A new rock brittleness index based on energy evolution and crack development characteristics

Abstract

Reliable evaluation of rock brittleness is crucial for understanding rock failure behavior and ensuring the stability and safety of underground mining and rock engineering. However, no universally accepted index currently exists, and many proposed indices exhibit limitations in terms of reliability, physical interpretation, and applicability across different rock types and stress conditions. This study introduces a novel brittleness index that integrates both energy dissipation and crack development characteristics, offering a more comprehensive and physically grounded assessment of rock brittleness. The new index is established based on the correlation between energy dissipation, acoustic emission parameters, and brittleness, providing a more robust framework that better reflects the fundamental mechanisms of brittle failure. To validate the new brittleness index, triaxial cyclic loading damage-controlled tests were performed on two representative rock types: siltstone (a porous, weakly cemented rock) and granite (a dense, crystalline rock). These tests generated quantitative data on energy evolution and acoustic emission parameters, which were analyzed to investigate brittleness evolution under varying confining pressures. The results show that the new brittleness index exhibits a nonlinear, monotonic decrease with increasing confining pressure for both siltstone and granite. Furthermore, under identical confining pressure conditions, granite exhibits higher brittleness index values than siltstone. Overall, the new brittleness index demonstrates strong stability and applicability, making it suitable for rocks with different characteristics and stress environments.

Keywords

Mining engineering / Rock brittleness / Plastic dissipation energy / Damage dissipation energy / Acoustic emission / Triaxial cyclic loading

References

[1] A. Morley, Strength of Materials, tenth ed., Longmans, Green, London, 1944.

[2] M. Hetenyi, Handbook of Experimental Stress Analysis, first ed., Wiley, New York, 1950.

[3] J.G. Ramsay, Folding and Fracturing of Rocks, first ed., McGraw-Hill, London, 1967.

[4] B.R. Lawn, D.B. Marshall, Hardness, toughness, and brittleness: an indentation analysis, J. Am. Ceram. Soc. 62 (7-8) (1979) 347-350.

[5] F.Z. Meng, H. Zhou, C.Q. Zhang, R.C. Xu, J.J. Lu, Evaluation methodology of brittleness of rock based on post-peak stress-strain curves, Rock Mech. Rock Eng. 48 (5) (2015) 1787-1805.

[6] L. Tutluoğlu, İ.F. Öge, C. Karpuz, Relationship between pre-failure and post-failure mechanical properties of rock material of different origin, Rock Mech. Rock Eng. 48 (1) (2015) 121-141.

[7] L.F. Liu, M. Guan, H.T. Zhao, H.P. Wang, T.Y. Gao, Y. Jiang, Brittleness evaluation method of shale based on confining pressure correction, Acta Geophys. 70 (1) (2022) 211-223.

[8] C. Ai, J. Zhang, Y.W. Li, J. Zeng, X.L. Yang, J.G. Wang, Estimation criteria for rock brittleness based on energy analysis during the rupturing process, Rock Mech. Rock Eng. 49 (12) (2016) 4681-4698.

[9] Y. Zhang, X.T. Feng, C.X. Yang, Q. Han, Z.F. Wang, R. Kong, Evaluation method of rock brittleness under true triaxial stress states based on pre-peak deformation characteristic and post-peak energy evolution, Rock Mech. Rock Eng. 54 (3) (2021) 1277-1291.

[10] H. Munoz, A. Taheri, E.K. Chanda, Fracture energy-based brittleness index development and brittleness quantification by pre-peak strength parameters in rock uniaxial compression, Rock Mech. Rock Eng. 49 (12) (2016) 4587-4606.

[11] I.R. Kivi, M. Ameri, H. Molladavoodi, Shale brittleness evaluation based on energy balance analysis of stress-strain curves, J. Petrol. Sci. Eng. 167 (2018) 1-19.

[12] Z. Zhao, X.P. Zhou, Digital microscopic multiphase heterogeneity representation and its effects on micromechanics and cracking behaviors of geomaterials, Rock Mech. Rock Eng. 57 (9) (2024) 7443-7459.

[13] Z. Zhao, Y.D. Shou, X.P. Zhou, Microscopic cracking behaviors of rocks under uniaxial compression with microscopic multiphase heterogeneity by deep learning, Int. J. Min. Sci. Technol. 33 (4) (2023) 411-422.

