Research On Optimization Of Non-circular Slip Surface According To Direct Search Method

Usually, calculation of the safety factor and determination of the potential critical slip surface of a slope can be divided into two stages:first, calculating the safety factor of a given slip surface, second, finding the minimum safety factor among all the possible slip surfaces. The purpose of this paper is focused on the second stage and the optimization of non-circular slip surface has been studied in this paper. The problem of optimization of non-circular slip surface is equal to the problem of nonlinear optimization. Among all the nonlinear optimization methods, direct search method has been wildly used in a lot of practical problems which showed that direct search method has the advantage of strong robustness and high search efficiency which leads to a very good result. Owing to the big advantages that direct search method has, this paper introduces a new method of optimization of non-circular slip surface based on the theory of direct search which is called "combination method of circular and non-circular". The reliability and efficiency of the new method has been proved by three examples and one practical project. Main work of this paper can be summarized as follow:(1) Basic theory of direct search method and three classical types of direct search method have been explained.(2) Pattern search method which is used in optimization of circular slip surfaces has been modified by changing the control variables from center and radius of the circle to three points on the circle. The ability to find the global minimum of this method has been proved by two examples.(3) According to the papers about the application of direct search method in optimization of non-circular slip surface, a new method of optimization of non-circular slip surface has been introduced based on "alternating variable method" and "quadratic fit". Examples show that this method is very efficient in finding the local minimum but sometimes fail to find the global minimum by being stuck into the local minimum which makes this method very sensitive to initial slip surface.(4) Combination of the method for optimization of circular slip surface and non-circular slip face that are introduced by this paper created a new method for optimization of non-circular slip surface which finds the critical circular slip surface first, then searches the critical non-circular slip surface using the critical circular slip surface as the initial slip surface. This new method is called as "combination method of circular and non-circular (CMCN)" by this paper.(5) CMCN method has been used in three non-homogeneous slope examples and comparison with the results obtained by other methods proves the validity of CMCN method.(6) CMCN method has also been used in a practical project and the practicability of this new method has been proved.