Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 498

explained by all possible models with small proof loads but can be best explained by only
one model at the higher proof loads ( Figure 13.14 ).

13.4 IMPleMentatIon oF Value oF
InForMatIon aSSeSSMent

There are useful tools that facilitate the implementation of the framework for assessing the
value of information. Both analytical and numerical methods are described in the following
sections.

13.4.1 analytical methods
A useful set of analytical methods for implementing Bayes' Theorem is available for select
cases of prior and posterior distributions for model parameters and likelihood functions
that are updated with random sampling (i.e., statistical independence between individual
measurements or observations). These cases are referred to as conjugate pairs since the form
for the prior distribution fits nicely with the form of the likelihood function in deriving an
analytical result for the posterior distribution, which has the same form as the prior distri-
bution. These results are widely published (e.g., Benjamin and Cornell 1970; Ang and Tang
2007); a summary of commonly used cases is presented in Table 13.1 .
When analytical results are available for implementing Bayes' Theorem, it may be pos-
sible with simple decision problems to develop analytical results for assessing the value of
information.

13.4.2 Illustrative example: Design quality
control program for compacted fill
To illustrate the derivation of analytical tools, consider an example of designing a quality
assurance/quality control (QA/QC) program for a compacted fill. The quality of the fill
to serve as a foundation for future construction will be indicated by its undrained shear
strength. The decision to be made is how many tests of undrained shear strength to conduct
during the construction of the fill.
Assume the undrained shear strength, X , is normally distributed with a mean value, M X ,
that is uncertain and an inherent standard deviation due to spatial variations and test-
ing error, σ X , that is equal to 200 psf. Model uncertainty in the mean strength is repre-
sented by a normal distribution with a mean value, μ μ = 1000 psf, and a standard deviation,
σ μ = 150 psf.
The cost of implementing a foundation design depends on the design shear strength that
is used, which is denoted as x *. The smaller the design shear strength, the greater the cost
of the foundation: Implementation cost = $20(1000- x *), where x * is in pounds per square
foot. If the actual strength, x , is less than the design strength, then the foundation will settle
excessively and there is an associated failure cost of $100,000.
The testing program will consist of n-independent measurements of the undrained shear
strength and it has a cost that is proportional to the number of tests: Test cost = $100n.
The decision tree for selecting the optimal design strength is shown in Figure 13.22 . The
design strength is obtained by minimizing the expected cost:

x ∗ − µ

′

µ

ECxC ( | ∗ ) = + C × P Failure ( ) = ( 20 − 04 . x ∗ ) + 100 × Φ

(13.20)

Implementation Failure

σσ

2

+

′ 2

X µ