Fig. 3: Strain curve of an intact pipeline.

a Time series variation curves for circumferential strain at 12 measurement points (R1-R12). The axial force load was 0–147 s, and the pipeline was primarily subjected to axial tensile deformation. The circumferential strain R1-R12 generated compressive strain via Poisson’s action. After the axial force loading was completed, internal pressure was applied, which significantly increased the circumferential strain. b Time series variation curves for axial strain at 12 measuring points (R13-R24). The pipeline’s axial strain increased linearly during the axial force loading stage. The pipeline primarily deformed along its circumference during the internal pressure loading stage. The axial strain remained stable, with a small amplitude of variation. As the internal pressure exceeded 9.05 MPa, the pipeline’s deformation concentrated at the burst position. With the expansion, the axial strain at measuring points R15 and R18 near the burst location increased. The measuring point R17 at the edge of the expansion zone significantly reduced axial strain with compression.