摘要
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。
Using the upper bound method with inclined interface blocks, the optimization methods shouldbe adopted to search for critical sliding mode with the global minimize factor of safety. Because the optimi-zation variables include slip surface positions and inclined interface angles, the freedom and nonlinearityare increasing significantly and searching for the global minimize factor of safety becomes more difficult. Inthis paper,a mathematical model of sliding mode optimization is provided,considering the slip surface slid-ing along the weak interlayer or not. In order to generate proper sliding modes during the random searchprocess, some geometrical constraints are introduced, finally the optimization problem is converted to theminimize problem with multi-degree of freedom and bound constraints. Combined with genetic algorithm andparticle swarm algorithm,some typical examples are analyzed. The result shows that the mathematical mod-el proposed in this paper can avoid generating the unreasonable sliding modes during the random searchprocess, with the result that the optimization efficiency is improved significantly and the non-convergenceof numerical calculation is avoided. Combined the mathematical model with the global optimization algo-rithms,the solution obtained is reasonable and very close to the limit equilibrium solution.
作者
孙平
陈玺
王玉杰
SUN Ping;CHEN Xi;WANG Yujie(Department of Geotechnique Engineering,China Institute of Water Resources and Hydropower Research,Beijing 100048,China;Institute of Water Resources and Hydro-electric Engineering,Xi'an University of Technology,Xi'an 710048,China)
出处
《水利学报》
EI
CSCD
北大核心
2018年第6期741-748,756,共9页
Journal of Hydraulic Engineering
基金
国家重点研发计划课题(2017YFC1501103
2016YFC0401804)
国家自然科学基金项目(51709282)
关键词
边坡稳定
临界滑动模式
斜条分上限法
全局优化
slope stability
critical sliding mode
upper bound method with inclined interface blocks
global optimization model