Acta Geotechnica

, Volume 11, Issue 1, pp 191–207 | Cite as

Effect of coupling excess pore pressure and deformation on nonlinear seismic soil response

  • Silvana Montoya-NogueraEmail author
  • Fernando Lopez-Caballero
Research Paper


The excess pore pressure (\(\Delta p_w\)) generation and consequent reduction in effective stress lead to the softening of a liquefiable soil deposit that can alter ground motions in terms of amplitude, frequency content and duration. However, total stress models, which are the most currently used, do not take into account coupling of excess pore pressures and soil deformations. To assess this effect, two analyses were made: (1) a Biot hydraulic and mechanical computation of a saturated soil deposit with coupling pore pressures and soil deformations and (2) a mechanical computation of a decoupled model with same initial behaviour. Both analyses were performed with a fully nonlinear elastoplastic multi-mechanism model. As \(\Delta p_w\) depends on the soil properties, two soils were analysed: loose-to-medium and medium-to-dense sand. The results regarding the profile of maximum accelerations and shear strains, the surface accelerations and their corresponding response spectra are analysed. The mean values of the normalized response spectra ratio of surface accelerations between the coupled and decoupled model show a deamplification of low and high frequencies (i.e. at frequencies lower than 1.0 Hz and higher than 10 Hz) that tend to increase with the liquefaction zone size. Coupling of \(\Delta p_w\) and soil deformation is therefore of great importance to accurately model the ground motion response. On the contrary, while peak acceleration predictions could be conservative, the amplification on the low frequencies could be largely underestimated which could be highly prejudicial for flexible buildings.


Earthquake engineering Liquefaction Numerical modelling Site response Soil nonlinearity 


