边坡可靠性分析中g-line失效域及Copula优度评价研究

针对岩土体抗剪强度参数联合分布模型中Copula优度评价问题,借助g-line给出了一种边坡失效域的抗剪强度参数表征方法,并利用积分途径得到了不同Copula及不同安全系数条件下算例边坡的失效概率,以此探讨了不同Copula计算结果的差异性,重点分析了S_n(p_c)、AIC、RMSE及Bias指标下各Copula的评价效果,并以上述各指标值为评价对象,分别计算了各Copula的熵权系数,从而给出了一种加权组合的Copula形式。结果表明,二次多项式拟合g-line的效果良好,此时边坡失效域可由抗剪强度参数独立表征;常用的评价指标得出的最优Copula结果不唯一,当不能有效地识别最优Copula时,可采用加权组合的Copula进行可靠性分析,能减小计算误差,有效地消除不同Copula引起的失效概率差异性,也能避免因直接采用某些Copula而引起的对边坡可靠度偏保守或者过高估计的问题。

Investigation of failure domain by using g-line and optimum evaluation of Copulas in slope reliability analysis

The identification of optimum evaluation for different Copulas in shear strength parameters of soils (i.e., cohesion c and internal friction angle φ) is a challenge. According to the g-line, an approach to determine the failure domain of soils in terms of shear strength parameters is given. Thus, the failure probability of an instanced slope can be calculated directly by using the integral approach under different Copulas and safety factors, meantime, the differences of the results are discussed. The effects of evaluation of different Copulas are discussed mainly in terms of S_n(p_c), AIC, RMSE and Bias. After employing the above-mentioned index values as the evaluation objects, the entropy weights of the selected Copulas are calculated, and then a weighted combined Copula is proposed. The results show that using a quadratic polynomial can fit the g-line well, and the failure domain of slope can be represented by the shear strength parameters respectively. The optimum copula is not accordant when using the common evaluation indices, such as AIC, RMSE, Bias and S_n(p_c). When the optimum Copula is not identified accurately, a weighted combined Copula is recommended because it can effectively control the discrepancies and avoid the excessive or conservative estimation of slope reliability.