Mathematical Reconstruction Analysis of a Natural Fracture Network in Rock Based on a Modified Fisher Model and Its Numerical Realization

ABSTRACT Fractures are one of the most critical factors influencing the mechanical properties of rocks. To explore the quantitative description method of fracture networks in natural rock masses and achieve precise mathematical reconstruction of the stochastic distribution characteristics of natural fractures, the apparent fracture distribution characteristics of 499 fractures in 12 standard specimens were investigated. The results show that there is a significant correlation among the density, length, and dip angle of fractures in different directions. Based on this, a quantitative description method for fracture networks that considers the relationship between fracture density and orientation is proposed. Combined with the Fisher model, the probability density distribution function of natural fracture orientation density was established. Using this method, the equivalent numerical analysis model of rock specimens containing natural fractures was reconstructed on the RFPA platform, and numerical experiments of triaxial loading and unloading were performed on the reconstructed equivalent fractured rock numerical model. This method can quantitatively describe the geometric distribution characteristics of fractures in natural rocks. The modified Fisher model enables the visual reconstruction of natural fracture networks, offering an effective technical approach for building equivalent numerical analysis models of rocks with natural fractures. It is highly valuable for studying the coupled mechanical behavior of multi‐physical fields in natural fractured rocks and provides an equivalent analysis method for visualizing and analyzing the damage process of natural fractured rocks.