  1. 1.
    Aubry D, Hujeux JC, Lassoudière F, Meimon Y (1982) A double memory model with multiple mechanisms for cyclic soil behavior. In: International symposium Num Mod Geomech, Balkema, pp 3–13Google Scholar
  2. 2.
    Aubry D, Modaressi A (1996) GEFDyn—manuel scientifique. LMSSMat, Julliet, Ecole Centrale Paris, FranceGoogle Scholar
  3. 3.
    Bazzurro P, Cornell CA (2004) Nonlinear soil-site effects in probabilistic seismic-hazard analysis. Bull Seismol 94(6):2110–2123CrossRefGoogle Scholar
  4. 4.
    Been K, Jefferies MG (1985) A state parameter for sands. Géotechnique 35(2):99–112CrossRefGoogle Scholar
  5. 5.
    Beresnev IA, Wen KL (1996) Nonlinear site response: a reality? Bull Seismol Soc Am 86(6):1964–1978Google Scholar
  6. 6.
    Bernardie S, Foerster E, Modaressi H (2006) Non-linear site response simulations in Chang-Hwa region during the 1999 Chi-Chi earthquake, Taiwan. Soil Dyn Earthq Eng 26:1038–1048CrossRefGoogle Scholar
  7. 7.
    Bird JF, Bommer JJ (2004) Earthquake losses due to ground failure. Eng Geol 75:147–179CrossRefGoogle Scholar
  8. 8.
    Bonilla F, Tsuda K, Pulido N, Régnier J, Laurendeau A (2011) Nonlinear site response evidence of K-NET and KiK-net records from the 2011 off the Pacific coast of Tohoku Earthquake. Earth Planets Space 63(7):785–789CrossRefGoogle Scholar
  9. 9.
    Bradley B, Dhakal R, MacRae G, Cubrinovski M (2010) Prediction of spatially distributed seismic demands in specific structures: ground motion and structural response. Earthq Eng Struct Dyn 39(5):501–520Google Scholar
  10. 10.
    Byrne PM, Park S-S, Beaty M, Sharp M, Gonzalez L (2004) Numerical modeling of liquefaction and comparison with centrifuge tests. Can Geotech J 41(2):193–211CrossRefGoogle Scholar
  11. 11.
    Carrilho Gomes R, Santos JA, Modaressi-Farahmand Razavi A, Lopez-Caballero F (2014) Validation of a strategy to predict secant shear modulus and damping of soils with an elastoplastic model. KSCE Journal of Civil Engineering, in printGoogle Scholar
  12. 12.
    Chin BH, Aki K (1991) Simultaneous study of the source, path, and site effects on strong ground motion during the 1989 Loma Prieta earthquake: a preliminary result on pervasive nonlinear site effects. Bull Seismol Soc Am 81(5):1859–1884Google Scholar
  13. 13.
    Costa D’Aguiar S, Modaressi-Farahmand-Razavi A, Dos Santos JA, Lopez-Caballero F (2011) Elastoplastic constitutive modelling of soil structure interfaces under monotonic and cyclic loading. Comput Geotech 38(4):430–447CrossRefGoogle Scholar
  14. 14.
    Darendeli MB (2001) Development of a new family of normalized modulus reduction and material damping curves. PhD thesis, The University of Texas, Austin, TexasGoogle Scholar
  15. 15.
    Dickenson SE, Seed RB (1996) Nonlinear dynamic response of soft and deep cohesive soil deposits. In: Proceedings of the international workshop on site response subjected to strong earthquake motions, volume 2, Yokosuka, Japan, pp 67–81Google Scholar
  16. 16.
    Foerster E, Modaressi H (2007b) Nonlinear numerical methods for earthquake site response analysis II—case studies. Bull Earthq Eng 5(3):325–345CrossRefGoogle Scholar
  17. 17.
    Foerster E, Modaressi H (2007) A diagonal consistent mass matrix for earthquake site response simulations. In: 4th international conference on earthquake geotechnical engineering, Thessaloniki, GreeceGoogle Scholar
  18. 18.
    Hartvigsen A (2007) Influence of pore pressures in liquefiable soils on elastic response spectra. Master’s thesis. University of WashingtonGoogle Scholar
  19. 19.
    Hujeux JC (1985) Génie Parasismique: Une loi de comportement pour le chargement cyclique des sols, v. davidovici edition. Presses ENPC, Champs-sur-Marne, pp 278–302Google Scholar
  20. 20.
    Idriss IM (1990) Influence of local site conditions on earthquake ground motions. In: Proceedings of IV U.S. Nat. Conf. on earthquake engineering, volume 1, Palm Springs, CaliforniaGoogle Scholar
  21. 21.
    Iervolino I, Cornell CA (2005) Record selection for nonlinear seismic analysis of structures. Earthq Spectra 21(3):685–713CrossRefGoogle Scholar
  22. 22.
    Ishihara K (1993) Liquefaction and flow failure during earthquakes. Géotechnique 43(3):351–415CrossRefGoogle Scholar
  23. 23.
    Jafarian Y, Abdollahi AS, Vakili R, Baziar MH, Noorzad A (2011) On the efficiency and predictability of strain energy for the evaluation of liquefaction potential: a numerical study. Comput Geotech 38(6):800–808CrossRefGoogle Scholar
  24. 24.
    Kontoe S, Zdravkovic L, Potts D (2008) An assessment of time integration schemes for dynamic geotechnical problems. Comput Geotech 35(2):253–264CrossRefGoogle Scholar
  25. 25.
    Koutsourelakis S, Prévost JH, Deodatis G (2002) Risk assessment of an interacting structure–soil system due to liquefaction. Earthq Eng Struct Dyn 31:851–879CrossRefGoogle Scholar
  26. 26.
    Kramer SL, Hartvigsen AJ, Sideras SS, Ozener PT (2011) Site response modeling in liquefiable soil deposits. In: 4th IASPEI/IAEE international symposium: effects of surface geology on seismic motion, pp 1–12Google Scholar
