Geotechnical and Geological Engineering

, Volume 31, Issue 1, pp 229–248 | Cite as

A Strain-Rate Dependent Clay Constitutive Model with Parametric Sensitivity and Uncertainty Quantification

Original Paper


This paper presents a strain-rate dependent plastic constitutive model for clays. Based on the concepts of critical-state soil mechanics and bounding surface plasticity theory, the model reproduces the mechanical response of clays under triaxial and simple shear loading conditions. The model parameters are determined for Boston Blue Clay, London Clay and Kaolin Clay, and the performance of the model in simulating the mechanical response of these clays is demonstrated for low to medium strain rates. The sensitivity of each model parameter is checked by perturbing the calibrated values by ±20 %. Subsequently, a probabilistic analysis using Monte Carlo simulations is performed by treating the model parameters as random variables and the impact of the statistics of the parameters on the undrained shear strength is investigated.


Clay Constitutive relations Plasticity Rate-dependence Sensitivity analysis Probabilistic analysis Monte Carlo simulations 



This material is based upon work supported by the U.S. Department of Homeland Security under Grant Award Number 2008-ST-061-TS002. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security.


  1. Adachi T, Oka F (1982) Constitutive equations for normally consolidated clay based on elasto-viscoplasticity. Soils Found 22(4):57–70CrossRefGoogle Scholar
  2. Been K, Jefferies MG (1985) A state parameter for sands. Géotechnique 35(2):99–112CrossRefGoogle Scholar
  3. Biscontin G, Pestana JM (2001) Influence of peripheral velocity on vane shear strength of an artificial clay. ASTM Geotech J 24(4):423–429Google Scholar
  4. Chakraborty T (2009) Development of a clay constitutive model and its application to pile boundary value problems. Ph.D. Thesis, Purdue University, West Lafayette, Indiana, USAGoogle Scholar
  5. Dafalias YF (1982) Bounding surface elastoplasticity-viscoplasticity for particulate cohesive media. In: Vermeer PA, Luger HJ (eds) International union of theoretical and applied mechanics conference on deformation and failure of granular materials, pp 97–107Google Scholar
  6. Dafalias YF, Manzari MT (2004) Simple plasticity sand model accounting for fabric change effects. J Eng Mech ASCE 130(6):622–634Google Scholar
  7. Dafalias YF, Papadimitriou AG, Li XS (2004) Sand plasticity model accounting for inherent fabric anisotropy. J Eng Mech ASCE 130(11):1319–1333CrossRefGoogle Scholar
  8. Dafalias YF, Manzari MT, Papadimitriou AG (2006) SANICLAY: simple anisotropic clay plasticity model. Int J Numer Anal Methods Geomech 30:1231–1257Google Scholar
  9. Díaz-Rodríguez JA, Martínez-Vasquez JJ, Santamarina JC (2009) Strain-rate effects in Mexico City soil. J Geotech Geoenviron Eng ASCE 135(2):300–305CrossRefGoogle Scholar
  10. Gasparre A (2005) Advanced laboratory characterization of London clay. Ph.D. Thesis, Imperial College LondonGoogle Scholar
  11. Gasparre A, Nishimura S, Coop MR, Jardine RJ (2007a) The influence of structure on the behaviour of London clay. Géotechnique 57(1):19–31CrossRefGoogle Scholar
  12. Gasparre A, Nishimura S, Minh NA, Coop MR, Jardine RJ (2007b) The stiffness of natural London clay. Géotechnique 57(1):33–37CrossRefGoogle Scholar
  13. Hájek V, Mašín D, Boháč J (2009) Capability of constitutive models to simulate soils with different OCR using a single set of parameters. Comput Geotech 36:655–664CrossRefGoogle Scholar
  14. Hambly EC (1972) Plane strain behaviour of remoulded normally consolidated Kaolin. Géotechnique 22:301–317CrossRefGoogle Scholar
  15. Hardin BO (1978) The nature of stress-strain behavior of soils. In: State-of-the-Art Report, Proceedings of the ASCE specialty conference on earthquake engineering and soil dynamics, Pasadena, pp 3–90Google Scholar
  16. Hight DW, McMillan F, Powell JJM, Jardine RJ, Allenou CP (2003) Some characteristics of London clay. Characterization of engineering properties of natural soils, Balkema, pp 851–908Google Scholar
