Fractal description of rock joints based on digital image processing technique

Joint roughness has an essential in?uence on the shear behavior of rock joints. Fractal dimensions (D) can be used to effectively reflect the roughness property contributed by the secondary asperity; however, it is not ideal to represent the asperity contributed by the first-order asperity. On the basis of the asperity of a rough joint occurring on many scales, the fractal parameter is used to show the roughness character offered by the secondary asperity, while the degree of a waviness (w_d) is used to reflect the roughness property at the first order. In this respect, joint roughness coefficient is represented using the fractal dimensions (D) and degree of the waviness (w_d), and their relationship is established. On the other hand, in virtue of the difficulties in calculating the value of D in engineering practices, a procedure is provided for obtaining the fractal dimension based on the digital image of rock joints. It will be helpful for applying the fractal dimension to describing the JRC in engineering practices.