Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 507

Expected consequence
for the decision given
a simulation

Simulated
information ( )
given a model
parameter (q)

Updated probability of
the model parameters
(q) given simulated
information ( )

Expected
consequence for the
decision averaged
over all information

Likelihood of simulated
information ( ) given a
model parameter (q)

Updated probability
of consequences for
each alternative

Simulated model
parameters (q)
from prior for q

Value of information analysis for four test piles 5.42

5.96

E (Cost| Data)

E (Cost| No data)

r i, j 0.54

0.5 Value of information

Random
gradient
for unit
side shear

Correlated
random test
results (kN)

P (pile
does not
fail)

P ( 1 , 2 , 3 , 4 |q) P (q | 1 , 2 , 3 , 4 )

P (C| )

30m
pile

35m
pile

q (kPa/m) 1.0 1.3 1.6 1.0 1.3 1.6

$1,000

1 2 3 4

1
2
3
4
5
6
7

1.6
1.3
1.0
1.0
1.0
1.0
1.3

603
887
725
673
559
1004
727

826
776
598
627
776
1246
764

645
1181
590
702
715
791
575

708
699
826
416
357
571
982

1.3E-03
2.2E-05
1.5E-03
3.1E-03
3.1E-03
1.3E-05
4.5E-04

2.8E-03
1.2E-03
2.8E-03
2.2E-03
2.2E-03
1.0E-03
2.6E-03

1.4E-03
2.3E-03
1.3E-03
7.5E-04
7.3E-04
2.3E-03
1.9E-03

0.235
0.006
0.265
0.509
0.517
0.004
0.09

0.508
0.344
0.497
0.368
0.363
0.310
0.52

0.257
0.650
0.238
0.123
0.120
0.686
0.39

0.956
0.987
0.953
0.925
0.924
0.988
0.974

0.994
0.998
0.994
0.990
0.990
0.999
0.997

6.47
5.07
6.50
6.74
6.74
5.03
5.68

Figure 13.30 Excerpt from Excel ® spreadsheet illustrating value of information assessment with Monte
Carlo simulation.

probability distributions for pile capacity ( Figure 13.14 ). For small proof loads, the informa-
tion is less valuable because it is unlikely that a pile will be loaded to failure, meaning that
the results will not be able to discriminate between the different models of pile capacity.
Likewise, for large proof loads, the information is less valuable because it is unlikely that a
pile will survive the proof load.

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

ρ εi, εj
= 1.0

ρ εi, εj
= 0.75

ρ εi, εj
= 0.50

ρ εi, εj
= 0.25

ρ εi, εj
= 0.0

0 2 4 6

Number of test piles

8 10

Figure 13.31 Value of information versus number of load tests for pile foundation design.