Failure characteristics and the energy criterion of rock with a through-going joint under true-triaxial unloading conditions: Insights from the DEM model

Abstract

Excavation unloading damages rock masses, with preferential failure along geological defects in rock engineering, which may induce catastrophe geological hazards. It is important to study the failure of jointed rock under true-triaxial unloading conditions. 3D DEM true-triaxial unloading modeling tests on rock with through-going joint considering the contributing factors, that is, the joint inclination, the initial confining pressure, and the unloading point, were conducted to study the rock mechanical properties, cracking behaviors, and failure characteristics. Six typical rock failure modes were summarized based on the development of main cracks, and the associated cracking mechanisms were studied by analysis of the ratio of tensile crack to shear crack. An energy criterion determining whether unloading-induced rock failure occurs instantaneously was proposed by comparing the accumulated elastic strain energy at the unloading point in true-triaxial unloading simulations with the limit elastic strain energy stored in rocks in biaxial compression modeling tests. Furthermore, the strength characteristics and applicability of the Mogi–Coulomb failure criterion in describing the failure of specimens with through-going joint under true-triaxial unloading conditions were studied. This study provides some new insights into true-triaxial unloading-induced failure of jointed rock, which may be valuable for revealing the mechanism of rock instabilities influenced by geological defects in deep excavations.

Keywords

cracking behavior / energy criterion / joint / rock failure mode / true-triaxial unloading modeling test

References

[1] Al-Ajmi AM, Zimmerman RW. Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min Sci. 2005; 42(3): 431-439.

[2] Bozzano F, Lenti L, Martino S, Montagna A, Paciello A. Earthquake triggering of landslides in highly jointed rock masses: reconstruction of the 1783 Scilla rock avalanche (Italy). Geomorphology. 2011; 129(3): 294-308.

[3] Brady BHG, Brown ET. Rock Mechanics: For Underground Mining. 3rd ed. Springer Dordrecht; 2006.

[4] Chang C, Haimson B. A failure criterion for rocks based on true triaxial testing. Rock Mech Rock Eng. 2012; 45: 1007-1010.

[5] Cho N, Martin CD, Sego DC. A clumped particle model for rock. Int J Rock Mech Min Sci. 2007; 44(7): 997-1010.

[6] Du J, Huang X, Yang G, et al. UDEC modelling on dynamic response of rock masses with joint stiffness weakening attributed to particle crushing of granular fillings. Rock Mech Rock Eng. 2023; 56: 1823-1841.

[7] Fakhimi A, Villegas T. Application of dimensional analysis in calibration of adiscrete element model for rock deformation and fracture. Rock Mech Rock Eng. 2007; 40(2): 193-211.

[8] Fan W, Tang G, Han D, Yang H. An innovative test to study cracking behavior of fractured rock-like material under stepped excavation unloading. Bull Eng Geol Environ. 2023; 82: 461.

[9] Feng F, Chen S, Han Z, Golsanami N, Liang P, Xie Z. Influence of moisture content and intermediate principal stress on cracking behavior of sandstone subjected to true triaxial unloading conditions. Eng Fract Mech. 2023; 284: 109265.

[10] Feng G, Ma Q, He Z, et al. Time-delayed failure process of granite and its energy evolution and acoustic emission characteristics. Eng Fail Anal. 2024; 157: 107854.

[11] Feng G, Feng X, Chen B, Xiao Y. Microseismic sequences associated with rockbursts in the tunnels of the Jinping II hydropower station. Int J Rock Mech Min Sci. 2015; 80: 89-100.

[12] Gao Y, Feng X, Wang Z, Zhang X. Strength and failure characteristics of jointed marble under true triaxial compression. Bull Eng Geol Environ. 2020; 79: 891-905.

[13] Gong F, Dai J, Xu L. A strength-stress coupling criterion for rockburst: inspirations from 1114 rockburst cases in 197 underground rock projects. Tunn Undergr Space Technol. 2023; 142: 105396.

[14] Gong F, Si X, Li X, Wang S. Experimental investigation of strain rockburst in circular caverns under deep three-dimensional high-stress conditions. Rock Mech Rock Eng. 2018; 52: 1459-1474.

[15] Gong F, Wu W, Ren L. Rockburst process and strength-weakening effect of the high-stress circular tunnel under internal unloading. J Rock Mech Geotech Eng. 2022; 15(4): 864-885.

[16] Gong F, Yan J, Luo S, Li X. Investigation on the linear energy storage and dissipation laws of rock materials under uniaxial compression. Rock Mech Rock Eng. 2019; 52: 4237-4255.