[14] Z. Zhao, H.F. Lu, Deep learning interprets failure process of coal reservoir during CO₂-desorption by 3D reconstruction techniques , Energy 282 (2023) 128802.

[15] D.M. Jarvie, R.J. Hill, T.E. Ruble, R.M. Pollastro, Unconventional shale-gas systems: The Mississippian Barnett Shale of north-central Texas as one model for thermogenic shale-gas assessment, AAPG Bull. 91 (4) (2007) 475-499.

[16] R. Rickman, M. Mullen, E. Petre, B. Grieser, D. Kundert, A practical use of shale petrophysics for stimulation design optimization: All shale plays are not clones of the Barnett shale, in: SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 2008.

[17] D. Buller, S. Hughes, J. Market, E. Petre, D. Spain, T. Odumosu, Petrophysical evaluation for enhancing hydraulic stimulation in horizontal shale gas wells, in: SPE Annual Technical Conference and Exhibition, Florence, Italy, 2010.

[18] V. Hucka, B. Das, Brittleness determination of rocks by different methods, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 11 (10) (1974) 389-392.

[19] M.K. Özfırat, H. Yenice, F. Şimşir, O. Yaralı, A new approach to rock brittleness and its usability at prediction of drillability, J. Afr. Earth Sci. 119 (2016) 94-101.

[20] R. Altindag, Correlation of specific energy with rock brittleness concepts on rock cutting, J. S. Afr. Inst. Min. Metall. 103 (3) (2003) 163-171.

[21] R. Altindag, Assessment of some brittleness indexes in rock-drilling efficiency, Rock Mech. Rock Eng. 43 (3) (2010) 361-370.

[22] S. Yagiz, C. Gokceoglu, Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness, Expert. Syst. Appl. 37 (3) (2010) 2265-2272.

[23] A.E. Dursun, M.K. Gokay, Cuttability assessment of selected rocks through different brittleness values, Rock. Mech. Rock. Eng. 49 (4) (2016) 1173-1190.

[24] A. Tarokh, J. Peng, A. Fakhimi, J.F. Labuz, Evaluation of brittleness from spalling and bending tests, in: the 50th U.S. Rock Mechanics/Geomechanics Symposium, Houston, Texas, USA, 2016.

[25] Z.S. Liu, Z.D. Sun, New brittleness indexes and their application in shale/clay gas reservoir prediction, Petrol. Explor. Dev. 42 (1) (2015) 129-137.

[26] A.W. Bishop, The influence of progressive failure on the choice of the method of stability analysis, Géotechnique 21 (2) (1971) 168-172.

[27] V. Hajiabdolmajid, P. Kaiser, Brittleness of rock and stability assessment in hard rock tunneling, Tunn. Undergr. Space Technol. 18 (1) (2003) 35-48.

[28] X.C. Gong, C.C. Sun, A new tablet brittleness index, Eur. J. Pharm. Biopharm. 93 (2015) 260-266.

[29] Y. Wang, C.H. Li, Y.Z. Hu, X.L. Zhou, A new method to evaluate the brittleness for brittle rock using crack initiation stress level from uniaxial stress-strain curves, Environ. Earth Sci. 76 (23) (2017) 799.

[30] Y.J. Xia, L.C. Li, C.A. Tang, X.Y. Li, S. Ma, M. Li, A new method to evaluate rock mass brittleness based on stress-strain curves of class I, Rock Mech. Rock Eng. 50 (5) (2017) 1123-1139.

[31] J.C. Guo, Z.H. Zhao, S.G. He, H. Liang, Y.X. Liu, A new method for shale brittleness evaluation, Environ. Earth Sci. 73 (10) (2015) 5855-5865.

[32] Z.Q. Guo, M. Chapman, X.Y. Li, Exploring the effect of fractures and microstructure on brittleness index in the Barnett Shale, in: SEG Technical Program Expanded Abstracts 2012, Society of Exploration Geophysicists, 2012.

[33] X.Y. Luan, B.R. Di, J.X. Wei, X.Y. Li, K.R. Qian, J.Y. Xie, P.B. Ding, Laboratory measurements of brittleness anisotropy in synthetic shale with different cementation, in: SEG Technical Program Expanded Abstracts 2014, Society of Exploration Geophysicists, 2014.

[34] S.Z. Sun, K.N. Wang, P. Yang, X.G. Li, J.X. Sun, B.H. Liu, K. Jin, Integrated prediction of shale oil reservoir using pre-stack algorithms for brittleness and fracture detection, in: International Petroleum Technology Conference, Beijing, China, 2013.

