Skip to main content
Log in

Formulation and validation of a constitutive model for sands in monotonic shear

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

A constitutive model for sands in monotonic shear is presented. The model is designed to simulate the behavior of sands in the whole stress and strain range of engineering interest with enough accuracy for practical usage. Material parameters were chosen to be state independent and easy to calibrate using conventional testing procedures. The formulation is based on effective stresses, pressure-dependent hyperelasticity, non-associative elastoplasticity, an isotropic hardening law and Rowe’s stress-dilatancy theory. The implementation of Rowe’s stress-dilatancy theory within the framework of elastoplasticity theory is discussed. It is found that Rowe’s theory produces a volumetric plastic strain rate function that has a discontinuity in its first derivative w.r.t. stress, and a smoothed form is proposed instead. Finally, some experimental tests are simulated and the results are briefly discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  1. Been K, Jefferies G (1985) A state parameter for sands. Geotechnique 35(2):99–112

    Article  Google Scholar 

  2. Benz T, Vermeer A, Schwab R (2008) A small-strain overlay model. Int J Numer Anal Meth Geomech. doi 10.1002/nag.701

  3. Bolton M (1986) The strength and dilatancy of sands. Geotechnique 36(1):65–78

    Article  Google Scholar 

  4. Bolton M (1987) The strength and dilatancy of sands: discussion. Geotechnique 37(2):219–226

    Article  Google Scholar 

  5. Brinkgreve R, Broere W, Waterman D (2006) Plaxis users manual. ISBN-10: 90-76016-02-X

  6. Casagrande A (1936) Characteristics of cohesionless soils affecting the stability of slopes and earth fills. J Boston Soc Civil Eng 23(1):13–32

    Google Scholar 

  7. Casagrande A (1975) Liquefaction and cyclic deformation of sands—a critical review. V PCSMFE Buenos Aires, Argentina, vol 5, pp 1–35

  8. Cubrinovski M, Ishihara K (1998) Modelling of sand behaviour based on state concept. Soil Found 38(3):115–127

    Google Scholar 

  9. Dafalias Y, Popov E (1975) A model of nonlinearly hardening materials for complex loadings. Acta Mech 21:173–192

    Article  MATH  Google Scholar 

  10. Dafalias Y, Manzari M (2004) Simple plasticity sand model accounting for fabric change effects. J Eng Mech 130(6):622–634

    Article  Google Scholar 

  11. de Beer E (1965) Influence of the mean normal stress on the shearing resistance of sand. VI ICSMFE Montreal, Canada, vol 1, pp 165–169

  12. Duncan J, Chang C (1970) Nonlinear analysis of stress and strain in soils. J Soil Mech Found Div ASCE 96(SM5):1629–1653

    Google Scholar 

  13. Fukushima S, Tatsuoka F (1984) Strength and deformation characteristics of saturated sand at extremely low pressures. Soil Found 24(4):30–48

    Google Scholar 

  14. Guo P, Stolle D (2004) The extension of Rowe’s stress-dilatancy model to general stress condition. Soil Found 44(4):1–10

    Google Scholar 

  15. Guo P, Wan R (2007) Rational approach to stress-dilatancy modelling using an explicit micromechanical formulation. In Bifurcations, Instabilities, Degradation in Geomechanics, Springer, doi 10.1007/978-3-540-49342-6_10

  16. Hardin B, Richart F (1963) Elastic wave velocities in granular soils. J Soil Mech Found Div ASCE 89(SM1):33–65

    Google Scholar 

  17. Hardin B, Drnevich V (1972) Shear modulus and damping in soils: measurement and parameter effects. J Soil Mech Found Div ASCE 98(SM6):603–624

    Google Scholar 

  18. Ishihara K (1993) Liquefaction and flow failure during earthquakes. The 33rd Rankine lecture. Geotechnique 43:349–415

    Google Scholar 

  19. Jefferies M (1993) Nor-sand: a simple critical state model for sand. Geotechnique 43:91–103

    Article  Google Scholar 

  20. Kim M, Lade P (1988) Single hardening constitutive model for frictional materials I. Plastic potential function. Comput Geotech 5(4):307–324

    Article  Google Scholar 

  21. Kokusho T (1980) Cyclic triaxial test of dynamic soil properties for wide strain range. Soil Found 20(2):45–60

    Google Scholar 

  22. Kondner R (1963) Hyperbolic stress–strain response; cohesive soils. J Soil Mech Found Div ASCE 78(SM1):115–143

    Google Scholar 

  23. Lade P (1977) Elastoplastic stress–strain theory for cohesionless soil with curved yield surfaces. Int J Solids Struct 13:1019–1035

    Article  MATH  Google Scholar 

  24. Lade P (1988) Double hardening constitutive model for soils: parameter determination and predictions for two sands. Proc. cleveland workshop const Eq granular non-cohesive soils, pp 367–382

  25. Lade P, Kim M (1988) Single hardening constitutive model for frictional materials II. Yield criterion and plastic work contours. Comput Geotech 6(1):13–30

    Article  Google Scholar 

  26. Lade P, Kim M (1988) Single hardening constitutive model for frictional materials III. Comparison with experimental data. Comput Geotech 6(1):31–48

