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  Title A statistical analysis of full-scale fracture propagation test data
  Author(s) Dr Andrew Cosham, Dr Ronald Koers, Dr Robert M Andrews, and Tanja Schmidt  
  Abstract A PIPE IN A FULL-SCALE fracture propagation test is classified as either a propagate pipe or an arrest pipe. The semi-empirical methods, such as the AISI Formula, the Battelle Short Formula or the Two Curve Model, for predicting the toughness required to arrest a running ductile fracture do not necessarily correctly predict the results of the full- scale tests. In some cases, the fracture has propagated through a pipe joint in which it was predicted to arrest (a non- conservative error), and in other cases it has arrested in a pipe joint through which it was predicted to propagate (a conservative error). A statistical analysis of these errors, based on the principles of discrimination and classification, and Bayes’ theorem, can be used to estimate the probability that a pipe is a propagate pipe given the ratio of the measured toughness to the predicted toughness. The probability that a pipe is a propagate pipe can then be used to estimate an upper bound to the length of a running fracture in a pipeline.

A data set of full-scale fracture propagation tests conducted using air or lean natural gas has been compiled, based on the earlier data sets compiled by Re et al., 1995 [1] and Vogt et al., 1983 [2] for the European Pipeline Research Group, but with reference back to the original (published) sources. The total number of data points in the revised data set, excluding tests conducted using line pipe of Grade L625 (API 5L X90) and above, is 226.

The European Pipeline Research Group has used this data set to conduct a statistical analysis of the Short Formula. Four correction factors have been considered: Leis, 1997 [10]; Eiber, 2008 [13, 14]; Wilkowski et al., 1977 [9]; and Wilkowski et al., 2000 [15].

A multiplier to be applied to the toughness predicted using the Short Formula with a correction factor to, for example, ensure that at least half of the pipe in a pipeline is predicted to be arrest pipe, or that there is a 95% probability of arrest within five pipe joints, is calculated.

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