Page 66 - Reliability and Maintainability of In service Pipelines

Pipeline Inspection and Maintenance 55

resistance of the structure at time t. The failure occurs when the stress becomes
greater than the resistance of the structure. More details about the limit state con-
cept in reliability analysis can be seen in Chapter 3, Methods for Structural
Reliability Analysis.
There are many known failure modes for pipelines. Identifying the dominating
failure modes depends on the definition of the physical model for the system,
which involves consideration of loads or any other contributing parameters.
Traditionally the most important parameters involved in the analysis of pipes are
loads, pipe mechanical properties, pipe geometry, and soil characteristics in the
case of buried pipes (Moser and Folkman, 2008). External loadings and corrosion,
which acts through reduction of the pipe wall thickness, affect the failure condi-
tion of the pipeline.
Several limit states (failure modes) can be considered in the failure analysis of
pipes. Normally the limit states are those which are controlled in designing stage
of pipeline (Moser, 2010).
Longitudinal deflection: Nonuniform soil compaction along with overexcava-
tion can be the reason behind nonuniform bedding, which leads to longitudinal
deflection of the pipe.
Pipeline deflection is considered as a serviceability failure, with the limit state
function presented as follows:

GY; Y max ; tð Þ 5 YtðÞ 2 Y max ð2:2Þ
If the deflection (i.e., YtðÞ) exceeds the allowable longitudinal deflection
threshold (i.e., Y max ), the deflection failure will happen. Longitudinal deflection
can be calculated by Eq. (2.3),(Gorenc et al., 2005).
P s L 3
Y 5 ð2:3Þ
250EI
The critical value for longitudinal deflection suggested by Gorenc et al., 2005
is as follows:
5L 3
Y max 5 ð2:4Þ
384EI
Ring deflection: It is also necessary to study the ring deflection of pipe and
make sure it does not reach 5% of inside diameter of pipe to prevent ring
deflection failure (Moser and Folkman, 2008). Ring deflection also can be con-
sidered as a serviceability failure with the limit state function presented as
Eq. (2.5).
G ΔX; D i ; tð Þ 5 ΔXtðÞ 2 0:05D i ð2:5Þ