Page 144 - Reliability and Maintainability of In service Pipelines

Case Studies on the Application of Structural Reliability 131

elasticity of 185 GPa. It is also assumed that the corrosion does not alter the
dimensions of the internal pipe diameter.

5.2.1 PROBLEM FORMULATION

The start point of the structural reliability analysis is defining limit state functions
(i.e., failure modes) as discussed in Section 3.3. A limit state is a condition of a
structure beyond which it does not fulfill the relevant design criteria. Eq. (4.1) pre-
sented the general formulation for limit state function of a structure subject to a time
varying process (e.g., corrosion). The failure occurs when the stress (StðÞ) becomes
greater than the resistance of the structure (RtðÞ).
When assessing the overall failure of a pipeline, it is important to consider the
impact that each individual failure mode has on the pipeline system as a whole.
The system failure analysis (see Section 3.4) is used to determine the interactions
of the different limit states. Similarly, this type of failure analysis allows for the
calculation of the overall system failure when the different failure modes are
combined in parallel or series systems (Kołowrocki, 2008). For this case study, a
series system failure analysis for estimating the probability of failure of steel
water pipelines will be developed.

5.2.1.1 Limit State Functions
There are many known failure modes for buried pipelines. Identifying the domi-
nating failure modes depends on the definition of 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 flexible
buried pipes are loads, soil stiffness, and pipe stiffness (Moser and Folkman,
2008). External loadings and corrosion, which act through reduction of the pipe
wall thickness, affect the failure condition of the pipeline.
The limit states to be considered in the failure analysis of steel water pipes
have been presented in Table 5.3. These limit states are those which are con-
trolled in the design stage of a buried flexible pipeline (Moser, 2010).
Nonuniform soil compaction along with overexcavation can be the reason
behind nonuniform bedding, which leads to longitudinal deflection of the pipe.
Flexible pipes are able to deform and move away from pressure. However, if the
bending deflection exceeds the allowable longitudinal deflection threshold, the
deflection failure will happen. Excessive bending can also result in flexural fail-
ure. It is also necessary to study the ring deflection of pipe and make sure it does
not reach 5% of the inside diameter of pipe to prevent ring deflection failure
(Moser and Folkman, 2008).