Comptes Rendus
An empirical statistical constitutive relationship for rock joint shearing considering scale effect
Comptes Rendus. Mécanique, Volume 347 (2019) no. 8, pp. 561-575.

The scale effect of rock joint shearing is of great significance in rock engineering. Most existing shear constitutive models could describe the pre- and post-peak deformation of rock joints, but only in one particular scale, that is, those existing models will fail to depict the rock joint shearing in different length scales. Therefore, this study aims to establish a constitutive relationship for rock joints with considering the scale effect. Based on the assumption of a random statistical distribution of rock material strength and statistical mesoscopic damage theory, damage variables are defined as the ratio of the number of damaged elements to the total number in the shear process. Together with the nonlinear relationship between the microelement failure and the joint scale, an empirical statistical constitutive relationship for joint is established. And then, the determination method of constitutive relationship parameters and the variation laws with the scale are discussed. Results show that the predicted results of the proposed empirical relationship not only agree well with the experimental results but also fully describe nonlinear deformation, pre-peak softening, post-peak softening, residual stage, and other mechanical properties of the shear deformation of joint with different dimensions, thereby demonstrating the rationality of the constitutive relationship. The physical meaning of the constitutive relationship parameters is clear, and the expressions of the constitutive relationship parameters can be deduced from the experimental results. In addition, the influence of scale effect on the shear deformation of rock joints can be quantified using parameters, which help accurately describe the action form of scale effect.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2019.08.001
Keywords: Rock joints, Scale effect, Constitutive relationship, Statistical damage, Shear behavior

Hang Lin 1; Shijie Xie 1; Rui Yong 2; Yifan Chen 1; Shigui Du 2

1 School of Resources and Safety Engineering, Central South University, Changsha, Hunan, 410083, China
2 Ocean College, Zhejiang University, Zhoushan, Zhejiang 316000, China
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Hang Lin; Shijie Xie; Rui Yong; Yifan Chen; Shigui Du. An empirical statistical constitutive relationship for rock joint shearing considering scale effect. Comptes Rendus. Mécanique, Volume 347 (2019) no. 8, pp. 561-575. doi : 10.1016/j.crme.2019.08.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.08.001/

[1] Y. Zhao; L. Zhang; W. Wang; J. Tang; H. Lin; W. Wan Transient pulse test and morphological analysis of single rock fractures, Int. J. Rock Mech. Min. Sci., Volume 91 (2017), pp. 139-154

[2] C. Zhang; C. Pu; R. Cao; T. Jiang; G. Huang The stability and roof-support optimization of roadways passing through unfavorable geological bodies using advanced detection and monitoring methods, among others, in the Sanmenxia Bauxite Mine in China's Henan Province, Bull. Eng. Geol. Environ. (2019) | DOI

[3] Y. Wang; H. Lin; Y. Zhao; X. Li; P. Guo; Y. Liu Analysis of fracturing characteristics of unconfined rock plate under edge-on impact loading, Eur. J. Environ. Civ. Eng. (2019), pp. 1-16 | DOI

[4] Y. Zhang; N. Huang Numerical study on the shear-flow behavior and transport process in rough rock fractures, C. R. Mecanique, Volume 346 (2018), pp. 877-886 | DOI

[5] Y. Shen; Y. Wang; Y. Yang; Q. Sun; T. Luo; H. Zhang Influence of surface roughness and hydrophilicity on bonding strength of concrete-rock interface, Constr. Build. Mater., Volume 213 (2019), pp. 156-166

[6] H. Lin; Z. Xiong; T. Liu; R. Cao; P. Cao Numerical simulations of the effect of bolt inclination on the shear strength of rock joints, Int. J. Rock Mech. Min. Sci., Volume 66 (2014), pp. 49-56 | DOI

[7] J.Y. Shen; M. Karakus Determination of Mohr–Coulomb shear strength parameters from generalized Hoek–Brown criterion for slope stability analysis, Rock Mech. Rock Eng., Volume 45 (2012), pp. 123-129

[8] J. Shen; R. Jimenez Predicting the shear strength parameters of sandstone using genetic programming, Bull. Eng. Geol. Environ. (2018), pp. 1-16

[9] F. Huang; J. Shen; M. Cai; C. Xu An empirical UCS model for anisotropic blocky rock masses, Rock Mech. Rock Eng. (2019), pp. 1-13

[10] Y. Xu; F. Dai; T. Zhao; N.W. Xu; Y. Liu Fracture toughness determination of cracked chevron notched Brazilian disc rock specimen via griffith energy criterion incorporating realistic fracture profiles, Rock Mech. Rock Eng., Volume 49 (2016), pp. 1-11

[11] R.E. Goodman; R.L. Taylor; T.L. Brekke Closure on a model for the mechanics of jointed rock, J. Soil Mech. Found. Div., Volume 94 (1970), pp. 637-660

[12] S. Saeb; B. Amadei Modelling rock joints under shear and normal loading, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. (1992), pp. 267-278

