# A Novel Carbon Fiber Composite Material for the Simulation of Damage Evolution in Thick Aquifers
## 3 Damage Self-Sensing Performance of CFSSM
### The Corresponding Relationship of D-RCR for CFSSM  
During the three-point bending test, the variation characteristics of \(RCR\) and \(D\) in CFSSM were continuously monitored, and the \(D\)-\(RCR\) curves were plotted. For each concentration, three specimens were tested. The final \(D\)-\(RCR\) curve for each concentration was obtained by fitting the curves of the three specimens, as shown in Figure 7. As the carbon fiber mass fraction increases, the correlation between \(RCR\) and \(D\) becomes more significant. Grouping by carbon fiber mass fraction, the correlations between \(RCR\) and \(D\) are as follows.  
When the carbon fiber mass fraction falls between 0% and 1%, the correlation between \(RCR\) and \(D\) is ambiguous, as the two do not exhibit concurrent growth. In Figure 7a, with the \(D\) range from 0 to 0.51, \(RCR\) grows slowly and consistently lags behind \(D\). In Figure 7b, with the \(D\) ranges from 0 to 0.1 and 0.32 to 0.9, \(RCR\) rises slowly. In Figure 7c, with the strain range from 0.12 to 0.56, \(RCR\) fluctuates for a long time and over a wide range.  
Between 1.5% and 2% carbon fiber mass fraction, a significant correlation is observed between \(RCR\) and \(D\), as both exhibit a generally consistent growth trend. In Figure 7e, both \(RCR\) and \(D\) increase together. The fluctuations are smaller and more stable compared with Figure 7d.  
This indicates that as the carbon fiber content increases, the material's ability to characterize rock mass damage and fracture progressively strengthens. When the carbon fiber content reaches 2 wt%, each point's damage coefficient \(D\) corresponds to a unique \(RCR\), which can effectively reflect the degree of damage in the specimen throughout the damage and fracture process. Therefore, CFSSM with 2 wt% carbon fiber content is selected for subsequent similar material simulation tests. Furthermore, when the \(RCR\) of this CFSSM exceeds 11.2%, it signifies that the material has been completely fractured.  
Figure 6: Resistivity monitoring results of CFSSM during curing period.  
This finding indicates that, when the mass fraction of carbon fibers exceeds 1.5%, the electrical conductivity of the CFSSM composite reaches the lower limit of the percolation threshold [29], thereby significantly enhancing its self-sensing capability for structural health monitoring. Beyond this critical concentration, a continuous conductive network is formed within the matrix, enabling efficient electron transport. This markedly improves the material's sensitivity to structural changes, such as strain or cracking. The result not only verifies the effectiveness of carbon fibers as conductive fillers but also provides a theoretical basis for optimizing their content in sensing-functional composites.  
The CFSSM with 2% carbon fiber content, which exhibits excellent self-sensing damage properties, is selected to establish the relationship between strain and \(RCR\), as shown in Figure 8. As the strain in the CFSSM increases, the \(RCR\) initially remains nearly constant, indicating minimal changes in the material's resistance at lower strain levels. This is followed by a gradual increase in \(RCR\), which corresponds to the early stages of material deformation. Finally, at higher strain levels, the \(RCR\) experiences a sharp rise, reflecting significant damage or the onset of failure within the material structure, as evidenced by the steep slope in the graph. The figure clearly illustrates this transition, with a gradual change at first, followed by a marked increase in resistance, which signifies the material's response to increasing strain and the progression of damage. This trend demonstrates the material's sensitivity to strain, making it a useful tool for damage detection and monitoring in similar material model tests.