Programming Development And Application Of Three Dimensional Limit Equilibrium Method For Slope Stability Based On Matlab

Slope stability analysis has been a hot topic for scholars at home and abroad.Based on Mohr-Coulomb yield criterion and the static equilibrium on the basis of two-dimensional limit equilibrium method,is one of the most commonly used methods in slope stability analysis.Two-dimensional limit equilibrium method assumes that the slope is in plane strain state,only a limited number of 2D profile instead of the real 3D spatial stability analysis of the landslide mass and ignore the influence of lateral boundary,the calculation results are too conservative.Three dimensional limit equilibrium law considers the sliding force on the side of the sliding surface.Based on the previous work,this paper continues to study the three dimensional limit equilibrium method.In view of Chinese scholars,breaking through the traditional assumption of the force acting on the column and presenting a more rigorous three-dimensional limit equilibrium method.In this paper,the method is improved in the process of solving the equations of safety factor,and the solution of the integral term in the equation is solved by using the idea of the discrete integral and the summation.Based on Matlab,the program is developed for several classical two-dimensional methods and the improved three-dimensional limit equilibrium method.Finally,three numerical examples and nine landslides are used to validate and apply the program developed in this paper:1.In view of the strict three-dimensional limit equilibrium method proposed by Chinese scholars,this paper adopts the idea of the discrete integral and the summation to improve the solution process.Calculation of vertex coordinates of each discrete part of the surface after simplifying and combining the discrete surface,equation is used to compute the discrete points of each part,and then for each equation can be obtained and the value of the integral,Finally,the equilibrium equations are constructed according to the 4 equilibrium equations of the whole sliding body.The results show that the more discrete parts,the closer to the fixed value and the higher precision.2.Based on the Matlab,the improved Sarma method,Janbu method,Bishop method,transfer coefficient method and the strict three dimensional limit equilibrium method are developed.In order to facilitate the conversion of data,this paper also compiles the data file conversion program,which enhances the usability of the program.Combined with two classical examples,the algorithm is verified.The improved Sarma method,Janbu method and Bishop method are used to verify the numerical example.The example two is used to verify the three dimensional limit equilibrium method.Example 1,the calculation results of Janbu method and Bishop method is more conservative,the improved Sarma method considering lateral force,so the results are relatively large,the overall results of the three methods are similar,the M-P method is more strict and two-dimensional calculation results in similar.Example 2 and 3,compared to the previous 3D limit equilibrium method,proposed by several safety coefficient is relatively close to;This paper method and the three-dimensional M-P method,the three-dimensional Spencer method meet the three direction of the force equilibrium condition and part of moment balance,the theoretical model is relatively tight,so the calculation result is close to.Results fully show the rationality and reliability of the calculating program.3.In view of the design of the landslide support,in order to have a global awareness of the thrust to the space distribution.Based on the traditional transfer coefficient method,and take an calculation example of a typical landslide accumulation in southwest China,thrusts of points in the whole slope are calculated,and the result is showed in the three dimensional space.the slope is divided into grids of m rows and n rows firstly.Thrusts of each grid point are calculated through the program,then the results are shown as three-dimensional surfaces.Spatial visualization of thrusts is carried out to do further study of its vertical and horizontal distribution.The results show that,vertical thrusts increase as the safety factor increase,and the increasing degree decreases.The vertical thrusts decrease with the decrease of angles of slip surfaces and thickness.The horizontal distribution of the thrusts is nearly double-linear.4.In order to realize the visualization of the input and the calculation results,wedesign a GUI interface based on Matlab.This interface will be the development of several kinds of limit equilibrium method and landslide thrust program as a background program is used to calculate the interface provides a calculation method,the choice of parameters in the input and the output results of the calculation of interface at a glance,easy to understand,at the same time can provide great convenience for engineering application.