关键词: 均质边坡, 失效概率, g-line曲线, Copula函数, 数值积分

Abstract: 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.

Key words: homogeneous slope, failure probability, g-line curve, Copula function, numerical integration