Seepage-Fractal Characteristics of Fractured Media Rock Materials Due to High-Velocity Non-Darcy Flow

Abstract

Under the influence of internal and external factors, a fracture network is easily generated in concrete and rock, which seriously endangers project safety. Fractal theory can be used to describe the formation and development of the fracture network and characterize its structure. Based on the flow balance in the node balance field, Forchheimer’s law is introduced to derive the control equation of high-velocity non-Darcy flow in the fracture network. The fracture network is established according to the geological parameters of Sellafield, Cumbria, England. A total of 120 internal fracture networks are intercepted according to 10 dimensions (1 m, 2 m, …, 10 m) and 12 directions (0°, 30°, ..., 330°). The fractal dimension, equivalent hydraulic conductivity (K), and equivalent non-Darcy coefficient (β) of the fracture network are calculated, and the influence of the fractal dimension on K and β is studied. The results indicate that the fractal dimension of the fracture network has a size effect; with the increase in the size, the fractal dimension of the fracture network undergoes three stages: rapid increase, slow increase, and stabilization. In the rapid increase stage, K and β do not exist. In the slow increase stage, K exists and is stable, and β does not exist. In the stabilization stage, K and β both exist and are stable. The principal axes of the fitted seepage ellipses of K and β are orthogonal, and the main influencing factors are the direction and continuity of the fracture.

Investigation and Application of Fractals in Civil Engineering Materials

“…Fractal theory can be used to describe the formation and development of the fracture network and to characterize its structure. In Zhao et al's [4] work in this Special Issue, the fractal dimension, equivalent hydraulic conductivity (K), and equivalent non-Darcy coefficient of the fracture network are calculated, and the influence of the fractal dimension on K is studied. The results indicate that the fractal dimension of the fracture network has a sizable effect on K; with the increase in size, the fractal dimension of the fracture network undergoes three stages: rapid increase, slow increase, and stabilization.…”