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.