EP 1130-2-500
27 Dec 96
APPENDIX D
INTRODUCTION TO AN ASSESSMENT OF STRUCTURAL RELIABILITY
D-1. Introduction. The objective is to introduce methodology to be used to evaluate the
reliability of civil works structures for various modes of performance. These reliability measures
are intended to be used in analyses for prioritizing structural rehabilitation. The results of a
reliability analysis are used to provide a condition ranking of the structure or component. Basic
references are provided herein. A decision making flow chart is provided as Figure D-1, and
reporting requirements for reliability analyses are presented in paragraph D-8.
a. Traditionally, evaluations of structural adequacy have been expressed by safety factors.
A safety factor can always be expressed as the ratio of capacity to demand. The safety factor
concept, however, has shortcomings as a measure of the relative reliability of structures for
different performance modes. A primary deficiency is that parameters (material properties,
strengths, loads, etc.) must be assigned single, precise values when the appropriate values may in
fact be uncertain. The use of precisely defined single values in an analysis is the deterministic
approach. Thus, the safety factor reflects both the condition of the structure and the engineers'
judgement and degree of conservatism in assigning values to parameters.
b. The probabilistic approach extends the safety factor concept to explicitly incorporate
uncertainty in the parameters. This uncertainty can be quantified through statistical analysis of
existing data or judgmentally assigned. Even if judgmentally assigned, the probabilistic results
will be more meaningful than a deterministic analysis because the engineer provides a measure of
the certainty of his or her judgement in each parameter.
D-2. Basic Principles.
a. Random Variables. In the probabilistic approach the parameters are treated as random
variables. Random variables assume a range of values in accordance with a function termed a
probability density function or probability distribution. Although the value of a parameter is
uncertain or variable, the probability density function quantifies the likelihood that the value of the
random variable lies in any given interval. When parameters are defined as random variables,
functions of these parameters such as safety factor also become random variables and can be
expressed in probabilistic terms.
b. Probability of Unsatisfactory Performance. An engineering reliability analysis
determines the probability of unsatisfactory performance, Pr(u), defined as the probability that the
value of a function which characterizes the performance of the system exceeds some limit state.
These performance functions, or performance modes, are deterministic functions which are used
in design or analysis and should define reasonable performance levels expected to occur over the
service life of the project or component. Failure modes for civil works type structures are difficult
to define deterministically, however, and describe a condition which is unacceptable for USACE
projects, i.e., failure of a structure or component. Therefore, performance modes such as
calculation of deflections, cracking or loss of section which can be more readily defined
deterministically are used in order to detect adverse conditions prior to failure.
D-1
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