Stability Analysis Of Rock Slope Based On Cusp Catastrophe Theory

In recent years,geological disasters such as slope collapse often occur,and the catastrophic consequences caused by it seriously threaten the safety of human life and property.There are many mountains and complex terrains in China,especially in the southwestern region,where landslides are particularly serious.Reasonable and effective evaluation of the stability of rock slope has been widely concerned by scholars at home and abroad.The establishment of accurate mathematical model to describe the state of slope instability system is the key link for slope management.However,since the slope collapse usually has significant abruptness and leap,the conventional calculus calculation can not describe this discontinuous change phenomenon.Therefore,it is of great theoretical value and practical significance to explore and analyze the stability of the slope.At present,there are many factors affecting the stability of slope,and the relationship is complicated.The conventional calculus calculation can't describe the problem of energy change.The main methods at home and abroad are limit equilibrium method and finite element method.These methods have certain deficiencies to some extent..Although the limit equilibrium method is simple in calculation,the reliability of the method is reduced due to the simplification of the method.The finite element method can better reflect the stress-strain relationship of each point in the rock slope,but it cannot be used for the large displacement landslide problem.Therefore,based on previous studies,this paper comprehensively considers various factors affecting rock slope stability,and introduces orthogonal test method for sensitivity analysis and superior combination analysis.Therefore,based on the mathematical basis of the catastrophe theory,the potential function unique to the rock slope system is calculated and a catastrophe model describing its instability is established,and then the mechanical conditions and instability mechanism are calculated.In this paper,by analyzing the basic factors such as the factors affecting the stability of rock slope,the type of structure and the failure mechanism,the safety stability coefficient of rock slope is taken as the research object,and the orthogonal test method is introduced to perform sorting and better combination analysis of sensitivity ofthe factors affecting the safety stability coefficient.On the basis of the orthogonal experiment,the factors that have a significant influence on the safety and stability factors are selected as the influencing factors,and the multi-factors and multi-levels of the slopes are selected in the common range of the influencing factors,and combined with the theoretical basis of the catastrophe theory.The mechanical conditions and criteria for the instability of the slope of the study area are derived by the cusp catastrophe method and the limit equilibrium method respectively.The results show that the limit equilibrium method is theoretically a method to analyze the stability of rock slopes rigorously.However,in practice,the reliability of the results is reduced due to the simplification of the assumptions in the calculation process.When using the cusp catastrophe model to evaluate the stability of rock slope,the effects of various factors on the stability of rock slope are considered comprehensively.The results are safer than the limit equilibrium method,which indicates that the cusp catastrophe method has higher feasibility in actual geological engineering analysis and evaluation.