ETL 1110-2-547
30 Sep 95
APPENDIX B: INTRODUCTION TO PROBABILITY AND
RELIABILITY IN GEOTECHNICAL ENGINEERING
R % Pr f
B-1. Introduction
'1
R ' 1 & Pr f
a. The objective of this ETL is to introduce some
basic elements of engineering reliability analysis
Pr f
'1&R
applicable to geotechnical structures for various modes
of performance. These reliability measures are
intended to be sufficiently consistent and suitable for
(2) In the engineering reliability literature, the
application to economic analysis of geotechnical
term failure is used to refer to any occurrence of an
structures of water resource projects. References are
adverse event under consideration, including simple
provided which should be consulted for detailed
events such as maintenance items. To distinguish
discussion of the principles of reliability analyses.
adverse but noncatastrophic events (which may require
repairs and associated expenditures) from events of
b. Traditionally, evaluations of geotechnical
catastrophic failure (as used in the dam safety context),
adequacy are expressed by safety factors. A safety
the term probability of unsatisfactory performance
factor can be expressed as the ratio of capacity to
Pr(U) is sometimes used. An example would be slope
demand. The safety concept, however, has short-
stability where the safety factor is below the required
comings as a measure of the relative reliability of
minimum safety factor but above 1.0. Thus, for this
geotechnical structures for different performance
case, reliability is defined as:
modes. A primary deficiency is that parameters
(material properties, strengths, loads, etc.) must be
R ' 1 & Pr U
assigned single, precise values when the appropriate
values may in fact be uncertain. The use of precisely
defined single values in an analysis is known as the
b. Contexts of reliability analysis.
deterministic approach. The safety factor using this
approach reflects the condition of the feature, the
(1) Engineering reliability analysis can be used in
engineer's judgment, and the degree of conservatism
several general contexts:
incorporated into the parameter values.
The estimation of the reliability of a new
c. Another approach, the probabilistic approach,
structure or system upon its construction and
extends the safety factor concept to explicitly incor-
first loading.
porate uncertainty in the parameters. This uncertainty
can be quantified through statistical analysis of existing
The estimation of the reliability of an existing
data or judgmentally assigned. Even if judgmentally
structure or system upon a new loading.
assigned, the probabilistic results will be more
meaningful than a deterministic analysis because the
The estimation of the probability of a part or
engineer provides a measure of the uncertainty of his
system surviving for a given lifetime.
or her judgment in each parameter.
Note that the third context has an associated time
interval, where as the first two involve measures of the
B-2. Reliability Analysis Principles
overall adequacy of the system in response to a load
event.
a. The probability of failure.
(2) Reliability for the first two contexts can be
(1) Engineering reliability analysis is concerned
calculated using the capacity-demand model and
with finding the reliability R or the probability of
quantified by the reliability index $. In the capacity-
failure Pr(f) of a feature, structure, or system. As a
demand model, uncertainty in the performance of the
system is considered reliable unless it fails, the
structure or system is taken to be a function of the
reliability and probability of failure sum to unity:
B-1
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