Statistical damage constitutive model based on the Hoek-Brown criterion

• Autorzy: Chen, Yifan , Lin, Hang , Wang, Yixian , Xie, Shijie , Zhao, Yanlin , Yong, Weixun
• Języki publikacji: EN

Abstrakty

EN

The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.

Słowa kluczowe

PL

skała; naprężenie; uszkodzenie

EN

Hoek-Brown criterion; statistical damage constitutive model; conventional triaxial tests; Weibull distribution

• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2021
• Tom: Vol. 21, no. 3
• Strony: 556--564
• Opis fizyczny: Bibliogr. 49 poz., rys., wykr.

Twórcy

autor

Chen, Yifan

• School of Resource and Safety Engineering, Central South University, Changsha 410083, Hunan, China,

autor

Lin, Hang

• School of Resource and Safety Engineering, Central South University, Changsha 410083, Hunan, China,

autor

Wang, Yixian

• School of Civil Engineering, Hefei University of Technology, Hefei 230009, China,

autor

Xie, Shijie

• School of Resource and Safety Engineering, Central South University, Changsha 410083, Hunan, China,

autor

Zhao, Yanlin

• School of Energy and Safety Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China,

autor

Yong, Weixun

• Kunming Prospecting Design Institute of China Nonferrous Metals Industry Co., Ltd, Kunming 650051, Yunan, China,

