Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 175

Table 3.20 Number of calculations required for the reliability
methods where N is the number of variables
Reliability method

Number of calculations

Taylor Series

2N + 1

Point Estimate 2 N

Simplified Hasofer Lind Depends on iterations, generally

more than Taylor Series or Point
Estimate

Monte Carlo Simulation

Typically > 5000

3.13.1 Significance of the variables
Because of the few extra calculations required, the Taylor Series method is the simplest
reliability method available to calculate probability of failure. Another advantage of the
Taylor Series method is that it allows an engineer to see how significant each variable is
to the overall factor of safety. As each variable is decreased or increased by the standard
deviation, the factor of safety is calculated. It is therefore easy to see which variables
have the largest effect on the factor of safety. Seeing these effects is difficult with the
PEM because more than one variable is changed at a time. It is also difficult to see these
effects with the Simplified Hasofer Lind method for the same reason. When performing
Monte Carlo simulations using @Risk™ a sensitivity analysis is also performed by the
program. This makes it very easy to see which variables influence the factor of safety
calculation.

3.13.2 accuracy
The precision with which P f can be computed depends primarily on the accuracy with which
the most likely values and the standard deviations of the variables that define the problem
can be estimated. In geotechnical engineering applications, where data are often sparse and
estimated values of parameters and their standard deviations are themselves uncertain, com-
puted values of P f cannot be expected to be highly precise. Here, accuracy of the methods is
discussed independent of choosing the standard deviation. The following observations can
be made when comparing the methods:

1. Values of P f computed assuming that the factors of safety are normally or lognormally
distributed are both equally as accurate when compared to the Monte Carlo method
results.

2. Values of P f computed by the PEM, assuming normal distribution of the factor of
safety, are consistently higher than the Monte Carlo values.

3. The Simplified Hasofer Lind method more closely agrees with the results of the Monte
Carlo simulation than the Taylor Series or the PEMs.

3.14 SuMMarY

It is important to remember that estimates of the probability of failure are just that—esti-
mates. Their value lies in their order of magnitude—is it 0.1%, 1%, or 10%? These orders
of magnitude, 0.1%, 1%, and 10% can be viewed as low, medium (or normal), and high.
Additional digits, such as 1.76%, do not add more value to the estimate.