    Article  Google Scholar 

  27. Lee K, Seed H (1967) Drained strength characteristics of sands. J Soil Mech Found Div ASCE 93(SM6):117–141

    Google Scholar 

  28. Maeda K, Miura K (1999) Confining stress dependency of mechanical properties of sands. Soil Found 39(1):53–67

    Google Scholar 

  29. Maeda K, Miura K (1999) Relative density dependency of mechanical properties of sands. Soil Found 39(1):69–79

    Google Scholar 

  30. Manzari M, Dafalias Y (1997) A two-surface critical plasticity model for sand’. Geotechnique 47(2):255–272

    Article  Google Scholar 

  31. Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc Jpn Soc Civil Eng 233:59–70

    Google Scholar 

  32. Molenkamp F (1988) A simple model for isotropic non-linear elasticity of frictional materials. Int J Numer Anal Meth Geomech 12(5):467–475

    Article  Google Scholar 

  33. Núñez E (1991) Propiedades mecánicas de materiales granulares incoherentes. Acad Nac Cs Ex Fís Nat Buenos Aires 46:71–89

    Google Scholar 

  34. Pestana J, Whittle A (1995) Compression model for cohesionless soils. Geotechnique 45(4):611–631

    Article  Google Scholar 

  35. Pestana J, Whittle A, Salvati L (2002) Evaluation of a constitutive model for clays and sands: Part I—sand behaviour. Int J Numer Anal Meth Geomech 26(2):1097–1121

    Article  MATH  Google Scholar 

  36. Poulos S (1981) The steady state of deformation. J Geot Eng Div ASCE 107(5):553–562

    Google Scholar 

  37. Richart F, Hall J, Woods D (1970) Vibrations of soils and foundations. Int Series Theo Appl Mech. Prentice-Hall, Englewood Cliffs, p 414

    Google Scholar 

  38. Rowe P (1962) The stress dilatancy relation for static equilibrium of an assembly of particles in contact. Proc Royal Soc 269:500–527

    Article  Google Scholar 

  39. Rowe P (1971) Stress–strain relationships for particulate materials at equilibrium. Proc Perf Earth Earth Support Struct 3:327–359

    Google Scholar 

  40. Santamarina JC, Cascante G (1996) Stress anisotropy and wave propagation—a micromechanical review. Can Geot J 33:770–782

    Article  Google Scholar 

  41. Santamarina JC (2001) Soils and waves. Wiley ISBN 978-0-471-49058-6

  42. Schanz T, Vermeer P, Bonnier P (1999) The hardening soil model: formulation and verification. Proc Plaxis Symp Beyond 2000 Comp Geotech Balkema, The Netherlands, pp 55–58

  43. Sfriso A (2007) A constitutive model for sands: Evaluation of predictive capability. Proc XIII CPMS, pp 242–247

  44. Sfriso A (2008) Numerical assessment of the deformation of CFRD dams during earthquakes. Proc XII IACMAG 4054: 4061

  45. Sfriso A (2009) The friction angle and dilatancy of sands. XVII ICSMGE, Alexandria, Egypt, pp 433–435

  46. Tatsuoka F, Shibuya S (1992) Deformation characteristics of soils and rocks from field and laboratory tests. Inst Ind Sc U Tokio 37(1), N° 235, 136 p

    Google Scholar 

  47. Tatsuoka F, Siddiquee M, Park C, Sakamoto M, Abe F (1993) Modelling stress strain relations of sand. Soil Found 33(2):60–81

    Google Scholar 

  48. Teachavorasinskum S, Shibuya S, Tatsuoka F (1991) Stiffness of sands in monotonic and cyclic loading in simple shear. Proc ASCE Geot Eng Congress Boulder, vol 1, pp 7863–7878

  49. Trautmann C, Kulhawy F (1987) CUFAD—A computer program for compression and uplift foundation analysis and design. Report EPRI EL-4540-CCM

  50. Verdugo R, Ishihara K (1996) The steady state of sandy soils. Soil Found 36(2):81–91

    Google Scholar 

  51. Wan R, Guo P (1999) A pressure and density dependent dilatancy model for granular materials. Soil Found 39(6):1–11

    Google Scholar 

  52. Wanatowski D, Chu J (2006) Strain softening of K0-consolidated Changi sand under plane strain conditions. Acta Geotech I:29–42. doi:10.1007/s11440-006-0004-x

    Article  Google Scholar 

  53. Woodward P, Molenkamp F (1999) Application of an advanced multi surface kinematic constitutive soil model. Int J Numer Anal Meth Geomech 23(15):1995–2043

    Article  MATH  Google Scholar 

  54. Yamashita S, Jamiolkowski M, Lo Presti D (2000) Stiffness nonlinearity of three sands. J Geot Geoenv Eng ASCE 126(10):929–938

    Article  Google Scholar 

Download references

Acknowledgments

The first author gratefully acknowledges many valuable suggestions, discussions and advice given by Prof. Eduardo Núñez.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Sfriso.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sfriso, A., Weber, G. Formulation and validation of a constitutive model for sands in monotonic shear. Acta Geotech. 5, 257–272 (2010). https://doi.org/10.1007/s11440-010-0127-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-010-0127-y

Keywords

Navigation