LRFD calibration of simple limit state functions in geotechnical soil-structure design - Risk and Reliability in Geotechnical Engineering - page 341

Figure 8.4 shows a plot of load bias values versus nominal (predicted) load Q n . The
visual impression is that load bias values are uncorrelated with predicted load values.
This is a necessary condition to allow the limit state function to be expressed in terms
of bias values ( Equation 8.8 ) . If this condition is not satisfied, then the load model can
be improved to remove this dependency or different load factors can be assigned to dif-
ferent ranges of predicted load. Statistical tests such as Spearman's rank correlation test
can be used to examine the hypothesis that X Q and Q n are uncorrelated at (say) a level

(a) 3 (b) 3

Outliers Outliers

2 2

1 1

0 0

Normal fit to all data
n = 93
μ Q = 1.00
COV Q = 0.316

-1 -1

Outliers

Lognormal fit to all data
n = 93
μ Q = 1.00
COV Q = 0.316

-2 -2

Outliers

-3 0.3 -3 0.3

0.5 1.0 1.5 2.0 1 2

Load bias, X Q Load bias, X Q

Load factor, γ Q

1.12 1.47

0.0 0.5 1.0 1.5 2.0

(c) 3 (d) 1.0 0.0

0.03

Lognormal fit
to upper tail
μ Q = 1.20
COV Q = 0.108

0.9 0.1

2

0.8 0.2

0.7 0.3

1

0.37

0.6 0.4

0.5 0.5

0

0.4 0.6

-1

0.3 0.7

Lognormal fit
to filtered data
n = 89
μ Q = 1.00
COV Q = 0.283

0.2 0.8

-2

Filtered data
n = 89

0.1 0.9

0.0 1.0

-3 0.3

1 2 0.0 0.5 1.0 1.5 2.0

Load bias, X Q Load bias, X Q

Figure 8.3 Load bias data: (a) Unfiltered data with normal fit, (b) unfiltered data with lognormal fit, (c) fil-
tered data with lognormal fit, (d) cumulative and exceedance fractions.