[13] S. Bandis; A. Lumsden; N. Barton Fundamentals of rock joint deformation, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., Volume 20 (1983), pp. 249-268

[14] G. Grasselli Manuel rocha medal recipient shear strength of rock joints based on quantified surface description, Rock Mech. Rock Eng., Volume 39 (2006), p. 295

[15] R. Simon; M. Aubertin; H. Mitri A non-linear constitutive model for rock joints to evaluate unstable slip. Vail Rocks 1999, Proc. 37th US Symposium on Rock Mechanics (USRMS), American Rock Mechanics Association, 1999

[16] M.E. Plesha Constitutive models for rock discontinuities with dilatancy and surface degradation, Int. J. Numer. Anal. Methods Geomech., Volume 11 (2005), pp. 345-362

[17] J. Wang; Y. Ichikawa; C. Leung A constitutive model for rock interfaces and joints, Int. J. Rock Mech. Min. Sci., Volume 40 (2003), pp. 41-53

[18] C.S. Desai; Y. Ma Modelling of joints and interfaces using the disturbed-state concept, Int. J. Numer. Anal. Methods Geomech., Volume 16 (1992), pp. 623-653

[19] X.P. Zhou; J. Bi; Q.H. Qian Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws, Rock Mech. Rock Eng., Volume 48 (2015), pp. 1097-1114

[20] A. Liu; G. Tian; Q. Zhang; W. Lin; J. Jiang Shear relaxation characteristics of rock joints under stepwise loadings, C. R. Mecanique, Volume 346 (2018), pp. 1179-1191 | DOI

[21] R. Sahlaoui; K. Sab; J-V. Heck Yield strength of masonry-like structures containing thin adhesive joints: 3D or 2D-interface model for the joints?, C. R. Mecanique, Volume 339 (2011), pp. 432-438 | DOI

[22] Y.F. Chen; H. Lin Consistency analysis of Hoek–Brown and equivalent Mohr–Coulomb parameters in calculating slope safety factor, Bull. Eng. Geol. Environ. (2018), pp. 1-13 | DOI

[23] J. Shen; M. Karakus Three-dimensional numerical analysis for rock slope stability using shear strength reduction method, Can. Geotech. J., Volume 51 (2014), pp. 164-172

[24] H. Pratt; A. Black; W. Brown; W. Brace The effect of speciment size on the mechanical properties of unjointed diorite, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. (1972), pp. 513-516

[25] N. Barton; V. Choubey The shear strength of rock joints in theory and practice, Rock Mech. Rock Eng., Volume 10 (1977), pp. 1-54

[26] S. Du; M. Huang; Z.Y. Luo; R.D. Jia; Y.M. Wang Scale effects of undulation amplitude of rock joints, Q. J. Eng. Geol. (2010)

[27] T-S. Ueng; Y-J. Jou; I-H. Peng Scale effect on shear strength of computer-aided-manufactured joints, J. Geoengin., Volume 5 (2010), pp. 29-37

[28] M. Bahaaddini; P. Hagan; R. Mitra; B. Hebblewhite Scale effect on the shear behaviour of rock joints based on a numerical study, Eng. Geol., Volume 181 (2014), pp. 212-223

[29] H. Liu; X. Yuan A damage constitutive model for rock mass with persistent joints considering joint shear strength, Can. Geotech. J., Volume 52 (2015), pp. 3107-3117

[30] J-J. Dong; Y-W. Pan A hierarchical model of rough rock joints based on micromechanics, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. (1996), pp. 111-123

[31] F. Vallier; Y. Mitani; M. Boulon; T. Esaki; F. Pellet A shear model accounting scale effect in rock joints behavior, Rock Mech. Rock Eng., Volume 43 (2010), pp. 581-595 | DOI

[32] Y. Wang; P. Guo; X. Li; H. Lin; Y. Liu; H. Yuan Behavior of fiber-reinforced and lime-stabilized clayey soil in triaxial tests, Appl. Sci., Volume 9 (2019), p. 900

[33] W. Weibull A statistical distribution function of wide applicability, J. Appl. Mech., Volume 18 (1951), pp. 293-297

[34] J. Ji; C. Zhang; Y. Gao; J. Kodikara Reliability-based design for geotechnical engineering: an inverse FORM approach for practice, Comput. Geotech., Volume 111 (2019), pp. 22-29

[35] J. Ji; C. Zhang; Y. Gao; J. Kodikara Effect of 2D spatial variability on slope reliability: a simplified FORM analysis, Geosci. Front., Volume 9 (2018), pp. 1631-1638

[36] Y. Wang; P. Guo; H. Lin; X. Li; Y. Zhao; B. Yuan et al. Numerical analysis of fiber-reinforced soils based on the equivalent additional stress concept, Int. J. Geomech. (2019) | DOI

