Strength parameters evolution model based on energy principle in brittle rock under triaxial loading and unloading tests

Abstract

Understanding brittle rock strength evolution is crucial for deep underground engineering design, particularly for projects at burial depths exceeding 1000 m. While the Cohesion Weakening and Frictional Strengthening (CWFS) model effectively predicts brittle rock failure patterns, existing CWFS models rely predominantly on empirical fitting with complex parameter determination procedures. This study conducted extensive triaxial cyclic loading-unloading tests to investigate the distribution and evolution of elastic and dissipative energy. Through theoretical derivation, the physical meanings of parameters in the logistic dissipation energy evolution model were elucidated, demonstrating that these parameters are independent of confining pressure. A rock damage variable was defined as the ratio of cumulative dissipated energy to residual dissipated energy, which is expressed as a function of normalized plastic strain. Nonlinear evolution equations for cohesion and internal friction angle were then formulated based on the principle that strength parameter evolution corresponds to energy dissipation. Building upon these evolution equations, a modified triple-shear energy criterion (MTSEC) was established. Fitting results from triaxial loading-unloading tests under various confining pressures demonstrate excellent agreement between the MTSEC and experimental data. The proposed model was implemented in FLAC^3D software and validated through field measurements of excavation-induced damage zones in the Jinping deep underground laboratory.

Keywords

triaxial cyclic loading and unloading testing / brittle failure / energy evolution model / cohesion weakening friction strengthening (CWFS) / strength model

References

[1] Duan K, Ji Y-l, Wu W, et al. . Unloading-induced failure of brittle rock and implications for excavation-induced strain burst. Tunnelling and Underground Space Technology, 2019, 84: 495-506 J]

[2] Guo S-f, Qi S-w, Zhan Z-f, et al. . Plastic-strain-dependent strength model to simulate the cracking process of brittle rocks with an existing non-persistent joint. Engineering Geology, 2017, 231: 114-125 J]

[3] Kim J S, Lee K S, Cho W 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]

[4] Lee K H, Lee I M, Shin Y J. Brittle rock property and damage index assessment for predicting brittle failure in excavations. Rock Mechanics and Rock Engineering, 2012, 45(2): 251-257 J]

[5] Cai M, Kaiser P K, Tasaka Y, et al. . Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(5): 833-847 J]

[6] Cui J, Jiang Q, Feng X-t, et al. . Equivalent elastic compliance tensor for rock mass with multiple persistent joint sets: Exact derivation via modified crack tensor. Journal of Central South University, 2016, 23(6): 1486-1507 J]

[7] Hajiabdolmajid V, Kaiser P, Martin C D. Mobilised strength components in brittle failure of rock. Géotechnique, 2003, 53(3): 327-336 J]

[8] Rafiei Renani H, Martin C D. Cohesion degradation and friction mobilization in brittle failure of rocks. International Journal of Rock Mechanics and Mining Sciences, 2018, 106: 1-13 J]

[9] Walton G. Initial guidelines for the selection of input parameters for cohesion-weakening-friction-strengthening (CWFS) analysis of excavations in brittle rock. Tunnelling and Underground Space Technology, 2019, 84: 189-200 J]

[10] Cabezas R, Vallejos J. Nonlinear criterion for strength mobilization in brittle failure of rock and its extension to the tunnel scale. International Journal of Mining Science and Technology, 2022, 32(4): 685-705 J]

[11] Sinha S, Walton G. A progressive S-shaped yield criterion and its application to rock pillar behavior. International Journal of Rock Mechanics and Mining Sciences, 2018, 105: 98-109 J]

[12] Fu B, Hu L-h, Tang C-n. Experimental and numerical investigations on crack development and mechanical behavior of marble under uniaxial cyclic loading compression. International Journal of Rock Mechanics and Mining Sciences, 2020, 130: 104289 J]

[13] Walton G, Diederichs M S. A mine shaft case study on the accurate prediction of yield and displacements in stressed ground using lab-derived material properties. Tunnelling and Underground Space Technology, 2015, 49: 98-113 J]

[14] Perras M A, Wannenmacher H, Diederichs M S. Underground excavation behaviour of the queenston formation: Tunnel back analysis for application to shaft damage dimension prediction. Rock Mechanics and Rock Engineering, 2015, 48(4): 1647-1671 J]

[15] Edelbro C. Numerical modelling of observed fallouts in hard rock masses using an instantaneous cohesion-softening friction-hardening model. Tunnelling and Underground Space Technology, 2009, 24(4): 398-409 J]

[16] Renani H R, Martin C D. Modeling the progressive failure of hard rock pillars. Tunnelling and Underground Space Technology, 2018, 74: 71-81 J]

[17] Luo S, Gong F-q. Evaluation of energy storage and release potentials of highly stressed rock pillar from rockburst control perspectives. International Journal of Rock Mechanics and Mining Sciences, 2023, 163: 105324 J]