  27. 27.
    Kramer SL (1996) Geotechnical earthquake engineering, 1st edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  28. 28.
    Kuhl D, Crisfield MA (1999) Energy-conserving and decaying algorithms in non-linear structural dynamics. Int J Numer Methods Eng 45:569–599CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Lopez-Caballero F, Modaressi-Farahmand-Razavi A, Modaressi H (2007) Nonlinear numerical method for earthquake site response analysis I—elastoplastic cyclic model and parameter identification strategy. Bull Earthq Eng 5(3):303–323CrossRefGoogle Scholar
  30. 30.
    Lopez-Caballero F, Modaressi-Farahmand-Razavi A (2010) Assessment of variability and uncertainties effects on the seismic response of a liquefiable soil profile. Soil Dyn Earthq Eng 30(7):600–613CrossRefGoogle Scholar
  31. 31.
    Lopez-Caballero F, Modaressi A (2011) Numerical analysis: specification and validation of used numerical methods. FP7-SME-2010-1-262161. PREMISERI project, Paris, FranceGoogle Scholar
  32. 32.
    Modaressi H, Benzenati I (1994) Paraxial approximation for poroelastic media. Soil Dyn Earthq Eng 13(2):117–129CrossRefGoogle Scholar
  33. 33.
    Popescu R, Prevost JH, Deodatis G (2005) 3D effects in seismic liquefaction of stochastically variable soil deposits. Géotechnique 55(1):21–31CrossRefGoogle Scholar
  34. 34.
    Popescu R, Prévost JH, Deodatis G, Chakrabortty P (2006) Dynamics of nonlinear porous media with applications to soil liquefaction. Soil Dyn Earthq Eng 26(6):648–665CrossRefGoogle Scholar
  35. 35.
    Raghunandan M, Liel AB (2013) Effect of ground motion duration on earthquake-induced structural collapse. Struct Saf 41:119–133CrossRefGoogle Scholar
  36. 36.
    Roscoe KH, Pooroshasb HB (1963) A fundamental principle of similarity in model tests for earth pressure problems. In: Proceedings of 2nd Asian regional conference on soil mechanics, volume 1,Tokyo, pp 134–140Google Scholar
  37. 37.
    Ruiz S, Saragoni GR (2009) Free vibration of soils during large earthquakes. Soil Dyn Earthq Eng 29:1–16CrossRefGoogle Scholar
  38. 38.
    Saez E (2009) Dynamic non-linear soil structure interaction. PhD thesis, Ecole Centrale ParisGoogle Scholar
  39. 39.
    Saez E, Lopez-Caballero F, Modaressi-Farahmand-Razavi A (2013) Inelastic dynamic soil–structure interaction effects on moment-resisting frame buildings. Eng Struct 51(1):166–177CrossRefGoogle Scholar
  40. 40.
    Schnabel PB, Lysmer J, Seed HB (1972) SHAKE: a computer program for earthquake response analysis of horizontally layered sites. Report No. EERC 72–12. Earthquake Engineering Research CenterGoogle Scholar
  41. 41.
    Seed HB, Murarka J, Lysmer J, Idriss IM (1976) Relationships between maximum acceleration, maximum velocity, distance from source and local site conditions for moderately strong earthquakes. Bull Seismol Soc Am 66(4):1323–1342Google Scholar
  42. 42.
    Shinozuka M, Ohtomo K (1989) Proceedings of the second US-Japan workshop in liquefaction, large ground deformation and their effects on lifelines, technical report Spatial severity of liquefaction, NCEER, pp 193–206Google Scholar
  43. 43.
    Sica S, Pagano L, Modaressi A (2008) Influence of past loading history on the seismic response of earth dams. Comput Geotech 35(1):61–85CrossRefGoogle Scholar
  44. 44.
    Sorrentino L, Kunnath S, Monti G, Scalora G (2008) Seismically induced one-sided rocking response of unreinforced masonry facades. Eng Struct 30(8):2140–2153CrossRefGoogle Scholar
  45. 45.
    Trifunac MD, Brady AG (1975) A study on the duration of strong earthquake ground motion. Bull Seismol Soc Am 65(3):581–626Google Scholar
  46. 46.
    Yoshida N (2013) Applicability of total stress seismic ground response analysis under large earthquakes. In: COMPDYN2013: 4th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering, Kos Island, Greece, p 13Google Scholar
  47. 47.
    Youd TL, Idriss IM, Andrus RD, Arango I, Castro G, Christian JT, Dobry R, Finn WDL, Leslie F, Hynes ME, Ishihara K, Koester JP, Liao SS, William F, Martin GR, Mitchell JK, Moriwaki Y, Power MS, Robertson PK, Seed RB, Stokoe II, Kenneth H (2001) Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. J Geotech Geoenviron Eng 127(10):816–833CrossRefGoogle Scholar
  48. 48.
    Yu G, Anderson JG, Siddharthan R (1993) On the characteristics of nonlinear soil response. Bull Seismol Soc Am 83(1):218–244Google Scholar
  49. 49.
    Zienkiewicz OC, Shiomi T (1984) Dynamic behavior of saturated porous media: the generalised Biot formulation and its numerical solution. Int J Numer Anal Methods Geomech 8(1):71–96CrossRefzbMATHGoogle Scholar
  50. 50.
    Z ienkiewicz OC, Taylor RL (1991) The Finite element method, solid and fluid mechanics, dynamics and non-linearity, vol 2, 4th edn. McGraw-Hill Book Company, LondonGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Silvana Montoya-Noguera
    • 1
    Email author
  • Fernando Lopez-Caballero
    • 1
  1. 1.Ecole Centrale ParisChatenay MalabryFrance

Personalised recommendations