On the anisotropic Mohr-Coulomb criterion of fractured rock masses based on the discrete fracture network
WANG Peitao1，2，3，LIU Cao1，3，MA Chi1，3，REN Fenhua1，3，CAI Meifeng1，3
(1. Key Laboratory of Ministry of Education for Efficient Mining and Safety of Metal Mine，University of Science and Technology Beijing，Beijing 100083，China；2. State Key Laboratory of Water Resource Protection and Utilization in Coal Mining，
Beijing 100011，China；3. School of Civil and Resources Engineering，University of Science and Technology Beijing，
Beijing 100083，China)
Abstract：The spatial distribution and roughness characteristics of the structural planes have a significant impact on the anisotropic properties of jointed rock mass，which are important factors affecting the engineering stability. To study the influence of roughness on the mechanical properties of anisotropy of jointed rock mass，a rough joint network model was established based on the fractal theory. Numerical compression tests considering varied rotation angles and confining pressures were conducted. Comparison of failure modes and acoustic emission characteristics between the fractal fracture model and the linear fracture model were performed. The results show that significant differences exist consideing the joint roughness，comparing the mechanical behaviours，AE charateristics and size effect. Meanwhile，a quantitative analysis of the anisotropy of the compressive strength and shear strength parameters of the jointed rock mass was conducted. The anisotropic Mohr circles based on the least squares principle were discussed. The biaxial compressive strength and shear strength parameters of the jointed rock mass show slight anisotropy. Differences of peak stresses，Mohr circle shapes and shear properties were verified under different loading directions. Influence of the geometry of the discrete faractures on the strength and fracture patterns was verified. The results will provide a novel and scientific model for characterizing the fractured rock mass and give a good reference for analysing the anisotropic shear behaviours of jointed rock masses.
王培涛1，2，3，刘 操1，3，马 驰1，3，任奋华1，3，蔡美峰1，3. 基于离散裂隙网络的岩体各向异性莫尔–库仑表征方法研究[J]. 岩石力学与工程学报, 2023, 42(S1): 3266-3280.
WANG Peitao1，2，3，LIU Cao1，3，MA Chi1，3，REN Fenhua1，3，CAI Meifeng1，3. On the anisotropic Mohr-Coulomb criterion of fractured rock masses based on the discrete fracture network. , 2023, 42(S1): 3266-3280.
[1] 李术才，刘洪亮，李利平，等. 基于数码图像的掌子面岩体结构量化表征方法及工程应用[J]. 岩石力学与工程学报，2017，36(1)：1–9.(LI Shucai，LIU Hongliang，LI Liping，et al. A quantitative method for rock structure at working faces of tunnels based on digital images and its application[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(1)：1–9.(in Chinese))
[2] CHEN L，WU S C，JIN A B，et al. The evolution regularity and influence factor analysis of zonal disintegration around deep jointed rock mass：a numerical study based on DEM[J]. Bulletin of Engineering Geology and the Environment，2021，81(1)：37–53.
[3] 张丰收，李猛利，张重远，等. 高地应力下深部岩芯饼化裂缝发展规律及机制研究[J]. 岩石力学与工程学报，2022，41(3)：533–542.(ZHANG Fengshou，LI Mengli，ZHANG Chongyuan，et al. Study on fracture propagation and formation mechanism of core discing at depth under high in-situ stresses[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(3)：533–542.(in Chinese))
[4] 张嘉凡，徐荣平，刘 洋，等. 冻融循环作用下注浆裂隙岩体微观孔隙演化规律及剪切力学行为研究[J]. 岩石力学与工程学报，2022，41(4)：676–690.(ZHANG Jiafan，XU Rongping，LIU Yang，et al. Study on micro-pore evolution law and shear mechanical behavior of grouting fractured rock mass under freeze-thaw cycle[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(4)：676–690. (in Chinese))
[5] CHEN G Q，LI H，WEI T，et al. Searching for multistage sliding surfaces based on the discontinuous dynamic strength reduction method[J]. Engineering Geology，2021，286(4)：106086.
