 4th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  15. Chopra AK (2010) Elastic response spectrum: a historical note. Earthq Eng Struct Dyn 36(1):3–12Google Scholar
  16. 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):452–462Google Scholar
  17. CJJ (2012) Urban bridge seismic specification (CJJ 166-2011). Architecture and Building Press, Beijng (in Chinese) Google Scholar
  18. Clough RW, Penzien J (1993) Dynamics of structures, 2nd edn. McGraw-Hill Inc, New YorkGoogle Scholar
  19. Der Kiureghian A, Neuenhofer A (1992) Response spectrum method for multi-support seismic excitations. Earthq Eng Struct Dyn 21(8):713–740Google Scholar
  20. Du XL, Zhao M (2010a) Stability and identification for rational approximation of frequency response function of unbounded soil. Earthq Eng Struct Dyn 39(2):165–186Google Scholar
  21. 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):937–946Google Scholar
  22. Eurocode 8 (2003) Design of structures for earthquake resistance. European Committee for Standardization, BrusselsGoogle Scholar
  23. 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, CambridgeGoogle Scholar
  24. GB (2010) Code for seismic design of buildings (GB 50011-2010). China Architecture and Building Press, Beijing (in Chinese) Google Scholar
  25. GB (2014) Code for seismic design of urban rail transit structures (GB 50909-2014). China Planning Press, Beijing (in Chinese) Google Scholar
  26. Gupta VK, Trifunac MD (1991) Seismic response of multistoried buildings including the effects of soil–structure interaction. Soil Dyn Earthq Eng 10(8):414–422Google Scholar
  27. Hashash YMA, Hook JJ, Schmidt B, Yao IC (2001) Seismic design and analysis of underground structures. Tunn Undergr Space Technol 16(4):247–293Google Scholar
  28. Hatzigeorgiou GD, Beskos DE (2010) Soil–structure interaction effects on seismic inelastic analysis of 3-D tunnels. Soil Dyn Earthq Eng 30(9):851–861Google Scholar
  29. Hu YX (2006) Earthquake engineering. Seismological Press, Beijing (in Chinese) Google Scholar
  30. 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 61:26–39Google Scholar
  31. ICC (2003) International building code (IBC). International Code Council, Falls ChurchGoogle Scholar
  32. Kaul MK (1978) Stochastic characterization of earthquakes through their response spectrum. Earthq Eng Struct Dyn 6(5):497–509Google Scholar
  33. Kishida A, Takewaki I (2010) Response spectrum method for kinematic soil–pile interaction analysis. Adv Struct Eng 13(1):181–198Google Scholar
  34. 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):36–55Google Scholar
  35. 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 79:250–262Google Scholar
  36. 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):161–184Google Scholar
  37. Liu GH, Lian JJ, Liang CL, Zhao M (2017) An effective approach for simulating multi-support earthquake underground motions. Bull Earthq Eng 15(11):4635–4659Google Scholar
  38. Lou M, Wang H, Chen X, Zhai Y (2011) Structure–soil–structure interaction: literature review. Soil Dyn Earthq Eng 31(12):1724–1731Google Scholar
  39. Luco JE, Contesse L (1973) Dynamic structure–soil–structure interaction. Bull Seismol Soc Am 63(4):1289–1303Google Scholar
  40. 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):637–649Google Scholar
  41. 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 279–340Google Scholar
  42. 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):05–930Google Scholar
  43. 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, BerkeleyGoogle Scholar
  44. 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):96–102Google Scholar
  45. 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):1029–1051Google Scholar
  46. 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):732–736Google Scholar
  47. Sutharshana S, Mcguire W (1988) Non-linear response spectrum method for three-dimensional structures. Earthq Eng Struct Dyn 16(6):885–900Google Scholar
  48. 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, IndiaGoogle Scholar
  49. Tongaonkar NP, Jangid RS (2003) Seismic response of isolated bridges with soil–structure interaction. Soil Dyn Earthq Eng 23(4):287–302Google Scholar
  50. Tsinidis G (2017) Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking. Tunn Undergr Space Technol 62:1–22Google Scholar
  51. 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):2903–2929Google Scholar
  52. Tsinidis G, Pitilakis K, Madabhushi G (2016b) On the dynamic response of square tunnels in sand. Eng Struct 125:419–437Google Scholar
  53. 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 59:199–214Google Scholar
  54. 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):207–218Google Scholar
  55. Wang Z, Der Kiureghian A (2015) Multiple-support response spectrum analysis using load-dependent Ritz vectors. Earthq Eng Struct Dyn 43(15):2283–2297Google Scholar
  56. 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):187–192Google Scholar
  57. Wolf JP (1985) Dynamic soil–structure interaction. Prentice Hall, Upper Saddle RiverGoogle Scholar
  58. Wolf JP (1988) Soil–structure-interaction analysis in time domain. Prentice Hall, Upper Saddle RiverGoogle Scholar
  59. Wolf JP (1994) Foundation vibrational analysis using simple physical models. Prentice Hall, Upper Saddle RiverGoogle Scholar
  60. Yu RF, Zhou XY (2007) Simplifications of CQC method and CCQC method. Earthq Eng Eng Vib 6(1):65–76Google Scholar
  61. Yu RF, Zhou XY (2008) Response spectrum analysis for non-classically damped linear system with multiple-support excitations. Bull Earthq Eng 6(2):261–284Google Scholar
  62. Yu HT, Cai C, Guan XF, Yuan Y (2016) Analytical solution for long lined tunnels subjected to travelling loads. Tunn Undergr Space Technol 58:209–215Google Scholar
  63. Yu H, Yuan Y, Bobet A (2017) Seismic analysis of long tunnels: a review of simplified and unified methods. Undergr Space 2:73–87Google Scholar
  64. 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):1074–1104Google Scholar
  65. 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):573–588Google Scholar
  66. 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):1850099Google Scholar
  67. 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 334:111–137Google Scholar
  68. 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 109–138Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Mi Zhao
    • 1
    • 2
    Email author
  • Zhidong Gao
    • 1
    • 2
  • Xiuli Du
    • 1
    • 2
  • Junjie Wang
    • 3
  • Zilan Zhong
    • 1
    • 2
  1. 1.Key Laboratory of Urban Security and Disaster Engineering of Ministry of EducationBeijing University of TechnologyBeijingChina
  2. 2.Beijing Collaborative Innovation Center for Metropolitan TransportationBeijing University of TechnologyBeijingChina
  3. 3.College of Civil EngineeringTongji UniversityShanghaiChina

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