Copula理论下基于g-line失效域的边坡可靠性分析

Copula-based slope reliability analysis using g-line failure domain

针对边坡失效概率计算中功能函数难以确定、多重积分计算不便等问题,提出了Copula理论下基于g-line失效域的边坡可靠性分析方法。首先简要介绍了Copula理论,给出了基于Copula理论的边坡可靠性分析步骤,进而探讨了一般均质边坡的g-line曲线拟合形状及表征边坡失效域的抗剪强度参数范围,结果表明,二次多项式能很好拟合g-line曲线,内摩擦角和黏聚力可表征g-line曲线下的边坡失效域。以一均质边坡为例,通过在g-line失效域内积分,得出了3种Copula函数下边坡的失效概率,均与FORM及MCS法得出的结果比较接近,从而验证了Copula理论下基于g-line失效域的边坡可靠性分析方法的合理性。最后,讨论了不同Copula函数下失效概率计算结果的差异性随安全系数变化的特点,认为在低失效概率(高安全系数)时,可靠性分析结果对Copula函数类型比较敏感,应重视不同Copula函数类型引起的计算结果差异性及最优化问题的研究。

To overcome difficulties in calculating the failure probability of slopes such as determining the performance function and solving multiple integration, a Copula-based method for analyzing slope reliability through the g-line failure domain was proposed in the present paper. Firstly, the Copula theory was briefly introduced and the procedures of Copula-based slope reliability analysis were presented. Then we discussed the g-line curve-fitting shapes of general homogeneous slopes and the range of shear strength parameters which represented the slope failure domain. It is found that the g-line curve can be fitted as the quadratic polynomial and the slope failure domain under the g-line curve can be represented by the friction angle and cohesion. Taking a homogeneous slope as an example, the failure probabilities of three different types of Copula functions were obtained by integrating the g-line failure domain. The results approximate to those calculated by traditional methods such as FORM and MCS, which demonstrate the reasonability of the Copula-based method for analyzing slope reliability using the g-line failure domain. Finally, we discussed the characteristics of the failure probabilities calculated by different Copula functions change with the safety factor. When the failure probability was low or the safety factor was high, the results are sensitive to the type of Copula function. Therefore, attention should be paid to the study of the different results caused by different function types and of the optimization problem.