Bibliografia

• [1] Zhao YL, Zhang CS, Wang YX, Lin H. Shear-related roughness classification and strength model of natural rock joint based on fuzzy comprehensive evaluation. Int J Rock Mech Mining Sci. 2021;137:17. https://doi.org/10.1016/j.ijrmms.2020.104550.
• [2] Cook N. The failure of rock. Int J Rock Mech Mining Sci Geomech Abstracts. 1965;2:389–403.
• [3] Wang SS, Xu WY. A coupled elastoplastic anisotropic damage model for rock materials. Int J Damage Mech. 2020;29:1222–45. https://doi.org/10.1177/1056789520904093.
• [4] Shao S, Shao SJ, Wang Q. Strength criteria based on shear failure planes and test verification on loess. Geotech Test J. 2019;42:347–64.
• [5] Geng HS, Xu HF, Gao L, Chen L, Wang B, Zhao X. Elastic modulus and strength of rock-like material with locked-In stress. Math Probl Eng. 2018;2018:1–17.
• [6] Hoek E, Brown ET. Empirical strength criterion for rock masses. J Geotech Eng Div. 1980;106:1013–35.
• [7] Feng WL, Qiao CS, Niu SJ, Yang Z, Wang T. An improved nonlinear damage model of rocks considering initial damage and damage evolution. Int J Damage Mech. 2020;29:1117–37. https://doi.org/10.1177/1056789520909531.
• [8] Chen Y, Lin H, Ding X, Xie S. Scale effect of shear mechanical properties of non-penetrating horizontal rock-like joints. Environ Earth Sci. 2021;80:192. https://doi.org/10.1007/s12665-021-09485-x.
• [9] Lin H, Zhang X, Wang YX, Yong R, Fan X, Du SG, et al. Improved nonlinear Nishihara shear creep model with variable parameters for rock-like materials. Adv Civil Eng. 2020;2020:7302141. https://doi.org/10.1155/2020/7302141.
• [10] Krajcinovic D, Silva MAG. Statistical aspects of the continuous damage theory. Int J Solids Struct. 1982;18:551–62.
• [11] Tang CA. Catastrophe in rock unstable failure. Beijing: Beijing: China Coal Industry Publishing House; 1993.
• [12] Chen K. Constitutive model of rock triaxial damage based on the rock strength statistics. Int J Damage Mech. 2020;29:1487–511. https://doi.org/10.1177/1056789520923720.
• [13] Liu DQ, He MC, Cai M. A damage model for modeling the complete stress-strain relations of brittle rocks under uniaxialcompression. Int J Damage Mech. 2018;27:1000–19. https://doi.org/10.1177/1056789517720804.
• [14] Cao W, Fang Z, Tang X. A study of statistical constitutive model for soft and damage rock. Chin J Rock Mechan Eng.1998;17:628–33.
• [15] Cao WG, Zhao MH, Liu CX. Study on the model and its modifying method for rock softening and damage based on Weibull random distribution. Chin J Rock Mechan Eng. 2004;23:3226–31.
• [16] Cao WG, Zhang S. Study on the statistical analysis of rock damage based on Mohr-Coulomb criterion. J Hunan University. 2005;32:43–7.
• [17] Cao WG, Zhao MH, Liu CX. Study on rectified method of Mohr Coulomb strength criterion for rock. Chin J Rock Mechan Eng. 2005;24:2403–8.
• [18] Lin H, Lei D, Yong R, Jiang C, Du S. Analytical and numerical analysis for frost heaving stress distribution within rock joints under freezing and thawing cycles. Environ Earth Sci. 2020;79:305. https://doi.org/10.1007/s12665-020-09051-x.
• [19] Zhang HM, Yuan C, Yang GS, Wu LY, Hossein M. A novel constitutive modelling approach measured under simulated freeze–thaw cycles for the rock failure. Eng Comp. 2019;35:1–14.
• [20] Shi C, Jiang XX, Zhu ZD, Hao ZQ. Study of rock damage constitutive model and discussion of its parameters based on Hoek-Brown criterion. Chin J Rock Mechan Eng. 2011;30:2647–52.
• [21] Cao RL, He SH, Wei J, Wang F. Study of modified statistical damage softening constitutive model for rock considering residual strength. Rock Soil Mech. 2013;34:1652–67.
• [22] Hoek E, Brown ET. The HoekeBrown failure criterion and GSI-2018 edition. J Rock Mech Geotech Eng. 2019;11:445–63.
• [23] Hoek E, Brown ET. Underground excavations in rocks. London: Institution of Mining and Metallurgy; 1980.
• [24] Shen J, Shu Z, Cai M, Du S. A shear strength model for anisotropic blocky rock masses with persistent joints. Int J Rock Mech Mining Sci. 2020;134:104430. https://doi.org/10.1016/j.ijrmms.2020.104430.
• [25] Shen JY, Jimenez R. Predicting the shear strength parameters of sandstone using genetic programming. Bull Eng Geology Environ. 2018;77:1647–62. https://doi.org/10.1007/s10064-017-1023-6.
• [26] Hoek E, Brown ET. Practical estimates of rock mass strength. Int J Rock Mech Mining Sci. 1997;34:1165–86.
• [27] Hoek E. Strength of rock and rock masses. ISRM News J. 1994;2:4–16.
• [28] Hoek E. Hoek-Brown failure criterion-2002 edition. In Proceedings of the fifth North American rock mechanics symposium. 2002; 1:18–22.
• [29] Deng C, Hu H, Zhang T, Chen J. Rock slope stability analysis and charts based on hybrid online sequential extreme learning machine model. Earth Sci Inf. 2020;13:729–46.
• [30] Schwartz AE. Failure of rock in the triaxial shear test. Rolla, USA: US Symposium on Rock Mechanics; 1964. p. 109–51.
• [31] Mogi K. Pressure dependence of rock strength and transition from brittle fracture to ductile flow. Bulletin Earthquake Research Institute; 1966. p. 215–32.
• [32] Kaiser PK, Kim B, Bewick RP, Valley B. Rock mass strength at depth and implications for pillar design. In: Van Sint Jan M, Y P, editors. Deep mining 2010, Proceedings of the fifth international seminar on deep and high stress mining. Santiago, Chile: Australian Centre for Geomechanics; 2010. p. 463–76.
• [33] Bewick RP, Kaiser PK, Amannc F. Strength of massive to moderately jointed hard rock masses. J Rock Mech Geotech Eng. 2019;11:126–39.
• [34] Zhang X, Lin H, Wang YX, Yong R, Zhao YL, Du SG. Damage evolution characteristics of saw-tooth joint under shear creep condition. Int J Damage Mech. 2021;30:453–80. https://doi.org/10.1177/1056789520974420.
• [35] Zhang X, Lin H, Wang Y, Zhao Y. Creep damage model of rock mass under multi-level creep load based on spatio-temporal evolution of deformation modulus. Arch Civil Mech Eng. 2021;21:71. https://doi.org/10.1007/s43452-021-00224-4.
• [36] Desai GFS. Constitutive model with strain softening. Int J Solids Struct. 1987;23:733–50.
• [37] Zhang HM, Meng XZ, Yang GS. A study on mechanical properties and damage model of rock subjected to freeze-thaw cycles and confining pressure. Cold Regions Sci Technol. 2020;174:14. https://doi.org/10.1016/j.coldregions.2020.103056.
• [38] Zhang M, Wang F, Yang Q. Statistical damage constitutive model for rocks based on triaxial compression tests. Chin J Geotech Eng. 2013;35:1965–71.
• [39] Xie S, Lin H, Wang Y, Cao R, Yong R, Du S, et al. Nonlinear shear constitutive model for peak shear-type joints based on improved Harris damage function. Arch Civil Mech Eng.2020;20:95. https://doi.org/10.1007/s43452-020-00097-z.
• [40] Lyu Q, Tan JQ, Dick JM, Liu Q, Gamage RP, Li L, et al. Stress-Strain Modeling and Brittleness Variations of Low-Clay Shales with CO2/CO2-Water Imbibition. Rock Mech Rock Eng. 2018;52:2039–52.
• [41] Gao F, Xie HP, Zhao P. Fractal properties of Weibull modulus and strenth of the rock. Chin Sci Bull. 1993;38:1427–30.
• [42] Xu SL, Zhao GF. A study on probability model of fracture toughness of concrete. Chin Civil Eng J. 1988;21:10–23.
• [43] Li YW, Jia D, Rui ZH, Peng JY, Fu CK, Zhang J. Evaluation method of rock brittleness based on statistical constitutive relations for rock damage. J Petrol Sci Eng. 2017;153:123–32.
• [44] Chen S, Qiao C, Ye Q, Khan MU. Comparative study on three-dimensional statistical damage constitutive modified model of rock based on power function and Weibull distribution. Environ Earth Sci. 2018;77:108–16.
• [45] Zheng YR. Principle of geotechnical plastic mechanics: generalized plastic mechanics. Beijing: China Building Industry Press; 2002.
• [46] Chou YL, Huang SY, Sun LY, Wang IJ, Yue GD, Cao W, et al. Mechanical model of chlorine salinized soil-steel block interface based on freezing and thawing. Rock Soil Mech. 2019;40:41–52.
• [47] Wang JB, Song ZP, Zhao BY, Liu XR, Liu J, Lai JX. A study on the mechanical behavior and statistical damage constitutive model of sandstone. Arab J Sci Eng. 2018;43:5179–92. https://doi.org/10.1007/s13369-017-3016-y.
• [48] Yang SQ, Jiang YZ. Triaxial mechanical creep behavior of sand-stone. Mining Sci Technol (China). 2010;20:339–49.
• [49] Tan C, Yuan MD, Shi YS, Zhou BS, Li H. Statistical damage constitutive model for cemented sand considering the residual strength and initial compaction phase. Adv Civil Eng. 2018;2018:1410893.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)

Identyfikatory

DOI

10.1007/s43452-021-00270-y