The mechanism of stability of fault system inducing roof water-inrush

This paper analyzes the strain stability during mining, which often causes a water inrush. Mining couses costant stress on the fault zone, which is a loading process on the system composed of fault material and surrounding medium. A cusp catastrophe model is presented and the necessary and sufficient conditions leading to fault systems are discussed. The fault zone is assumed to be planar and is a combination of two media: medium-1 is elastic-brittle or strain-hardening and medium-2 is strain-softening. The shear stress-strain constitutive model for the strain-softening medium is described by the Weibull's distribution law. It was found that the instability of a fault system mainly relies on the ratio between the stiffness of medium1 to the post-peak stiffness of the strain-softening medium, and the homogeneity index of strain-softening medium and the bifurcation point,k <= 1, which is the turning point of the fault system from stability to potential instability. One can judge the occurrence of fault instability from this feature and regard the indexDas a parameter, which reflects the precursory abnormality of a fault.