Research on Applicability of the Mohr-Wedge Criterion Including Rock Critical State

doi:10.12068/j.issn.1005-3026.2021.04.016

Abstract

Abstract: The Mohr-Wedge (MW) strength criterion is a theoretical formula， which is derived based on the rock wedge failure mechanics model and the partial differential equation related to the principal stresses. The MW criterion can be easily understood by using the dimensional analysis to arrange the multiple parameters with corresponding physical meanings. To analyze the applicability of the MW criterion including the rock critical state， the Mohr-Coulomb criterion， the Hoek-Brown criterion and the exponential criterion were selected as the comparison objects， and the average absolute error MAE was used as the evaluation index in order to quantitatively compare the accuracy of the four criteria in predicting rock strength. The results show that when the confining pressure is less than the rock critical state confining pressure σ_○cr-M， the MW criterion has certain applicability. When the confining pressure is greater than σ_○cr-M， the rock strength predicted by the four criteria is different due to the different rock critical state confining pressure. Therefore， a method to predict rock strength under different rock critical state confining pressures was proposed， which can provide some reference for choosing the value of rock critical state confining pressure.

Key words: rock critical state; Mohr-Wedge criterion; dimensional analysis; rock strength criterion; confining pressure

CLC Number:

TU45

ZHANG Jing， REN Feng-yu， HE Rong-xing， OUYANG Zhi-hua. Research on Applicability of the Mohr-Wedge Criterion Including Rock Critical State[J]. Journal of Northeastern University(Natural Science), 2021, 42(4): 567-575.

