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Methods for Structural Reliability Analysis 95


           corrosion or combined corrosion and fractures were included within the observed
           data model.
             Teixeira et al. (2008) used both Monte Carlo simulation method and FORM
           for assessing the reliability of corrosion affected pipelines subjected to internal
           pressure.
             A methodology for predicting remaining life of corroded underground steel
           gas pipelines was presented by Li et al. (2009). They took the effect of random-
           ness of pipeline corrosion into account by developing a mechanically-based prob-
           abilistic model. Monte Carlo simulation was employed in their study to calculate
           the remaining safe life and its cumulative distribution function.
             Yamini (2009) also used different reliability analysis methods (Monte Carlo
           simulation, FORM, and SORM) for failure analysis of CI water mains. In his
           study two failure modes were considered individually. A failure mode was
           defined as the point at which the corrosion depth is more than the maximum
           acceptable decrease in pipe wall thickness and another failure mode was defined
           as the time at which total stresses exceed the pipe strength capacity.
             Lee et al. (2010) also used a FORM to evaluate the time-dependent reliability
           index for a fully deteriorated piping component rehabilitated with fiber-reinforced
           plastic (FRP), considering the demand of internal fluid pressure, external soil
           pressure, and traffic loading.
             Zhou (2011) developed a methodology to carry out the time-dependent reli-
           ability evaluation of a pressurized steel gas pipeline containing an active corro-
           sion defect by taking into account the time-dependency of the internal pressure.
             A methodology for predicting remaining life of corroded underground steel
           gas pipelines was presented by Li et al. (2009). They took the effect of random-
           ness of pipeline corrosion into account by developing a mechanically-based prob-
           abilistic model. Monte Carlo simulation was employed in their study to calculate
           the remaining safe life and its cumulative distribution function. Li and
           Mahmoodian (2013) used an analytical first passage reliability method for estima-
           tion of failure probability of corrosion affected CI water pipes. Their study was
           limited to uniform corrosion rate; while in practice aging pipelines normally pos-
           sess corrosion pits or cracks.
             Qin (2014) developed a Monte Carlo simulation-based methodology to evalu-
           ate the time-dependent system reliability of corroding pipelines in terms of three
           different potential failure modes, namely small leak, large leak, and rupture. In
           his study only the corrosion depth was considered as the time-dependent parame-
           ter and corrosion length was treated as a time-independent parameter.
             Mahmoodian and Li (2015) developed a stochastic model for the stress inten-
           sity factor and a time-variant analysis method based on gamma process concept
           to quantify the failure probability. In their study two types of stresses (i.e., hoop
           and axial) were considered for two cases of corrosion (i.e., external and internal).
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