A Simplified form of Grasselli's 3D Roughness Measure θ _max ^* /(C + 1)

Excerpt

Joint surface morphology has a significant impact on the shear strength and hydromechanical behavior of rock joints, further influencing engineering stability and safety. Barton and Choubey (1977) developed a morphological parameter, the joint roughness coefficient (JRC), to quantify joint surface topography, which is recommended by the International Society for Rock Mechanics (ISRM 1981) and is currently used in engineering applications. Based on the ten standard profiles, the JRC of a profile extracted from a natural rock joint can be determined through visual comparison, which was proven to be subjective and can lead to biased representation of joint roughness (Tatone and Grasselli 2009). Many researchers have focused their attention on developing statistical parameters to quantify JRC more precisely, including Z₂ (the root mean square of the first derivative of the profile) (Tse and Cruden 1979; Yu and Vayssade 1991), SF (the mean square of the first derivative of the profile) (Tse and Cruden 1979; Yu and Vayssade 1991), and R_p (roughness profile index) (El-Soudani 1978; Maerz et al. 1990; Yu and Vayssade 1991). These two-dimensional parameters are capable of describing profile roughness in different directions. However, the parameters cannot distinguish the morphological characteristics of a rough surface in the forward or backward directions (Yang et al. 2016). Apart from statistics, fractal dimension has also been suggested as a JRC identification method (Turk et al. 1987; Odling 1994; Xie et al. 1999) based on the fractal theory developed by Mandelbrot (1967). …