The dilatancy/contractancy of soil is of particular importance for compaction, consolidation, liquefaction, etc. Interestingly, constitutive relations are often unsatisfactory in modelling volume changes in the sense that their predictions deviate considerably from each other. This scatter is pronounced in problems with stress rotation. Therefore, in this paper some selected constitutive relations are investigated with respect to their performance at stress rotation. The obtained numerical simulations are compared with each other and also with experimental results from the $1\gamma 2\epsilon $ and the hollow cylinder apparatuses.

Revised: 2019-09-19

Accepted: 2019-10-14

Published online: 2019-11-25

Keywords: Principal stress rotation, Constitutive Model, Hypoplasticity, Barodesy, Sanisand

@article{OGEO_2019__1__A4_0, author = {Schranz, Fabian and Fellin, Wolfgang and Kolymbas, Dimitrios}, title = {Comparative performance of some constitutive models in stress rotation}, journal = {Open Geomechanics}, eid = {4}, publisher = {Alert Geomaterials}, volume = {1}, year = {2019}, doi = {10.5802/ogeo.3}, language = {en}, url = {opengeomechanics.centre-mersenne.org/item/OGEO_2019__1__A4_0/} }

Schranz, Fabian; Fellin, Wolfgang; Kolymbas, Dimitrios. Comparative performance of some constitutive models in stress rotation. Open Geomechanics, Volume 1 (2019) , article no. 4, 11 p. doi : 10.5802/ogeo.3. https://opengeomechanics.centre-mersenne.org/item/OGEO_2019__1__A4_0/

[1] Principal Stress Rotation: A Missing Parameter, Journal of the Geotechnical Engineering Division, Proceedings of ASCE, Volume 106 (1980) no. 4, pp. 419-433

[2] Effects of Rotation of the Principal Stress Axes and of the Intermediate Principal Stress on the Shear Strength, Proceedings of the Sixth International Conference on Soil Mechanics and Foundation Engineering, Volume I (1965), pp. 179-183

[3] Small-strain stiffness of soils and its numerical consequences, Mitteilung des Instituts für Geotechnik, IGS, 2007 no. 55 http://www.uni-stuttgart.de/igs/content/publications/igs_dissertationen/diss_benz.pdf (Zugl.: Stuttgart, Univ., Diss., 2006)

[4] Rütteldruckverdichtung als plastodynamisches Problem (Deep vibrocompaction as plastodynamic problem), Advances in Geotechnical Engineering and Tunnelling, Volume 2, Balkema, 2000

[5] Non-coaxiality and energy dissipation in granular materials., Soils and Foundations, Volume 40 (2000) no. 2, pp. 49-59 | Article

[6] Flow theory for sand during rotation of principal stress direction., Soils and Foundations, Volume 31 (1991) no. 4, pp. 121-132 | Article

[7] Modelling the Deformation of Sand during Cyclic Rotation of Principal Stress Directions, International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics (1991), pp. 7-12

[8] Model for the deformation of sand during rotation of principal stress directions., Soils and Foundations, Volume 33 (1993) no. 3, pp. 105-117 | Article

[9] Energy dissipation and post-bifurcation behaviour of granular soils, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 31 (2007) no. 3, pp. 435-455 | Article | Zbl 1196.74118

[10] Non-coaxial version of Rowe’s stress-dilatancy relation, Granular Matter, Volume 11 (2009) no. 2, pp. 129-137 | Article | Zbl 1178.74037

[11] Modeling of the simple shear deformation of sand: effects of principal stress rotation, Acta Geotechnica, Volume 4 (2009) no. 3, pp. 193-201 | Article

[12] Hypoplastizität und Granulometrie einfacher Korngerüste, Veröffentlichung des Institutes für Bodenmechanik und Felsmechanik, Volume 142, Karlsruhe: Inst. für Bodenmechanik und Felsmechanik, 1997

[13] The development of a new hollow cylinder apparatus for investigating the effects of principal stress rotation in soils, Géotechnique, Volume 33 (1983) no. 4, pp. 355-383 | Article

