## 4 Conclusions  
Burst pressure of pipeline with restrained and unrestrained concentric dent-crack defects was investigated in this study, considering the effect of varying crack geometry, dent depth, and denting pressure. Predicted burst pressures are compared with burst pressure of longitudinally cracked pipes without dents. Lastly, the effect of releasing the indenter from pipe surface when the pipe is operating at its maximum allowable operating pressure on crack propagation was assessed. Specimens with unrestrained concentric dent-crack defects with dent depth of 2% OD formed at zero denting pressure had the same burst pressure as plain cracked specimens, but dent-crack defects were more injurious than plain cracks with increasing dent depth and denting pressures. A 0.2 t deep crack in dents formed at zero pressure was not problematic because the affected specimen sustained the MAOP of the pipe without the crack propagating, for crack lengths \(\leq\) 200 mm and dent depths \(\leq\) 6% OD. Unrestrained dents of depth 6% OD formed at pressures \(>\) 0.3 P\({}_{\rm y}\), with cracks of depth \(\geq\) 0.2 t, did not sustain the MAOP of the pipe. The cracks propagated at pressures lower than MAOP of the pipe, and risk of bursting at pressure lower than MAOP increased with crack length and denting pressure. Specimens with restrained dent-crack defects had higher burst pressure than the corresponding specimens with unrestrained dent-crack defects and releasing the restraint at MAOP did not propagate 0.2 t deep cracks but propagated 0.5 t deep cracks. Risk of propagation and bursting increased with crack length, denting pressure, and dent depth. All cracks with length \(>\) 60 mm propagated but only those of length \(>\) 100 mm propagated until the pipes burst when dent restraint was released at MAOP of the pipe. Increasing crack depth, crack length, and dent depth were more detrimental to pipe integrity than increasing denting pressure. But, deep dents (\(>\)4% OD) disproportionately increased the effect of the other defect parameters on pipeline integrity and burst pressure. Pipelines with restrained concentric dent-crack defects are safe for service at maximum allowable operating pressure of the pipe if the restraints remain in position on the pipe surface. Integrity of pipelines with unrestrained concentric dent-cracks vary with defect geometry. Affected pipelines retain significant strength and may be maintained in service with careful assessment. Although only two crack depths were considered in this study, the results suggest that dent-crack defects are not too severe on integrity of pipelines subjected to monotonically increasing pressure. A study involving more crack depths and locations within dents other than the dent center (apex) is required for a broader understanding of the effect of dent-crack defects on the integrity of pipelines. Our future work will investigate more crack depths and the effect of cracks located in the flank of dents on burst pressure. Additionally, the fatigue life of pipelines with dent-crack defects, which has not been the focus of the present study, will be investigated. The authors have agreed upon the following credit statement for this manuscript. Conceptualization: A.O., Y.L., and S.A.; Methodology: A.O. and S.A.; Investigation: A.O. and S.A.; Formal Analysis: A.O., Y.L., and S.A.; Resources: S.A., N.Y.-G., M.K., and R.C. ; Writing--original draft preparation: A.O. and Y.L. ; Writing--review and editing: Y.L., S.A., R.C., and N.Y.-G.; Supervision: S.A.; Project administration: S.A.; Funding acquisition: S.A., N.Y.-G., R.C., and M.K. All authors have read and agreed to the published version of the manuscript. The authors wish to acknowledge funding received from NSERC and Enbridge Pipelines Inc. The authors declare no conflict of interest. Any information or data pertaining to Enbridge Employee Services Canada Inc., or its affiliates, contained in this paper was provided to the authors with the express permission of Enbridge Employee Services Canada Inc., or its affiliates.