uncertainty in the values of various parameters used in

A definition of the limit state (e.g., ln *(FS) *=

calculating some measure of performance, such as the

0).

factor of safety.

A method to estimate the expected value and

(3) In the third context, reliability over a future

standard deviation of the limit state given the

time interval is calculated using parameters developed

expected values and standard deviations of the

from actual data on the lifetimes or frequencies of

parameters (e.g., the Taylor's series or point

failure of similar parts or systems. These are usually

estimate methods).

taken to follow the exponential or Weibull probability

distributions. This methodology is well established in

electrical, mechanical, and aerospace engineering

where parts and components routinely require periodic

(1) For rehabilitation studies of geotechnical

replacement. This approach produces a *hazard*

structures, the reliability index is used as a "relative

measure of reliability or confidence in the ability of a

time period. These functions are used in economic

structure to perform its function in a satisfactory

analysis of proposed geotechnical improvements. The

manner."

development of hazard functions is not part of this

ETL.

(2) The analysis methods used to calculate the

reliability index should be sufficiently accurate to rank

(4) For reliability evaluation of most geotechnical

the relative reliability of various structures and

structures, in particular existing levees, the capacity-

components. However, reliability index values are not

demand model will be utilized, as the question of

absolute measures of probability. Structures,

interest is the probability of failure related to a load

components, and performance modes with higher

event rather than the probability of failure within a

indices are considered more reliable than those with

time interval.

lower indices. Experience analyzing geotechnical

structures will refine these techniques.

measure of the reliability of an engineering system that

reflects both the mechanics of the problem and the

uncertainty in the input variables. This index was

developed by the structural engineering profession to

provide a measure of comparative reliability without

of failure or unsatisfactory performance is defined as

having to assume or determine the shape of the

the probability that the demand on a system or

probability distribution necessary to calculate an exact

component exceeds the capacity of the system or

value of the probability of failure. The reliability

component. The capacity and demand can be

index is defined in terms of the expected value and

combined into a single function (*the performance*

standard deviation of the performance function, and

permits comparison of reliability among different

demand taken as the *limit state*. The *reliability R *is

structures or modes of performance without having to

the probability that the limit state will not be achieved

calculate absolute probability values. Calculating the

or crossed.

reliability index requires:

A deterministic model (e.g., a slope stability

illustrated for slope stability analysis in Figure B-1.

analysis procedure).

Using the expected value and standard deviation of the

random variables *c *and *N *in conjunction with the

A performance function (e.g., the factor of

Taylor*s series method or the point estimate method,

safety from UTEXAS2).

the expected value and standard deviation of the

factor of safety can be calculated. If it is assumed that

The expected values and standard deviations

the factor of safety is lognormally distributed, then the

of the parameters taken as random variables

natural log of the factor of safety is normally distri-

(e.g., *E[N] *and *F*N).

buted. The performance function is taken as the log of

B-2

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