Determining of the Joint Roughness Coefficient (JRC) of Rock Discontinuities Based on the Theory of Random Fields

This work intends to embed the estimation of the joint roughness coefficient (JRC) in the framework of random fields. The random field method is a probabilistic approach which involves modeling of the spatial variability of the pertinent physical quantities as a fundamental part of the (assumed) underlying probabilistic structure. Although this method is one of higher complexity in regard of the presumed background knowledge, it encodes naturally subtler information about the rock surface roughness. It is noted that, the proposed random field approach considers automatically the scale of the problem (no correction factor is needed), whilst the JRC estimates appear to be more stable (compared to those derived from Z2 or SF) in the sense that images of the same profile but of different quality give similar results for its roughness. The present work could also be useful in advanced probabilistic rock slope stability analysis based on random fields. In such a case, the required spatial correlation length θ can be obtained by the proposed θ = 145.5 σ/JRC relationship (σ = variance of the profile). The JRC can be obtained through tilt tests, push or pull tests, or matching roughness profiles, whilst σ can be obtained from inspection of the digitized profile.