Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 144

100%

CDF for s F = 0.23

90%

CDF for s F = 0.38

80%

70%

60%

50%

40%

Normal
probability of
failure = 1.5%

Normal
probability of
failure = 9.4%

30%

20%

10%

0% 0.5

1 1.5

F = Factor of safety

2 2.5

Figure 3.12 Illustration of the effect of standard deviation on probability of failure for F = 1.50.

(1.6 * 0.23 = 0.38) increases the P f by more than 6 times. Thus, a 60% increase in uncer-
tainty results in more than a six-fold increase in the probability of failure, all other things
being equal.

3.4 ProbabIlItY oF FaIlure anD FaCtor oF SaFetY

3.4.1 What is “failure?”
The phrase “probability of failure” comes from the theory of probability and reliability,
which is neutral with regard to consequences of failure. The event described as “failure”
need not necessarily be catastrophic. For example, if the factor of safety against a retain-
ing wall sliding was less than 1.0, the wall might slide a short distance, the sliding move-
ment would result in a decrease in the earth pressure, and sliding would stop. If the earth
pressure increased at a later time due to creep in the backfill or due to some other cause,
another increment of sliding might result. Eventually, if repeated episodes of sliding resulted
in significant displacement of the wall, this behavior could be considered to be unsatisfac-
tory performance of the wall, but probably not a catastrophic failure. However, if the factor
of safety against instability of a soil slope was less than 1.0, large movements might occur,
perhaps suddenly. Such movements could indeed be catastrophic, resulting in significant
damage to structures on or below the slope, or even a threat to life. In recognition of the
important difference between catastrophic failure and less significant performance prob-
lems, the Corps of Engineers use the term “probability of unsatisfactory performance” to
describe more benign occurrences (U.S. Army Corps of Engineers, 1997).
Whatever terminology is used, it is important to keep in mind the real consequences of
the event analyzed, and not to be blinded by the word “failure” when the term “probability