A dynamic strength criterion of rock materials based on energy theory
ZHOU Changtai1，2，3，XIE Heping1，2，3，ZHU Jianbo1，2
(1. Guangdong Provincial Key Laboratory of Deep Earth Sciences and Geothermal Energy Exploitation and Utilization，Shenzhen University，Shenzhen，Guangdong 518060，China；2. Institute of Deep Earth Sciences and Green Energy，Shenzhen University，Shenzhen，Guangdong 518060，China；3. College of Water Resource and Hydropower，Sichuan University，Chengdu，Sichuan 610065，China)
Abstract：The current rock failure criteria fail to fully consider the influence of engineering disturbances，leading to potential disasters. Therefore，there is an urgent need to develop a dynamic rock failure criterion considering the effect of the strain rate. Exploring the strength law of rock materials from the perspective of energy transformation in the overall failure process proves to be an effective approach. Thus，this study investigates the dynamic failure criterion based on energy theory. Drawing inspiration from the dynamic strength and overall failure laws of rock materials，a novel continuity function for the strain energy release dispersion coefficient considering the external stress environment was constructed. This function can accurately reflect the influence of the confining pressure on the energy release direction of rock materials. Additionally，the critical value Gcd，which represents the dynamic maximum energy release rate of rock material considering the strain rate effect，was established by introducing a unified dynamic uniaxial compressive strength model. Finally，the dynamic failure criterion considering the strain rate effect was proposed based on the maximum dynamic energy release rate of rock materials. The results demonstrate a good agreement between the theoretical predictions of the proposed rock dynamic strength criterion and the experimental results obtained from three different types of rock or rock-like materials. This criterion provides a better description of the nonlinear dynamic strength characteristics of rock or rock-like materials. Furthermore，the results indicate that the newly constructed energy dynamic failure criterion has a clear physical and mechanical meaning. The findings of this study have important engineering significance for studying the yield and failure characteristics of rock materials under dynamic disturbances.
周昌台1，2，3，谢和平1，2，3，朱建波1，2. 基于能量理论的岩石动态破坏准则[J]. 岩石力学与工程学报, 2023, 42(8): 1890-1898.
ZHOU Changtai1，2，3，XIE Heping1，2，3，ZHU Jianbo1，2. A dynamic strength criterion of rock materials based on energy theory. , 2023, 42(8): 1890-1898.
[1] HOEK E，BROWN E T. The Hoek-Brown failure criterion and GSI – 2018 edition[J]. Journal of Rock Mechanics and Geotechnical Engineering，2019，11(3)：445–463.
[2] 谢和平，陈忠辉. 岩石力学[M]. 北京：科学出版社，2004：52–59.(XIE Heping，CHEN Zhonghui. Rock mechanics[M]. Beijing：Science Press，2004：52–59.(in Chinese))
[3] 俞茂宏. 双剪理论及其应用[M]. 北京：科学出版社，1998：59–130. (YU Maohong. Unified strength theory and its applications[M]. Beijing：Science Press，1998：59–130.(in Chinese))
[4] YU M H. Advances in strength theories for materials under complex stress state in the 20th Century[J]. Advances in Mechanics，2004，34(4)：529–560.
[5] TRESCA H. Mémoire sur l’écoulement des corps solides soumis à de fortes pressions[J]. Comptes Rendus Mécanique，Rend，1864，59：754–758.
[6] DRUCKER D C，PRAGER W. Soil mechanics and plastic analysis on limit design[J]. Journal of Applied Mathematics，1952，10(2)：157–165.
[7] GUEST J J. On the strength of ductile materials under combined stress[J]. Philosophical Magazine，1899，17(1)：202.
[8] 谢和平，鞠 杨，黎立云. 基于能量耗散与释放原理的岩石强度与整体破坏准则[J]. 岩石力学与工程学报，2005，24(17)：3 003–3 010. (XIE Heping，JU Yang，LI Liyun. Criteria for strength and structural failure of rocks based on energy dissipation release principles[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(17)：3 003– 3 010.(in Chinese))
[9] XIE H，ZHU J，ZHOU T，et al. Conceptualization and preliminary study of engineering disturbed rock dynamics[J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources，2020，6：1–14.
[10] 朱建波，马斌文，谢和平，等. 煤矿矿震与冲击地压的区别与联系及矿震扰动诱冲初探[J]. 煤炭学报，2022，47(9)：3 396–3 409.(ZHU Jianbo，MA Binwen，XIE Heping，et al. The differences and connections between mining seismicity and coal bursts in coal mines and preliminary study on coal bursts induced by mining seismicity[J]. Journal of China Coal Society，2022，47(9)：3 396–3 409.(in Chinese))
[11] GRADY D E，LIPKIN J. Criteria for impulsive rock fracture[J]. Geophysical Research Letters，1980，7(4)：255–258.
