KSCE Journal of Civil Engineering

, Volume 20, Issue 2, pp 609–622 | Cite as

Validation of a strategy to predict secant shear modulus and damping of soils with an elastoplastic model

  • Rui Carrilho GomesEmail author
  • Jaime A. Santos
  • Arézou Modaressi-Farahmand Razavi
  • Fernando Lopez-Caballero
Geotechnical Engineering


The assessment of seismic site effects such as ground motion and permanent displacement requires the accurate description of the soil's stress-strain-strength relationship under irregular cyclic loading from small to medium and at large strains. The main objective of this paper is to enhance and validate the performance of an elastoplastic constitutive law in modelling non-linear soil behaviour, with particular attention to the stiffness and damping evolution with deformation. First, a simple and rational strategy is presented to derive model parameters related to shear hardening based on experimental data. Secondly, as the elastoplastic law tends to overestimate damping in the large strain range in comparison with experimental data (Ishihara, 1996; Puzrin, 2012), a new parameter is introduced in the model to overcome this issue. The modified model response exhibits lower stiffness than the standard one. For sands, an effective reduction of the damping factor is achieved and good agreement is obtained for hysteretic loop and straindependent stiffness and damping curves. For clays, the reduction in damping is also achieved for large strains, but it also has a significant effect on the soil stiffness. Finally, numerical simulations of one-dimensional ground seismic response show that for sands the new parameter has no visible effect on the seismic soil response due to maximum shear strain level achieved, while for clays the reduction in both damping and stiffness occurs.


elastoplastic model model parameter derivation dynamic properties of soils seismic site effects numerical simulation 


