Finite-Element Analysis of Failure in Transversely Isotropic Geomaterials
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
The strength and failure behaviors of geomaterials, such as soils and rocks, are commonly anisotropic because of lamination and sedimentation. The main purpose of this study is to investigate the effect of anisotropy on the localization pattern and bearing capacity of geostructures by finite-element simulation. To this aim, an extended Drucker-Prager yield criterion is developed for transversely isotropic geomaterials based on the Cosserat continuum. In this criterion, the internal frictional angle is related to the material principal direction and the mixed invariant of the stress tensor and the microstructure tensor. The corresponding stress update and consistent elastoplastic tangent modulus matrix are presented. Numerical results show that the localization pattern and the bearing capacity of the geostructures are very sensitive to the material principal direction as well as the anisotropic degree.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are pleased to acknowledge the support of this work by the National Natural Science Foundation of China through Contract/Grant Nos. 10802060 and 11172216 and the Natural Key Basic Research and Development Program of China (973 Program) through Contract/Grant Nos. 2010CB732005 and 2010CB731502.
References
ABAQUS 6.10-1 [Computer software]. Waltham, MA, Dassault Systèmes.
Abelev, A. V., and Lade, P. V. (2003). “Effects of cross anisotropy on three-dimensional behavior of sand. I: Stress–strain behavior and shear banding.” J. Eng. Mech., 160–166.
Alsaleh, M. I., Voyiadjis, G. Z., and Alshibli, K. A. (2006). “Modelling strain localization in granular materials using micropolar theory: Mathematical formulations.” Int. J. Numer. Anal. Methods Geomech., 30(15), 1501–1524.
Alshibli, K. A., Alsaleh, M. I., and Voyiadjis, G. Z. (2006). “Modelling strain localization in granular materials using micropolar theory: Numerical implementation and verification.” Int. J. Numer. Anal. Methods Geomech., 30(15), 1525–1544.
Arthur, J. R. F., Chua, K. S., and Dunstan, T. (1977). “Induced anisotropy in a sand.” Géotechnique, 27(1), 13–30.
Arthur, J. R. F., and Menzies, B. K. (1972). “Inherent anisotropy in a sand.” Géotechnique, 22(1), 115–128.
Azami, A., Pietruszczak, S., and Guo, P. (2010). “Bearing capacity of shallow foundations in transversely isotropic granular media.” Int. J. Numer. Anal. Methods Geomech., 34(8), 771–793.
Budhu, M. (2008). Soil mechanics and foundations, Wiley, New York.
Casagrande, A., and Carillo, N. (1944). “Shear failure of anisotropic materials.” J. Boston Soc. Civ. Eng., 31(4), 74–81.
Chang, C. S., and Yin, Z.-Y. (2010). “Micromechanical modeling for inherent anisotropy in granular materials.” J. Eng. Mech., 830–839.
Cosserat, E., and Cosserat, F. (1909). Theory of deformable bodies, Trans. D. H. Delphenich. Hermann et Fils, Paris.
Dassault Systèmes. (2010). ABAQUS/CAE user's manual, version 6.10-EF1, Waltham, MA.
De Borst, R. (1991). “Simulation of strain localization: a reappraisal of the micropolar continuum.” Eng. Comput., 8(4), 317–332.
Duveau, G., Shao, J. F., and Henry, J. P. (1998). “Assessment of some failure criteria for strongly anisotropic materials.” Mech. Cohes.-Frict. Mater., 3(1), 1–26.
Eringen, A. C., and Edelen, D. G. B. (1972). “On non-local elasticity.” Int. J. Eng. Sci., 10(3), 233–248.
Gao, Z., Zhao, J., and Yao, Y. (2010). “A generalized anisotropic failure criterion for geomaterials.” Int. J. Solids Struct., 47(22–23), 3166–3185.
Kong, Y., Zhao, J., and Yao, Y. (2013). “A failure criterion for cross-anisotropic soils considering microstructure.” Acta Geotech., 8(6), 665–673.
Lade, P. V. (2007). “Modeling failure in cross-anisotropic frictional materials.” Int. J. Solids Struct., 44(16), 5146–5162.
Lade, P. V. (2008). “Failure criterion for cross-anisotropic soils.” J. Geotech. Geoenviron. Eng., 117–124.
Lade, P. V. (2013). “Three-dimensional failure in geomaterials: Experimentation and modeling.” Constitutive modeling of geomaterials, Springer, Berlin, 47–58.
Lade, P. V., and Abelev, A. V. (2003). “Effects of cross anisotropy on three-dimensional behavior of sand. II: Volume change behavior and failure.” J. Eng. Mech., 167–174.
Li, X., and Tang, H. (2005). “A consistent return mapping algorithm for pressure-dependent elastoplastic Cosserat continua and modeling of strain localization.” Comput. Struct., 83(1), 1–10.
Li, X. S., and Dafalias, Y. F. (2002). “Constitutive modeling of inherently anisotropic sand behavior.” J. Geotech. Geoenviron. Eng., 868–880.
Muhlhaus, H. B., and Aifantis, E. C. (1991). “A variational principle for gradient plasticity.” Int. J. Solids Struct., 28(7), 845–857.
Muhlhaus, H. B., and Vardoulakis, I. (1987). “The thickness of shear bands in granular materials.” Géotechnique, 37(3), 271–283.
Needleman, A. (1988). “Material rate dependence and mesh sensitivity in localization problems.” Comput. Meth. Appl. Mech. Eng., 67(1), 69–85.
Oda, M. (1993). “Inherent and induced anisotropy in plasticity theory of granular soils.” Mech. Mater., 16(1–2), 35–45.
Pietruszczak, S., Lydzba, D., and Shao, J. F. (2002). “Modelling of inherent anisotropy in sedimentary rocks.” Int. J. Solids Struct., 39(3), 637–648.
Pietruszczak, S., and Mroz, Z. (2000). “Formulation of anisotropic failure criteria incorporating a microstructure tensor.” Comput. Geotech., 26(2), 105–112.
Pietruszczak, S., and Mroz, Z. (2001). “On failure criteria for anisotropic cohesive-frictional materials.” Int. J. Numer. Anal. Methods Geomech., 25(5), 509–524.
Xiao, Y., Liu, H., and Yang, G. (2012). “Formulation of cross-anisotropic failure criterion for granular material.” Int. J. Geomech., 182–188.
Zhong, S.-Y., Xu, W.-Y., and Ling, D. (2011). “Influence of the parameters in the Pietruszczak–Mroz anisotropic failure criterion.” Int. J. Rock. Mech. Min. Sci., 48(6), 1034–1037.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 15 • Issue 6 • December 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 31, 2013
Accepted: Sep 17, 2014
Published online: Oct 9, 2014
Published in print: Dec 1, 2015
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.