Modeling Roughness of Rock Discontinuity Surfaces: A Signal Analysis Approach

Barton’s (1973) model for estimating the peak shear strength of rock discontinuity surfaces includes an input variable, called joint roughness coefficient (JRC). Using this model, Barton and Choubey (1977) empirically determined the JRC values of a large number of discontinuities and designated a set of ten roughness profiles (Fig. 1) that represents the JRC range of 0–20. These ten profiles continue to function as a practical tool for visually matching and assigning corresponding JRC values to discontinuity surfaces. A growing number of studies designed to quantify the profile matching process show that the JRC values of the original ten profiles correlate reasonably well with a variety of mathematical expressions of roughness (Tse and Cruden 1979; Yu and Vayssade 1991; Tatone and Grasselli 2010; Jang et al. 2014). On the other hand, a close inspection of these profiles reveals inconsistent transitions in the nature of roughness of subsequent profiles, often displaying sudden changes in the characteristics of the most prominent morphological features. This raises several important questions: (1) why do these ten profiles perform in the given order? (2) to what extent do slight and/or local changes along a profile influence its shear strength (and therefore JRC)? and (3) will the same degree of correlation and/or confidence interval hold for any subset of discontinuity profiles other than the original ten? These questions can be explored by physical experiments and numerical simulations, or by decoding the constituent structure of roughness profiles with signal analysis. This technical note is designed to shed light on these questions using the latter approach, and to pave the way for development of a physically based roughness quantification method that is consistent (in expressing morphology and assigning ranking), explicit (in its procedures and assumptions) and comprehensive (in equally efficient representation for all possible roughness patterns).