Li Sumei, Chen Zuyu, Lu Feng
(Institute of Structural Materials, China Academy of Water Resources and Hydropower Research)
mention
This paper briefly introduces the search problem of landslide sliding surface and genetic algorithm, and tries to use genetic evolutionary algorithm to search the most possible sliding surface from the combination of arbitrary sliding surfaces of slope, that is, the sliding surface with the lowest safety factor. As an example, the application of genetic algorithm in the landslide analysis of the right bank of the intake of Tianshengqiao II Hydropower Station is analyzed.
Keywords slope; Safety factor; Genetic algorithm; European monetary union plan.
1. Introduction
In the process of slope stability analysis by slice method, it is a key step to determine the critical slip surface with the smallest safety factor from the set of possible slip surfaces. This is a problem of determining the minimum functional safety factor of the independent variable function of the sliding surface shape. Because of the complexity of the actual situation, the analytical method for finding this minimum value is difficult to put into practice. From the practical point of view, the method of solving the minimum safety factor of slope based on the optimization principle is more effective and convenient to apply. These methods include "exhaustive method", "golden section method" and "Powell method", but they can only be applied to the case of arc sliding surface or arc-straight sliding surface (improved arc method). Sun Jun applied the complex method to the fractured sliding surface with multiple degrees of freedom, and achieved good results, which was more in line with the rock slope. Chen Zuyu put forward the simplex method, which makes the optimization method of searching the most dangerous sliding surface of slope more effective and will not miss the possible minimum value. Simplex method program has been applied in many engineering, scientific research and educational units at home and abroad, and it has been continuously improved with the increase of applied engineering cases [1]. Simplex method makes the research and application of optimization method in rock slope stability analysis a big step forward. As an optimization method, genetic algorithm is a bionic optimization algorithm developed in recent years. Some scholars at home and abroad try to use genetic algorithm to search the slope sliding surface with the minimum safety factor in order to obtain better results. Literature [2] applies this algorithm to the heterogeneous soil slope with arbitrary shape based on the assumption of circular slip surface, and the search objective is to minimize the center and radius of circular slip surface. In this paper, on the basis of reference [1] and reference [2], the genetic algorithm is applied to search the minimum safety factor slip surface of arbitrary slope. According to the engineering practice experience, it is mainly the sliding surface of broken line combination. 2. Genetic algorithm and its application in geotechnical engineering.
As mentioned above, the problem of searching the most dangerous sliding surface of slope is the functional extreme value of safety factor on the shape of sliding surface. The main means of numerical method to solve this problem is iterative operation. The general iteration method is easy to fall into the trap of local minimum, and there is an "infinite loop" phenomenon, which leads to the failure of iteration. Genetic algorithm overcomes this shortcoming and is a global optimization algorithm.
In the long process of evolution, organisms have been developing from lower organisms to higher organisms, which can be said to be a wonderful optimization process. This is the result of natural environment selection. People study the phenomenon of biological evolution and conclude that the evolution process includes replication, hybridization, mutation, competition and selection. Inspired by the process of biological inheritance and evolution, some scholars put forward genetic algorithm. In the algorithm, genetic organisms are called individuals, and the adaptability of individuals to the environment is expressed by fitness. The fitness value depends on the chromosome of the individual. In the algorithm, chromosomes are usually represented by a string of numbers, and one bit in the string of numbers corresponds to a gene. A certain number of individuals form a group. All individuals undergo selection, hybridization and mutation to generate a new population, which is called a new generation.
The flow of the genetic algorithm calculation program can be expressed as follows [3]:
The first step in preparation
(1) Choose an appropriate coding scheme to convert variables (features) into chromosomes (number strings with length m). Usually coded in binary.
(2) Select appropriate parameters, including population size (number of individuals m), crossover probability PC and mutation probability Pm.
(3) Determine the fitness function f(x). F(x) should be a positive value.
The second step is to form an initial population (including m individuals). In the problem of slope sliding surface search, the possible sliding surface groups analyzed are taken as the initial groups.
The third step is to calculate the fitness value fi of each chromosome (string) and the total fitness value of the population.
The fourth step is to choose.
