遗传算法在斜条分上限法中的应用探讨

 应用斜条分上限解法求解边坡稳定、地基极限承载力等问题时，需要借助优化手段寻求最优的上限解。由于斜条分法中增加了条间倾角作为优化自变量，导致优化变自量增加，传统的数值优化算法经常陷入局部极值的陷阱。本文以无重力地基承载力问题为例，通过基于非均匀变异的微型遗传算法求解其临界滑移模式。发现改进后的遗传算法具有较好的全局搜索能力和局部收敛能力，能使问题较好地收敛到闭合解；采用改进遗传算法与单纯形法结合或滑裂面坐标和条块界面角分开优化的方式可以得到更为精确的解答。最后用该数值方法对地基承载力公式中考虑地基土重力的经验系数进行了对比验证。

DISCUSSION ON APPLICATION OF GENETIC ALGORITHM TO UPPER BOUND METHOD WITH INCLINED INTERFACE BLOCKS

Using the upper bound method with inclined interface blocks，the slope stability and ultimate bearing capacity problems are solved to obtain the best upper bound solutions by virtue of the numerical approach. The traditional numerical optimization algorithms always stuck in local minima because of the inclined interface angles as optimization variables. In this paper，taking the bearing capacity of non-gravity foundation for example，the micro-genetic algorithm combined with nonuniform mutation algorithm is introduced to search the critical failure modes. The results show that the improved genetic algorithm can make the problem converging strongly to the theoretical solution，which is better than traditional numerical optimization algorithms in global searching and local convergence ability. More accurate solution can be obtained by combining the improved genetic algorithm with simplex method or optimizing slip surface coordinates and inclined interface angles separately. Finally，the empirical factor of bearing capacity formula with the joined influence of soil weight is verified by this numerical method.