Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 495

1.0

Load test result for 30-m
long pile = 700 kN

0.8 Prior

Updated

0.6

0.51

0.33 0.33 0.33

0.4

0.27

0.22

0.2

0.0

0.9 1.3 1.6
Gradient of unit side shear versus depth (kPa/m)

Figure 13.17 Prior and updated probability distributions for model parameter given one pile load test result
in pile foundation design.

The likelihood function in this case is a function of the sample mean of the individual load
test results, m ε . This likelihood function is shown in Figure 13.19 as a function of the num-
ber of independent tests for an example set of test results; the likelihood function becomes
significantly sharper as the number of independent tests increases.
The test results may not be independent; there may be a systematic variation due to spatial
proximity or measurement error as well as an independent variation. If the total variation

0.947 0.958

(a) 1.0

Load test result for 30-m
long pile = 700 kN

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Prior
Updated

E ( C ) = $6.870
E ( C /Data) = $6,410

0.053

0.042

4500 49,500

Consequence ($ per pile)

Pile length = 30 m

0.993 0.995

(b) 1.0

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Load test result for 30-m
long pile = 700 kN

Prior
Updated

E ( C ) = $6.550
E ( C /Data) = $6,460

0.007 0.005

6125 67,375

Consequence ($ per pile)

Pile length = 35 m

Figure 13.18 Prior and updated probability distributions for consequences given one pile load test result for
alternative pile lengths in pile foundation design.