Stability Analysis Of Homogeneous Soil Slop Based On Variational Method

Slope stability analysis is a classic and important topic of geotechnical engineering.Due to the complexity of the instability mechanism and the diversity of incentives,the theory of slope stability analysis and the understanding of landslide disasters are worth further exploration.In the commonly used slope stability analysis,the traditional limit equilibrium method is widely used.It can not be solved because it only uses the static equilibrium in the limit state.Then various static assumptions are introduced which are proved unreasonable and unnecessary.Based on the traditional limit equilibrium method,this paper introduces the variational method to analyze the slope stability problem.The advantage is that it does not need any assumption,only the slip surface function and its upper normal stress distribution function are regarded as unknown functions,and the objective function is regarded as the functional of these two unknown functions,and it is transformed into solving unconstrained functional extremum problem.The main work of the thesis is as follows:(1)The development history of the limit equilibrium variation method is reviewed comprehensively based on the date collected by author and the research status at domestic and abroad is expounded.And it briefly introduces the basis of variational method.(2)By using the global limit equilibrium variation method,a detailed theoretical derivation and solution process is given.And the expressions of the critical slip surface function and stress function and the solution method of the safety factor are obtained.Based on the international classic slope exam questions,the critical slip surface and safety factor under various special conditions and general conditions are analyzed with the variation of soil strength parameters c ??.And the influence of the crack at the top of the slope on the stability of the slope is considered.(3)Furthermore,the optimization algorithm of the limit equilibriumvariation method is proposed combined the geometrical characteristic of the critical slip surface which has been obtained.And the theoretical completeness of the method is proved from both geometric and physical meanings.(4)Based on the actual failure mechanism of the slope soil,the defects of the safety factor definition in the current project are discussed,and the definition of the safety factor under the new concept is given.The safety factor and the position of the most dangerous slip surface under the influence of various influencing factors are discussed separately,and compared with the strength reduction method,and the difference of the results is analyzed.(5)Write a MATLAB program to solve the theoretical formulas derived above.