[12] ZHAO J. Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock[J]. International Journal of Rock Mechanics and Mining Sciences，2000，37(7)：1 115–1 121.
[13] 钱七虎，戚承志. 岩石、岩体的动力强度与动力破坏准则[J]. 同济大学学报：自然科学版，2008，36(12)：1 599–1 605.(QIAN Qihu，QI Chengzhi. Dynamic strength and dynamic fracture criteria of rock and rock mass[J]. Journal of Tongji University，2008，36(12)：1 599–1 605.(in Chinese))
[14] 宫凤强，司雪峰，李夕兵，等. 基于应变率效应的岩石动态Mohr-Coulomb准则和Hoek-Brown准则研究[J]. 中国有色金属学报，2016，26(8)：1 763–1 773.(GONG Fengqiang，SI Xuefeng，LI Xibing et al. Rock dynamic Mohr-Coulomb and Hoek-Brown criteria based on strain rate effect[J]. The Chinese Journal of Nonferrous Metals，2016，26(8)：1 763–1 773.(in Chinese))
[15] SI X F，GONG F Q，LI X B，et al. Dynamic Mohr-Coulomb and Hoek-Brown strength criteria of sandstone at high strain rates[J]. International Journal of Rock Mechanics and Mining Sciences，115(13)：48–59.
[16] QIAN Q H，QI C Z，WANG M Y. Dynamic strength of rocks and physical nature of rock strength[J]. Journal of Rock Mechanics and Geotechnical Engineering，2009，1(1)：1–10.
[17] 杜修力，王国盛，路德春. 混凝土材料非线性多轴动态强度准则[J]. 中国科学：技术科学，2014，44(12)：1 319–1 332.(DU Xiuli，WANG Guosheng，LU Dechun. Nonlinear multiaxial dynamic strength criterion for concrete material[J]. Scientia Sinica：Technologica，2014，44(12)：1 319–1 332.(in Chinese))
[18] 马林建，阳 发，王明洋，等. 考虑应变率效应的广义Hoek-Brown 动态强度准则[J]. 岩土力学，2017，38(增2)：27–32.(MA Linjian，YANG Fa，WANG Mingyang，et al. Generalized Hoek-Brown dynamic strength criterion incorporating strain rate effect[J]. Rock and Soil Mechanics，2017，38(Supp.2)：27–32.(in Chinese))
[19] 路德春，李 萌，王国盛，等. 静动组合载荷下混凝土率效应机理及强度准则[J]. 力学学报，2017，49(4)：940–952.(LU Dechun，LI Meng，WANG Guosheng，et al. Study on strain rate effect and strength criterion of concrete under static-dynamic coupled loading[J]. Chinese Journal of Theoretical and Applied Mechanics，2017，49(4)：940–952.(in Chinese))
[20] MASUDA K，MIZUTANI H，YAMADA I. Experimental study of strain-rate dependence and pressure dependence of failure properties of granite[J]. Journal of Physics of the Earth，1987，35(1)：37–66.
[21] OLSSON W. A. The compressive strength of tuff as a function of strain rate from 10–6 to 103/sec[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1991，28(1)：115–118.
[22] HAO Y，HAO H，LI Z X. Influence of end friction confinement on impact tests of concrete material at high strain rate[J]. International Journal of Impact Engineering，2013，60：82–106.
