Research On Seismic Stability Evaluation Method Of Slope Based On Catastrophe Theory

The landslide phenomenon in China's geological disasters accounts for 76.2%,especially in rural areas with weak protection conditions,which has caused great harm to people's property and personal safety.Studying the stability of slope has important significance for effectively preventing and controlling landslide disasters and safe construction of engineering construction.Previous research methods have mostly adopted the limit equilibrium method,which is limited to the existence of assumptions and it is difficult to reflect the true slope condition.The catastrophe theory is suitable for studying complex nonlinear system problems.The catastrophe progression method is a new method to solve this problem derived from the catastrophe theory.The method is superior to the catastrophe theory in terms of computational complexity and difficulty.Based on the catastrophe progression method,the orthogonal experiment design principle is used to optimize the experimental scheme.The normalization formula is used to obtain the catastrophe grade value,and finally the stability evaluation table of the slope state is obtained,which is used to efficiently evaluate the slope state.The main research contents and results of the article are:(1)The basic principle of catastrophe theory is studied,and the shape of catastrophe models are deduced based on the potential function.Finally,by comparing the models,it is concluded that cusp catastrophe model and swallowtail catastrophe model are more widely used in solving practical engineering problems.Then,the basic principle and implementation steps of the catastrophe progression method are introduced.At the same time,the normalized formula of the catastrophe models are deduced,which lays a foundation for the application of the catastrophe progression method in the following chapters.(2)Time-history dynamic analysis is carried out for a set of slope examples in the orthogonal experimental scheme.Firstly,the natural vibration frequency and the natural vibration period of the slope structure are obtained by modal analysis,and then the mass and stiffness damping coefficients are obtained through calculation.Finally,the following conclusions are obtained: First,the combined displacement at the slope top is the largest in the time-history analysis of the dynamic displacement,and the closer to the border,the bigger.Second,during the time history analysis of the slope dynamic stress,the first principal stress and the third principal stress at the turn of the slope are the largest,followed by the slope foot and the slope top.(3)For the time-history dynamic stability analysis of slope under earthquake conditions,the paper use modal analysis to get the natural frequency and natural vibration period of the slope.Then,11 slope monitoring points are used to analyze the dynamic displacement response process and dynamic stress response process.First,the horizontal and vertical dynamic displacements are the largest at the top of the slope,followed by the waist and foot of the slope;the first and third principal stresses at the waist of the slope reach the maximum,followed by the foot and the top of the slope.Second,the horizontal and vertical dynamic displacements of the slope gradually increase with the increase of altitude.For the dynamic stress situation,the extreme values of the first and third principal stresses appear at the lower monitoring point No.11.(4)The catastrophe progression method is applied to study the seismic stability of slope,and the following conclusions are obtained: First,the change trend of safety factor are and catastrophe progression value basically the same,which shows that the catastrophe progression value can be used to evaluate the slope stability as the safety factor.Second,the evaluation table of slope stability state is obtained through the change characteristics of catastrophe progression value and safety factor.When the catastrophe value is less than 0.65,the slope is in instability state;when the range is 0.65 and 0.78,the slope is in metastable state;when the value is greater than 0.78,the slope is in a state of safety and stability.The accuracy of the evaluation table is 86.7% through the verification of slope example.Slope stability analysis is an extremely complex problem involving a variety of influencing factors.The paper only considers the bulk density and seismic load for the external factors of slope instability,but has not studied other influencing factors.How to analyze the influence of other factors and the coupling effects of various influencing factors on the stability of slope is an urgent problem to be solved in the current research.In addition,the paper establishes the internal structure of the slope under ideal conditions,and does not consider the existence of weak layers,joints and cracks inside the slope.This problem is a difficult problem in the study of slope stability.This kind of problem needs more profound research.