Modeling and simulation of bivariate distribution of shear strength parameters using copulas - Risk and Reliability in Geotechnical Engineering - page 108

Table 2.11 Comparison of probabilities of failure associated with different copulas and nominal factors of safety

a = [0.40, 0.58 m] b = [1.40, 1.64 m] λ = [1.00, 1.95] ρ = [ − 0.50, − 0.88]

Copula FS n = 1.03 FS n = 1.17 FS n = 1.30 FS n = 1.03 FS n = 1.17 FS n = 1.30 FS n = 1.03 FS n = 1.17 FS n = 1.30 FS n = 1.03 FS n = 1.17 FS n = 1.30

Gaussian 1 1 1 1 1 1 1 1 1 1 1 1

Plackett 1.17 1.84 3.89 1.17 1.84 3.89 1.17 1.98 7.17 1.17 3.78 2.45 × 10 4

Frank 1.14 1.60 2.92 1.14 1.60 2.92 1.14 1.75 5.47 1.14 2.96 1.13 × 10 4

No.16 1.68 4.77 21.68 1.68 4.77 21.68 1.68 5.88 87.45 1.68 7.39

7.54 × 10 4

Note: The value is calculated by p f / p f Gaussian .