Determination of Joint Roughness Coefficient of 2D Rock Joint Profile Based on Fractal Dimension by Using of the Gene Expression Programming

Rock joint roughness influence the shear behavior of rock joints, which have been extensively studied in last a few decades. Various parameters were recommended to quantify the joint roughness, in these parameters, the joint roughness coefficients (JRC value) were widely applied to depict the joint roughness quantitatively by many researchers. Through analysis the references, it is found that the empirical formula of the JRC value based on fractal dimension were commonly adopted, however, the empirical formulas were determined frequently by a limited number of data point, meanwhile, the type of empirical formula were chosen based on the researchers’ subjectively. For obtaining a suitable and objective empirical formula of JRC values based on fractal dimension, a large number of experimental data were collected from the references, by using the gene expression programming method, an empirical formula was determined objectively. The obtained formula can reflect the relationship between the JRC values and fractal dimension extensively, the empirical formula is \( JRC = 21.0810 - \frac{0.0656}{(\sqrt D - 0.9969)D} \).