# Complex Network Modeling and Analysis of Microfracture Activity in Rock Mechanics
## 4 Results and Discussion
### Analysis of Microfracture Activity  
To explain the behavior of microfractures in detail, we separate the changing part of the curve and establish a model of the microfracture network at multiple times in this stage. Apart from the peak value observed in the average clustering coefficient curve, each microfracture clustering event is also associated with a noticeable peak value on the average degree curve. As microcracks begin to cluster, the deformation of the rock transitions into an unstable crack growth stage. Subsequently, microcracks continue to propagate, expand, cluster, overlap, and exhibit other behaviors. Overall, on the basis of the variation patterns of the average degree and average clustering coefficient of microfractures, the microfracture process of granite can be divided into four main stages, as depicted in Figure 16.  
Silence period (75%\(\sigma_{\rm p}\)): During the compaction stage (I) and linear elastic stage (II) of the granite sample, as well as the initial and middle stages of the stable crack growth stage (III), acoustic emission events are rare and discrete. The occurrence of fracture points is highly random, with only a few appearing sporadically. As the sample approaches the expansion point, localized finite expansion occurs at the fracture points, leading to the formation of random microcracks. Microcrack growth period (75%\(\sigma_{\rm p}\) to 87%\(\sigma_{\rm p}\)): During the transition from the stable crack growth stage to the unstable crack growth stage, there is a localized expansion of microcracks within the rock. This leads to a notable aggregation event of microcracks. Concurrently, the volumetric strain of the granite increases, causing the rock volume to shift from contraction to dilation, indicating the onset of the unstable crack growth stage. During this period, the primary activity of microfractures was expansion and continuation. The average degree of the microfracture network continuously fluctuates, indicating that fracture points in the rock appear randomly and are related to each other. Additionally,  
Figure 16: The change rules of the average degree and average clustering coefficient. (before \(\sigma\)cd \(\sim\) op). the average clustering coefficient of the network only exhibits a few maximum values (2 times), suggesting that microfractures in the rock experience limited aggregation events. Therefore, in the early stage of unstable crack growth, the main activity of microfractures is connectivity propagation. The cluster increasing period (87%\(\sigma_{\text{p}}\) to 95%\(\sigma_{\text{p}}\)): When microcracks expand to a certain extent, because of damage accumulation, the sum of the dissipated energy released by stable crack growth and the elastic strain energy stored by rock deformation is not enough to meet the mechanical energy absorbed by the rock, and more microcracks occur in the rock interior faster. Faster and more microfractures exhibit more obvious aggregation. During this period, the activity of microfractures is more obvious than that in the previous stage, and clustering events mainly occur around the initial clustering events. According to the previous analysis, the clustering of nodes can greatly improve the average value of nodes. Therefore, owing to the occurrence of random fractures and expansion, the average degree of the microfracture network will fluctuate, and with increasing strain, the microfracture aggregation will increase, and the average degree will increase overall. In summary, the behavior of microcracks changes to rapid growth and local aggregation. Centralized clustering and overlapping period (after 95%\(\sigma_{\text{p}}\) to after \(\sigma_{\text{p}}\)): As several distinct local aggregations of microcracks occur, the internal damage within the rock accumulates to a very high level. During this phase, due to significant aggregation events, the average degree of the microcrack network increases to a relatively high level.