高边坡结构可靠度的二次处理有限元分析

本文依据强度折减理论,利用MIDAS/GTS有限元软件,分析计算了高边坡结构的安全系数K,找到边坡滑裂带的位置。在此基础上,对有限元输入数据和输出结果进行二次处理,建立基本随机变量c,f与滑裂带中单元的最大(和最小)主应力σ1(和σ3)的拟合关系f1(和f3),将其代入高边坡结构的功能函数Z中,使Z由隐式形式变为显式。基于该显式表示的Z,利用Monte Carlo法计算滑裂带中所有失效单元的可靠指标β1,并将其单元面积A1作为权重系数,经过加权平均得到边坡结构的整体可靠指标β。上述方法使得结合有限元软件计算边坡结构的整体可靠度得以简化。经实例分析可知,本文提出的方法是合理可行的,可使边坡结构整体可靠性分析得以简化,也可为高边坡结构整体可靠性分析提供理论参考。

FINITE ELEMENT METHOD BASED RELIABILITY ANALYSIS FOR STABILITY OF HIGH SLOPE STRUCTURE

Based on the strength reduction theory, the factor of safety K of high slope structure is calculated using finite element method (FEM) (software -MIDAS/GTS). The sliding strip of slope structure is found at first. The input data and the output data used in the FEM are disposed again. Then the relation f1 (and f3) between basic random variables c,f and σ1 (and σ3), which are most (and least) main stress, may be found. So, the high slope structural function Z can be changed into explicit form from the original implicit form using above relation f1 and f3. Based on this explicit function Z, the reliability index β1 of each failure element within a sliding strip is computed using Monte Carlo method. The area Ai of above element is taken as weight coefficient. Then the slope structural whole reliability index β can be given based on the mean value, which is the result of all the failure elements βi multiplied by Ai . The result of example shows that the present method is reasonable and feasible. It may simplify the computation program of slope structural whole reliability. And it can also be taken as a theory reference in high slope structural stability analysis.