基于交替变量局部梯度法对土质边坡的三维稳定性分析  

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

作　　者：孙树林[1,2] 王天宇[1] 刘小芳[1] 余文平[1] 夏银枫 

机构地区：[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

出　　处：《岩土力学》2014年第3期759-764,共6页Rock and Soil Mechanics

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。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.

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 

分 类 号：TU432[建筑科学—岩土工程]