Bulletin of Earthquake Engineering

, Volume 17, Issue 1, pp 159–180 | Cite as

SPH-FEM coupled simulation of SSI for conducting seismic analysis on a rectangular underground structure

  • Sunbin Liang
  • Zhiyi ChenEmail author
Original Research


A reliable simulation of soil–structure interaction (SSI) is the precondition for understanding properly the dynamic response characteristics and earthquake disaster mechanism of underground structures. This paper adopts Smoothed Particle Hydrodynamics-Finite Element Method (SPH-FEM) coupled method to address the SSI issue. The coupled method takes advantage of the convenience of SPH in simulating the particle features of soils. The advantages of the presented method are capable of tracking the location information and motion of soils at any moment, and the deformation process inside the near-structure soils can also be captured during an earthquake. Meanwhile, it can also be made use of the accuracy of FEM in handling boundary issues and solving structural dynamics. Analysis results indicate that not only the racking deformation mode is observed, but also a rocking vibration mode that is non-negligible can be found for a rectangular underground structure under transverse seismic excitation. The rocking vibration mode is shown as the incline of top and bottom slabs, which is caused by the asymmetric seismic action on two opposite side-walls resulting from the different soil–structure contact status. The analysis clearly shows that the seismic earth pressure is a result of the interaction between soil and structure in an earthquake. The distribution and magnitude of seismic earth pressure are influenced by the magnitude of soil deformation and soil–structure contact status.


SPH-FEM coupled method Soil–structure interaction (SSI) Rectangular underground structure Seismic analysis 



This research was supported by the National Natural Science Foundation of China (Grant Nos. 41472246, 51778464), Key laboratory of Transportation Tunnel Engineering (TTE2014-01), and “Shuguang Program” supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission. All supports are gratefully acknowledged.