References

[1]Shou Y，Zhou X，Qian Q.A critical condition of the zonal disintegration in deep rock masses:CrossMark strain energy density approach ［J］.Theoretical and Applied Fracture Mechanics，2018，97:322-332.
[2]Matthew D，Joseph P，Mary M，et al.Pseudo-static failure modes and yield accelerations in rock slopes ［J］.International Journal of Rock Mechanics and Mining Sciences，2018，102:1-14.
[3]蔡美峰，何满潮，刘东燕.岩石力学与工程［M］.北京:科学出版社，2010.(Cai Mei-feng，He Man-chao，Liu Dong-yan.Rock mechanics and engineering ［M］.Beijing:Science Press，2010.)
[4]Mohr O.Welche umstande bedingen die elastizitatsgrenze und den bruch eines materials ［J］.Zeitschrift des Vereins Deutscher Ingenieure，1900，44:1524-1530.
[5]Balmer G.A general analytical solution for Mohr envelope ［J］.American Society for Testing and Materials，1952，52:1260-1271.
[6]Ucar R.Determination of shear failure envelope in rock masses ［J］.International Journal of Rock Mechanics Engineering，1986，112(3):303-315.
[7]Kumar P.Shear failure envelope of Hoek-Brown criterion for rockmass ［J］.Tunnelling and Underground Space Technology，1998，13(4):453-458.
[8]Hoek E，Brown E T.Empirical strength criterion for rock masses ［J］.Journal of Geotechnical and Geoenvironmental Engineering，1980，106(GT9):1013-1035.
[9]Hoek E，Wood D，Shah S.A modified Hoek-Brown failure criterion for jointed rock masses［C］//Proceedings of the Rock Characterization.London:British Geotechnical Society，1992:209-214.
[10]Vutukuri V S，Lama R D，Saluja S S.Handbook on mechanical properties of rocks ［M］.Clausthal:Transform Technology Publications，1974.
[11]Sankhaneel W，Gabriel W.A progressive S-shaped yield criterion and its application to rock pillar behavior ［J］.International Journal of Rock Mechanics and Mining Sciences，2018，105:98-109.
[12]Shen J Y，Jimenez R，Karakus M，et al.A simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength ［J］.Rock Mechanics and Rock Engineering，2014，47:357-369.
[13]Ouyang Z，Elsworth D.A phenomenological failure criterion for brittle rock ［J］.Rock Mechanics and Rock Engineering，1991，24:133-153.
[14]张晶，欧阳治华，郭宏强，等.Mohr-Wedge岩石破坏准则适用性研究［J］.矿业研究与开发，2016，36(11):19-25.(Zhang Jing，Ouyang Zhi-hua，Guo Hong-qiang，et al.Research on the applicability of Mohr-Wedge rock failure criterion ［J］.Mining Research and Development，2016，36(11):19-25.)
[15]Mogi K.Fracture and flow of rocks under high triaxial compression ［J］.Journal of Geophysical Research Atmospheres，1971，76(5):1255-1269.
[16]Signh M，Raj A，Singh B.Modified Mohr-Coulomb criterion for non-linear triaxial and polyaxial strength on intact rocks ［J］.International Journal of Rock Mechanics and Mining Sciences，2001，48(4):546-555.
[17]Al-Ajmi A M，Zimmerman R W.Relation between the Mogi and the Coulomb failure criteria ［J］.International Journal of Rock Mechanics and Mining Sciences，2005，42:431-439.
[18]俞茂宏.线性和非线性的统一强度理论［J］.岩石力学与工程学报，2007，26(4):662-669.(Yu Mao-hong.Linear and nonlinear unified strength theory ［J］.Chinese Journal of Rock Mechanics and Engineering，2007，26(4):662-669.)
[19]周小平，钱七虎，杨海清.深部岩体强度准则［J］.岩石力学与工程学报，2008，27(1):117-123.(Zhou Xiao-ping，Qian Qi-hu，Yang Hai-qing.Strength criteria of deep rock mass ［J］.Chinese Journal of Rock Mechanics and Engineering，2008，27(1):117-123.)
[20]You M Q.Mechanical characteristics of the exponential strength criterion under conventional triaxial stresses ［J］.International Journal of Rock Mechanics and Mining Sciences，2010，47(2):195-204.
[21]Yamaji A，Sato K.Stress inversion meets plasticity theory:a review of the theories of fault-slip analysis from the perspective of the deviatoric stress-strain space ［J］.Journal of Structural Geology，2019，125:296-310.
[22]Hoek E.Strength of jointed rock masses ［J］.Geotechnique，1983，23(3):187-223.
[23]徐松林，吴文，王广印，等.大理岩等围压三轴压缩全过程研究Ⅰ:三轴压缩全过程的峰前、峰后卸围压全过程实验［J］.岩石力学与工程学报，2001，20(6):763-767.(Xu Song-lin，Wu Wen，Wang Guang-yin，et al.Study on complete procedures of marble under triaxial compression Ⅰ:testing study on complete procedure of triaxial compression and the processes of unloading confining at the pre-peak and post-peak ［J］.Chinese Journal of Rock Mechanics and Engineering，2001，20(6):763-767.)
[24]杨圣奇，苏承东，徐卫亚.大理岩常规三轴压缩下强度和变形特性的试验研究［J］.岩土力学，2005，26(3):475-478.(Yang Sheng-qi，Su Cheng-dong，Xu Wei-ya.Experimental investigation on strength and deformation properties of marble under conventional triaxial compression ［J］.Rock and Soil Mechanics，2005，26(3):475-478.)
[25]Barton N.Shear strength criteria for rock，rock joints，rockfill and rock masses:problems and some solutions ［J］.Journal of Rock Mechanics and Geotechnical Engineering，2013，5:249-261.
[26]Peng S，Johnson A M.Crack growth and faulting in cylindrical specimens of chelmsford granite ［J］.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1972，9(1):37-86.
[27]Walter J.Failure of granite under compression ［J］.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1977，14(4):209-215.
[28]Mogi K.Experimental rock mechanics ［M］.London:Taylor and Francis，2007.
[29]Swanson S R，Brown W S.An observation of loading path independence of fracture in rock ［J］.International Journal of Rock Mechanics and Mining Sciences，1971，8:277-281.
[30]汪斌，朱杰兵，邬爱清，等.高应力下岩石非线性强度特性的试验验证［J］.岩石力学与工程学报，2010，29(3):542-548.(Wang Bin，Zhu Jie-bing，Wu Ai-qing，et al.Experimental validation of nonlinear strength property of rock under high geostress ［J］.Chinese Journal of Rock Mechanics and Engineering，2010，29(3):542-548.)［31］Von K T.Festigkeitsversuche unter all seitigem Druck ［J］.Zeit Vereins Deutscher Ingenieure，1911，55:1749-1759.［32］Barton N.The shear strength of rock and rock joints ［J］.International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts，1976，13:255-279.［33］李斌，王大国，刘艳章，等.三轴条件下改进的Hoek-Brown准则的修正［J］.煤炭学报，2017，42(5):1173-1181.(Li Bin，Wang Da-guo，Liu Yan-zhang，et al.Improvement of modified Hoek-Brown criterion under conventional triaxial compression conditions ［J］.Journal of China Coal Society，2017，42(5):1173-1181.)