Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 506

Simulate set of model parameters from prior
probability distribution for model parameters

Simulate a set of information from the probability
distribution for information given a set of model
parameters

Update the prior probability distribution for the
model parameters based on the information

Repeat N times and
approximate the
expected consequence
for the decision as the
sample average from
the N simulations

Update the prior probability distribution for the consequence of each
decision alternative based on the updated probability distribution for the
model parameters

Calculate the updated expected consequence for each
decision alternative based on the updated probability
distribution for the consequence

Establish the expected consequence for the decision as the
maximum expected consequence among the decision
alternatives

Figure 13.29 Conceptual flow chart to approximate value of information numerically.

of the possible sets of information, which generally will involve sampling from multivariate
probability distributions, can be facilitated using Markov Chain Monte Carlo methods (e.g.,
Hastings 1970).

13.4.4 Illustrative example: Pile foundation load tests
The pile foundation design problem described earlier ( Figures 13.12 through 13.21 ) provides
an example to illustrate the use of numerical methods in assessing the value of information
from pile load tests. An excerpt from an Excel ® spreadsheet used to approximate the value
of information is shown in Figure 13.30 .
The value of information is shown for load tests to failure in Figure 13.31 . For each point
on these graphs, 10 sets of 10,000 realizations were used producing 95% confidence bounds
on the estimated value for the value of information that are all smaller than ±1% of the
estimate. There are diminishing returns in increasing the value of information by increas-
ing the number of load tests. For independent test results, the value of perfect information
is approached with 10 load tests. The value of information from multiple tests decreases
as the correlation between test results increases (i.e., the contribution of systematic varia-
tions to the total variations increases). Also, the number of tests required to achieve perfect
information increases as the correlation between test results increases; at the limit of perfect
correlation, it is not possible to achieve perfect information no matter how many load tests
are performed ( Figure 13.31 ).
The value of information is shown for proof load tests in Figure 13.32 . The value of infor-
mation is greatest when the proof load is at 800 kN, which is near the center of the possible