Analysis of the stability of earthen slopes and optimization of the sliding surface of slopes using the optimization algorithm

Dissertation for Master's Degree

Civil Engineering Department, Soil and Foundation Mechanics

Summary

One of the most important and at the same time most difficult topics in soil mechanics is the problem of the stability of gables.  Analyzing the stability of soil slopes in order to determine the most probable rupture process or in other words to find the lowest reliability factor is one of the important issues of geotechnical engineering. Among the mentioned methods, the optimization methods inspired by nature have been used the most to determine the most critical slip surface. Among various optimization methods, the method that can find the critical slip surface in a shorter time and with less analysis volume is more superior than other methods. One of the new optimization methods is the bird community method. In this thesis, the modified Bishop's method and its combination with the bird community algorithm, which is one of the non-classical and modern optimization methods, is used to find the critical slip surface of earthen slopes. In this thesis, a quick method to optimize the sliding surface of earthen slopes with the help of bird community algorithm and the modified Bishop method is presented. Keywords: slope stability, optimization, sliding surface, Bishop, confidence factor. Chapter 1. General. 1-1- Introduction.

Analyzing the stability of earth slopes in order to determine the most probable rupture process or in other words to find the lowest confidence factor is one of the important issues of geotechnical engineering. The methods used by researchers to find the slip surface can be divided into general categories. These three categories are: (A) Numerical method of calculation of changes (B) Soil mass method (C) Optimization method inspired by . Among the mentioned methods, optimization methods inspired by nature have been used the most to determine the most critical sliding level. The optimization of the slip surface of the gables is one of the unconstrained optimization problems that today these methods have a good range, although there is still a lot of possibility for their expansion. Among the various optimization methods, the method that can find the critical slip surface in a shorter time and with a smaller amount of analysis is more superior than other methods. Therefore, by collecting, comparing and analyzing the results obtained from various optimization methods, it is possible to choose and suggest the appropriate method for analyzing engineering problems. With the research and investigation even carried out regarding different optimization algorithms for the analysis of earthen slopes, the following result has been obtained in the above research: To find the slip surface in earthen slopes, using the bird community algorithm is suitable for the reasons mentioned below. One of the new optimization methods is the community method, and the advantages of the above method compared to other methods are as follows: 1- It has an easy mechanism to use Computer

2-Checking simple mathematical relationships

3-Using the objective function itself instead of using its derivatives unlike other methods

4- The high speed of convergence pointed to the solution of this algorithm.

Regarding the importance of determining the critical sliding level of gables, in this research, an attempt is made to analyze the gables using the modified Bishop method and combine it with the bird community algorithm and select the appropriate stability variables. Shirvani provides a suitable solution to reduce the amount of analysis and faster convergence of the algorithm. The optimization methods that have been used so far have their own limitations and problems, for example Aria and, using the conjugate gradient method, have determined the critical non-circular slip surface on the slopes. In this method, the first-order derivative of the confidence factor function is needed, which is highly complicated in some problems.  also used the simplex method to find the rupture level, which in this method has a high probability of getting involved in the local optimum. In recent years, Malkawi has used the Monte Carlo method to optimize the sliding surface, which according to the concepts of the Monte Carlo optimization method, using this method for modeling is difficult and time-consuming.Kombi and his colleagues and Mohammad Hossein Bagheripour and Ehsan Shahsundi have used the genetic algorithm to find the sliding surface of earthen slopes, which is more difficult and time-consuming due to the concepts of the genetic algorithm optimization method and the convergence speed of this method than the bird community optimization method. Cheng and his colleagues have used the bird algorithm to find the non-circular sliding surface in earthen slopes. Shui Lee has used the bird community algorithm to optimize the stability of Ash Dam. The bird community algorithm has also been used in the optimization of other engineering problems, including Perez and Behdinan, who used the bird community algorithm to optimize the strength of composite bars. Lee et al. have used the bird community algorithm to optimize structures with pin joints. Yang et al. have used the modified bird community algorithm to adapt dynamic problems. 1-2- Objectives of the thesis In this thesis, Bishop's method has been modified and combined with the bird community algorithm, which is one of the non-classical and modern optimization methods, to find the critical slip surface of the gables. Soil is used. The combination of Bishop's method and the algorithm of the bird community has caused that, unlike some methods used to optimize the stability of the roof, this method does not require a lot of time to repeat the analysis of the problem and avoid complex mathematical calculations. This method has an easy mechanism for simulating the problem for computer use and has the ability to combine it with other optimization methods. Another important advantage of the bird community algorithm compared to the aforementioned optimization methods is that it greatly reduces the possibility of getting involved in local optimization by selecting variables and determining the parameters of the algorithm, and with a higher probability than many optimization methods, the overall optimal solution can be found. Khaki is presented with the help of bird community algorithm and modified Bishop method. Authors' investigations and researches have shown that it is possible to speed up the bird community method to find the overall optimum by choosing more suitable variables and correctly determining the parameters of the algorithm. In this research, pleasure, the variables of the center of the circle and the starting points of the sliding surface have been selected as the variables of the problem. By analyzing and analyzing the problem, he determined suitable parameters for the algorithm, that the selection of these variables will prevent the production of additional sliding circles that are not decisive for the surface of the roof, and prevent additional repetition of the program to find the minimum confidence factor, as a result, it will lead to a faster convergence of the algorithm. earthen terraces in different ways to choose the right method for analyzing earthen terraces in this research.

The third chapter is related to the familiarization of general optimization methods and optimization methods that have been used so far for earthen terraces.

The fourth chapter has fully explained the bird community algorithm and its applications and the operation of the program prepared in this research, which is used to analyze and optimize the most likely sliding surface of earthen terraces.

The fifth chapter deals with the sensitivity analysis of the parameters of the bird community algorithm and the determination of the variables of Bishop's method and the solution of practical examples to prove the accuracy and validity of the proposed method, the results of which are given in the form of graphs and tables at the end of each example.

Chapter Two

Research background

2-1- Introduction

One of the most important and at the same time the most difficult topics in soil mechanics is the problem of the stability of gables.  Landslides occur in very different situations. These landslides may interfere with the natural slopes or cause the stability of the man-made hills to collapse. The occurrence of these slips may happen all at once or may last several months or even years. The stability of gables [1] has always been one of the topics of interest among genetic engineers, the importance of this issue is more evident when the sliding of a gable causes huge irreparable damages.