Study on the velocity of P waves across a single joint based on fractal and damage theory

As waves cross rock joints, the wave velocity is difficult to determine due to joint irregular surfaces. In this paper, a new RGB (red, green and blue) color model is established, and by applying this model, a new calculation method of the image fractal dimension (IFD) of joint surfaces is proposed. Based on this new calculation method, the relationship between P wave velocity and the image fractal dimension of joint surfaces is obtained, and the velocity of P waves across joints is formulated. The ultrasonic tests for rock specimens with a single joint are conducted to confirm the new formula of the velocity of P waves across joints. The test results agree well with the analytical solution presented in this paper. The results show that the velocity of P waves across joints decreases with the increase of joint surface roughness.