Noncoaxial Theory of Plasticity Incorporating Initial Soil Anisotropy
Publication: International Journal of Geomechanics
Volume 19, Issue 12
Abstract
In this paper, a noncoaxial plane strain soil model is developed in the framework of initial soil strength anisotropy that is described by taking the internal friction angle to be a function of principal stress orientations. The conventional Mohr-Coulomb (M-C) yield criterion is generalized to give an anisotropic yield criterion, with the curve in the deviatoric stress space forming an ellipse. Both rotational and eccentric ellipses are discussed. The formulation of noncoaxial constitutive equations is described by a general form in terms of the plastic strain rate. In this form, the plastic strain rate is divided into two parts: the conventional component that is derived from the classical plastic potential theory and the noncoaxial component that is assumed to be tangential to the yield surface. The newly proposed model is validated by the analytical calculations and discrete element modeling (DEM) simulation results in simple shear tests. Conclusions can be drawn that this model is generally capable of capturing the DEM observations of simple shear testing.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 51609204) and the National Key Research and Development Program (Grant No. 2016YFC0802205). The author would like to thank Yuan, the writer of a thesis that provided the data (Yuan 2015).
References
Abbo, A. J. 1997. “Finite element algorithms for elastoplasticity and consolidation.” Ph.D. thesis, Dept. of Civil, Surveying, and Environmental Engineering, Univ. of Newcastle.
Ai, J., P. A. Langston, and H. S. Yu. 2014. “Discrete element modelling of material non-coaxiality in simple shear flows.” Int. J. Numer. Anal. Methods Geomech. 38 (6): 615–635. https://doi.org/10.1002/nag.2230.
Anand, L. 1983. “Plane deformations of ideal granular materials.” J. Mech. Phys. Solids 31 (2): 105–122. https://doi.org/10.1016/0022-5096(83)90045-5.
Arthur, J., K. Chua, and T. Dunstan. 1977. “Induced anisotropy in a sand.” Geotechnique 27 (1): 13–30. https://doi.org/10.1680/geot.1977.27.1.13.
Booker, J., and E. Davis. 1972. “A general treatment of plastic anisotropy under conditions of plane strain.” J. Mech. Phys. Solids 20 (4): 239–250. https://doi.org/10.1016/0022-5096(72)90003-8.
Borja, R. I., K. M. Sama, and P. F. Sanz. 2003. “On the numerical integration of three-invariant elastoplastic constitutive models.” Comput. Methods Appl. Mech. Eng. 192 (9–10): 1227–1258. https://doi.org/10.1016/S0045-7825(02)00620-5.
Cai, Y., H.-S. Yu, D. Wanatowski, and X. Li. 2012. “Noncoaxial behavior of sand under various stress paths.” J. Geotech. Geoenviron. Eng. 139 (8): 1381–1395. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000854.
Davis, E. 1968. “Theories of plasticity and failure of soil masses.” Chap. 6 in Soil-mechanics—Selected topics, edited by I. K. Lee. London: Butterworths.
Drescher, A., and G. D. J. De Jong. 1972. “Photoelastic verification of a mechanical model for the flow of a granular material.” J. Mech. Phys. Solids 20 (5): 337–340. https://doi.org/10.1016/0022-5096(72)90029-4.
Gu, X., L. Lu, and J. Qian. 2017. “Discrete element modeling of the effect of particle size distribution on the small strain stiffness of granular soils.” Particuology 32 (Jun): 21–29. https://doi.org/10.1016/j.partic.2016.08.002.
Handy, R. L. 2001. “Does lateral stress really influence settlement?” J. Geotech. Geoenviron. Eng. 127 (7): 623–626. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:7(623).
Hansen, B. 1961. “Shear box tests on sand.” In Proc., 5th Int. Conf. on Soil Mechanics Foundation Engineering, 127–131. Paris: Dunod.
Harris, D. 1993. “Constitutive equations for planar deformations of rigid-plastic materials.” J. Mech. Phys. Solids 41 (9): 1515–1531. https://doi.org/10.1016/0022-5096(93)90038-H.
He, Y., Y. Liu, Y. Zhang, and R. Yuan. 2019. “Stability assessment of three-dimensional slopes with cracks.” Eng. Geol. 252 (Mar): 136–144. https://doi.org/10.1016/j.enggeo.2019.03.001.
Huang, M., X. Lu, and J. Qian. 2010. “Non-coaxial elasto-plasticity model and bifurcation prediction of shear banding in sands.” Int. J. Numer. Anal. Methods Geomech. 34 (9): 906–919. https://doi.org/10.1002/nag.838.
Li, X., and Y. Dafalias. 2004. “A constitutive framework for anisotropic sand including non-proportional loading.” Geotechnique 54 (1): 41–55. https://doi.org/10.1680/geot.2004.54.1.41.
Pande, G. N., and K. Sharma. 1983. “Multi-laminate model of clays—A numerical evaluation of the influence of rotation of the principal stress axes.” Int. J. Numer. Anal. Methods Geomech. 7 (4): 397–418. https://doi.org/10.1002/nag.1610070404.