[35] J.J. Chen, G.Z. Zhang, H.Z. Chen, X.Y. Yin, The construction of shale rock physics effective model and prediction of rock brittleness, in: SEG Technical Program Expanded Abstracts 2014, Society of Exploration Geophysicists, 2014.

[36] X.R. Huang, J.P. Huang, Z.C. Li, Q.Y. Yang, Q.X. Sun, W. Cui, Brittleness index and seismic rock physics model for anisotropic tight-oil sandstone reservoirs, Appl. Geophys. 12 (1) (2015) 11-22.

[37] X.P. Yue, T. Wen, Y. Gao, W.J. Jia, Y.K. Wang, M.Y. Hu, Evaluation method for determining rock brittleness in consideration of plastic deformation in pre-peak and failure energy in post-peak, Appl. Sci. 13 (23) (2023) 12711.

[38] X.G. Zhao, M. Cai, A mobilized dilation angle model for rocks, Int. J. Rock Mech. Min. Sci. 47 (3) (2010) 368-384.

[39] H.R. Renani, C.D. Martin, Cohesion degradation and friction mobilization in brittle failure of rocks, Int. J. Rock Mech. Min. Sci. 106 (2018) 1-13.

[40] S.J. Miao, Z.J. Liu, X.G. Zhao, L.K. Ma, Y.W. Zheng, D.H. Xia, Plastic and damage energy dissipation characteristics and damage evolution of Beishan granite under triaxial cyclic loading, Int. J. Rock Mech. Min. Sci. 174 (2024) 105644.

[41] F.Q. Gong, J.Y. Yan, X.B. Li, S. Luo, A peak-strength strain energy storage index for rock burst proneness of rock materials, Int. J. Rock Mech. Min. Sci. 117 (2019) 76-89.

[42] F.Q. Gong, P.L. Zhang, K. Du, A novel staged cyclic damage constitutive model for brittle rock based on linear energy dissipation law: Modelling and validation, Rock Mech. Rock Eng. 55 (10) (2022) 6249-6262.

[43] M. Nouri, G. Khanlari, B. Rafiei, V. Sarfarazi, M. Zaheri, Estimation of brittleness indexes from petrographic characteristics of different sandstone types (Cenozoic and Mesozoic sandstones), Markazi Province, Iran, Rock Mech. Rock Eng. 55 (4) (2022) 1955-1995.

[44] V. Sarfarazi, M.F. Maraji, H. Haeri, Crack growth properties in granite specimens consisting non-persistent joint under punch shear through test, Anal. Numer. Method. Min. Eng. 12 (33) (2021) 17-26.

[45] J. Jin, P. Cao, Y. Chen, C.Z. Pu, D.W. Mao, X. Fan, Influence of single flaw on the failure process and energy mechanics of rock-like material, Comput. Geotech. 86 (2017) 150-162.

[46] L. Qiao, L. Chen, G. Dasgupta, Q.W. Li, Y. Li, Surface characterization and frictional energy dissipation characteristics of deep granite under high stress conditions, Rock Mech. Rock Eng. 52 (5) (2019) 1577-1589.

[47] Z.J. Liu, S.J. Miao, M.C. Liang, P.J. Yang, Z.Q. Zhao, N.D. Chang, Characteristics and association mechanism of energy dissipation and crack development in siltstone under triaxial cyclic loading and unloading, Rock Mech. Rock Eng. 57 (12) (2024) 10399-10425.

[48] D. Lefebvre, F. Ellyin, Cyclic response and inelastic strain energy in low cycle fatigue, Int. J. Fatigue 6 (1) (1984) 9-15.

[49] Z.M. Li, T. Liu, Z.L. Cui, Study on elastic-plastic damage constitutive model of frozen soil based on energy dissipation theory, Appl. Mech. Mater. 423-426 (2013) 1187-1192.

[50] J. Vilhelm, V. Rudajev, T. Lokajíček, R. Živor, Application of autocorrelation analysis for interpreting acoustic emission in rock, Int. J. Rock Mech. Min. Sci. 45 (7) (2008) 1068-1081.

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

[52] X.L. Liu, Z. Liu, X.B. Li, F.Q. Gong, K. Du, Experimental study on the effect of strain rate on rock acoustic emission characteristics, Int. J. Rock Mech. Min. Sci. 133 (2020) 104420.