[14] Sand response to cyclic rotation of principal stress directions as induced by wave loads, Soils and Foundations, Volume 23 (1983) no. 4, pp. 11-26 | Article

[15] “$1\gamma 2\epsilon $”: A New Shear Apparatus to Study the Behavior of Granular Materials, Geotechnical Testing Journal, Volume 15 (1992) no. 2, pp. 129-137 | Article

[16] Deformation of granular materials due to rotation of principal axes, Géotechnique, Volume 48 (1998) no. 5, pp. 605-619 | arXiv:http://dx.doi.org/10.1680/geot.1998.48.5.605 | Article

[17] Barodesy: a new constitutive frame for soils, Géotechnique Letters, Volume 2 (2012), pp. 17-23 | Article

[18] Introduction to barodesy, Géotechnique, Volume 65 (2015) no. 1, pp. 52-65 | Article

[19] A generalized hypoelastic constitutive law, Proc. XI Int. Conf. Soil Mechanics and Foundation Engineering, San Francisco, Volume 5 (1985), 2626 pages

[20] An outline of hypoplasticity, Archive of Applied Mechanics, Volume 61 (1991) no. 3, pp. 143-151 | Article | Zbl 0734.73023

[21] Deformation behavior of anisotropic dense sand under principal stress axes rotation., Soils and Foundations, Volume 26 (1986) no. 1, pp. 36-52 | Article

[22] Soil Behaviour and Critical State Soil Mechanics, Cambridge University Press, 1990 | Zbl 0743.73023

[23] Hypoplastic model for cohesionless soils with elastic strain range, Mechanics of Cohesive-frictional Materials, Volume 2 (1997) no. 4, pp. 279-299 | Article

[24] Stress non-uniformity in a hollow cylinder torsional sand specimen, Geomechanics and Geoengineering, Volume 2 (2007) no. 2, pp. 117-122 | arXiv:https://doi.org/10.1080/17486020701377124 | Article

[25] SANISAND-FN: An evolving fabric-based sand model accounting for stress principal axes rotation, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 43 (2019) no. 1, pp. 97-123 | Article

[26] Yielding and flow of sand under principal stress axes rotation., Soils and Foundations, Volume 30 (1990) no. 1, pp. 87-99 | Article

[27] Une analogie mécanique pour les terres sans cohésion, Comptes rendus hebdomadaires des séances de l’Académie des sciences, Volume 243 (1956), p. 125-126

[28] Vergleichsstudie zur Kompressibilität und zu den Scherparametern von Ton aus Ödometer- und Rahmenscherversuchen, geotechnik, Volume 40 (2017) no. 3, pp. 204-217 | Article

[29] A critical assessment of stress nonuniformities in hollow cylinder test specimens., Soils and Foundations, Volume 31 (1991) no. 1, pp. 60-72 | Article

[30] SANISAND: Simple anisotropic sand plasticity model, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 32 (2008) no. 8, pp. 915-948 | Article | Zbl 1273.74309

[31] The Non-Linear Field Theories of Mechanics, Springer, 1992 | Article

[32] Drained Deformation Behavior of Anisotropic Sands during Cyclic Rotation of Principal Stress Axes, Journal of Geotechnical and Geoenvironmental Engineering, Volume 136 (2010) no. 11, pp. 1509-1518 | arXiv:http://ascelibrary.org/doi/pdf/10.1061/%28ASCE%29GT.1943-5606.0000378 | Article

[33] The Steady State of Sandy Soils., Soils and Foundations, Volume 36 (1996) no. 2, pp. 81-91 http://ci.nii.ac.jp/naid/110003946012 | Article

[34] A hypoplastic relation for granular materials with a predefined limit state surface, Mechanics of Cohesive-frictional Materials, Volume 1 (1996) no. 3, pp. 251-271 | Article

[35] Undrained anisotropy and rotational shear in granular soil, Géotechnique, Volume 57 (2007) no. 4, pp. 371-384 | arXiv:https://doi.org/10.1680/geot.2007.57.4.371 | Article