  17. Hinchberger SD, Rowe KR (1998) Evaluation of the predictive ability of two elasticviscoplastic constitutive models. Can Geotech J 35:769–789CrossRefGoogle Scholar
  18. Hinchberger SD, Qu G, Lo KY (2010) Constitutive approach for rate-sensitive anisotropic structured clays. Int J Numer Anal Methods Geomech 34(17):1797–1830CrossRefGoogle Scholar
  19. Hueckel T, Nova R (1979) Some hysteresis effects of the behavior of geologic media. Int J Solids Struct 15(8):625–642CrossRefGoogle Scholar
  20. Jung BC, Biscontin G (2006) Modeling of strain rate effects on clay in simple shear. In: Proceedings of GeoCongress 2006, pp 1–6Google Scholar
  21. Kaliakin VN, Dafalias YF (1990a) Theoretical aspects of the elastoplastic-viscoplastic bounding surface model for cohesive soils. Soils Found 30(3):11–24CrossRefGoogle Scholar
  22. Kaliakin VN, Dafalias YF (1990b) Verification of the elastoplastic-viscoplastic bounding surface model for cohesive soils. Soils Found 30(3):25–36CrossRefGoogle Scholar
  23. Kavazanjian E, Mitchell JK (1980) Time-dependent deformation behavior of clays. J Geotech Geoenviron Eng ASCE 106(6):611–630Google Scholar
  24. Ladd CC, Edgers L (1972) Consolidated-undrained direct simple shear tests on Boston Blue Clay. Research Report R72-82, Department of Civil Engineering, MIT, Cambridge, MAGoogle Scholar
  25. Ladd CC, Varallyay J (1965) The influence of the stress system on the behavior of saturated clays during undrained shear. Research Report No R65-11, Department of Civil Engineering, MIT, Cambridge, MAGoogle Scholar
  26. Leroueil S, Marques MES (1996) State of the art on the importance of strain rate and temperature effects in geotechnical engineering. ASCE Conv Wash Geotech Special Publ 61:1–60Google Scholar
  27. Leroueil S, Kabbaj M, Tavenas F, Bouchard R (1985) Stress-strain rate relation for the compressibility of sensitive natural clays. Géotechnique 35(2):159–180CrossRefGoogle Scholar
  28. Li XS (2002) A sand model with state-dependent dilatancy. Géotechnique 52(3):173–186CrossRefGoogle Scholar
  29. Li XS, Dafalias YF (2000) Dilatancy of cohesionless soils. Géotechnique 50(4):449–460CrossRefGoogle Scholar
  30. Ling HI, Yue D, Kaliakin V, Themelis NJ (2002) An anisotropic elasto-plastic bounding surface model for cohesive soils. J Eng Mech ASCE 128(7):748–758CrossRefGoogle Scholar
  31. Loukidis D, Salgado R (2009) Modeling sand response using two-surface plasticity. Comput Geotech 36:166–186CrossRefGoogle Scholar
  32. Manzari MT, Dafalias YF (1997) A critical state two-surface plasticity model for sands. Géotechnique 47(2):255–272CrossRefGoogle Scholar
  33. Martindale H (2011) Rate-dependent behavior of clay. M.S. Thesis, University of Connecticut, Storrs, Connecticut, USAGoogle Scholar
  34. Matešić L, Vucetic M (2003) Strain-rate effect on soil secant modulus at small cyclic strains. J Geotech Geoenviron Eng ASCE 129(6):536–549CrossRefGoogle Scholar
  35. Mukabi JN, Tatsuoka F (1999) Influence of reconsolidation stress history and strain rate on the behaviour of kaolin over a wide range of strain. 12th ARC: geotechnics for Developing Africa, Durban, South Africa, pp 365–377Google Scholar
  36. Nakai T, Matsuoka H (1986) A generalized elastoplastic constitutive model for clay in three-dimensional stresses. Soils Found 26(3):81–98CrossRefGoogle Scholar
  37. Nishimura S (2005) Laboratory study on anisotrophy of natural London clay. Ph.D. Thesis, Imperial College LondonGoogle Scholar
  38. Ngo T, Mendis P, Gupta A, Ramsay J (2007) Blast loading and blast effects on structures—an overview. EJSE Int Special Issue Load Struct 7:76–91Google Scholar
  39. Ohmaki S (1979) Mechanical model for the stress-strain behaviour of normally consolidated cohesive soil. Soils Found 19(3):29–44CrossRefGoogle Scholar
  40. Ortiz M, Simo JC (1986) An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int J Numer Methods Eng 23:353–366CrossRefGoogle Scholar