[6] 王 刚，宋磊博，刘夕奇，等. 非贯通节理花岗岩剪切断裂力学特性及声发射特征研究[J]. 岩土力学，2022，43(6)：1 533–1 545. (WANG Gang，SONG Leibo，LIU Xiqi，et al. Shear fracture mechanical properties and acoustic emission characteristics of discontinuous jointed granite[J]. Rock and Soil Mechanics，2022，43(6)：1 533–1 545.(in Chinese))
[7] 柯志强，王环玲，徐卫亚，等. 含横向节理的柱状节理岩体力学特性试验研究[J]. 岩土力学，2019，40(2)：660–667.(KE Zhiqiang，WANG Huanling，XU Weiya，et al. Experimental study of mechanical behaviour of artificial columnar jointed rock mass containing transverse joints[J]. Rock and Soil Mechanics，2019，40(2)：660–667.(in Chinese))
[8] 陈卫忠，王鲁瑀，谭贤君，等. 裂隙岩体地下工程稳定性研究发展趋势[J]. 岩石力学与工程学报，2021，40(10)：1 945–1 961.(CHEN Weizhong，WANG Luyu，TAN Xianjun，et al. State-of-the-art and development tendency of the underground engineering stability of fractured rock mass. Chinese Journal of Rock Mechanics and Engineering，2021，40(10)：1 945–1 961.(in Chinese))
[9] BARTON N. Review of a new shear strength criterion for rock joints[J]. Engineering Geology，1973，7(4)：287–332.
[10] GE Y F，KULATILAKE PHSW，TANG H M，et al．Investigation of natural rock joint roughness[J]. Computers and Geotechnics，2014，55(12)：290–305.
[11] YUAN W，LIU S F，TAN H H，et al. A new approach for quantifying the two-dimensional joint roughness coefficient(JRC) of rock joints[J]. Environmental Earth Sciences，2021，80(15)：484–496.
[12] 赵炼恒，于诚浩，黄栋梁，等. 基于离散傅立叶变换的岩石节理形貌分析与随机重构[J]．铁道科学与工程学报，2017，14(8)：1 606–1 613.(ZHAO Lianheng，YU Chenghao，HUANG Dongliang，et al. Fourier-based reconstruction of rock joint and the statistical analysis of its morphology[J]. Journal of Railway Science and Engineering，2017，14(8)：1 606–1 613.(in Chinese))
[13] 陈 曦，曾亚武. 粗糙节理的改进形貌表征方法及采样点距效应[J]. 浙江大学学报：工学版，2021，55(11)：2 161–2 169.(CHEN Xi，ZENG Yawu. Improved morphology characterization method and sampling effect of rough rock joint[J]. Journal of Zhejiang University：Engineering Science，2021，55(11)：2 161–2 169.(in Chinese))
[14] 王培涛，任奋华，谭文辉，等. 单轴压缩试验下粗糙离散节理网络模型建立及力学特性[J]. 岩土力学，2017，38(增1)：70–78.(WANG Peitao，REN Fenhua，TAN Wenhui，et al. Model of roughness discrete fractures network for uniaxial compressive test and its mechanical properties[J]. Rock and Soil Mechanics，2017，38(Supp.1)：70–78. (in Chinese))
[15] 王培涛，刘 雨，章 亮，等. 基于3D打印技术的裂隙岩体单轴压缩特性试验初探[J]. 岩石力学与工程学报，2018，37(2)：364–373.(WANG Peitao，LIU Yu，ZHANG Liang，et al. Preliminary experimental study on uniaxial compressive properties of 3D printed fractured rock models[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(2)：364–373.(in Chinese))
[16] 王培涛，黄正均，任奋华，等. 基于3D打印的含复杂节理岩石直剪特性及破坏机制研究[J]. 岩土力学，2020，41(1)：46–56.(WANG Peitao，HUANG Zhengjun，REN Fenhua，et al. Research on direct shear behaviour and fracture patterns of 3D-printed complex jointed rock models[J]. Rock and Soil Mechanics，2020，41(1)：46–56.(in Chinese))
[17] 王培涛，任奋华，蔡美峰. 基于离散元方法的粗糙性节理岩体直剪力学及尺寸效应特性[J]. 煤炭学报，2018，43(4)：976–983.(WANG Peitao，REN Fenhua，CAI Meifeng. Mechanical analysis and size effect of rough discrete fractures network model under direct shear tests based on particle flow code[J]. Journal of China Coal Society，2018，43(4)：976–983.(in Chinese))
[18] WANG P T，REN F H，CAI M F. Influence of joint geometry and roughness on the multiscale shear behaviour of fractured rock mass using particle flow code[J]. Arabian Journal of Geosciences，2020，13(1)：165–179.
