# Modeling of the simple shear deformation of sand: effects of principal stress rotation

- 595 Downloads
- 10 Citations

## Abstract

The paper presents a simple constitutive model for the behavior of sands during monotonic simple shear loading. The model is developed specifically to account for the effects of principal stress rotation on the simple shear response of sands. The main feature of the model is the incorporation of two important effects of principal stress on stress–strain response: anisotropy and non-coaxiality. In particular, an anisotropic failure criterion, cross-anisotropic elasticity, and a plastic flow rule and a stress–dilatancy relationship that incorporate the effects of non-coaxiality are adopted in the model. Simulations of published experimental results from direct simple shear and hollow cylindrical torsional simple shear tests on sands show the satisfactory performance of the model. It is envisioned that the model can be valuable in modeling in situ simple shear response of sands and in interpreting simple shear test results.

## Keywords

Constitutive model Dilatancy Granular materials Non-coaxiality Simple shear## References

- 1.Arthur JRF, Rodriguez JDC, Chua KS, Dunstan T (1980) Principal stress rotation: a missing parameter. J Geotech Eng Div ASCE 106(4):419–433Google Scholar
- 2.Arthur JRF, Menzies B (1972) Inherent anisotropy in a sand. Geotechnique 22:115–128Google Scholar
- 3.Chaudhary SK, Kuwano J, Hayano Y (2004) Measurement of quasi-elastic stiffness parameters of dense Toyoura sand in hollow cylindrical apparatus and triaxial apparatus with bender elements. Geotech Test J 27(1):1–13CrossRefGoogle Scholar
- 4.Cole ERL (1967) Soils in the simple shear apparatus. Ph.D. thesis. Cambridge UniversityGoogle Scholar
- 5.Fioravante V (2000) Anisotropy of small strain stiffness of Ticino and Kenya sands from seismic wave propagation measured in triaxial testing. Soils Found 40(4):129–142Google Scholar
- 6.Frydman S, Talesnick M (1991) Simple shear of isotropic elasto-plastic soil. Int J Num Anal Meth Geomech 15(4):251–270zbMATHCrossRefGoogle Scholar
- 7.Gutierrez M, Ishihara K (2000) Non-coaxiality and energy dissipation in granular materials. Soils Found 40(2):49–59Google Scholar
- 8.Gutierrez M, Vardoulakis I (2006) Energy dissipation and post-bifurcation behavior of granular soils. Int J Num Anal Meth Geomech 31(3):435–455CrossRefGoogle Scholar
- 9.Gutierrez M, Wang J (2008) Non-coaxial version of Rowe’s stress–dilatancy relation. Granural Matter 11:129–137CrossRefGoogle Scholar
- 10.Gutierrez M, Ishihara K, Towhata I (1993) Flow theory for sand during rotation of principal stress direction. Soils Found 31(4):121–132Google Scholar
- 11.Jung Y-H, Chung CK, Finno RJ (2004) Development of nonlinear cross-anisotropic model for the pre-failure deformation of geomaterials. Comp Geotech 31:89–102CrossRefGoogle Scholar
- 12.Kuwano R, Jardine RJ (2002) On the applicability of cross-anisotropic elasticity to granular materials at very small strains. Geotechnique 52:727–749CrossRefGoogle Scholar
- 13.Miura K, Miura S, Toki S (1986) Deformation behavior of anisotropic sand under principal axes rotation. Soils Found 26(1):36–52Google Scholar
- 14.Moroto N (1987) On deformation of granular material in simple shear. Soils Found 27(1):77–85Google Scholar
- 15.Ochiai H (1975) The behaviour of sands in direct shear tests. J Jpn Soc Soil Mech Found Eng 15(4):93–100Google Scholar
- 16.Oda M (1975) On the relation
*τ*/*σ*_{n}=*κ*tan*ψ*in the simple shear test. Soils Found 15(4):35–41MathSciNetGoogle Scholar - 17.Oda M (1981) Anisotropic strength of cohesionless sands. J Geotech Eng ASCE 107(GT9):1219–1231Google Scholar
- 18.Oda M, Konishi J (1974) Rotation of principal stresses in granular material during simple shear. Soils Found 14(4):39–53Google Scholar
- 19.Osinov VA, Wu W (2006) Simple shear in sand with an anisotropic hypoplastic model. Geomech Geoeng 1(1):43–50CrossRefGoogle Scholar
- 20.Prevost J, Høeg K (1975) Reanalysis of simple shear soil testing. Can Geotech J 13:418–429CrossRefGoogle Scholar
- 21.Richart FE, Hall JR, Woods RD (1970) Vibrations of soils and foundations. Int Ser Theor Appl Mech. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
- 22.Roscoe KH (1970) The influence of strains in soil mechanics—10th Rankine Lecture. Geotechnique 20(2):129–170Google Scholar
- 23.Rowe PW (1962) The stress–dilatancy relation for static equilibrium of an assembly of particles in contact. Proc R Soc Lond Ser A Math Phys Sci 269(1339):500–527CrossRefGoogle Scholar
- 24.Tatsuoka F (1987) Discussion on the strength and dilatancy of sands. Geotechnique 37(2):219–226CrossRefGoogle Scholar
- 25.Vardoulakis I, Georgopoulos IG (2005) The “stress–dilatancy” hypothesis revisited: shear-banding related instabilities. Soils Found 45(2):61–76Google Scholar
- 26.Yang Y, Yu HS (2006) Numerical simulations of simple shear with non-coaxial soil models. Int J Num Anal Meth Geomech 30(1):1–19CrossRefGoogle Scholar
- 27.Yoshimine M, Özay R, Sezen A, Ansal A (1999) Undrained plane strain shear tests on saturated sand using a hollow cylinder torsional shear apparatus. Soils Found 39(2):131–136Google Scholar
- 28.Zeng X, Ni B (1999) Stress-induced anisotropic
*G*_{max}of sands and its measurement. J Geotech Geoenviron Eng ASCE 125(9):741–749CrossRefGoogle Scholar