  1. ABAQUS Inc. (2014) ABAQUS/Analysis user’s manual-version 6.14. Providence, RI, USAGoogle Scholar
  2. Attaway S, Heinstein MW, Swegle J (1994) Coupling of smooth particle hydrodynamics with the finite element method. Nucl Eng Des 150(2–3):199–205CrossRefGoogle Scholar
  3. Campbell J, Vignjevic R, Libersky LD (2000) A contact algorithm for smoothed particle hydrodynamics. Comput Methods Appl Mech Eng 184(1):49–65CrossRefGoogle Scholar
  4. Chen ZY, Liu ZQ (2018) Effects of central column aspect ratio on seismic performances of subway station structures. Adv Struct Eng 24(1):14–29CrossRefGoogle Scholar
  5. Chen ZY, Chen W, Bian GQ (2014) Seismic performance upgrading for underground structures by introducing shear panel dampers. Adv Struct Eng 17(9):1343–1358CrossRefGoogle Scholar
  6. Chen ZY, Chen W, Li YY, Yuan Y (2016) Shaking table test of a multi-story subway station under pulse-like ground motions. Soil Dyn Earthq Eng 82:111–122CrossRefGoogle Scholar
  7. CHN Code GB50007 (2011) Code for design of building foundation. China Planning Press, Beijing (in Chinese) Google Scholar
  8. CHN Code GB50909 (2014) Code for seismic design of urban rail transit structures. China Planning Press, Beijing (in Chinese) Google Scholar
  9. Cilingir U, Madabhushi SPG (2011) A model study on the effects of input motion on the seismic behavior of tunnels. Soil Dyn Earthq Eng 31:452–462CrossRefGoogle Scholar
  10. Dai ZL, Huang Y, Cheng HL, Xu Q (2017) SPH model for fluid-structure interaction and its application to debris flow impact estimation. Landslides 14(3):917–928CrossRefGoogle Scholar
  11. Deng YH, Dashti S, Hushmand A, Davis C, Hushmand B (2016) Seismic response of underground reservoir structures in sand: evaluation of class-c and c1 numerical simulations using centrifuge experiments. Soil Dyn Earthq Eng 85:202–216CrossRefGoogle Scholar
  12. Desai CS, Zaman MM, Lightner JG, Siriwardane HJ (1984) Thin-layer elements for interfaces and joints. Int J Numer Anal Methods Geomech 8(1):19–43CrossRefGoogle Scholar
  13. Du Y, Zhang F, Zhang A, Ma L, Zheng J (2016) Consequences assessment of explosions in pipes using coupled FEM-SPH method. J Loss Prev Process Ind 43:549–558CrossRefGoogle Scholar
  14. Durante MG, Di Sarno L, Taylor CA, Mylonakis G, Simonelli AL (2016) Experimental evaluation of soil–pile–structure interaction. Earthq Eng Struct Dyn 45(7):1041–1061CrossRefGoogle Scholar
  15. Elkhoraibi T, Hashemi A, Ostadan F (2014) Probabilistic and deterministic soil structure interaction analysis including ground motion incoherency effects. Nucl Eng Des 269(4):250–255CrossRefGoogle Scholar
  16. Elnashai AS, Di Sarno L (2015) Fundamentals of earthquake engineering: from source to fragility. Wiley and Sons, UKGoogle Scholar
  17. Evard AE (1988) Beyond N-body: 3D cosmological gas dynamics. Mon Not R Astron Soc 235:934–991Google Scholar
  18. Gerolymos N, Gazetas G (2006) Winkler model for lateral response of rigid caisson foundations in linear soil. Soil Dyn Earthq Eng 26(5):347–361CrossRefGoogle Scholar
  19. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(3):375–389CrossRefGoogle Scholar
  20. Goodman RE, Taylor RL, Brekke TL (1968) A model for the mechanics of jointed rock. J Soil Mech Found Div 94(3):637–660Google Scholar
  21. Govindjee S (1997) Accuracy and stability for integration of Jaumann stress rate equations in spinning bodies. Eng Comput 14(1):14–30CrossRefGoogle Scholar
  22. Groenenboom PHL, Cartwright BK (2009) Hydrodynamics and fluid–structure interaction by coupled SPH-FE method. J Hydraul Res 48(sup1):61–73CrossRefGoogle Scholar
  23. Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253CrossRefGoogle Scholar
  24. Huang Y, Dai ZL (2014) Large deformation and failure simulations for geo-disasters using smoothed particle hydrodynamics method. Eng Geol 168(1):86–97CrossRefGoogle Scholar
  25. Huo H, Bobet A, Fernández G, Ramírez J (2005) Load transfer mechanisms between underground structure and surrounding ground: evaluation of the failure of the Daikai station. J Geotech Geoenviron 131(12):1522–1533CrossRefGoogle Scholar
  26. Hushmand A, Dashti S, Davis C, Zhang M, Ghayoomi M, McCartney JS, Lee Y, Hu J (2016) Seismic performance of underground reservoir structures: insight from centrifuge modeling on the influence of structure stiffness. J Geotech Geoenviron 142(7):04016020CrossRefGoogle Scholar