[17] Hadjigeorgiou J, Esmaieli K, Grenon M. Stability analysis of vertical excavations in hard rock by integrating a fracture system into a PFC model. Tunn Undergr Space Technol. 2009; 24(3): 296-308.

[18] Hatzor Y, He B, Feng X. Scaling rockburst hazard using the DDA and GSI methods. Tunn Undergr Space Technol. 2017; 70: 343-362.

[19] He M, Ding M, Yuan Z, Zhao J, Luo B, Ma X. Numerical simulation of rock bursts triggered by blasting disturbance for deep-buried tunnels in jointed rock masses. Comput Geotech. 2023; 161: 105609.

[20] He M, Wang Q. Rock dynamics in deep mining. Int J Min Sci Technol. 2023; 33(9): 1065-1082.

[21] He M, Miao J, Feng J. Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions. Int J Rock Mech Min Sci. 2010; 47(2): 286-298.

[22] He M, Nie W, Zhao Z, Guo W. Experimental investigation of bedding plane orientation on the rockburst behavior of sandstone. Rock Mech Rock Eng. 2012; 45: 311-326.

[23] Hu H, Lu Y, Xia B, Luo Y, Peng J, Li Y. Damage characteristics of sandstone with different crack angles subjected to true triaxial cyclic loading and unloading. Theor Appl Fract Mech. 2022; 121: 103444.

[24] Hu L, Feng X, Xiao Y, et al. Effects of structural planes on rockburst position with respect to tunnel cross-sections: a case study involving a railway tunnel in China. Bull Eng Geol Environ. 2020; 79: 1061-1081.

[25] Ji H, Liu R, Yu L, Zhu X. Influence of joint inclination on mechanical behaviors of shales during unloading-induced slip processes. Int J Rock Mech Min Sci. 2023; 170: 105487.

[26] Jiang H, Yang Y, Chorzepa MG. A generalized Mogi–Coulomb failure criterion for rocks. Int J Geomech. 2023; 23(4): 04023024.

[27] Keneti A, Sainsbury BA. Review of published rockburst events and their contributing factors. Eng Geol. 2018; 246: 361-373.

[28] Li J, Liu D, He M, Guo Y. True triaxial experimental study on the variation characteristics of rockburst with the number of fast unloading surfaces. Rock Mech Rock Eng. 2023; 56(8): 5585-5606.

[29] Li X, Feng F, Li D, Du K, Ranjith PG, Rostami J. Failure characteristics of granite influenced by sample height-to-width ratios and intermediate principal stress under true-triaxial unloading conditions. Rock Mech Rock Eng. 2018; 51: 1321-1345.

[30] Liang D, Zhang N, Liu H, Fukuda D, Rong H. Hybrid finite-discrete element simulator based on GPGPU-parallelized computation for modelling crack initiation and coalescence in sandy mudstone with prefabricated cross-flaws under uniaxial compression. Eng Fract Mech. 2021; 247: 107658.

[31] Liu D, Sun J, Li R, et al. Experimental study on the effect of unloading rate on gneiss rockburst. J Rock Mech Geotech Eng. 2024; 16(6): 2064-2076.

[32] Liu F, Ma T, Tang C, Chen F. Prediction of rockburst in tunnels at the Jinping II hydropower station using microseismic monitoring technique. Tunn Undergr Space Technol. 2018; 81: 480-493.

[33] Liu S, Wang Z, Kou M, Zhang Y, Wang Y. Phase-field simulations of unloading failure behaviors in rock and rock-like materials. Theor Appl Fract Mech. 2023; 126: 103936.

[34] Lu W, Zhu Z, He Y, Que X. Strength characteristics and failure mechanism of a columnar jointed rock mass under uniaxial, triaxial, and true triaxial confinement. Rock Mech Rock Eng. 2021; 54: 2425-2439.

[35] Luo S, Gong F. Evaluation of energy storage and release potentials of highly stressed rock pillar from rockburst control perspectives. Int J Rock Mech Min Sci. 2023; 163: 105324.

[36] Manouchehrian A, Cai M. Numerical modeling of rockburst near fault zones in deep tunnels. Tunn Undergr Space Technol. 2018; 80: 164-180.

[37] Mogi K. Fracture and flow of rocks under high triaxial compression. J Geophys Res. 1971; 76(5): 1255-1269.

[38] Oreskes N, Shrader-Frechette K, Belitz K. Verification, validation, and confirmation of numerical models in the earth sciences. Science. 1994; 263(5147): 641-646.

