Abstract：The complex failure process of natural rock masses is a primary factor contributing to the unpredictability of natural disasters. To gain a deeper understanding of rock mass failure modes, we propose a numerical model that simulates the mixed tension-shear failure process of rocks, based on the ordinary state-based peridynamics method. This model integrates the maximum principal stress criterion and the Mohr-Coulomb criterion into the material damage identification process. The propagation paths of tensile and shear cracks during rock failure are determined by evaluating the ratio of fracture energy released from different failure bonds to the total fracture energy. Additionally, corresponding quantification parameters are introduced to characterize crack propagation. The model’s effectiveness in identifying crack propagation is validated through uniaxial compression tests on rock samples with prefabricated cracks. Finally, we investigate the effects of confining pressure, inclination angle of prefabricated cracks, and the height-to-diameter ratio on crack propagation morphology, peak strength, and structural damage indices of the rock. The results demonstrate that confining pressure suppresses the expansion of tensile cracks. As confining pressure increases, the failure mode of rock samples gradually transitions from tensile splitting failure to mixed tension-shear failure, and ultimately to shear failure, significantly increasing peak strength. The inclination angle of prefabricated cracks influences peak strength by altering crack propagation morphology; when the inclination angle is 30°, the rock sample exhibits more tensile cracks, resulting in lower peak compressive strength. Conversely, at an inclination angle of 90°, the increase in shear cracks significantly enhances peak compressive strength. A decrease in the height-to-diameter ratio of the rock sample prolongs the coplanar shear crack extension path and increases the number of tensile cracks. Simultaneously, the friction effect at the end face is significantly enhanced, suppressing tensile crack expansion and consequently improving compressive strength.
华 涛，申林方，王志良，李松波，陈 骞，李 泽. 基于近场动力学方法岩石拉伸–剪切混合破坏过程数值计算[J]. 岩石力学与工程学报, 2025, 44(S2): 258-269.
HUA Tao, SHEN Linfang, WANG Zhiliang, LI Songbo, CHEN Qian, LI Ze. Numerical simulation of rock tension-shear mixed failure process based on peridynamics method. , 2025, 44(S2): 258-269.
[1] WONG L，EINSTEIN H. Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences，2009，46(2)：239–249.
[2] SHEN B，STEPHANSSON O. Numerical analysis of mixed mode I and Mode II fracture propagation[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts，1993，30(7)：861–867.
[3] 彭 捷，李永红，刘海南，等. 榆神矿区大砭窑煤矿地面塌陷与地裂缝发育规律[J]. 中国煤炭，2015，41(10)：37–41.(PENG Jie，LI Yonghong，LIU Hainan，et al. Development law of surface collapse and ground fractures in Dabianyao Coal Mine in Yulin—Shenmu mining area[J]. China Coal，2015，41(10)：37–41.(in Chinese))
[4] ALLÈGRE C J，LE MOUEL J L，PROVOST A. Scaling rules in rock fracture and possible implications for earthquake prediction[J]. Nature，1982，297(5861)：47–49.
[5] 赵阳升. 岩体力学发展的一些回顾与若干未解之百年问题[J]. 岩石力学与工程学报，2021，40(7)：1 297–1 336.(ZHAO Yangsheng. Retrospection on the development of rock mass mechanics and the summary of some unsolved centennial problems[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(7)：1 297–1 336.(in Chinese))
[6] 王苏生，杨圣奇，田文岭，等. 预制裂隙岩石裂纹扩展相场模拟方法研究[J]. 岩石力学与工程学报，2023，42(2)：365–377.(WANG Susheng，YANG Shengqi，TIAN Wenling，et al. Research on phase-field simulation method of crack propagation of rock with pre-existing fissures[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(2)：365–377.(in Chinese))
[7] LIU T，LIN B，YANG W. Mechanical behavior and failure mechanism of pre-cracked specimen under uniaxial compression[J]. Tectonophysics，2017，712：330–343.
[8] PAN W，WANG X，LIU Q，et al. Non-parallel double-crack propagation in rock-like materials under uniaxial compression[J]. International Journal of Coal Science and Technology，2019，6(3)：372–387.
