| Slope stability and bearing capacity analysis have wide application prospect and practical significance in civil engineering and hydraulic engineering, which can be solved by unified numerical method as their analytical methods belong to the same theoretical system. The proposing of the upper bound method with inclined interface blocks makes it possible for the establishment of the unified method. However, the upper bound method contains the process of searching for the critical failure mode by optimization method, which is also the key point. The traditional numerical optimization algorithms always stuck in local minima when the inclined interface angles are added as optimization variables, as well as slip surface coordinates. Therefore, a global optimization algorithm needs to be proposed to solve this problem. As an efficient parallel stochastic global optimization algorithm, Genetic Algorithms does not rely on the gradient information of the objective function in the optimization process, therefore especially suitable for dealing with the complex nonlinear, multi-degree of freedom and multi-extremal problems, just like searching for the critical failure modes of upper bound method. According to the characteristics of optimization problems, some improvements are introduced in Genetic Algorithms. Therefore, the contents of this paper are listed as follow:The basic principles of upper bound method are recalled, including the upper bound theorem and the principle of virtual work. The solving process, integral equations and the construction of critical slip mode are introduced, and the difficulty of finding the critical slip mode is discussed.After introducing the basic principles and operating steps of Genetic Algorithms, Genetic Algorithms is applied in upper bound method to obtain the critical slip mode, meanwhile, the generation of initial slip surface, the selection of fitness function and genetic operators, and the treatment of unreasonable slip surface are discussed. For the drawback of premature in simple genetic algorithm, the micro-genetic algorithm combined with non-uniform mutation algorithm is introduced to improve its global searching ability, and the joint optimization process with simplex method is added after the improved genetic algorithm finished. Taking a simple slope and bearing capacity of non-gravity foundation for example, the results show that the improved genetic algorithm can make the problem converging strongly to the same critical failure mode for different initial slip surfaces, which is better than traditional numerical optimization algorithms in global searching and local convergence ability.The upper bound method is applied in ultimate bearing capacity to obtain the upper bound solutions of empirical factor of bearing capacity formula with the joined influence of cohesion, loads and soil weight by virtue of improved genetic algorithm. By comparing the upper bound solutions with the theoretical or experience solutions, the results show that the upper bound solutions of Ne and Nq have little difference with the theoretical solutions, and that of N. is closed to Vesic’s experience solution.The application of the upper bound method in deep anti-sliding stability analysis of concrete gravity dam foundation is discussed. The conformity between upper bound method and equal safety factor method is proved though a simple dam example with double sliding surfaces. Finally, the upper bound method is applied to the stability analysis of the Xiangjiaba concrete gravity dam, and the results of stability analysis are discussed, considering the angle of force between blocks. The results show that critical factor of safety obtained by optimization algorithm meet the requirements of K≥3.0in the specification. For those safety factors which do not meet, let the angle be equal to3°, then critical factor of safety will meet the requirements of specification. |