[53] A.M. Dziewonski, T.A. Chou, J.H. Woodhouse, Determination of earthquake source parameters from waveform data for studies of global and regional seismicity, J. Geophys. Res. 86 (B4) (1981) 2825-2852.

[54] C.C. Graham, S. Stanchits, I.G. Main, G. Dresen, Comparison of polarity and moment tensor inversion methods for source analysis of acoustic emission data, Int. J. Rock Mech. Min. Sci. 47 (1) (2010) 161-169.

[55] J. Wang, W.D. Song, S. Cao, Y.Y. Tan, Mechanical properties and failure modes of stratified backfill under triaxial cyclic loading and unloading, Int. J. Min. Sci. Technol. 29 (5) (2019) 809-814.

[56] F. Chen, Z.Q. Sun, J.C. Xu, J.Y. Zhang, A composite material model for investigation of micro-fracture mechanism of brittle rock subjected to uniaxial compression, J. Cent. South Univ. Technol. 8 (4) (2001) 258-262.

[57] X.Z. Li, H.W. Yan, X. Che, A micromechanics-based model of direct tensile fracture in brittle rocks under confining pressure, Int. J. Geomech. 23 (5) (2023) 04023040.

[58] M.Z. Yang, H.X. Huang, Y. Yang, Durability prediction of brittle rocks based on type-I crack extension theory, Theor. Appl. Fract. Mech. 115 (2021) 103044.

[59] X.P. Zhou, Y.J. Lian, L.N.Y. Wong, F. Berto, Understanding the fracture behavior of brittle and ductile multi-flawed rocks by uniaxial loading by digital image correlation, Eng. Fract. Mech. 199 (2018) 438-460.

[60] H. Zhang, Z.Z. Wang, Z.L. Song, Y.Z. Zhang, T.T. wang, W.C. Zhao, Acoustic emission characteristics of different brittle rocks and its application in brittleness evaluation, Geomech. Geophys. Geo-Energ. Geo-Resour. 7 (2) (2021) 48.

[61] Q.L. Yao, T. Chen, C.J. Tang, M. Sedighi, S.W. Wang, Q.X. Huang, Influence of moisture on crack propagation in coal and its failure modes, Eng. Geol. 258 (2019) 105156.

[62] H. Wang, M. Fall, S.J. Miao, Characteristics of fracture changes and fatigue failure signals for siltstone under cyclic loading, Int. J. Rock Mech. Min. Sci. 174 (2024) 105645.

[63] L.J. Dong, Y.H. Zhang, S.J. Bi, J. Ma, Y.H. Yan, H. Cao, Uncertainty investigation for the classification of rock micro-fracture types using acoustic emission parameters, Int. J. Rock Mech. Min. Sci. 162 (2023) 105292.

[64] J. Bi, Y. Zhao, Z.J. Wu, J.S. Li, C.L. Wang, Research on crack classification method and failure precursor index based on RA-AF value of brittle rock, Theor. Appl. Fract. Mech. 129 (2024) 104179.

[65] C.D. Martin, N.A. Chandler, The progressive fracture of Lac du Bonnet granite, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (6) (1994) 643-659.

[66] M.M. He, B.Q. Huang, C.H. Zhu, Y.S. Chen, N. Li, Energy dissipation-based method for fatigue life prediction of rock salt, Rock Mech. Rock Eng. 51 (5) (2018) 1447-1455.

[67] Q.B. Meng, J.F. Liu, B.X. Huang, Z.Z. Zhang, J.K. Long, J.Y. Wu, Experimental analysis of the height-diameter ratio effect of rock energy under uniaxial cyclic loading-unloading conditions, Bull. Eng. Geol. Environ. 82 (7) (2023) 283.

[68] S. Pagliara, R. Thendiyath, M. Palermo, Energy dissipation over large-scale roughness for both transition and uniform flow conditions, Int. J. Civ. Eng. 13 (3) (2015) 341-346.

[69] W. Yao, Y.Y. Cai, J. Yu, J.F. Zhou, S.Y. Liu, B.X. Tu, Experimental and numerical study on mechanical and cracking behaviors of flawed granite under triaxial compression, Measurement 145 (2019) 573-582.

[70] M.B. Gao, T.B. Li, Y. Gao, Y. Zhang, Q.W. Yang, Z.H. He, Q.Q. He, A method to evaluation rock brittleness based on statistical damage constitutive parameters, Front. Earth Sci. 10 (2023) 1020834.