Calculate the selection probability Pi=fi/F and the cumulative probability of each string. Generally, the selection is made by simulating the algorithm of rotating Hua Lun. According to the size of Pi, it is divided into sectors with different sizes. Rotate m times to select m strings. The steps realized on the computer are: generating a random number r between [0, 1], and if r
intersect
(1) generates a random number between [0, 1] for each string, if r >；; Pc, and then the strings participate in the crossover operation, so after selecting a group that participates in the crossover, they are randomly paired.
(2) For each pair, a random number between [1, m] is generated to determine the intersection position.
Step 6 mutation
If the probability of change is Pm, the expected value of the number of digits that may change is Pm ×m×M, and each digit changes with equal probability. Specifically, a random number r between [0, 1] is generated for each bit in each string, and if r
If the number of new individuals reaches m, a new group has been formed, and the third step is turned; Otherwise, go to the fourth step to continue the genetic operation. Until the individual with the maximum fitness is found or the maximum evolutionary algebra is reached.
Because the selection probability is determined by the fitness value, that is, the chromosome with large fitness value has higher selection probability, which makes selection play the role of "survival of the fittest". Crossover makes chromosomes exchange information, combined with selection rules, so that excellent information can be retained and bad information can be discarded. Mutation is a gene mutation, the purpose of which is to produce a new variety with substantial differences. Although genetic algorithm is a random algorithm, it is directional, and its "random selection by probability" method is a tool in the directional search method. It is this unique search method that makes the genetic algorithm naturally avoid the local minimum trap that other optimization algorithms often encounter. The effectiveness of genetic algorithm in searching the optimal results has not been strictly proved mathematically, but its effectiveness has been reflected in many professional applications. As far as the current level of scientific understanding is concerned, genetic algorithm is a reliable method for the non-differentiable functional extreme value problem of safety factor of rock slope on the shape of sliding surface. 3. Genetic algorithm is used to search the slope sliding surface with minimum safety factor of arbitrary shape.
When looking for the most dangerous sliding surface of slope (especially rock slope), the actual shape of sliding surface is very complicated, and the main structural surface of rock mass and the shape of slope play a controlling role. From the past practical engineering experience, it can be concluded that the section shape of the sliding surface of rock slope in the sliding direction is a broken line, which is formed by connecting the structural surface of rock mass with the shear failure surface of local geotechnical materials. In this way, the problem of searching the most dangerous sliding surface can be simplified to the problem of optimizing from the combination of broken sliding surfaces. In this paper, genetic evolution algorithm is used to solve this problem.
(1) defines the objective function of genetic algorithm.
The objective function is defined as the safety factor of the slope, and the fitness value of the solution is expressed by the safety factor. When searching the most dangerous sliding surface of slope, the smaller the safety factor of the solution, the better the adaptability.
(2) Determination of initial population
According to the engineering geological survey records and experience of the slope, several slip surface shapes are preliminarily drawn up. As shown in figure 1, the sliding surface consists of point sequence Ai(xi, yi) (i= 1,? , n) means. Arrange the coordinates (xi, yi) of the point sequence AI as x 1y 1x2xy2? XNyN form, binary coding forms chromosomes. For the suggested sliding surface shape, the corresponding safety factor is calculated by EMU program [4].
(3) determine the search scope
According to experience, the possible range of coordinates (,yi) of each point Ai is determined. In this range, the shape of slope slip surface leading to the minimum safety factor is searched.
(4) Calculation
All the suggested slip surface shapes (chromosomes) of the initial population are submitted to the genetic algorithm program for calculation. See the previous article for the specific process.
4. Case analysis [4]
Figure 1 Schematic Diagram of Landslide on the Right Bank of the Intake of Tianshengqiao Ⅱ Hydropower Station
Take the landslide on the right bank of the intake of Tianshengqiao II Hydropower Station as an example, and figure 1 is its calculation diagram. The landslide is about 30m high with a total volume of more than 7000m3, which is mainly composed of Quaternary scouring sediments and construction waste. See table 1 for physical and mechanical parameters.