  41. Papadimitriou AG, Bouckovalas GD (2002) Plasticity model for sand under small and large cyclic strains: a multiaxial formulation. Soil Dyn Earthq Eng 22(3):191–204CrossRefGoogle Scholar
  42. Papadimitriou AG, Manzari MT, Dafalias YF (2005) Calibration of a simple anisotropic plasticity model for soft clays. In: Proceedings, GeoFrontiers conference of ASCE, January 24–26, Austin, TX, Geotechnical Special Publication No. 128, pp 415–424Google Scholar
  43. Perzyna P (1963) The constitutive equations for rate sensitive plastic materials. Q Appl Math 20:321–332Google Scholar
  44. Perzyna P (1966) Fundamental problems in viscoplasticity. Adv Appl Mech 9:244–377Google Scholar
  45. Pestana JM, Whittle AJ, Gens A (2002) Evaluation of a constitutive model for clays and sands: part II—clay behavior. Int J Numer Anal Meth Geomech 26:1123–1146CrossRefGoogle Scholar
  46. Prashant A, Penumadu D (2005) A laboratory study of normally consolidated kaolin clay. Can Geotech J 42(1):27–37CrossRefGoogle Scholar
  47. Randolph, M. F. (2004). “Characterisation of soft sediments for offshore applications. Proc. 2nd Int. Conf. on Site Characterisation, Porto 1, pp 209–231Google Scholar
  48. Randolph MF, Wroth CP (1981) Application of the failure state in undrained simple shear to the shaft capacity of driven piles. Géotechnique 31(1):143–157CrossRefGoogle Scholar
  49. Santagata MC, Germaine JT, Ladd CC (2005) Factors affecting the initial stiffness of cohesive soils. J Geotech Geoenviron Eng 131(4):430–441CrossRefGoogle Scholar
  50. Santagata M, Germaine JT, Ladd CC (2007) Small-Strain nonlinearity of normally consolidated clay. J Geotech Geoenviron Eng 133(1):72–82CrossRefGoogle Scholar
  51. Schlue BF, Moerz T, Kreiter S (2010) Influence of shear rate on undrained vane shear strength of organic harbor mud. J Geotech Geoenviron Eng 136(10):1437–1447CrossRefGoogle Scholar
  52. Sheahan TC (1991) An experimental study of the time-dependent undrained shear behavior of resedimented clay using automated stress path equipment. Ph.D. Thesis, MIT, Cambridge, MAGoogle Scholar
  53. Sheahan TC (2005) A soil structure index to predict rate dependence of stress-strain behavior. Testing, modeling and simulation in geomechanics, ASCE, Geotechnical Special Publication, no. 143, pp 81–97Google Scholar
  54. Sheahan TC, Ladd CC, Germaine JT (1996) Rate dependent undrained shear behaviour of saturated clay. J Geotech Geoenviron Eng ASCE 122(2):99–108CrossRefGoogle Scholar
  55. Silvestri V, Yong RN, Soulie M, Gabriel F (1986) Controlled-strain, controlled-gradient and standard consolidation testing of sensitive clays. In: Yong RN, Townsend FC (eds) Proceedings of consolidation of soils: testing and evaluation: a symposium, issue 892, ASTM Committee D-18 on Soil and Rock, pp 433–450Google Scholar
  56. Sorensen KK, Baudet BA, Simpson B (2007) Influence of structure on the time-dependent behaviour of a stiff sedimentary clay. Géotechnique 57(1):113–124CrossRefGoogle Scholar
  57. Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice, 3rd edn. Wiley, New YorkGoogle Scholar
  58. Vaid YP, Campanella RG (1974) Triaxial and plane strain behavior of natural clay. J Geotech Eng Div 100(3):207–224Google Scholar
  59. Vermeer PA (1978) A double hardening model for sand. Géotechnique 28(4):413–433CrossRefGoogle Scholar
  60. Wang ZL, Dafalias YF, Shen CK (1990) Bounding surface hypoplasticity for sand. J Eng Mech ASCE 116(5):983–1001CrossRefGoogle Scholar
  61. Zhou H, Randolph MF (2007) Computational techniques and shear band development for cylindrical and spherical penetrometers in strain-softening clay. Int J Geomech 7(4):287–295CrossRefGoogle Scholar
  62. Zienkiewicz OC, Cormeau IC (1974) Viscoplasticity, plasticity and creep in elastic solids: a unified numerical solution approach. Int J Numer Methods Eng 8:821–828CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of ConnecticutStorrsUSA
  2. 2.Department of Civil EngineeringIndian Institute of TechnologyDelhiIndia
  3. 3.Department of Civil and Environmental EngineeringUniversity of WaterlooWaterlooCanada

Personalised recommendations