[18] Liu X-p, Jiang Q, Li S-j, et al. . Energy characteristics of progressive damage of Jinping marble under cyclic loading and unloading. Rock and Soil Mechanics, 2024, 45(8): 2373-2386 J]

[19] Zhang L-m, Cong Y, Meng F-z, et al. . Energy evolution analysis and failure criteria for rock under different stress paths. Acta Geotechnica, 2021, 16(2): 569-580 J]

[20] Xie H-p, Li L-y, Ju Y, et al. . Energy analysis for damage and catastrophic failure of rocks. Science China Technological Sciences, 2011, 54(S1): 199-209 J]

[21] Gong F-q, Zhang P-l, Luo S, et al. . Theoretical damage characterisation and damage evolution process of intact rocks based on linear energy dissipation law under uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 2021, 146: 104858 J]

[22] Ning J-g, Wang J, Jiang J-q, et al. . Estimation of crack initiation and propagation thresholds of confined brittle coal specimens based on energy dissipation theory. Rock Mechanics and Rock Engineering, 2018, 51(1): 119-134 J]

[23] Xie H-p, Li L-y, Peng R-d, et al. . Energy analysis and criteria for structural failure of rocks. Journal of Rock Mechanics and Geotechnical Engineering, 2009, 1(1): 11-20 J]

[24] Gong F-q, Yan J-y, Luo S, et al. . Investigation on the linear energy storage and dissipation laws of rock materials under uniaxial compression. Rock Mechanics and Rock Engineering, 2019, 52(11): 4237-4255 J]

[25] Gao H, Zheng Y-r, Feng X-t. Study on energy yield criterion of geomaterials. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(12): 2437-2443[J]

[26] Li Z, Zhou H, Hu D-w, et al. . Yield criterion for rocklike geomaterials based on strain energy and CMP model. International Journal of Geomechanics, 2020, 20(3): 04020013 J]

[27] Ulusay R. The ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 2007–2014, 2015, Cham. Springer International Publishing M]

[28] Xin J, Jiang Q, Zhai D, et al. . Shear-induced rockburst of double-tunnel rocks subjected to shear loading: A comparative analysis. Journal of Central South University, 2023, 30(12): 4207-4229 J]

[29] Tang M-y, Gao M-z, Li S-w, et al. . Failure behavior and energy evolution characteristics of deep roadway sandstone under different microwave irradiation modes. Journal of Central South University, 2023, 30(1): 214-226 J]

[30] Feng G-l, Ma J-g, Chen B-r, et al. . Microseismic energy and intensity criterion of rockburst in deep TBM tunnels: A case study of the Neelum-Jhelum hydropower project. Journal of Central South University, 2023, 30(5): 1695-1709 J]

[31] Gong F-q, Luo S, Jiang Q, et al. . Theoretical verification of the rationality of strain energy storage index as rockburst criterion based on linear energy storage law. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(6): 1737-1746 J]

[32] Miao S-j, Liu Z-j, Zhao X-g, et al. . Energy dissipation and damage characteristics of Beishan granite under cyclic loading and unloading. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(5): 928-938[J]

[33] Liu D-q, Guo Y-p, Li J-y, et al. . Experimental study on damage and failure energy evolution of brittle rocks under uniaxial compression. Journal of Engineering Geology, 2023, 31(3): 843-853[J]

[34] Alidaryan M, Khosravi M H, Bahaaddini M, et al. . Mobilization of cohesion and friction angle of intact rocks in the shearing process. Rock Mechanics and Rock Engineering, 2023, 56(11): 8221-8233 J]

[35] Taheri A, Zhang Y-b, Munoz H. Performance of rock crack stress thresholds determination criteria and investigating strength and confining pressure effects. Construction and Building Materials, 2020, 243: 118263 J]

[36] Potra F A, Wright S J. Interior-point methods. Journal of Computational and Applied Mathematics, 2000, 124(1–2): 281-302 J]

[37] Zheng M-z, Li S-j, Feng Z-j, et al. . Three-dimensional stress variation characteristics in deep hard rock of CJPL-II project based on in-situ monitoring. International Journal of Mining Science and Technology, 2024, 34(2): 179-195 J]

[38] Xu D-p, Zhou Y-y, Qiu S-l, et al. . Elastic modulus deterioration index to identify the loosened zone around underground openings. Tunnelling and Underground Space Technology, 2018, 82: 20-29 J]

[39] Feng X-t, Wang Z-f, Zhou Y-y, et al. . Modelling three-dimensional stress-dependent failure of hard rocks. Acta Geotechnica, 2021, 16(6): 1647-1677 J]

[40] Yang Y, Jiang Q, Liu J, et al. . Equivalent constitutive model for jointed rock masses and its application in large underground Caverns. International Journal of Geomechanics, 2023, 23: 04022259 J]

RIGHTS & PERMISSIONS

Central South University