[9] 张 科，刘享华，李 昆，等. 含孔多裂隙岩石力学特性与破裂分形维数相关性研究[J]. 岩石力学与工程学报，2018，37(12)：2 785– 2 794.(ZHANG Ke，LIU Xianghua，LI Kun，et al. Investigation on the correlation between mechanical characteristics and fracturing fractal dimension of rocks containing a hole and multi-flaws[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(12)：2 785– 2 794.(in Chinese))
[10] HAN Z，LI J，LI D，et al. 3D spatial fracture behavior of sandstone containing a surface flaw under uniaxial compression[J]. International Journal of Rock Mechanics and Mining Sciences，2023，171：105583.
[11] LI J，DUAN K，MENG H，et al. On the mechanical properties and failure mechanism of conglomerate specimens subjected to triaxial compression tests[J]. Rock Mechanics and Rock Engineering，2023，56(2)：973–995.
[12] 刘之喜，孟祥瑞，赵光明，等. 真三轴压缩下砂岩的能量和损伤分析[J]. 岩石力学与工程学报，2023，42(2)：327–341.(LIU Zhixi，MENG Xiangrui，ZHAO Guangming，et al. Energy and damage analysis of sandstone under true triaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(2)：327–341.(in Chinese))
[13] 李地元，陈昱达. 单轴压缩下岩石裂纹扩展应力阈值识别与验证[J]. 岩石力学与工程学报，2023，42(增1)：3 121–3 130.(LI Diyuan，CHEN Yuda. Identification and verification of stress threshold for rock crack propagation under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(Supp.1)：3 121–3 130.(in Chinese))
[14] ZHOU X P，WANG Y T，ZHANG J Z，et al. Fracturing behavior study of three-flawed specimens by uniaxial compression and 3D digital image correlation：sensitivity to brittleness[J]. Rock Mechanics and Rock Engineering，2019，52(3)：691–718.
[15] ZHANG W，GUO W，WANG Z. Influence of lateral pressure on mechanical behavior of different rock types under biaxial compression[J]. Journal of Central South University，2022，29(11)：3 695–3 705.
[16] BI J，NING L，ZHAO Y，et al. Analysis of the microscopic evolution of rock damage based on real-time nuclear magnetic resonance[J]. Rock Mechanics and Rock Engineering，2023，56(5)：3 399–3 411.
[17] 郑安兴，罗先启，陈振华. 基于扩展有限元法的岩体水力劈裂耦合模型[J]. 岩土力学，2019，40(2)：799–808.(ZHENG Anxing，LUO Xianqi，CHEN Zhenhua. Hydraulic fracturing coupling model of rock mass based on extended finite element method[J]. Rock and Soil Mechanics，2019，40(2)：799–808.(in Chinese))
[18] CAO Y，WANG W，SHEN W，et al. A new hybrid phase-field model for modeling mixed-mode cracking process in anisotropic plastic rock-like materials[J]. International Journal of Plasticity，2022，157：103395.
[19] ROY P，PATHRIKAR A，DEEPU S P，et al. Peridynamics damage model through phase field theory[J]. International Journal of Mechanical Sciences，2017，128：181–193.
[20] BIE Y，REN H，YAN H，et al. The unified nonlocal peridynamics- based phase-field damage theory[J]. Theoretical and Applied Fracture Mechanics，2023，126：103980.
[21] HAN Z，XIE S，LI D. Discrete element study on the mechanical behavior of flawed rocks under dynamic compression[J]. Theoretical and Applied Fracture Mechanics，2022，121：103516.
[22] MA G W，WANG X J，REN F. Numerical simulation of compressive failure of heterogeneous rock-like materials using SPH method[J]. International Journal of Rock Mechanics and Mining Sciences，2011，48(3)：353–363.
[23] SILLING S. Reformulation of elasticity theory for discontinuities and long-range forces[J]. Journal of the Mechanics and Physics of Solids，2000，48(1)：175–209.
[24] 刘造保，田 锋，周金鑫. 岩石脆性破坏全过程的准态基近场动力学方法[J]. 力学学报，2024，56(5)：1 395–1 410.(LIU Zaobao，TIAN Feng，ZHOU Jinxin. Quasi-state-based peridynamics method for the whole process of rock brittle failure[J]. Chinese Journal of Theoretical and Applied Mechanics，2024，56(5)：1 395–1 410.(in Chinese))
[25] ZHU Q，NI T. Peridynamic formulations enriched with bond rotation effects[J]. International journal of engineering science，2017，121：118–129.