Qian, J., W. Li, X. Gu, and K. Xu. 2016. “Influence of inherent anisotropy on the soil behavior in simple shear tests using DEM.” In Proc., Int. Conf. on Discrete Element Methods, 777–784. New York: Springer.
Qian, J., J. Yang, and M. Huang. 2008. “Three-dimensional noncoaxial plasticity modeling of shear band formation in geomaterials.” J. Eng. Mech. 134 (4): 322–329. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:4(322).
Roscoe, K. H. 1970. “The influence of strains in soil mechanics.” Geotechnique 20 (2): 129–170. https://doi.org/10.1680/geot.1970.20.2.129.
Roscoe, K. H., R. H. Bassett, and E. R. L. Cole. 1967. “Principal axes observed during simple shear of a sand.” In Vol. 1 of Proc., Geotechnical Conf. on Shear Strength Properties of Natural Soils and Rocks, 231–237. Oslo, Norway: Norwegian Geotechnical Institute.
Rudnicki, J. W., and J. Rice. 1975. “Conditions for the localization of deformation in pressure-sensitive dilatant materials.” J. Mech. Phys. Solids 23 (6): 371–394. https://doi.org/10.1016/0022-5096(75)90001-0.
Sadrnejad, S., and S. Shakeri. 2017. “Multi-laminate non-coaxial modelling of anisotropic sand behavior through damage formulation.” Comput. Geotech. 88 (Aug): 18–31. https://doi.org/10.1016/j.compgeo.2017.02.018.
Savage, J., and D. Lockner. 1997. “A test of the double-shearing model of flow for granular materials.” J. Geophys. Res.: Solid Earth 102 (B6): 12287–12294. https://doi.org/10.1029/97JB00779.
Spencer, A. 1964. “A theory of the kinematics of ideal soils under plane strain conditions.” J. Mech. Phys. Solids 12 (5): 337–351. https://doi.org/10.1016/0022-5096(64)90029-8.
Tejchman, J., and W. Wu. 2009. “Non-coaxiality and stress-dilatancy rule in granular materials: FE investigation within micro-polar hypoplasticity.” Int. J. Numer. Anal. Methods Geomech. 33 (1): 117–142. https://doi.org/10.1002/nag.715.
Tong, Z.-X., J.-M. Zhang, Y.-L. Yu, and G. Zhang. 2010. “Drained deformation behavior of anisotropic sands during cyclic rotation of principal stress axes.” J. Geotech. Geoenviron. Eng. 136 (11): 1509–1518. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000378.
Tsutsumi, S., and K. Hashiguchi. 2005. “General non-proportional loading behavior of soils.” Int. J. Plast. 21 (10): 1941–1969. https://doi.org/10.1016/j.ijplas.2005.01.001.
Wu, Y., X. Zhou, Y. Gao, L. Zhang, and J. Yang. 2019. “Effect of soil variability on bearing capacity accounting for non-stationary characteristics of undrained shear strength.” Comput. Geotech. 110 (Jun): 199–210. https://doi.org/10.1016/j.compgeo.2019.02.003.
Yang, L. 2013. “Experimental study of soil anisotropy using hollow cylinder testing.” Ph.D. dissertation, Nottingham Center for Geomechanics, Univ. of Nottingham.
Yang, Y., and H. Yu. 2006a. “Application of a non-coaxial soil model in shallow foundations.” Geomech. Geoeng. Int. J. 1 (2): 139–150. https://doi.org/10.1080/17486020600777101.
Yang, Y., and H. Yu. 2006b. “A non-coaxial critical state soil model and its application to simple shear simulations.” Int. J. Numer. Anal. Methods Geomech. 30 (13): 1369–1390. https://doi.org/10.1002/nag.531.
Yang, Y., and H. Yu. 2006c. “Numerical simulations of simple shear with non-coaxial soil models.” Int. J. Numer. Anal. Methods Geomech. 30 (1): 1–19. https://doi.org/10.1002/nag.468.
Yang, Y., and H.-S. Yu. 2010. “Numerical aspects of non-coaxial model implementations.” Comput. Geotech. 37 (1–2): 93–102. https://doi.org/10.1016/j.compgeo.2009.07.007.
Yu, H. S., and X. Yuan. 2006. “On a class of non-coaxial plasticity models for granular soils.” Proc. R. Soc. London A: Math. Phys. Eng. Sci. 462 (2067): 725–748. https://doi.org/10.1098/rspa.2005.1590.
Yu, H.-S. 2007. Plasticity and geotechnics. New York: Springer.
Yuan, R. 2015. “A non-coaxial theory of plasticity for soils with an anisotropic yield criterio.” Ph.D. thesis, Nottingham Center for Geomechanics, Univ. of Nottingham.
Yuan, R., H.-S. Yu, N. Hu, and Y. He. 2018. “Non-coaxial soil model with an anisotropic yield criterion and its application to the analysis of strip footing problems.” Comput. Geotech. 99 (Jul): 80–92. https://doi.org/10.1016/j.compgeo.2018.02.022.
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Published In
International Journal of Geomechanics
Volume 19 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Oct 28, 2018
Accepted: Apr 22, 2019
Published online: Oct 12, 2019
Published in print: Dec 1, 2019
Discussion open until: Mar 12, 2020
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