| By two fundamentally different phenomenon changes introduced mutation theory, combing the development of catastrophe theory, the basic form and its characteristics. Analyzed the stability of the system corresponding to different areas, which divided by bifurcation within the control plane. According to the results of previous studies, summarized the general steps to solve slope stability and other engineering problems based on cusp catastrophe theory.In this paper, by analyzing the diffraction pattern of the black rock XRD experiments show that: the main component of the black rock is quartz,muscovite, illite, chlorite and minor amounts of pyrite. Pyrite susceptible to oxidation, the resulting acidic water can cause chemical alteration mineralogy,and it cracks, shear strength. After a long period of erosion, black rock internally generated weak interlayer.Based on the black rock slope geological conditions, rock slope mechanics model was built, Considering the strain softening, water weakening of weak interlayer and rainfall and other factors, the cusp catastrophe model was established. Based on catastrophe theory to explain three slope evolution, such as the stability of the slope, type of slope instability and hysteresis synchronous type of slope instability, and give the necessary condition for instability failure of slope. For the stability of the slope, through a comparative analysis shows that: the cusp catastrophe model established in this paper is superior to the traditional limit equilibrium method stiffness.By analysis the actual project shows that: solving the problem of slope by cusp catastrophe model established in this paper is correctness, and is actually consistent. To make the calculation simple, fast, according to the results of this study, the program for the calculating the slope stability and slope instability critical factor was written by MATLAB language. |