Relationship between joint roughness coefficient and fractal dimension of rock fracture surfaces

Numerous empirical equations have been proposed to estimate the joint roughness coefficient (JRC) of a rock fracture based on its fractal dimension (D). A detailed review is made on these various methods, along with a discussion about their usability and limitations. It is found that great variation exists among the previously proposed equations. This is partially because of the limited number of data points used to derive these equations, and partially because of the inconsistency in the methods for determining D. The 10 standard profiles on which most previous equations are based are probably too few for deriving a reliable correlation. Different methods may give different values of D for a given profile. The h–L method is updated in this study to avoid subjectivity involved in identifying the high-order asperities. The compass-walking, box-counting and the updated h–L method are employed to examine a larger population of 112 rock joint profiles. Based on these results, a new set of empirical equations are proposed, which indicate that the fractal dimension estimated from compass-walking and the updated h–L method closely relate to JRC, whereas the values estimated from box-counting do not relate as closely.