[39] Peng S, Li X, Li C, Liang L, Huang L. Crack-closure behavior and stress-sensitive wave velocity of hard rock based on flat-joint model in particle-flow-code (PFC) modeling. Comput Geotech. 2024; 170: 106320.

[40] Potyondy DO, Cundall PA. A bonded-particle model for rock. Int J Rock Mech Min Sci. 2004; 41(8): 1329-1364.

[41] Ren J, Xiao M, Liu G. Rock macro–meso parameter calibration and optimization based on improved BP algorithm and response surface method in PFC 3D. Energies. 2022; 15(17): 6290.

[42] Scholtès L, Donzé FV. Modelling progressive failure in fractured rock masses using a 3D discrete element method. Int J Rock Mech Min Sci. 2012; 52: 18-30.

[43] Shang X, Zhou J, Liu F, Shen J, Liao X. A peridynamics study for the free-surface-assisted rock fragmentation caused by TBM disc cutters. Comput Geotech. 2023; 158: 105380.

[44] Si X, Li X, Gong F, Huang L, Liu X. Experimental investigation of failure process and characteristics in circular tunnels under different stress states and internal unloading conditions. Int J Rock Mech Min Sci. 2022; 154: 105116.

[45] Stead D, Wolter A. A critical review of rock slope failure mechanisms: the importance of structural geology. J Struct Geol. 2015; 74: 1-23.

[46] Su G, Li P, Xu H, Liu X. A two-step method for predicting rockburst using sound signals. Acta Geotech. 2023; 19: 273-303.

[47] Sun F, Guo J, Liu X, Zhang H. Strain rockburst evolution process under true triaxial condition with single face unloading due to tunnel excavation. Comput Geotech. 2023; 159: 105465.

[48] Trzeciak M, Sone H. Critical review of the Mogi failure criterion based on true-triaxial laboratory data analysis and theoretical considerations. Int J Rock Mech Min Sci. 2022; 159: 105220.

[49] Wang M, Lu Z, Zhao Y, Wan W. Peak strength, coalescence and failure processes of rock-like materials containing preexisting joints and circular holes under uniaxial compression: experimental and numerical study. Theoret Appl Fract Mech. 2023; 125: 103898.

[50] Wasantha PLP, Ranjith PG, Shao SS. Energy monitoring and analysis during deformation of bedded-sandstone: use of acoustic emission. Ultrasonics. 2014; 54(1): 217-226.

[51] Wong LNY, Li H. Numerical study on coalescence of two pre-existing coplanar flaws in rock. Int J Solids Struct. 2013; 50(22): 3685-3706.

[52] Wu T, Gao Y, Zhou Y, Li J. Experimental and numerical study on the interaction between holes and fissures in rock-like materials under uniaxial compression. Theoret Appl Fract Mech. 2020; 106: 102488.

[53] Xie H, Li L, Peng R, Ju Y. Energy analysis and criteria for structural failure of rocks. J Rock Mech Geotech Eng. 2009; 1: 11-20.

[54] Yao Z, Fang Y, Yu T, et al. Dynamic failure mechanism of tunnel under rapid unloading in jointed rockmass: a case study. Eng Fail Anal. 2022; 141: 106634.

[55] Zhang C, Feng XT, Zhou H, Qiu S, Wu W. Case histories of four extremely intense rockbursts in deep tunnels. Rock Mech Rock Eng. 2012; 45: 275-288.

[56] Zhang J, Du R, Chen Y, Huang Z. Experimental investigation of the mechanical properties and energy evolution of layered phyllite under uniaxial multilevel cyclic loading. Rock Mech Rock Eng. 2023; 56: 4153-4168.

[57] Zhang X, Wong LNY. Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach. Rock Mech Rock Eng. 2012; 45(5): 711-737.

[58] Zhang Y, Liu S, Kou M, Wang Z. Mechanical and failure characteristics of fissured marble specimens under true triaxial compression: insights from 3-D numerical simulations. Comput Geotech. 2020; 127: 103785.

[59] Zhou H, Meng F, Zhang C, Hu D, Yang F, Lu J. Analysis of rockburst mechanisms induced by structural planes in deep tunnels. Bull Eng Geol Environ. 2015; 74: 1435-1451.

[60] Zhu Z, Lu W, He Y, Que X. Experimental study on the strength failure characteristics of columnar jointed rock masses under three-dimensional stress. KSCE J Civil Eng. 2021; 25: 2411-2425.

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