Study On The Upper Bound Limit Analysis In Stability Of Slopes

Upper and lower bound limit analysis methods are effective tools in solving Geotechnical Engineering problems. The former is one of the most popular issues in the field of Geotechnical Engineering and it includes two main methods:analytical method and finite elements method. In this paper, some researches which focus on these two methods have been done in the application of slope stability. Based on the optimization theory, slope stability upper bound limit analysis method with nonlinear failure criterion and upper bound limit finite elements method have been studied. Specific contents are as follows:To study the slope stability upper bound limit analysis method with nonlinear failure criterion, the author first introduced the linear and nonlinear failure criteria and then described in detail the basic theory of limit analysis and mathematical programming.Under the nonlinear failure criterion, circumscribed linear method was introduced. By combining the slice method and limit analysis upper bound method, the author has deduced the implicit expressions of stability safety factor in slopes with different sliding surface. Slope stability factor and safety factor with a nonlinear failure criterion were calculated by using sequential quadratic planning techniques. The impact of a nonlinear failure criterion on slope stability was analyzed by a concrete example. Finally, some comparison with existing researches have been done, and the result shows that the method introduced by the paper is correct.In the upper bound theorem, slope was discreted by finite element discretizational method. The paper has obtained the ultimate load and the safety factor by the mathematical programming after constructing the unit speed mode and setting up a linear programming model. In order to verify the feasibility of the theory, the author has analyzed a specific example. The impacts of relevant parameters on the calculation results has already been analyzed.