[19] WANG P T，LIU C，QI Z W，et al. A rough discrete fracture network model for geometrical modeling of jointed rock masses and the anisotropic behaviour[J]. Applied Sciences，2022，12(3)：1–15.
[20] 周宏伟，谢和平，M A KWASNIEWSKI，等. 岩体节理表面形貌的各向异性研究[J]. 地质力学学报，2001，(2)：123–129.(ZHOU Hongwei，XIE Heping，M A KWASNIEWSKI，et al. Anisotropy study on the surface morphology of rock mass joints[J]. Journal of Geomechanics，2001，(2)：123–129.(in Chinese))
[21] JI H，YAN L，XU J R. Experimental investigation on anisotropic strength and deformation behaviors of columnar jointed rock mass in confined state[J]. International Journal of Geomechanics，2021，21(9)：06021022–06021022.
[22] MAAZALLAHI V，MAJDI A. Numerical appraisal of rock mass anisotropy effect on elastic deformations of a circular tunnel[J]. Arabian Journal of Geosciences，2020，13(13)：547–563.
[23] 郑程程，贺 鹏，王 刚，等. 隧道裂隙岩体结构信息解译与危石垮塌空间展布规律研究[J]. 岩石力学与工程学报，2022，41(3)：515–532.(ZHENG Chengcheng，HE Peng，WANG Gang，et al. Structure information interpretation of fractured rock mass and spatial distribution law of dangerous rock collapse in tunnels[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(3)：515–532.(in Chinese))
[24] JAEGER J C. Shear failure of anisotropic rocks[J]. GeoScience World，1960，97(1)：65.
[25] 阙相成，朱珍德，牛子豪，等. 不同截面柱状节理岩体变形及强度各向异性研究[J]. 岩土力学，2021，42(9)：2 416–2 426.(QUE Xiangcheng，ZHU Zhende，NIU Zihao，et al. Deformation and strength anisotropy of columnar jointed rock mass with different cross-sectional shapes[J]. Rock and Soil Mechanics，2021，42(9)：2 416–2 426.(in Chinese))
[26] 邓华锋，李 涛，李建林，等. 层状岩体各向异性声学和力学参数计算方法研究[J]. 岩石力学与工程学报，2020，39(增1)：2 725–2 732.(DENG Huafeng，LI Tao，LI Jianlin，et al. Study on calculation method of anisotropic acoustic and mechanical parameters of layered rock[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(Supp.1)：2 725–2 732.(in Chinese))
[27] YU J，YAO W，DUAN K，et al. Experimental study and discrete element method modeling of compression and permeability behaviors of weakly anisotropic sandstones[J]. International Journal of Rock Mechanics and Mining Sciences，2020，134：1–14.
