Modified Statistical Damage Constitutive Model of Rock Based on Normal Distribution

Due to the insufficiency of damage model, on the basis of studying deeply deformation and damage mechanism of the rock mass, considering the process and phenomenon of the damage of rock mass, damage part can be divided into two parts: the damage material and micro defects due to the change of damage material, then this paper puts forward a new definition of damage. Besides it proposes an impact factor γ which controls the relationship between two parts and the method of determining the parameters. Next, a new rock damage model is established through the analysis of microscopic stress of rock. Moreover, on the basis of the analysis of the relationship between effective stress and nominal stress and the introduction of statistical damage theory, this paper establish a statistical damage constitutive model of rock considering that Micro-unit strength obeys normal distribution. The model can well reflect the strain softening characteristic of rock mass and the strain hardening characteristic of rock mass, and the physical meanings of the model parameters are explicit .This model is more convenient for application. Finally, the rationality and feasibility of the model are identified through the comparative analysis of the existing research results and the previous results.