Technical Notes
Dec 17, 2021

Multiyield-Surface Implementation of a Simplified Three-Dimensional Hoek–Brown Strength Criterion

Publication: International Journal of Geomechanics
Volume 22, Issue 3

Abstract

This work presents the implementation of a simplified three-dimensional Hoek–Brown strength criterion using a multiyield-surface plasticity approach. The adopted three-dimensional simplification of the strength criterion accounts for the intermediate principal stress influence, maintaining the simplicity in the numerical implementation. This criterion corresponds to a paraboloid surface of circular cross section in the principal stress space. The introduction of multiple yield surfaces allows for a smooth definition of the nonlinear stress–strain behavior of the material. In addition, a kinematic hardening rule is adopted, allowing yield surfaces to translate with loading, enabling a hysteretic and path-dependent stress–strain response.

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Acknowledgments

The authors would like to acknowledge the support obtained from the FONDECYT-INICIACION research (Grant No 11181252) and from Universidad de Chile, Project U-Inicia Code (N° UI 24/2018).

References

Anyaegbunam, A. 2015. “Nonlinear power-type failure laws for geomaterials: Synthesis from triaxial data, properties, and applications.” Int. J. Geomech. 15 (1): 04014036. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000348.
Barton, N. 2013. “Shear strength criteria for rock, rock joints, rockfill and rock masses: Problems and some solutions.” J. Rock Mech. Geotech. Eng. 5 (4): 249–261. https://doi.org/10.1016/j.jrmge.2013.05.008.
Barton, N. 2016. “Non-linear shear strength for rock, rock joints, rockfill and interfaces.” Innov. Infrastruct. Solutions 1 (1): 1–19. https://doi.org/10.1007/s41062-016-0011-1.
Benz, T., R. Schwab, R. Kauther, and P. Vermeer. 2008. “A Hoek–Brown criterion with intrinsic material strength factorization.” Int. J. Rock Mech. Min. Sci. 2 (210–222): 45. https://doi.org/10.1016/j.ijrmms.2007.05.003.
Clausen, J., and L. Damkilde. 2008. “An exact implementation of the Hoek–Brown criterion for elasto-plastic finite element calculations.” Int. J. Rock Mech. Min. Sci. 45 (6): 831–847. https://doi.org/10.1016/j.ijrmms.2007.10.004.
Dai, Z., T. You, X. Xu, and Q. Zhu. 2018. “Removal of singularities in Hoek–Brown criterion and its numerical implementation and applications.” Int. J. Geomech. 18 (10): 04018127. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001201.
Dassault Systèmes. 2016. ABAQUS 2016—User subroutines reference guide. Providence, RI: SIMULIA.
Eberhardt, E. 2012. “The Hoek–Brown failure criterion.” Rock Mech. Rock Eng. 45 (6): 981–988. https://doi.org/10.1007/s00603-012-0276-4.
Fu, Z., S. Chen, and C. Peng. 2013. “Modeling cyclic behavior of rockfill materials in a framework of generalized plasticity.” Int. J. Geomech. 14 (2): 191–204. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000302.
Gu, Q., J. P. Conte, Z. Yang, and A. Elgamal. 2011. “Consistent tangent moduli for multi-yield-surface J2 plasticity model.” Comput. Mech. 48 (1): 97–120. https://doi.org/10.1007/s00466-011-0576-7.
Hoek, E., and E. Brown. 1980a. “Empirical strength criterion for rock masses.” J. Geotech. Geoenviron. Eng. 106: 1013–1035.
Hoek, E., and E. Brown. 1980b. Underground excavations in rock. London: Inst. of Mining and Metallurgy.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion-2002 edition.” In Vol. 1 of Proc., of NARMS-TAC, pp. 267–273. Toronto: University of Toronto Press.
Ismael, M., and H. Konietzky. 2019. “Constitutive model for inherent anisotropic rocks: Ubiquitous joint model based on the Hoek–Brown failure criterion.” Comput. Geotech. 105: 99–109. https://doi.org/10.1016/j.compgeo.2018.09.016.
Jiang, H. 2017. “Three-dimensional failure criteria for rocks based on the Hoek–Brown criterion and a general lode dependence.” Int. J. Geomech. 17 (8): 04017023. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000900.
Jiang, H., and J. Zhao. 2015. “A simple three-dimensional failure criterion for rocks based on the Hoek–Brown criterion.” Rock Mech. Rock Eng. 48 (5): 1807–1819. https://doi.org/10.1007/s00603-014-0691-9.
Khosravifar, A., A. Elgamal, J. Lu, and J. Li. 2018. “A 3D model for earthquake-induced liquefaction triggering and post-liquefaction response.” Soil Dyn. Earthquake Eng. 110: 43–52. https://doi.org/10.1016/j.soildyn.2018.04.008.
Kondner, R. L. 1963. “Hyperbolic stress–strain response: Cohesive soils.” J. Soil Mech. Found. Div. 89 (1): 115–144. https://doi.org/10.1061/JSFEAQ.0000479.
Kramer, S. 1996. Geotechnical earthquake engineering. London: Pearson.