  27. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a mesh-free particle method. World Scientific Press, SingaporeCrossRefGoogle Scholar
  28. Liu ZR, Cui GQ, Wang X (2014) Vibration characteristics of a tunnel structure based on soil–structure interaction. Int J Geomech 14(4):04014018CrossRefGoogle Scholar
  29. Lucy LB (1977) A numerical approach to the testing of fusion processes. Astron J 82:1013–1024CrossRefGoogle Scholar
  30. Monaghan JJ (1988) An introduction to SPH. Comput Phys Commun 48(1):89–96CrossRefGoogle Scholar
  31. Monaghan JJ (1989) On the problem of penetration in particle methods. J Comput Phys 82(1):1–15CrossRefGoogle Scholar
  32. Monaghan JJ, Gingold RA (1983) Shock simulation by the particle method SPH. J Comput Phys 52(2):374–389CrossRefGoogle Scholar
  33. Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1):135–143Google Scholar
  34. Morinishi K, Fukui T (2012) An Eulerian approach for fluid–structure interaction problems. Comput Fluids 65:92–98CrossRefGoogle Scholar
  35. Mühlhaus HB, Vardoulakis I (1988) The thickness of shear bands in granular materials. Geotechnique 37(3):271–283CrossRefGoogle Scholar
  36. Nam SH, Song HW, Byun KJ, Maekawa K (2006) Seismic analysis of underground reinforced concrete structures considering elasto-plastic interface element with thickness. Eng Struct 28(8):1122–1131CrossRefGoogle Scholar
  37. Osouli A, Zamiran S (2017) The effect of backfill cohesion on seismic response of cantilever retaining walls using fully dynamic analysis. Comput Geotech 89:143–152CrossRefGoogle Scholar
  38. Pitilakis K, Tsinidis G, Leanza A, Maugeri M (2014) Seismic behaviour of circular tunnels accounting for above ground structures interaction effects. Soil Dyn Earthq Eng 67:1–15CrossRefGoogle Scholar
  39. Samata S, Ohuchi H, Matsuda T (1997) A study of the damage of subway structures during the 1995 Hanshin-Awaji earthquake. Cem Concr Compos 19(3):223–239CrossRefGoogle Scholar
  40. Sedarat H, Kozak A, Hashash YMA, Shamsabadi A, Krimotat A (2009) Contact interface in seismic analysis of circular tunnels. Tunn Undergr Sp Technol 24(4):482–490CrossRefGoogle Scholar
  41. Taiwan Central Weather Bureau Seismological Center,
  42. Tsinidis G (2017) Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking. Tunn Undergr Sp Technol 62(1):1–22CrossRefGoogle Scholar
  43. Tsinidis G, Pitilakis K, Madabhushi G (2016) On the dynamic response of square tunnels in sand. Eng Struct 125:419–437CrossRefGoogle Scholar
  44. Ulgen D, Saglam S, Ozkan MY (2015) Assessment of racking deformation of rectangular underground structures by centrifuge tests. Geotech Lett 5(4):261–268CrossRefGoogle Scholar
  45. Vuyst TD, Vignjevic R, Campbell JC (2005) Coupling between meshless and finite element methods. Int J Impact Eng 31(8):1054–1064CrossRefGoogle Scholar
  46. Wang ZQ, Lu Y, Hao H, Chong K (2005) A full coupled numerical analysis approach for buried structures subjected to subsurface blast. Comput Struct 83(4–5):339–356CrossRefGoogle Scholar
  47. Wang ZQ, Lu Y, Bai CH (2011) Numerical simulation of explosion-induced soil liquefaction and its effect on surface structures. Finite Elem Anal Des 47(9):1079–1090CrossRefGoogle Scholar
  48. Wen WP, Zhai CH, Li S, Chang Z, Xie LL (2014) Constant damage inelastic displacement ratios for the near-fault pulse-like ground motions. Eng Struct 59(2):599–607CrossRefGoogle Scholar
  49. Xiao N, Zhou XP, Gong QM (2017) The modelling of rock breakage process by TBM rolling cutters using 3D FEM-SPH coupled method. Tunn Undergr Sp Technol 61:90–103CrossRefGoogle Scholar
  50. Zeghal M, Edil TB (2002) Soil structure interaction analysis: modeling the interface. Can Geotech J 39(3):620–628CrossRefGoogle Scholar
  51. Zhang JM, Shamoto Y, Tokimatsu K (1998a) Evaluation of earth pressures under any lateral deformation. Soils Found 38(1):15–33CrossRefGoogle Scholar
  52. Zhang JM, Shamoto Y, Tokimatsu K (1998b) Seismic earth pressure theory for retaining walls under any lateral displacement. Soils Found 38(2):143–163CrossRefGoogle Scholar
  53. Zlatanović E, Lukić DC, Prolović V, Bonić Z, Davidović N (2015) Comparative study on earthquake-induced soil–tunnel structure interaction effects under good and poor soil conditions. Eur J Environ Civ Eng 19(8):1000–1014CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Geotechnical EngineeringTongji UniversityShanghaiChina

Personalised recommendations