Abstract
Every macroscopic crack that leads to rock failure is a product of microcracks. Similar to fault events that occur at different locations during earthquakes, microfractures show chaotic and concentrated distributions within rocks and in different macroscopic fracture planes, respectively. Spatial distribution is used to describe the crack propagation process. In this study, we conducted true triaxial unloading and compression tests on cuboid granite samples to simulate real stress conditions, and the spatial coordinates of the microfractures were acquired using acoustic emission (AE) monitoring. Based on graph theory, we constructed the minimum spanning tree structure of AE events, analyzed the crack propagation according to the spatial correlation, and introduced two indexes of spatial correlation length and spatial correlation degree. Strongly correlated AE events exhibited a stronger ability to expand, and this clustering of AE events is called the fracture source. Furthermore, the local lowest point of the spatial correlation length corresponded to the formation time window of the fracture source on the macroscopic crack fracture surface. Results indicated that these fracture sources were distributed in the fracture surface space of each macroscopic crack and corresponded with the final crack morphology. Additionally, the spatial distribution of the fracture sources under different time windows demonstrated the evolution of the crack propagation path with time. Furthermore, we discussed the variation in the AE-dominant frequency in this critical time window, and the final result strongly verified the above statement.
Highlights
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The minimum spanning tree structure of acoustic emission events was constructed based on graph theory.
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The temporal variation of spatial correlation length was analyzed and its value described the degree of microfracture aggregation.
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The spatial correlation degree was proposed and strong correlation microcracks characterize the spatial evolution of macroscopic crack.
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Acknowledgements
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant no. 52074294), and Fundamental Research Funds for the Central Universities (Grant No. 2021YJSNY08).
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CW: methodology, validation, investigation, writing—original draft, review and editing, supervision, project administration. BW: methodology, software, formal analysis, investigation, data curation, writing—original draft, review and editing. CL, LH, LS, XX and PC: investigation.
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Wang, C., Wang, B., Li, C. et al. Investigation of the Spatial Correlation of Rock Crack Propagation Based on Graph Theory. Rock Mech Rock Eng 56, 1981–1993 (2023). https://doi.org/10.1007/s00603-022-03176-0
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DOI: https://doi.org/10.1007/s00603-022-03176-0