基于交替变量局部梯度法对土质边坡的三维稳定性分析

›› 2014, Vol. 35 ›› Issue (3): 759-764.

基于交替变量局部梯度法对土质边坡的三维稳定性分析

孙树林^{1, 2}，王天宇¹，刘小芳¹，余文平¹，夏银枫¹

1. 河海大学地球科学与工程学院, 南京 210098; 2. 河海大学水文水资源与水利工程科学国家重点实验室，南京 210098

收稿日期:2013-06-17 出版日期:2014-03-10 发布日期:2014-03-19
作者简介:孙树林，男，1963年生，博士，教授，博士生导师，主要从事地质环境与地质灾害方面的工作

Three-dimensional stability analysis of a soil slope based on alternating variable local gradient method

SUN Shu-lin^{1, 2}，WANG Tian-yu¹，LIU Xiao-fang¹，YU Wen-ping¹，XIA Yin-feng¹

1. College of Earth Sciences and Engineering, Hohai University, Nanjing 210098, China; 2. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China

Received:2013-06-17 Online:2014-03-10 Published:2014-03-19

摘要/Abstract

摘要： 临界滑动面的获得是土质边坡稳定性分析中一个必要的过程，然而现有分析方法难以保证该临界滑面的准确性，而且部分分析方法在计算过程中会陷入局部最小值陷阱。基于单变量方法和最速梯度法，提出了交替变量局部梯度法，该方法能够突破最优化方法应用在边坡稳定性分析上的瓶颈。首先，通过斯宾塞极限平衡方法和网格搜索法（或者其他确定临界滑面的方法），获得边坡初始椭球状临界滑面；其次，在该滑面上布置若干节点作为变量，目标函数为安全系数Fs关于空间节点坐标Zi的方程，为了使目标函数快速降低，沿负梯度方向循环优化每个节点，当满足一定精度要求时，即可获得三维土质边坡非圆弧状临界滑动面；最后，通过算例证明该方法可行，计算结果可靠。

关键词: 边坡稳定性, 非圆弧临界滑动面, 单变量方法, 最速梯度法, 交替变量局部梯度法

Abstract: It is necessary to obtain the critical slip surface in soil slope stability analysis. However, the existing analysis methods can not ensure the accuracy; and some analysis methods may fall into local minimum trap in the process of calculation. In order to obtain a non-spherical critical slip surface that is most similar with the actual slip surface, an alternating variable local gradient method is proposed based on univariate method and steepest descent method. This method can break through the bottleneck of optimization method applied to slope stability analysis. At first, the initial critical ellipsoidal slip surface of slope can be determined by Spencer limit equilibrium method and the grid search method (or any other method to determine the critical slip surface). Then, several nodes are arranged on the slip surface as variables; the objective function is an equation of safety factor Fs versus space node coordinates Zi; to make the value of objective function decrease fast, each node is optimized according to the negative gradient direction in every cycle. When the result meets the accuracy requirements, the non-spherical critical slip surface of the three-dimensional soil slope is obtained. Finally, this method is proved to be feasible and accurate by two examples.

Key words: slope stability, non-spherical critical slip surface, univariate method, steepest descent method, alternating variable local gradient method

中图分类号:

TU 432

孙树林，王天宇，刘小芳，余文平，夏银枫，. 基于交替变量局部梯度法对土质边坡的三维稳定性分析[J]. , 2014, 35(3): 759-764.

SUN Shu-lin ，WANG Tian-yu ，LIU Xiao-fang ，YU Wen-ping ，XIA Yin-feng，. Three-dimensional stability analysis of a soil slope based on alternating variable local gradient method[J]. , 2014, 35(3): 759-764.

参考文献

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