A Fractal Model for the Shear Behaviour of Large-Scale Opened Rock Joints

This paper presents a joint constitutive model that represents the shear behaviour of a large-scale opened rock joint. Evaluation of the degree of opening is made by considering the ratio between the joint wall aperture and the joint amplitude. Scale dependence of the surface roughness is investigated by approximating a natural joint profile to a fractal curve patterned in self-affinity. Developed scaling laws show the slopes of critical waviness and critical unevenness tend to flatten with increased sampling length. Geometrical examination of four 400-mm joint profiles agrees well with the suggested formulations involving multi-order asperities and fractal descriptors. Additionally, a fractal-based formulation is proposed to estimate the peak shear displacements of rock joints at varying scales, which shows a good correlation with experimental data taken from the literature. Parameters involved in the constitutive law can be acquired by inspecting roughness features of sampled rock joints. Thus, the model can be implemented in numerical software for the stability analysis of the rock mass with opened joints.

[1]  Norbert R. Morgenstern,et al.  THE ULTIMATE FRICTIONAL RESISTANCE OF ROCK DISCONTINUITIES , 1979 .

[2]  D. Cruden,et al.  ESTIMATING JOINT ROUGHNESS COEFFICIENTS , 1979 .

[3]  J. Oh,et al.  A constitutive model for a laboratory rock joint with multi-scale asperity degradation , 2016 .

[4]  Norbert H. Maerz,et al.  Joint roughness measurement using shadow profilometry , 1990 .

[5]  Michael Sakellariou,et al.  On the fractal character of rock surfaces , 1991 .

[6]  A. Malinverno.  A simple method to estimate the fractal dimension of a self‐affine series , 1990 .

[7]  Yujing Jiang,et al.  Estimating the relation between surface roughness and mechanical properties of rock joints , 2006 .

[8]  Pinnaduwa Kulatilake,et al.  Requirements for accurate quantification of self affine roughness using the roughness-length method , 1997 .

[9]  F. Lanaro.  Geometry, Mechanics and Transmissivity of Rock Fractures , 2001 .

[10]  B. Mandelbrot.  How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension , 1967, Science.

[11]  J. Oh,et al.  Effect of opening on the shear behavior of a rock joint , 2010 .

[12]  In-Mo Lee,et al.  Underestimation of roughness in rough rock joints , 2008 .

[13]  M. Leal-Gomes.  Some New Essential Questions About Scale Effects On the Mechanics of Rock Mass Joints , 2003 .

[14]  Lu Zhang,et al.  A new method estimating the 2D Joint Roughness Coefficient for discontinuity surfaces in rock masses , 2014 .

[15]  J. Oh,et al.  A joint shear model incorporating small-scale and large-scale irregularities , 2015 .

[16]  L. Jing,et al.  The scale dependence of rock joint surface roughness , 2001 .

[17]  N. Odling,et al.  Natural fracture profiles, fractal dimension and joint roughness coefficients , 1994 .

[18]  P. Kulatilake,et al.  Requirements for accurate quantification of self-affine roughness using the variogram method , 1998 .

[19]  B. Mandelbrot.  Self-Affine Fractals and Fractal Dimension , 1985 .

[20]  Giovanni Grasselli,et al.  Shear strength of rock joints based on quantified surface description , 2001 .

[21]  J. P. Seidel,et al.  Towards an understanding of joint roughness , 1995 .

[22]  F. Lanaro.  A random field model for surface roughness and aperture of rock fractures , 2000 .

[23]  Fulvio Tonon,et al.  Constitutive model for rock fractures: Revisiting Barton's empirical model , 2010 .

[24]  Richard F. Voss,et al.  Fractals in nature: from characterization to simulation , 1988 .

[25]  Giovanni Grasselli,et al.  An Investigation of Discontinuity Roughness Scale Dependency Using High-Resolution Surface Measurements , 2013, Rock Mechanics and Rock Engineering.

[26]  N. Barton,et al.  The shear strength of rock joints in theory and practice , 1977 .

[27]  N. Fardin.  The effect of scale on the morphology, mechanics and transmissivity of single rock fractures , 2003 .

[28]  F. Johansson.  Shear Strength of Unfilled and Rough Rock Joints in Sliding Stability Analyses of Concrete Dams , 2009 .

[29]  P. Hagan,et al.  Scale effect on the shear behaviour of rock joints based on a numerical study , 2014 .

[30]  N. Barton,et al.  Effects Of Block Size On The Shear Behavior Of Jointed Rock , 1982 .

[31]  J Muralha,et al.  ABOUT LNEC EXPERIENCE ON SCALE EFFECTS IN THE MECHANICAL BEHAVIOUR OF JOINTS . PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON SCALE EFFECTS IN ROCK MASSES, LOEN, NORWAY, JUNE 7-8 1990 , 1990 .

[32]  J. Oh,et al.  Experimental Studies on the Mechanical Behaviour of Rock Joints with Various Openings , 2016, Rock Mechanics and Rock Engineering.

[33]  Stephen R. Brown,et al.  Broad bandwidth study of the topography of natural rock surfaces , 1985 .

[34]  T. Belem,et al.  Fractal analysis of shear joint roughness , 1997 .

[35]  J. Carr,et al.  The fractal dimension as a measure of the roughness of rock discontinuity profiles , 1990 .

[36]  F. Johansson.  Influence of scale and matedness on the peak shear strength of fresh, unweathered rock joints , 2016 .

[37]  Zon-Yee Yang,et al.  Application of the self-affinity concept to the scale effect of joint roughness , 1999 .

[38]  W. R. Dearman,et al.  Characterization of rock joint surfaces by fractal dimension , 1987 .

[39]  Stavros Bandis.  Experimental studies of scale effects on shear strength, and deformation of rock joints , 1980 .

[40]  B. Mandelbrot.  How Long Is the Coast of Britain ? , 2002 .

[41]  Nick Barton,et al.  Experimental studies of scale effects on the shear behaviour of rock joints , 1981 .

[42]  B. Ladanyi,et al.  Simulation Of Shear Behavior Of A Jointed Rock Mass , 1969 .

[43]  Hui-Hai Liu,et al.  A Fractal-Based Model for Fracture Deformation Under Shearing and Compression , 2013, Rock Mechanics and Rock Engineering.

[44]  Jeong-gi Um,et al.  Accurate quantification of rock joint roughness and development of a new peak shear strength criterion for joints , 1997 .