Modeling and simulation of bivariate distribution of shear strength parameters using copulas - Risk and Reliability in Geotechnical Engineering - page 94

(a) 0.025 0.25

Histogram
TruncNormal
Lognormal
TruncGumbel
Weibull

Histogram
TruncNormal
Lognormal
TruncGumbel
Weibull

0.020 0.20

0.015 0.15

0.010 0.10

0.005 0.05

0.000 0.00

15 35 55 75 95 115 16 19 22 25 28 31

ϕ (º)

c (kPa)

(b) 0.020 0.15

Histogram
TruncNormal
Lognormal
TruncGumbel
Weibull

Histogram
TruncNormal
Lognormal
TruncGumbel
Weibull

0.016 0.12

0.012 0.09

0.008 0.06

0.004 0.03

0.000 0.00

14 17 20 23 26 29 32

0 30 60 90 120 150

ϕ (º)

c (kPa)

(c) 0.010 0.15

Histogram

Histogram
TruncNormal
Lognormal
TruncGumbel
Weibull

TruncNormal
Lognormal
TruncGumbel
Weibull

0.008 0.12

0.006 0.09

0.004 0.06

0.002 0.03

0.000

0.00

50 110 170 230 290 350 4 8 12 16 20 24

c (kPa) ϕ (º)

Figure 2.3 Histograms of measured data and PDFs of fitted marginal distributions. (a) CD dataset, (b) CU
dataset, and (c) UU dataset.

identified best-fit marginal distributions using AIC and BIC provide better fits to the proper-
ties of measured shear strength parameters than the other candidate marginal distributions.

2.3.3 Identification of best-fit copula
After determining the best-fit marginal distributions of c and ϕ, the next step is to identify
the copula that provides the best fit to the measured dependence structure between c and ϕ.