Effect of spatial correlation on the failure probability of pipelines under corrosion

Abstract

Corrosion in pipelines has been probabilistically modeled. However, the potential effect of spatial correlation of corrosion defects, in several segments of a pipeline, on its failure probability has not received much attention. In this paper, several degrees of spatial correlation are assumed for the corrosion in determined segments of a pipeline and their effects on the global reliability are examined. The pipeline is assumed to be a series system. The failure mode is considered to be controlled by the stresses due to internal pressure and the presence of corrosion. Component reliability is calculated by First Order Second Moment approximations. First order bounds are used to define the limits for the global failure probability by assuming first, either no correlation (independent pipeline segments) and, secondly, perfect correlation between segments. Then, second order bounds are estimated to improve the calculation of the failure probability by including the correlation coefficients mentioned above. The correlation degree between failure modes at two pipeline segments increases with the degree of correlation of the corrosion initial depths located at these segments. Also, for a correlation coefficient between corrosion depths larger than 0.6, its contribution to the correlation between failure modes becomes significant and, therefore, should be accounted for. When the specific correlation degree between corrosion defects at adjacent pipeline segments is considered in the calculation of an example pipeline failure probability, this probability is narrowly bounded between 0.58 and 0.59, as compared to the usual practice where this correlation is assumed to be either 0 or 1 for which the failure probability is bounded between 0.49 and 0.79. The formulation may be used to set optimal maintenance schedules for pipelines under corrosion.