JRMGE / Vol 10 / Issue 4

Article

An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

Baotang Shen, Jingyu Shi, Nick Barton


2018, 10(4): 645-652. doi:10.1016/j.jrmge.2018.04.002


Received: 2017-10-18 / Revised: 2018-04-26 / Accepted: 2018-04-28 / Available online: 2018-05-30

2018, 10(4): 645-652.

doi:10.1016/j.jrmge.2018.04.002


Received: 2017-10-18

Revised: 2018-04-26

Accepted: 2018-04-28

Available online: 2018-05-30


Abstract: In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now, leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD, and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comrehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.

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Baotang Shen, Jingyu Shi, Nick Barton, 2018. An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks. J. Rock Mech. Geotech. Eng. 10 (4), 645-652.

Article Data

Author(s) Information

Prof. Nick Barton
nickrbarton@hotmail.com

Nick Barton was born in 1944 in England. He obtained a BSc degree in Civil Engineering from King's College in 1966, and a PhD concerning shear strength and rock slope stability from Imperial College in 1971. He worked for two long periods at NGI in Oslo between 1971 and 2000, eventually as Division Director and then as Technical Advisor. He also worked for four years at TerraTek (subsequently Schlumberger) in Salt Lake City, and was Manager of Geomechanics from 1981 to 1984. Since 2000 he has had his own international rock engineering consultancy, Nick Barton & Associates, based in Oslo and São Paulo. He has consulted on hundreds of rock engineering projects in a total of 40 countries during 50 years, has 270 publications as first or single author, and has written two books, one on TBM prognosis, the other linking rock quality and seismic attributes of rock masses at all scales. He has 13 international awards including the 6th Müller Lecture of the International Society for Rock Mechanics (ISRM). He developed the widely used Q-system for classifying rock masses, and for selecting rock tunnel and cavern single-shell support in 1974. He was originator of the rock joint shear strength parameters JRC and JCS and co-developer of the resulting Barton-Bandis constitutive laws for rock joint modelling in 1982, which was incorporated as a sub-routine in UDEC-BB in 1985. He also developed the QTBM prognosis method and QSLOPE for selecting maintenance-free rock slope bench-face angles. His chief areas of consulting activity have been in hydropower tunnelling and cavern construction, nuclear waste disposal site characterization, metro tunnels and caverns, and site characterization at high dams. He has given more than 50 keynote lectures in international conferences.

Prof. Jingyu Shi
Jingyu.Shi@csiro.au

Dr. Jingyu Shi obtained his BEng in 1982 from Lanzhou University, China and PhD in 1988 from Nottingham University, UK. He has background in solid mechanics and worked on several projects in various fields of applied mathematics in several universities and CSIRO in Australia. His main experiences are in numerical modelling with various methods, including finite different method, finite volume method and boundary element method.