[23] 谢和平，鞠 杨，黎立云，等. 岩体变形破坏过程的能量机制[J]. 岩石力学与工程学报，2008，27(9)：1 729–1 740.(XIE Heping，JU Yang，LI Liyun，et al. Energy mechanism of deformation and failure of rock masses[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(9)：1 729–1 740.(in Chinese))
[24] 郭建强，刘新荣. 强度准则与岩爆判据统一的研究[J]. 岩石力学与工程学报，2018，37(增1)：3 340–3 352.(GUO Jianqiang，LIU Xinrong. Study on the uniformity between strength criterion and rockburst criterion[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(Supp.1)：3 340–3 352.(in Chinese))
[25] 郭建强，刘新荣，黄武锋，等. 基于弹性应变能的 Mohr-Coulomb 强度准则讨论[J]. 同济大学学报：自然科学版，2018，46(9)：1 168–1 174.(GUO Jianqiang，LIU Xinrong，HUANG Wufeng，et al. Discussion on M-C Strength criterion based on elastic strain energy[J]. Journal of Tongji University：Natural Science，2018，46(9)：1 168–1 174.(in Chinese))
[26] 张后全，徐建峰，贺永年，等. 脆性岩石真三轴能量强度准则研究[J]. 中国矿业大学学报，2012，41(4)：564–570.(ZHANG Houquan，XU Jianfeng，HE Yongnian，et al. Study of triaxial energy strength criterion for brittle rock material[J]. Journal of China University of Mining and Technology，2012，41(4)：564–570.(in Chinese))
[27] 高 红，郑颖人，冯夏庭. 岩土材料能量屈服准则研究[J]. 岩石力学与工程学报，2007，26(12)：2 437–2 443.(GAO Hong，ZHENG Yingren，FENG Xiating. Study on energy yield criterion of geomaterials[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(12)：2 437–2 443.(in Chinese))
[28] 周 辉，李 震，杨艳霜，等. 岩石统一能量屈服准则[J]. 岩石力学与工程学报，2013，32(11)：2 170–2 184.(ZHOU Hui，LI Zhen，YANG Yanshuang，et al. Unified energy yield criterion of rock[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(11)： 2 170– 2 184.(in Chinese))
[29] 郭建强，刘新荣，王军保，等. 基于弹性应变能的岩石强度准则[J].岩土力学，2016，37(增2)：129–136.(GUO Jianqiang，LIU Xinrong，WANG Junbao，et al. Investigation on strength criterion of rock based on elastic strain energy[J]. Rock and Soil Mechanics，2016，37(Supp.2)：129–136.(in Chinese))
[30] 赵忠虎，谢和平. 岩石变形破坏过程中的能量传递和耗散研究[J]. 四川大学学报：工程科学版，2008，40(2)：29–34.(ZHAO Zhonghu，XIE Heping. Energy transfer and energy dissipation in rock deformation and fracture[J]. Journal of Sichuan University：Engineering Science，2008，40(2)：29–34.(in Chinese))
[31] 刘晓辉，薛 洋，郑 钰，等. 冲击荷载下煤岩破碎过程能量释放研究[J]. 岩石力学与工程学报，2021，40(增2)：3 201–3 211.(LIU Xiaohui，XUE Yang，ZHENG Jue，et al. Research on energy release in coal rock fragmentation process under impact load[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(Supp.2)：3 201–3 211. (in Chinese))
[32] DOAN M L，GARY G. Rock pulverization at high strain rate near the San Andreas fault[J]. Nature Geoscience，2009，2(10)：709–712.
[33] 武仁杰，李海波，李晓锋，等．冲击载荷作用下层状岩石破碎能耗及块度特征[J]. 煤炭学报，2020，45(3)：1 053–1 060.(WU Renjie，LI Haibo，LI Xiaofeng，et al. Broken energy dissipation and fragmentation characteristics of layered rock under impact loading[J]. Journal of China Coal Society，2020，45(3)：1 053–1 060.(in Chinese))
[34] PENG J，CAI M，RONG G，et al. Determination of confinement and plastic strain dependent post-peak strength of intact rocks[J]. Engineering Geology，2017，218：187–196.
[35] 高 超. 页岩变形破坏的弹脆性特征及能量演化研究[博士学位论文][D]. 成都：四川大学，2019.(GAO Chao. The investigation of elastic-brittle deformation properties of shale and its failure energy evolution analysis[M. S. Thesis][D]. Chengdu：Sichuan University，2019.(in Chinese))
[36] GRADY D E，KIPP M E. The micromechanics of impact fracture of rock[J]. International Journal of Rock Mechanics and Mining Sciences Abstraction，1979，16(5)：293–302.
[37] KIMBERLEY J，RAMESH K T，DAPHALAPURKAR N P. A scaling law for the dynamic strength of brittle solids[J]. Acta Mater，2013，61(9)：3 509–3 521.
[38] LI X F，LI H B，ZHAO J. Grain-based discrete element method(GB-DEM) modelling of multi-scale fracturing in rocks under dynamic loading[J]. Rock Mechanics and Rock Engineering，2018，51：3 785–3 817.
[39] GONG F Q，SI X F，LI X B，et al. Dynamic triaxial compression tests on sandstone at high strain rates and low confining pressures with split Hopkinson pressure bar[J]. International Journal of Rock Mechanics and Mining Sciences，2019，113：211–219.
[40] DU H B，DAI F，LIU Y，et al. Dynamic response and failure mechanism of hydrostatically pressurized rocks subjected to high loading rate impacting[J]. Soil Dynamics and Earthquake Engineering，2020，129：105927.
[41] FU Q，BU M X，SU L，et al. Dynamic triaxial compressive response and failure mechanism of basalt fibre-reinforced coral concrete[J]. International Journal of Impact Engineering，2021，156：103930.
[42] ZHANG Q B，ZHAO J. A review of dynamic experimental techniques and mechanical behaviour of rock materials[J]. Rock Mechanics and Rock Engineering，2014，47(4)：1 411–1 478.
2023, Vol. 42 
