The present paper focuses on evaluation of existing methods for digitization and quantification of joint roughness. Repeated lidar scans of a number of natural rock joints were registered using Cloud Compare and MATLAB and were then interpolated onto a regular grid for averaging. Specifically, we used the average of many lidar scans to increase the precision in digitization of joint topology, which ultimately allowed us to apply the joint roughness quantification method of Tatone & Grasselli (2009). An average of 30 or more scans was found to provide sufficiently accurate data for surface roughness estimation. Ultimately, the strengths predicted based on these roughness values were compared to results obtained from constant normal load direct shear laboratory testing. Calculated peak shear strength values were found to have typical root-mean-squared errors on the order of 0.05-0.10 MPa for the rock joints considered.
In geomechanics, analysis of fracture roughness is often limited to subjective 2D profilometry analysis. The lack of consistently accurate, precise, and high-resolution tools for data collection has been the primary constraint for characterizing fracture roughness in three dimensions, particularly at the field-scale.
Work by Grasselli and Egger, 2003 showed that it is possible to properly digitize and analyze anisotropic fracture roughness in 3D at the laboratory scale. They developed an analysis method that utilizes the full 3D fracture geometry (as opposed to 2D transects) that is now well established for both roughness quantification and shear strength evaluation. Although this is the method that we apply in this study, other approaches for roughness quantification could be considered in future work, such as Fourier analysis (Renaud and Saichi, 2019), and directional tortuosity (Xiao, 2013).
Specifically, Grasselli and Egger, 2003 showed that the fraction of rock joint area with asperities oriented against the shear direction is responsible for the overall surface roughness. Once a given fracture surface digitized, it is possible to predict the influence of roughness on the anisotropic shear strength of discontinuities. Accordingly, Grasselli and Egger, 2003 proposed a series of equations to represent the relationship between the distribution of asperity dips and an overall surface roughness. Based on previous observations made by Yeo et al.,1998, and Gentier et al., 1997, at the laboratory scale and by Tannant and Kaiser, 1993, at the field scale, they determined that a surface with a larger proportion of steeply dipping asperities oriented against the shear direction should be considered to have a higher degree of roughness. This is mathematically expressed in Equation 1, where A0 is the proportion of the joint area with dip above an angular threshold of zero degrees (i.e., dipping opposite the shear direction), θ*max is the maximum apparent dip in a given shear direction, and C is a dimensionless non-linear fitting parameter that accounts for the distribution of dips. For a joint with no overall inclination, the value of A0 is anticipated to be approximately 0.5, as half of the asperities would face one way while the other half would be facing the other way.