边坡稳定极限分析斜条分上限法的全局优化方法

边坡稳定极限分析斜条分上限法需要寻求最小安全系数对应的临界滑动模式。由于待优化变量中包含了滑裂面位置与条块界面倾角,问题的自由度与非线性程度明显增加,寻找安全系数的整体极值变得十分困难。本文建立了任意形状滑裂面通过与不通过软弱夹层两种情况下斜条分上限法滑动模式优化的数学模型。为保证在随机搜索过程中生成合理的滑动模式,引入一系列约束条件,将临界滑动模式的搜索问题转化为一个有界约束的数学极小值问题,并结合遗传算法和粒子群算法两种全局优化方法,对多个典型算例进行对比分析。研究表明,提出的模型可以解决优化过程中生成不合理滑动模式的问题,不仅极大地提高了优化效率,而且可以避免数值计算不收敛的麻烦;将模型与全局优化算法相结合,在大多数情况下能够得到一个合理的、与极限平衡解十分接近的上限解,具有较好的全局收敛性。

A global optimization algorithm of upper bound method with inclined interface blocks for slope stability

Using the upper bound method with inclined interface blocks,the optimization methods should be adopted to search for critical sliding mode with the global minimize factor of safety.Because the optimization variables include slip surface positions and inclined interface angles,the freedom and nonlinearity are increasing significantly and searching for the global minimize factor of safety becomes more difficult.In this paper,a mathematical model of sliding mode optimization is provided,considering the slip surface sliding along the weak interlayer or not.In order to generate proper sliding modes during the random search process,some geometrical constraints are introduced,finally the optimization problem is converted to the minimize problem with multi-degree of freedom and bound constraints.Combined with genetic algorithm and particle swarm algorithm,some typical examples are analyzed.The result shows that the mathematical model proposed in this paper can avoid generating the unreasonable sliding modes during the random search process,with the result that the optimization efficiency is improved significantly and the non-convergence of numerical calculation is avoided.Combined the mathematical model with the global optimization algorithms,the solution obtained is reasonable and very close to the limit equilibrium solution.