Estimating crack closure and damage stress thresholds of rock during uniaxial compression based on axial plastic strain

Abstract

The quantitative determination of crack stress thresholds is of great significance to comprehend the deformation and failure of rock. In the study, we proposed a new model to estimate the crack closure and crack damage stress thresholds based on axial plastic strain. Then we compared the stress thresholds calculated by the proposed method with that by existing methods to validate the accuracy of our method. Finally, we discussed the effect of the error of elastic modulus on estimated stress thresholds. The results show that the crack closure and crack damage stresses predicted by the proposed method are very close to that by other methods. This indicates the proposed method can accurately identify the crack closure and crack damage stresses of rock materials. Moreover, the proposed method greatly reduces the dependence on elastic parameter and obtains the stress thresholds of crack closure and crack damage objectively. Based on the results, we developed a detailed flow chart for the proposed method to minimize the effect of elastic modulus.

Keywords

crack closure stress / crack damage stress / axial plastic strain / rock deformation / uniaxial compression

References

[1] BäckblomG, MartinC D. Recent experiments in hard rocks to study the excavation response: Implications for the performance of a nuclear waste geological repository. Tunnelling and Underground Space Technology, 1999, 14(3): 377-394 J]

[2] ZHOU Zi-long, WANG Pei-yu, CAI Xin, et al. Influence of water content on energy partition and release in rock failure: Implications for water-weakening on rock-burst proneness [J]. Rock Mechanics and Rock Engineering, 2023: 1–17. DOI: https://doi.org/10.1007/s00603-023-03379-z.

[3] DiederichsM S, KaiserP K, EberhardtE. Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(5): 785-812 J]

[4] DuJ-m, FangQ, WangG, et al. . Analytical solution of a circular lined tunnel with alterable mechanical property under hydrostatic stress and internal pressure. Journal of Central South University, 2022, 29(8): 2757-2770 J]

[5] LiX F, LiH B, LiuL W, et al. . Investigating the crack initiation and propagation mechanism in brittle rocks using grain-based finite-discrete element method. International Journal of Rock Mechanics and Mining Sciences, 2020, 127: 104219 J]

[6] XieS-j, LinH, ChenY-f, et al. . A new nonlinear empirical strength criterion for rocks under conventional triaxial compression. Journal of Central South University, 2021, 28(5): 1448-1458 J]

[7] WangH-q, ZhouZ-l, LiJ-p, et al. . Effects of earthquake on damage evolution and failure mechanism of key rock Pillars in underground engineering. Journal of Central South University, 2022, 29(9): 3125-3139 J]

[8] BieniawskiZ T. Mechanism of brittle fracture of rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1967, 4(4): 407-423 J]

[9] LajtaiE Z, CarterB J, Scott DuncanE J. Mapping the state of fracture around cavities. Engineering Geology, 1991, 31(3–4): 277-289 J]

[10] EberhardtE, SteadD, StimpsonB, et al. . Changes in acoustic event properties with progressive fracture damage. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(3–4): 71.e1-71.e12 J]

[11] ZhouZ-l, CaiX, LiX-b, et al. . Dynamic response and energy evolution of sandstone under coupled static-dynamic compression: Insights from experimental study into deep rock engineering applications. Rock Mechanics and Rock Engineering, 2020, 53(3): 1305-1331 J]

[12] MartinC D, ChandlerN A. The progressive fracture of Lac du Bonnet granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1994, 31(6): 643-659 J]

[13] DiederichsM S. Manuel rocha medal recipient rock fracture and collapse under low confinement conditions. Rock Mechanics and Rock Engineering, 2003, 36(5): 339-381 J]

[14] GongF-q, WuChen. Identifying crack compaction and crack damage stress thresholds of rock using load-unload response ratio (LURR)theory. Rock Mechanics and Rock Engineering, 2020, 53(2): 943-954 J]

[15] MartinC DThe strength of massive Lac du Bonnet granite around underground openings, 1993, Winnipeg, Manitoba, Canada, University of Manitoba[D]

[16] EberhardtE, SteadD, StimpsonB, et al. . Identifying crack initiation and propagation thresholds in brittle rock. Canadian Geotechnical Journal, 1998, 35(2): 222-233 J]

[17] CaiX, ChengC-q, ZhouZ-l, et al. . Rock mass watering for rock-burst prevention: Some thoughts on the mechanisms deduced from laboratory results. Bulletin of Engineering Geology and the Environment, 2021, 80(11): 8725-8743 J]

