Page 104 - Reliability and Maintainability of In service Pipelines

Methods for Structural Reliability Analysis 93

To calculate the probability of failure, they used the level II FOSM reliability
method. This method requires an iterative solution, when the random variables
are not normally distributed and the limit state function is nonlinear.
They developed their model in further studies (Ahammed and Melchers, 1997)
by considering the effect of following longitudinal stresses:

Longitudinal tensile stresses as a result of Poisson’s ratio effect from the out-
ward radial action of the internal fluid pressure.
Longitudinal thermal stresses.
Longitudinal stresses due to bending as a result of unevenness or settlement of
the pipeline bedding.
Camarinopoulos et al. (1999) used a combination of approximate quadrature
analytical and Monte Carlo method to evaluate the multiple integrals in their reli-
ability analysis for cast iron buried water pipes. They also used the model to
assess the sensitivity of structural reliability to the variation of some important
parameters such as wall thickness, unsupported length, and external corrosion
coefficient.
Yves and Patrick (2000) also presented a method to calculate the reliability of
the buried water pipes using maintenance records and the Weibull distribution for
underlying variables. The method appears to rely entirely on the historical data,
which in most cases is unknown.
Benmansour and Mrabet (2002) studied the reliability of buried concrete sew-
ers by using the FOSM method. They studied two typical cases to assess the
effect of loads on the circumferential and longitudinal behavior of pipes.
Therefore two limit state functions that they considered in their study were based
on longitudinal cracking and circular cracking due to bending moments. They did
not consider corrosion as a deterioration process, therefore their methodology was
a simple time-independent method.
Sinha and Pandey (2002) developed a model to estimate the failure probability
of aging pipelines prone to corrosion by using simulation-based probabilistic neu-
ral network analysis. The approximations in their neural network model can be
considered as a limitation of their methodology.
Sadiq et al. (2004) used Monte Carlo simulations to perform the reliability
analysis of CI water mains, considering axial and hoop stresses as acting loads in
a limit state function. The reduction in the factor of safety (FOS) of water mains
over time was computed, with a failure defined as a situation in which FOS
becomes smaller than one. The Monte Carlo simulations yielded an empirical
probability density function of time to failure, to which a lognormal distribution
was fitted leading to the derivation of a failure hazard function.
Davis et al. (2005) used Weibull probability distribution to account for varia-
tion in the degradation rate of asbestos cement sewers. A tensile failure model