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  1. Adachi, T. and Oka, F. (1982). “Constitutive equation for normally consolidated clays based on elasto-viscoplasticity.” Soils and Foundations, Vol. 22, No. 4, pp. 57–70.CrossRefGoogle Scholar
  2. Amorosi, A., Boldini, D., and Elia, G. (2010). “Parametric study on seismic ground response by finite element modelling.” Computers and Geotechnics, Vol. 37, Issue 4, June 2010, pp. 515–528.CrossRefGoogle Scholar
  3. Aubry, D., Hujeux, J.-C., Lassoudire, F., and Meimon, Y. (1982). “A double memory model with multiple mechanisms for cyclic soil behaviour.” Int. Symp. Numerical Models in Geomechanics, Balkema, pp. 3–13.Google Scholar
  4. Biarez, J. and Hicher, P.-Y. (1994). Elementary Mechanics of Soil Behaviour. Saturated remoulded soils, Balkema, Rotterdam, Netherlands.Google Scholar
  5. Dobry, R., Ladd, R. S., Yokel, F. Y., Chung, R. M., and Powell, D. (1982). Prediction of pore water pressure build-up and liquefaction of sands during earthquakes by the cyclic strain method, Building Science 138, National Bureau of Standards, Washington D.C.Google Scholar
  6. Gomes, R. C. (2009). Numerical modelling of the seismic response of the ground and circular tunnels, PhD Thesis, Technical University of Lisbon, Superior Technical Institute, Portugal (in Portuguese).Google Scholar
  7. Gomes, R. C., Santos, J. A., and Oliveira, C. S. (2006). “Design spectrumcompatible time histories for numerical analysis: Generation, correction and selection.” Journal of Earthquake Engineering, Vol. 10, No. 6, pp. 843–865.Google Scholar
  8. Gomes-Correia, A., Barros, J. M. C., Santos, J. A., and Sussumu, N. (2001). “An approach to predict shear modulus of soils in the range of 10- 6 to 10- 2 strain levels.” 4th International Conference on recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Prakash Press, San Diego, California.Google Scholar
  9. Hujeux, J.-C. (1985). “Une loi de comportement pour le chargement cyclique des sols.” Génie Parasismique, V. Davidovici, Presses ENPC, France, pp. 278–302.Google Scholar
  10. Idriss, I. M. (1990). “Response of soft soils sites during earthquakes.” Proceeding: H. Bolton Seed Memorial Symposium (J.M. Duncan, ed.), University of California, Berkeley, Vol. 2, pp. 273–289.Google Scholar
  11. Idriss, I. M. and Seed, H. B. (1968). “Seismic response of horizontal layers.” Journal Soil Mechanics Foundation Division, ASCE, Vol. 94, No. 4, pp. 1003–1031.Google Scholar
  12. Ishibashi, I. and Zhang, X. (1993). “Unified dynamic shear moduli and damping ratios of sand and clay.” Soils and Foundations, Vol. 33, No. 1, pp. 182–191.CrossRefGoogle Scholar
  13. Ishihara, K. (1996). Soil behaviour in earthquake geotechnics, Clarendon Press, Oxford, U.K.Google Scholar
  14. Iwasaki, T., Tatsuoka, F., and Takagi, S. (1978). “Shear moduli of sands under cyclic torsion shear loading.” Soils and Foundations, Vol. 18, No. 1, pp. 39–56.CrossRefGoogle Scholar
  15. Lade, P. V. and Duncan, J. M. (1975). “Elastoplastic stress-strain theory for cohesionless soil.” J. Geotech. Engr. Div., ASCE, Vol. 101(GT10), No. 10, pp. 1037–1053.Google Scholar
  16. Lopez-Caballero, F., Modaressi-Farahmand Razavi, A., and Modaressi, H. (2007). “Nonlinear numerical method for earthquake site response analysis I- elastoplastic cyclic model and parameter identification strategy.” In Bulletin of Earthquake Engineering, Vol. 5, No. 3, pp. 303–323.CrossRefGoogle Scholar
  17. Mayne, P. W. and Mitchell, J. K. (1988). “Profiling of overconsolidation ratio in clays by field vane.” Canadian Geotechnical Journal, Vol. 25, No. 1, pp. 150–157.CrossRefGoogle Scholar
  18. Mellal, A. (1997). Analyse des effects du comportement non linéaire des sols sur le mouvement sismique, PhD Thesis, École Centrale deParis, France.Google Scholar
  19. Mellal, A. (1999). “A comparative study between the equivalent-linear approach and an elasto-plastic model.” 9th International Conference on Soil Dynamics and Earthquake Engineering, SDEE'99, Bergen, Norway.Google Scholar
  20. Modaressi, A. and Lopez-Caballero, F. (2001). “Global methodology for soil behaviour identification and its application to the study of site effects.” 4th International Conference on recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Prakash Press, San Diego, California.Google Scholar
  21. Muravskii, G. (2005). “On description of hysteretic behaviour of materials.” International Journal of Solids and Structures, Vol. 42, Nos. 9–10, pp. 2625–2644.CrossRefzbMATHGoogle Scholar
  22. Phillips, C. and Hashash, Y. M. A. (2009). “Damping formulation for nonlinear 1D site response.” Soil Dynamics and Earthquake Engineering, Vol. 29, No. 7, pp. 1143–1158.CrossRefGoogle Scholar
  23. Pradham, T. (1990). The behaviour of sand subjected to monotonic and cyclic loadings, PhD Thesis, Kyoto University, Japan.Google Scholar
  24. Prevost, J. H. (1978). “Plasticity theory for soil stress-strain behavior.” J. Engr. Mech. Div., ASCE, Vol. 104(EM5), pp. 117–1194.Google Scholar
  25. Puzrin, A. M. (2012). Constitutive modelling in geomechanics, Springer- Verlag, Berlin, Heidelberg.CrossRefGoogle Scholar
  26. Santos, J. A. (1999). Caracterização de solos através de ensaios dinâmicos e cíclicos de torção. Aplicação ao estudo do comportamento de estacas sob acções horizontais estáticas e dinâmicas, PhD Thesis, Technical University of Lisbon, Superior Technical Institute, Portugal (in Portuguese).Google Scholar
  27. Santos, J. A. and Gomes-Correia, A. (2000). “Shear modulus of soils under cyclic loading at small and medium strain level.” 12th World Conference on Earthquake Engineering, Auckland, New Zealand.Google Scholar
  28. Santos, J. A. and Gomes-Correia, A. (2001). “Reference threshold shear strain of soil. Its application to obtain a unique strain-dependent shear modulus curve for soil.” XV International Conference on Soil Mechanics and Geotechnical Engineering, Istanbul, Turkey, Vol. 1, pp. 267–270.Google Scholar
  29. Santos, J. A., Gomes, R. C., and Antão, A. (2002). “Application of linear and elastoplastic models for the study of seismic local site effects.” 8th National Congress of Geotechnics-Congresso Nacional de Geotecnia, Vol. 3, pp. 1983–1994, LNEC, Lisbon, Portugal (in Portuguese).Google Scholar
  30. Schnabel, P. B., Lysmer, J., and Seed, H. B. (1972). SHAKE-A computer program for earthquake response analysis of horizontally layered sites, Report No. EERC 72–12, University of California, Berkeley, California.Google Scholar
  31. Tatsuoka, F., Iwasaki, T., and Takagi, Y. (1978). “Hysteretic damping of sands under cyclic loading and its relation to shear modulus.” Soils and Foundations, Vol. 18, No. 2, pp. 25–40.CrossRefGoogle Scholar
  32. Tatsuoka, F., Masuda, T., Siddiquee, M. S. A., and Koseki, J. (2003). “Modeling the stress strain relations of sand in cyclic plane strain loading.” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129, No. 6, pp. 450–467.CrossRefGoogle Scholar
  33. Vucetic, M. (1994). “Cyclic threshold shear strains in soils.” Journal of Geotechnical Engineering, ASCE Vol. 120, No. 12, pp. 2208–2228.CrossRefGoogle Scholar
  34. Vucetic, M. and Dobry, R. (1991). “Effect of soil plasticity on cyclic response.” Journal of Geotechnical Engineering, ASCE, Vol. 117, No. 1, pp. 89–107.CrossRefGoogle Scholar
  35. Yamashita, S., Kohata, Y., Kawaguchi, T., and Shibuya, S. (2001). “International round-Robin test organized by TC-29.” Advances Laboratory Stress–Strain Testing of Geomaterials, Swets & Zeitlinger Publishers.Google Scholar
  36. Yoshida, N., Kobayashi, S., Suetomi, I., and Miura, K. (2002). “Equivalent linear method considering frequency dependent characteristics of stiffness and damping.” Soil Dynamics and Earthquake Engineering, Vol. 22, Issue 3, pp. 205–222.CrossRefGoogle Scholar
  37. Zienkiewicz, O. C. and Shiomi, T. (1984). “Dynamic behaviour of saturated porous media: The generalised biot formulation and its numerical solution.” Int. J. Numer. Anal. Methods Geomech, Vol. 8, No. 1, pp. 71–96.CrossRefzbMATHGoogle Scholar
  38. Zienkiewicz, O. C. and Taylor, R. L. (1991). “The finite element method, solid and fluid mechanics.” Dynamics and Non-Linearity, Vol. 2, 4th Ed. McGraw-Hill Book Company, London.Google Scholar

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Rui Carrilho Gomes
    • 1
    Email author
  • Jaime A. Santos
    • 1
  • Arézou Modaressi-Farahmand Razavi
    • 2
  • Fernando Lopez-Caballero
    • 2
  1. 1.Civil Engineering Dept., Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.LMSSMat, CNRS UMR8579, Ecole Centrale ParisChatenay-Malabry CedexFrance

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