Relationship between the Fractal Dimension and Joint Roughness Coefficient

Abstract

An empirical relationship between the fractal dimension (D) and joint roughness coefficient (JRC) is described. The concepts of fractals and fractal dimension are introduced. A fractal dimension for joint and bedding planes is determined using elevation data measured along a line traversing these surfaces. Surfaces adjacent to Libby Dam, Montana are analyzed using the concept of the fractal dimension. The minimum resolution (spacing) of elevation measurements is 15.2 cm (0.5 ft), hence fractal dimensions describe large scale features of these surfaces. A JRC value is also determined visually for each surface. The empirical relationship between JRC and D is found to be: This expression has an error standard deviation of 1.24 JRC values. Moreover, the coefficient of determination for this equation is 0.979. The approximate relationship between the joint roughness coefficient and fractal dimension is: A 0.001 variation in the fractal dimension results in a 1 value variation in the joint roughness coefficient.