[18] TaheriA, ZhangY-b, MunozH. Performance of rock crack stress thresholds determination criteria and investigating strength and confining pressure effects. Construction and Building Materials, 2020, 243118263 J]

[19] KimJ S, LeeK S, ChoW J, et al. . A comparative evaluation of stress-strain and acoustic emission methods for quantitative damage assessments of brittle rock. Rock Mechanics and Rock Engineering, 2015, 48(2): 495-508 J]

[20] PengJ, CaiM, RongG, et al. . Stresses for crack closure and its application to assessing stress-induced microcrack damage. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(6): 1091-1100[J]

[21] ZhangZ-h, TangC-an. A novel method for determining the crack closure stress of brittle rocks subjected to compression. Rock Mechanics and Rock Engineering, 2020, 53(9): 4279-4287 J]

[22] XieS-j, HanZ-y, ShuR-h, et al. . A new method to determine the crack closure stress based on stress difference. Theoretical and Applied Fracture Mechanics, 2022, 119103337 J]

[23] ZhaoX G, CaiM, WangJ, et al. . Strength comparison between cylindrical and prism specimens of Beishan granite under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 2015, 7610-17 J]

[24] EberhardtE, StimpsonB, SteadD. Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mechanics and Rock Engineering, 1999, 32(2): 81-99 J]

[25] DuK, LiX-f, SuR, et al. . Shape ratio effects on the mechanical characteristics of rectangular prism rocks and isolated pillars under uniaxial compression. International Journal of Mining Science and Technology, 2022, 32(2): 347-362 J]

[26] TANG Ming-hao, WANG Gui-bin, CHEN Shi-wan, et al. An objective crack initiation stress identification method for brittle rock under compression using a reference line [J]. Rock Mechanics and Rock Engineering, 2021, 54(4). http://link.springer.com/article/10.1007/s00603-021-02479-y. DOI:https://doi.org/10.1007/s00603-021-02479-y.

[27] ZhaoX G, CaiM, WangJ, et al. . Objective determination of crack initiation stress of brittle rocks under compression using AE measurement. Rock Mechanics and Rock Engineering, 2015, 48(6): 2473-2484 J]

[28] ZhangX-p, WongL N Y, WangS-j, et al. . Engineering properties of quartz mica schist. Engineering Geology, 2011, 121(3–4): 135-149 J]

[29] AmannF, ButtonE A, EvansK F, et al. . Experimental study of the brittle behavior of clay shale in rapid unconfined compression. Rock Mechanics and Rock Engineering, 2011, 44(4): 415-430 J]

[30] ZhangB-c, LiangY-p, ZouQ-l, et al. . Determination of crack closure stress under constant-fatigue loading based on damage variable evolution. Theoretical and Applied Fracture Mechanics, 2022, 121: 103526 J]

[31] WuC, GongF-q, LuoYong. A new quantitative method to identify the crack damage stress of rock using AE detection parameters. Bulletin of Engineering Geology and the Environment, 2021, 80(1): 519-531 J]

[32] XueL, QinS-q, SunQ, et al. . A study on crack damage stress thresholds of different rock types based on uniaxial compression tests. Rock Mechanics and Rock Engineering, 2014, 47(4): 1183-1195 J]

[33] XieS-j, HanZ-y, LinHang. A quantitative model considering crack closure effect of rock materials. International Journal of Solids and Structures, 2022, 251111758 J]

[34] CaiM. Practical estimates of tensile strength and hoek-brown strength parameter m_i of brittle rocks. Rock Mechanics and Rock Engineering, 2010, 43(2): 167-184 J]

[35] ChangS H, LeeC I. Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(7): 1069-1086 J]

[36] ZhangX-p, LüG-g, ZhangQ, et al. . Uniaxial compression test for three stress thresholds of siliceous siltstone. Journal of Engineering Geology, 2020, 28(3): 441-449[J]

[37] PelletF L, KeshavarzM, Amini-HosseiniK. Mechanical damage of a crystalline rock having experienced ultra high deviatoric stress up to 1.7 GPa. International Journal of Rock Mechanics and Mining Sciences, 2011, 48(8): 1364-1368 J]

[38] ZhaoX G, CaiM, WangJ, et al. . Damage stress and acoustic emission characteristics of the Beishan granite. International Journal of Rock Mechanics and Mining Sciences, 2013, 64258-269 J]