[37] C. Tang; W. Yang; Y. Fu; X.JE.G. Xu A new approach to numerical method of modelling geological processes and rock engineering problems—continuum to discontinuum and linearity to nonlinearity, Eng. Geol., Volume 49 (1998), pp. 207-214

[38] C. Tang; H. Liu; P. Lee; Y. Tsui; L. Tham Numerical studies of the influence of microstructure on rock failure in uniaxial compression—part I: effect of heterogeneity, Int. J. Rock Mech. Min. Sci., Volume 37 (2000), pp. 555-569

[39] H. Lin; X. Ding; R. Yong; W. Xu; S. Du Effect of non-persistent joints distribution on shear behavior, C. R. Mecanique, Volume 347 (2019), pp. 477-489 | DOI

[40] S. Pirmohammad; M. Hojjati Mengharpey A new mixed mode I/II fracture test specimen: numerical and experimental studies, Theor. Appl. Fract. Mech., Volume 97 (2018), pp. 204-214 | DOI

[41] Y.X. Wang; S.B. Shan; C. Zhang; P.P. Guo Seismic response of tunnel lining structure in a thick expansive soil stratum, Tunn. Undergr. Space Technol., Volume 88 (2019), pp. 250-259 | DOI

[42] J. Justo; J. Castro; S. Cicero; M.A. Sánchez-Carro; R. Husillos Notch effect on the fracture of several rocks: application of the theory of critical distances, Theor. Appl. Fract. Mech., Volume 90 (2017), pp. 251-258 | DOI

[43] H. Lin; W. Xiong; Z. Xiong; F. Gong Three-dimensional effects in a flattened Brazilian disk test, Int. J. Rock Mech. Min. Sci., Volume 74 (2015), pp. 10-14 | DOI

[44] J. Lemaitre How to use damage mechanics, Nucl. Eng. Des., Volume 80 (1984), pp. 233-245

[45] Y. Liu; F. Dai A damage constitutive model for intermittent jointed rocks under cyclic uniaxial compression, Int. J. Rock Mech. Min. Sci., Volume 103 (2018), pp. 289-301 | DOI

[46] X. Fan; H. Lin; H. Lai; R. Cao; J. Liu Numerical analysis of the compressive and shear failure behavior of rock containing multi-intermittent joints, C. R. Mecanique, Volume 347 (2019), pp. 33-48 | DOI

[47] R. Cao; W. Tang; H. Lin; X. Fan Numerical analysis for the progressive failure of binary-medium interface under shearing, Adv. Civ. Eng. (2018) | DOI

[48] R.-h. Cao; P. Cao; H. Lin; G. Ma; Y. Chen Failure characteristics of intermittent fissures under a compressive-shear test: experimental and numerical analyses, Theor. Appl. Fract. Mech., Volume 96 (2018), pp. 740-757 | DOI

[49] J. Mazars; G. Pijaudier-Cabot Continuum damage theory—application to concrete, J. Eng. Mech., Volume 115 (1989), pp. 345-365

[50] S. Gentier; J. Riss; G. Archambault; R. Flamand; D. Hopkins Influence of fracture geometry on shear behavior, Int. J. Rock Mech. Min. Sci., Volume 37 (2000), pp. 161-174

[51] Y. Li; J. Oh; R. Mitra; B. Hebblewhite A constitutive model for a laboratory rock joint with multi-scale asperity degradation, Comput. Geotech., Volume 72 (2016), pp. 143-151

[52] Z.C. Tang; C.C. Xia; S.G. Xiao Constitutive model for joint shear stress–displacement and analysis of dilation, Chin. J. Rock Mech. Eng., Volume 30 (2011), pp. 917-925

[53] S.Q. Yang; W.Y. Xu; C.D. Su Study on statistical damage constitutive model of rock considering scale effect, Chin. J. Rock Mech. Eng., Volume 24 (2005), pp. 4484-4490

[54] M. Huang; S.G. Du; Z.Y. Luo; X.H. Ni Study of shear strength characteristics of simulation rock structural planes based on multi-size direct shear tests, Rock Soil Mech., Volume 34 (2013), pp. 3180-3186

[55] B. Amadei; J. Wibowo; S. Sture; R.H. Price Applicability of existing models to predict the behavior of replicas of natural fractures of welded tuff under different boundary conditions, Geotech. Geolog. Eng., Volume 16 (1998), pp. 79-128

[56] O. Hungr; D.F. Coates Deformability of joints and its relation to rock foundation settlement, Cangeotechj., Volume 15 (1978), pp. 239-249

[57] M. Zhang; Y. Lu; Q. Yang Failure probability and strength size effect of quasi-brittle materials, Chin. J. Rock Mech. Eng., Volume 29 (2010), pp. 1782-1789

[58] H. Zhou; G.T. Cheng; Y. Zhu; J. Chen; J.J. Lu; G.J. Cui et al. Experimental study of shear deformation characteristics of marble dentate joints, Rock Soil Mech., Volume 40 (2019), pp. 852-860

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