Bifurcation Analysis in Sands under True Triaxial Conditions with Coaxial and Noncoaxial Plastic Flow Rules
Publication: Journal of Engineering Mechanics
Volume 143, Issue 10
Abstract
An important point of shear banding is that during the rotation of principal stress directions, out-of-axes deformation plays a significant role and leads to noncoaxiality between principal stress and principal plastic-strain-rate directions. Although many research works have dealt with the effect of noncoaxiality under plane-strain loading conditions disregarding the intermediate principal stress, here, the effect of noncoaxility on the onset of strain localization is investigated under true triaxial conditions because both noncoaxiality and intermediate principal stress are important factors in the investigation of shear-band formation. Therefore, a three-dimensional (3D) noncoaxial elastoplastic model is proposed and incorporated in the single hardening constitutive model to capture the stress-strain relationships and predict the onset of strain localization under true triaxial conditions for the studied dense sand. The numerical simulations illustrate that the bifurcation points comply well with the peak of the stress-strain curves observed experimentally in true triaxial tests. No bifurcation point is observed in the hardening regime by numerical simulations or experimental results near the triaxial compression condition.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alshibli, K. A., Batiste, S. N., and Sture, S. (2003). “Strain localization in sand: Plane strain versus triaxial compression.” J. Geotech. Geoenviron. Eng., 483–494.
Arthur, J. R. F., Dunstan, T., Al-Ani, Q. A. J. L., and Assadi, A. (1977). “Plastic deformation and failure in granular media.” Géotechnique, 27(1), 53–74.
Bardet, J. P. (1990). “A comprehensive review of strain localization in elasto-plastic soils.” Comput. Geotech., 10(3), 163–188.
Bardet, J. P. (1991). “Orientation of shear bands in frictional soils.” J. Eng. Mech., 1466–1485.
Dafalias, Y. F. (1986). “Bounding surface plasticity. I: Mathematical foundation and hypoplasticity.” J. Eng. Mech., 966–987.
Desrues, J., and Chambon, R. (2002). “Shear band analysis and shear moduli calibration.” Int. J. Solids Struct., 39(13–14), 3757–3776.
Desrues, J., Lanier, J., and Stutz, P. (1985). “Localization of the deformation in tests on sand sample.” Eng. Fract. Mech., 21(4), 909–921.
Desrues, J., and Viggiani, G. (2004). “Strain localization in sand: An overview of the experimental results obtained in Grenoble using stereophotogrammetry.” Int. J. Numer. Anal. Methods Geomech., 28(4), 279–321.
Gao, Z., and Zhao, J. (2013). “Strain localization and fabric evolution in sand.” Int. J. Solids Struct., 50(22–23), 3634–3648.
Gao, Z., Zhao, J., Li, X. S., and Dafalias, Y. F. (2014). “A critical state sand plasticity model accounting for fabric evolution.” Int. J. Numer. Anal. Methods Geomech., 38(4), 370–390.
Gerard, G., and Becker, H. (1952). “Column behavior under conditions of impact.” J. Aeronaut. Sci., 19(1), 58–60.
Guo, N., and Zhao, J. (2016). “3D multiscale modeling of strain localization in granular media.” Comput. Geotech., 80, 360–372.
Gutierrez, M. (2011). “Effects of constitutive parameters on strain localization in sands.” Int. J. Numer. Anal. Methods Geomech., 35(2), 161–178.
Gutierrez, M., Ishilhara, K., and Towhata, I. (1991). “Flow theory for sand during rotation of principal stress direction.” Soils Found., 31(4), 121–132.
Gutierrez, M., and Vardoulakis, I. (2007). “Energy dissipation and post-bifurcation behaviour of granular soils.” Int. J. Numer. Anal. Methods Geomech., 31(3), 435–455.
Han, C., and Drescher, A. (1993). “Shear band in biaxial tests on dry coarse sand.” Soils Found., 33(1), 118–132.
Hashiguchi, K., and Tsutsumi, S. (2001). “Elastoplastic constitutive equation with tangential stress rate effect.” Int. J. Plast., 17(1), 117–145.
Hashiguchi, K., and Tsutsumi, S. (2003). “Shear band formation analysis in soils by the sub-loading surface model with tangential stress rate effect.” Int. J. Plast., 19(10), 1651–1677.
Hashiguchi, K., and Tsutsumi, S. (2007). “Gradient plasticity with the tangential subloading surface model and the prediction of shear-band thickness of granular materials.” Int. J. Plast., 23(5), 767–797.
Hill, J. (1962). “Accelerations waves in solids.” J. Mech. Phys. Solids, 10(1), 1–16.
