最优化方法在确定边坡最小安全系数方面的应用

本文探索最优化方法用于寻找边坡稳定分析中最小安全系数的可能性。在常规的边坡稳定分析中,需要多次试算许多滑裂面,比较相应的安全系数,其成果不仅粗糙,而且有可能不是事实上的最小值。采用最优化方法,可以用严格的数值分析方法找到最小安全系数及其相应的“临界滑裂面”。本文采用单形法,负梯度法和DFP法。通过对一系列算例的分析验证,可以发现,最优化方法和理论解以及穷举法的计算成果吻合。本文还列举了工程实例的分析结果以说明其在工程设计中的实用性。采用最优化方法,可以使设计工作大大简化,成果更为可靠。

The Use of the Method of Optimization for Minimizing Safety Factors in Slope Stability Analysis

This paper explores the feasibility of the use of the methods of optimization for minimizing the safety factors in slope stability analysis. The routine precedure of finding the minmium safety factor includes comparisons of a number of potential slip surfaces which are basically selected by experience and random search. Low efficiency and unreliability are problems commonly encountered in profession.The methods of optimization allow a mathematically rigorous and reliable searching for minimum safety factor and its associated &;quot;critical slip surface&;quot;. In this paper, the simplex, negative gradient and Davidon-Fletcher-Powell methods were employed. Test problems with a closed form solution and grid search solutions showed all the above mentioned methods were capable of providing accurate results. A case history analysis showed the feasibility of the methods. It is concluded that the methods of optimization provide powerful means for practitioners to facilitate their routine work in the calculation of the minimum safety factor.