A Fractal Model for Characterizing Hydraulic Properties of Fractured Rock Mass under Mining Influence

Abstract

In this paper, two basic assumptions are introduced: (1) The number and length distribution of fractures in fractured rock mass are in accordance with the fractal law. (2) Fluid seepage in the fractures satisfies the cubic law. Based on these two assumptions, the fractal model of parallel seepage and radial seepage in fractured rock mass is established, and the seepage tensor of fracture network which reflects the geometric characteristics and fractal characteristics of fracture network under two kinds of seepage is derived. The influence of fracture geometry and fractal characteristics on permeability is analyzed, and the validity and accuracy of the model are verified by comparing the calculated results of the theoretical model and physical model test. The results show that the permeability coefficient K of fracture network is a function of the geometric (maximum crack length Lmax, fractured horizontal projection length L0, diameter calculation section porosity Φ, fracture strike α, and fracture angle θ) and fractal characteristics (fracture network fractal dimension Df and seepage flow fractal dimension DT). With the increase of fractal dimension Df, the permeability coefficient increases. With the increase of DT, the permeability coefficient decreases rapidly. And the larger the Df (Df>1.5), the greater the change of permeability coefficient K with DT.