Ishilhara, K., and Towhata, I. (1983). “Sand response to cyclic rotation of principal stress directions as induced by wave loads.” Soils Found., 23(4), 11–26.
Jiang, M., Zhu, H., and Li, X. (2010). “Strain localization analyses of idealized sands in biaxial tests by distinct element method.” Front. Archit. Civ. Eng. China, 4(2), 208–222.
Kim, M. K., and Lade, P. V. (1988). “Single hardening constitutive model for frictional materials: I. Plastic potential Function.” Comput. Geotech., 5(4), 307–324.
Kolymbas, D. (1991). “An outline of hypoplasticity.” Arch. Appl. Mech., 61(3), 143–151.
Lade, P. V. (2003). “Analysis and prediction of shear banding under 3D conditions in granular materials.” Soils Found., 43(4), 161–172.
Lade, P. V., and Jakobsen, K. P. (2002). “Incrementalization of a single hardening constitutive model for frictional materials.” Int. J. Numer. Anal. Methods Geomech., 26(7), 647–659.
Lade, P. V., and Kim, M. K. (1988). “Single hardening constitutive model for frictional materials. II: Yield criterion and plastic work contours.” Comput. Geotech., 6(1), 13–29.
Lade, P. V., and Kim, M. K. (1995). “Single hardening constitutive model for soil, rock and concrete.” Int. J. Solids Struct., 32(14), 1963–1978.
Li, X. S., and Dafalias, Y. F. (2004). “A constitutive framework for anisotropic sand including nonproportional loading.” Géotechnique, 54(1), 41–55.
Manzari, M. T. (2004). “Application of micropolar plasticity to post failure analysis in geomechanics.” Int. J. Numer. Anal. Methods Geomech., 28(10), 1011–1032.
Molenkamp, F. (1985). “Comparison of frictional material models with respect to shear band initiation.” Géotechnique, 35(2), 127–143.
Mooney, M. A., Finno, R. J., and Viggiani, M. G. (1998). “A unique critical state for sand?” J. Geotech. Geoenviron. Eng., 1100–1108.
Papamichos, E., and Vardoulakis, I. (1995). “Shear band formation in sand according to non-coaxial plasticity model.” Géotechnique, 45(4), 649–661.
Regueiro, R. A., and Borja, R. I. (2001). “Plane strain finite element analysis of pressure-sensitive plasticity with strong discontinuity.” Int. J. Solids Struct., 38(21), 3647–3672.
Rice, J. R., and Rudnicki, J. W. (1980). “A note on some features of theory of the localization of deformation.” Int. J. Solids Struct, 16(7), 597–605.
Rudnicki, J. W., and Rice, J. R. (1975). “Conditions for the localization of the deformation in pressure sensitive dilatant materials.” J. Mech. Phys. Solids, 23(6), 371–394.
Sanborn, S. E., and Prévost, J. H. (2011). “Frictional slip plane growth by localization detection and the extended finite element method (XFEM).” Int. J. Numer. Anal. Methods Geomech., 35(11), 1278–1298.
Simo, J. C., Oliver, J., and Armero, F. (1993). “An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids.” Comput. Mech., 12(5), 277–296.
Stören, S., and Rice, J. R. (1975). “Localized necking in thin sheets.” J. Mech. Phys. Solids, 23(6), 421–441.
Vardoulakis, I. (1980). “Shear band inclination and shear modulus of sand in biaxial tests.” Int. J. Numer. Anal. Methods Geomech., 4(2), 103–119.
Vardoulakis, I., and Graf, B. (1985). “Calibration of constitutive models for granular materials using data from biaxial experiments.” Géotechnique, 35(3), 299–317.
Vardoulakis, I., and Sulem, J. (1995). Bifurcation analysis in geomechanics, Chapman & Hall, Glasgow, U.K.
Vermeer, P. A. (1990). “The orientation of shear bands in biaxial tests.” Géotechnique, 40(2), 223–236.
Wang, Q., and Lade, P. V. (2001). “Shear banding in true triaxial tests and its effect on failure in sand.” J. Eng. Mech., 754–761.
Yang, Z. X., Li, X. S., and Yang, J. (2007). “Undrained anisotropy and rotational shear in granular soil.” Geotechnique, 57(4), 371–384.
Zhao, J., and Guo, N. (2015). “The interplay between anisotropy and strain localisation in granular soils: A multiscale insight.” Géotechnique, 65(8), 642–656.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 143 • Issue 10 • October 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Jul 25, 2016
Accepted: Apr 28, 2017
Published online: Aug 4, 2017
Published in print: Oct 1, 2017
Discussion open until: Jan 4, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.