[26] WANG Y，WU W. A bond-level energy-based peridynamics for mixed-mode fracture in rocks[J]. Computer Methods in Applied Mechanics and Engineering，2023，414：116169.
[27] ZHANG H，ZHANG X，QIAO P Z. A new peridynamic mixed-mode bond failure model for interface delamination and homogeneous materials fracture analysiss[J]. Computer Methods in Applied Mechanics and Engineering，2021，379：113728.
[28] ZHAO Y，ZHANG L，WANG W，et al. Cracking and stress-strain behavior of rock-like material containing two flaws under uniaxial compression[J]. Rock Mechanics and Rock Engineering，2016，49(7)：2 665–2 687.
[29] YANG S Q，JING H W. Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression[J]. International Journal of Fracture，2011，168(2)：227–250.
[30] MADENCI E，OTERKUS E. Peridynamic theory and its applications[M]. New York：Springer，2014：38–57.
[31] SILLING S，EPTON M，WECKNER J，et al. Peridynamic states and constitutive modeling[J]. Journal of Elasticity，2007，88(2)：151–184.
[32] SILLING S，LEBOUCQ R. Convergence of peridynamics to classical elasticity theory[J]. Journal of Elasticity，2008，93(1)：13–37.
[33] 李 铮，郭德平，周小平，等. 模拟岩石中裂纹扩展连接的近场动力学方法[J]. 岩土力学，2019，40(12)：4 711–4 721.(LI Zheng，GUO Deping，ZHOU Xiaoping，et al. Numerical simulation of crack propagation and coalescence using peridynamics[J]. Rock and Soil Mechanics，2019，40(12)：4 711–4 721.(in Chinese))
[34] SILLING S A，EPTON M，WECKNER O，et al. Peridynamic states and constitutive modeling[J]. Journal of Elasticity，2007，88(2)：151–184.
[35] MADENCI E，OTERKUS E. Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening[J]. Journal of the Mechanics and Physics of Solids，2016，86：192–219.
[36] WANG Y，WU W. A bond-level energy-based peridynamics for mixed-mode fracture in rocks[J]. Computer Methods in Applied Mechanics and Engineering，2023，414：116169.
[37] YANG S，YANG D，JING H. An experimental study of the fracture coalescence behaviour of brittle sandstone specimens containing three fissures[J]. Rock Mechanics and Rock Engineering，2012，45(4)：563–582.
[38] 潘鹏志，周 辉，冯夏庭. 加载条件对不同尺寸岩石单轴压缩破裂过程的影响研究[J]. 岩石力学与工程学报，2008，27(增2)：3 636–3 642. (PAN Pengzhi，ZHOU Hui，FENG Xiating. Research on effect of loading conditions on failure processes of rocks with different sizes under uniaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2008，27(Supp.2)：3 636–3 642.(in Chinese))
[39] CHEN M，ZANG C，DING Z，et al. Effects of confining pressure on deformation failure behavior of jointed rock[J]. Journal of Central South University，2022，29(4)：1 305–1 319.
[40] LIU L，LI H，LI X，et al. Full-field strain evolution and characteristic stress levels of rocks containing a single pre-existing flaw under uniaxial compression[J]. Bulletin of Engineering Geology and the Environment，2020，79(6)：3 145–3 161.
[41] ZHANG G，WANG M，LI X，et al. Micro-and macrocracking behaviors in granite and molded gypsum containing a single flaw[J]. Construction and Building Materials，2021，292：123452.
[42] TUNCAY E，ÖZCAN N T，KALENDER A. An approach to predict the length-to-diameter ratio of a rock core specimen for uniaxial compression tests[J]. Bulletin of Engineering Geology and the Environment，2019，78(7)：5 467–5 482.
[43] 朱其志，闵中泽，王岩岩，等. 粉砂岩三轴压缩试验中的试样尺寸效应研究[J]. 岩石力学与工程学报，2019，38(增2)：3 296–3 303. (ZHU Qizhi，MIN Zhongze，WANG Yanyan，et al. Study on the size effect of silty sandstone samples under conventional triaxial compression[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp. 2)：3 296–3 303.(in Chinese))
[44] QI M，ZHAO G，XU W，et al. Influence of height-diameter ratio on rock compressive failure characteristics and damage evolution law[J]. Energies，2022，15(15)：5 557.
2025, Vol. 44 
