The Application of the Battelle “Short Formula” to the Determination of Ductile Fracture Arrest Toughness in Gas Pipelines
Bibliographic record
Abstract
Many models and formulae have been put forward, over the years, for the determination of the toughness necessary for the arrest of propagating ductile fracture in gas pipelines. One of the first, and most prominent, was that developed by Battelle Columbus Laboratories for the Pipeline Research Committee of the American Gas Association. As originally embodied, the model involved the comparison of curves expressing the variation of fracture velocity and of decompression wave velocity with pressure (the “two-curve model” — TCM). To aid in analysis, at a time long before a computer was available on every desk, a “short formula” (SF) was developed that provided a good fit to the results of the TCM for a substantial matrix of conditions. This SF has subsequently been adopted by several standards bodies and used widely in the analysis of the results of full-scale burst tests. Since the original description of the derivation of the SF is to be found only in a report to the PRC dating back to the Seventies, many in the pipeline industry today are left without a full appreciation of its range of validity. The present paper briefly discusses the original intent of the SF as a substitute for the TCM, and presents the results of extensive calculations comparing the results of the two. It can be concluded that the SF provides an excellent estimate of the results of the TCM over a very wide range of design and operating parameters, within the limitations inherent in the method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".