# Complex Network Modeling and Analysis of Microfracture Activity in Rock Mechanics
## 5 Conclusions  
This study integrates interdisciplinary theories--spatiotemporal single-link clusters, fractal theory, and graph theory--to develop a complex network model for rock microfractures using triaxial acoustic emission tests. The model offers new insights into predicting rock failure and enhancing engineering safety by analyzing microfracture evolution during rock deformation. It aids engineers in understanding failure mechanisms and designing better safety measures. In practical terms, it effectively monitors and forecasts rock stability in underground projects like tunnels and mines. By analyzing on-site acoustic emission data, the model identifies early instability warnings, enabling proactive accident prevention. The main conclusions are as follows:  
(i) The degree of distribution of microfracture networks follows a power law, typical of complex networks. Most microfracture points have low connectivity, with few points forming a highly connected \"core,\" indicating significant aggregation during rock deformation and failure;  
(ii) The rock microfracture network evolves significantly during deformation and failure. Initially, nodes are sparse and discrete, with low average degree and clustering coefficient. These parameters increase suddenly and continuously in the mid-loading stage, showing an upward trend. Notably, there's a marked rise in both the average degree and clustering coefficient in the late loading stages;  
(iii) The average degree, represented by the characteristic parameter \(<\!\!<\)\(>\), and the average clustering coefficient \(<\!\!<\)\(>\) of the rock microfracture network serve as indicators of microcrack propagation and the aggregation of fracture points during the rock fracture process. These results strongly reflect these phenomena;  
(iv) Microcrack activity begins in the middle stage of stable crack growth, especially near the expansion point, acting as a precursor to unstable crack growth. The process divides into three stages: propagation (\(\sim\)87%\(\sigma_{\rm p}\)), increased clustering (87%\(\sigma_{\rm p}\) to 95%\(\sigma_{\rm p}\)), and concentrated interaction (after 95%\(\sigma_{\rm p}\)). Initially, microcracks expand with weak clustering, but in later stages, intensified clustering and secondary rupture occur. When stress exceeds 95%\(\sigma_{\rm p}\), extensive microfracture aggregation and rapid expansion happen, often leading to macrocrack formation;  
(v) The abrupt increase in the characteristic parameter \(<\!\!<\)\(>\) (at about 95% of the peak stress, \(\sigma_{\rm p}\)) of the rock microfracture network serves as an indicator of imminent rock failure. Based on these findings, future research could explore the following directions:  
(i) Expanding the Sample Size: Investigating microfracture networks in rocks from different geological settings to generalize the findings and enhance the model's applicability;(ii) Integrating with Other Geomechanical Models: Combining the complex network model with other geomechanical models to provide a more comprehensive understanding of rock behavior under various stress conditions;  
(iii) Real-Time Monitoring Applications: Developing real-time monitoring systems using the complex network model to predict rock instability in practical engineering scenarios, such as underground mining and tunneling. Y.C. : Writing--Reviewing and Editing, Conceptualization, Methodology, Software. J.X. : Data curation, Writing--Original draft preparation. Y.P. : Visualization, Investigation. Q.Z. : Fund Support, Supervision. All authors have read and agreed to the published version of the manuscript. This work was supported by the general program of National Natural Science Foundation of China (41272333). The raw data supporting the conclusions of this article will be made available by the authors on request. This work was supported by the general program of the National Natural Science Foundation of China (41272333). At the same time, the author would like to thank the editors and reviewers for their profound comments and suggestions.