Table 1 Physical and mechanical properties of each soil layer
Shear strength index of soil density (g/cm3)
Internal friction angle cohesion (kPa)
① Construction waste1.8521.819.6
② Slope soil 1.85 2 1.8 0.0
③ Sandy soil 1.85 2 1.8 29.4
④ Sandy silt 1.85 20.8 34.3
⑤ River pebble and gravel 1.90 24.2 0.0
Before the landslide, the excavation of the retaining wall near the toe of the slope weakened the overall stability of the slope, so it can be concluded that the sliding surface of the landslide will pass by. This example will also ignore the influence of tensile cracks at the top of the slope in practical engineering. Five broken lines are selected to simulate the shape of sliding surface, and AiBiCiDiE(i= 1~4) is preliminarily determined as a possible sliding surface. The Y coordinate of the upper endpoint Ai of the sliding surface has been constrained, and the X and Y coordinates of the lower endpoint E have been determined, so the sliding surface has only 7 degrees of freedom. According to the requirements of genetic algorithm, the sliding surface is expressed as follows:
xAxByBxCyCxDyD
Table 2 lists the coordinates of four simulated sliding surfaces and the safety factor of EMU program analysis.
Table 2 Coordinate and safety factor of simulated sliding surface (coordinate unit m)
Safety factor of sliding surface xA xB yB xC yC xD yD
a 1b 1c 1d 1E 35.44 27.69 16.82 18.79 9.25 1 1.39 4 4.49 0.92
a2 B2 C2 D2 e 38. 15 30.60 20.69 23. 14 14.60 14. 12 8.37 0.99
a3 B3 C3 d3e 39.02 34. 18 18.47 26.28 10.4 1 16.07 4.58 1.02
a3 B3 C4 d4e 39.02 34. 18 18.47 25. 12 1 1.39 14.70 4.97 1。 03
Limit the search range of each degree of freedom to 2.0m. Four arranged digit strings are used as input data of genetic algorithm program for coding and calculation. After a lot of operations, the coordinate number string with the smallest safety factor is finally found in the largest group algebra (1000), and the following coordinates are formed after decoding:
(36.89,30.07)(33.25,2 1.52)(2 1.7 1,9.34)( 13.54,5.07)(0.0,0.0)
This is the sliding surface of ABCDE in figure 1 The corresponding safety factor obtained by genetic algorithm is 0.90. The slip surface form and safety factor are close to the actual situation.
5. Conclusion
Genetic algorithm is an efficient optimization algorithm, which can effectively solve the local minimum problem, the representation of nonlinear mapping relationship, the non-differentiability of nonlinear mapping relationship and other common optimization algorithms. The example results prove this characteristic. The main work of applying genetic algorithm to the search of landslide slip surface is to simplify the engineering problem into the form required by genetic algorithm, and it is necessary to refer to geological survey data and engineering experience in detail to make the simplified form close to the actual situation. For simplified search samples, the calculation of safety factor must be reliable, so some mature calculation programs, such as EMU, can be applied. After fully considering the actual engineering geological conditions and selecting practical search samples, the genetic algorithm program will certainly be able to search for the most likely sliding surface.
refer to
1 Chen zuyu, Shao changming, application of optimization method in determining the minimum safety factor of slope, journal of geotechnical engineering, 10, No.4, 1998.7.
2 Xiao Chuanwen, Liang Li, Lin, Application of Genetic Evolutionary Algorithm in Slope Stability Analysis, Journal of Geotechnical Engineering, Vol.20,No. 1,1998.
3 Zhou Ming, Sun Shudong, Principle and Application of Genetic Algorithm, National Defense Industry Press, 1999.6.
4. Chen Zuyu, Stability Analysis Program for Rock High Slope EMU, 1995.5.
Study on searching the minimum safety factor of slope by genetic algorithm
Feng Lu Chen Zuyu Li Sumei
(Structure and Materials Department, IWHR)
abstract
This paper introduces the search problem of minimum safety factor of slope and the principle of genetic algorithm. This theory has been used to solve this problem in order to find the most likely landslide. As an example, the application of genetic algorithm in the right bank landslide of Tianshengqiao Power Station is introduced.
Key words: slope, safety factor, genetic algorithm, EMU program.