Investigating the scale effects in strength of fractured rock mass

Based on the method of fractal geometry, the relationship between quantity and size of fracture in a rock mass can be studied. It was found that this relationship is power: Nd ¼ N0d D. Based on this result and theoretical analysis, the nonlinear relationship between rock mass strength and fracture quantity is found: Rc ¼ Rcm þ DRcExp½ BNd .the formula includes the residual strength of fractured rock mass Rcm, the difference in value ðDRcÞ between the intact rock strength Rc0 and the residual strength, and fracture quantity. Then, combining the relationship between fracture quantity and the size of rock mass, the formula of rock mass strength is found: Rc ¼ Rcm þ DRcExpð BN1m2ði 1ÞDl2 D E Þ. The formula includes fracture quantity, the fractal dimension of fracture quantity distribution and rock mass size. The results show that the attenuation index of rock mass strength is related to the fractal dimension of fracture quantity distribution: a ¼ 2 D.