Fold catastrophe model of rock dynamic destabilization

The problems existing in rock dynamic destabilization are discussed by use of the catastrophe theory. There are three equilibrium states for the cusp catastrophe model. One is unstable, the others are stable. One equilibrium state can reach another equilibrium state. For the fold catastrophe model there are two equilibrium states. One is stable, the other is unstable. One equilibrium state can not change to the other equilibrium state. According to the energy conservation principle, the equilibrium equation is established. A fold catastrophe model of rock dynamic destabilization is generalized by adopting a general form of material constitutive equation. The equations of deformation catastrophe and energy release of the material are obtained. The catastrophe material constitutive relationship of Weibull distribution is introduced into the generalized fold model.