Li, G. X. 1988. Triaxial experiments on dry and saturated rockfill materials used in Xiaolangdi earth dam. Research Rep. 17-1-2-88031. Beijing: Tsinghua Univ.
Marinos, V., P. Marinos, and E. Hoek. 2005. “The geological strength index: Applications and limitations.” Bull. Eng. Geol. Environ. 64 (1): 55–65. https://doi.org/10.1007/s10064-004-0270-5.
Melkoumian, N., S. Priest, and S. Hunt. 2009. “Further development of the three-dimensional Hoek–Brown yield criterion.” Rock Mech. Rock Eng. 42 (6): 835–847. https://doi.org/10.1007/s00603-008-0022-0.
Mercado, V., W. El-Sekelly, M. Zeghal, and T. Abdoun. 2017. “Identification of soil dynamic properties of sites subjected to bi-directional excitation.” Soil Dyn. Earthquake Eng. 92: 215–228. https://doi.org/10.1016/j.soildyn.2016.09.038.
Mroz, Z. 1967. “On the description of anisotropic workhardening.” J. Mech. Phys. Solids 15 (3): 163–175. https://doi.org/10.1016/0022-5096(67)90030-0.
Pan, X. D., and J. A. Hudson. 1988. “A simplified three dimensional Hoek–Brown yield criterion.” In ISRM Int. Symp., 95–103. Lisbon, Portugal: International Society for Rock Mechanics.
Parra-Colmenares, E. J. 1996. “Numerical modeling of liquefaction and lateral ground deformation including cyclic mobility and dilation response in soil systems.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Rensselaer Polytechnic Institute.
Prevost, J. H. 1985. “A simple plasticity theory for frictional cohesionless soils.” Int. J. Soil Dyn. Earthquake Eng. 4 (1): 9–17. https://doi.org/10.1016/0261-7277(85)90030-0.
Prevost, J. H. 1987. “Modeling the behavior of geomaterials.” In Geotechnical modeling and applications, edited by S. M. Sayed, 8–75. Houston, TX: Gulf Publishing Company.
Priest, S. 2010. “Comparisons between selected three-dimensional yield criteria applied to rock.” Rock Mech. Rock Eng. 43 (4): 379–389. https://doi.org/10.1007/s00603-009-0064-y.
Priest, S. (2012). “Three-dimensional failure criteria based on the Hoek–Brown criterion.” In The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014, 241–245. Dordrecht, Netherlands: Springer.
Rukhaiyar, S., and N. K. Samadhiya. 2015. “Effect of cyclic loading on Himalayan rocks.” In Proc., 5th Indian Young Geotechnical Engineers Conf.: Extended Abstracts. Vadodara, India: Indian Geotechnical Society.
Vakili, A. 2016. “An improved unified constitutive model for rock material and guidelines for its application in numerical modelling.” Comput. Geotech. 80: 261–282. https://doi.org/10.1016/j.compgeo.2016.08.020.
VandenBerge, D., and M. McGuire. 2019. “Practical use of modified Hoek–Brown criterion for soil slope stability analysis.” Geotech. Geol. Eng. 37 (6): 5441–5455. https://doi.org/10.1007/s10706-019-00991-1.
Vermeer, P., and R. De Borst. 1984. Non-associated plasticity for soils, concrete and rock. Delft, Netherlands: Delft Univ. of Technology.
Wan, R. G. 1992. “Implicit integration algorithm for Hoek–Brown elastic-plastic model.” Comput. Geotech. 14 (3): 149–177. https://doi.org/10.1016/0266-352X(92)90031-N.
Xiao, Y., H. Liu, Y. Chen, and J. Jiang. 2014. “Strength and deformation of rockfill material based on large-scale triaxial compression tests. I: Influences of density and pressure.” J. Geotech. Geoenviron. Eng. 140 (12): 04014070. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001176.
Yang, Z., and A. Elgamal. 2008. “Multi-surface cyclic plasticity sand model with Lode angle effect.” Geotech. Geol. Eng. 26 (3): 335–348. https://doi.org/10.1007/s10706-007-9170-3.
Yang, Z., A. Elgamal, and E. Parra. 2003. “Computational model for cyclic mobility and associated shear deformation.” J. Geotech. Geoenviron. Eng. 129 (12): 1119–1127. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:12(1119).
Zhang, L., and H. Zhu. 2007. “Three-dimensional Hoek–Brown strength criterion for rocks.” J. Geotech. Geoenviron. Eng. 133 (9): 1128–1135. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:9(1128).

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 3March 2022

History

Received: Dec 14, 2020
Accepted: Oct 12, 2021
Published online: Dec 17, 2021
Published in print: Mar 1, 2022
Discussion open until: May 17, 2022

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Assistant Professor, Dept. of Civil and Environmental Engineering, Universidad del Norte, Km. 5 Vía a Puerto Colombia, Barranquilla 081007, Colombia (corresponding author). ORCID: https://orcid.org/0000-0002-9585-189X. Email: [email protected]
William Fuentes
Director of Consulting Services, Pontificia Universidad Javeriana, Cra. 7 No. 40-62, Bogotá 110231, Colombia.
Felipe Ochoa-Cornejo
Assistant Professor, Dept. of Civil Engineering, Universidad de Chile, Av. Libertador Bernardo O'Higgins 1058, Santiago de Chile 837-0456, Chile.

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