[28] 王永艺，唐春安，夏英杰. 压缩条件下玄武岩柱各向异性及破裂机理数值模拟研究[J]. 水利与建筑工程学报，2021，19(4)：14–22. (WANG Yongyi，TANG Chunan，Xia Yingjie. Numerical simulation of anisotropy and fracture mechanism of columnar jointed basalts under compression[J]. Journal of Water Resources and Architectural Engineering，2021，19(4)：14–22.(in Chinese))
[29] ZHANG J，WU X H，CAI M F，et al. Particle flow simulation of anisotropic mechanical properties of cracked rock mass[J]. Geotechnical and Geological Engineering，2021，39(8)：5 917– 5 929.
[30] 王荣达，刘铁新，张 凯. 岩体节理面不同构成部分各向异性的研究[J]. 土工基础，2022，36(1)：29–32.(WANG Rongda，LIU Tiexin，ZHANG Kai. Study on the anisotropy of different components of rock mass joint surface[J]. Soil Engineering and Foundation，2022，36(1)：29–32.(in Chinese))
[31] 洪陈杰，黄 曼，夏才初，等. 岩体结构面各向异性变异系数的尺寸效应研究[J]. 岩土力学，2020，41(6)：2 098–2 109.(HONG Chenjie，HUANG Man，XIA Caichu，et al. Study of size effect on the anisotropic variation coefficient of rock joints[J]. Rock and Soil Mechanics，2020，41(6)：2 098–2 109.(in Chinese))
[32] BARTON N. A relationship between joint roughness and joint shear strength[C]// Proceedings of the International Symposium on Rock Fracture. Nancy，France：[s. n]，1971：1–8.
[33] BARTON N，CHOUBEY V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics and Rock Engineering，1977，10(1/2)：1–54.
[34] ODLING N E. Natural fracture profiles，fractal dimension and joint roughness coefficients[J]. Rock Mechanics and Rock Engineering，1994，27(3)：135–153.
[35] WANG P T，YANG T H，XU T，et al. Numerical analysis on scale effect of elasticity strength and failure patterns of jointed rock masses[J]. Geosciences Journal，2016，20(4)：539–549.
[36] DONG L，TONG X，MA J. Quantitative investigation of tomographic effects in abnormal regions of complex structures[J]. Engineering，2021，7(7)：1 011–1 022.
[37] DONG L，TONG X，HU Q，et al. Empty region identification method and experimental verification for the two-dimensional complex structure[J]. International Journal of Rock Mechanics and Mining Sciences，2021，147：104885.
[38] DONG L，CHEN Y，SUN D，et al. Implications for rock instability precursors and principal stress direction from rock acoustic experiments[J]. International Journal of Mining Science and Technology，2021，31(5)：789–798.
[39] 刘洪磊，王培涛，杨天鸿，等. 基于离散元方法的花岗岩单轴压缩破裂过程的声发射特性[J]. 煤炭学报，2015，40(8)：1 790–1 795. (LIU Honglei，WANG Peitao，YANG Tianhong，et al. Mechanical characteristics of granite under uniaxial compressive and AE monitoring test using particle flow code[J]. Journal of China Coal Society，2015，40(8)：1 790–1 795.(in Chinese))
[40] 田 勇，俞然刚，张 尹，等. 声发射特征在灰岩损伤识别及定量评估中的应用[J]. 工程科学与技术，2020，52(3)：115–122.(TIAN Yong，YU Rangang，ZHANG Yi，et al. Application of acoustic emission characteristics in damage identification and quantitative evaluation of limestone[J]. Advanced Engineering Sciences，2020，52(3)：115–122. (in Chinese))
[41] 邹宗兴，唐辉明，徐 伟，等. 三轴试验莫尔包络线模型拟合[J]. 地质科技情报，2011，30(3)：118–122.(ZOU Zongxing，TANG Huiming，XU Wei，et al. Moire envelope model fitting of triaxial test[J]. Geological Science and Technology Information，2011，30(3)：118–122.(in Chinese))
2023, Vol. 42 
