# Study on the Fracture Resistance of Mixed Fiber Concrete Lining in a Reverse Fault Tunnel
## 7 Discussion
### Correlation Analysis  
Through the above analysis, it can be obtained that \(\rho_{\text{sf}}\), \(\text{l}_{\text{sf}}/\text{d}_{\text{sf}}\) and \(\rho_{\text{pf}}\) have mutual influence on the extreme value of the maximum principal stress of the lining, and in order to further analyze the degree of influence of these three parameters and four combined variables (a total of seven variables), the [PERSON]'s correlation coefficient analysis in spss was used to obtain Figure 17. The theoretical distribution interval of the correlation coefficients in the table is \([-1,1]\), and in general, it is considered to have weak correlation in the range of 0.3-0.5, medium correlation in the range of 0.5-0.7, and strong correlation in the range of 0.7-0.9.  
Figure 16: Comparison of different admixture of fibers (S for single steel fiber, P for single polypropylene fiber, S-P for mixed steel-polypropylene fiber, PC for plain concrete).  
From Figure 17, it can be significantly observed that seven variables have a significant correlation with maximum principal stress and maximum longitudinal strain at arch crown, maximum shear strain at arch springing, compressive damage variable at arch springing, and tensile damage variable at arch springing. Among them, the four combined parameters are more relevant to the results than the three initial parameters.  
For the maximum principal stress and longitudinal strain at the arch crown, the most significant influence is \(\rho_{\text{pf}}\rho_{\text{sf}}\text{-}\text{l}_{\text{sf}}\text{/}\text{d}_{ \text{sf}}\), which indicates that the combined performance of steel-polypropylene fiber can significantly improve the bearing performance of the lining top.  
For shear strain at arch sidewall, it can be found that the correlation coefficient of \(\rho_{\text{pf}}\) is the lowest, and lower relative to several other variables, i.e., considering \(\rho_{\text{pf}}\) alone has less influence on the shear strain; at the same time, it can be found that several variables containing a factor of \(\rho_{\text{sf}}\) have a higher correlation with the shear strain, and the ones that consider \(\lambda_{\text{sf}}\) and those that consider the combination of the three variables have a high degree of correlation with it, so it can be assumed that \(\rho_{\text{sf}}\) has a determinative effect on the lining shear resistance.  
For the compressive damage variable and tensile damage variable at arch springing, the most important influencing factors are \(\rho_{\text{pf}}\rho_{\text{sf}}\text{-}\text{l}_{\text{sf}}\text{/}\text{d}_{ \text{sf}}\) and \(\rho_{\text{sf}}\text{-}\text{l}_{\text{sf}}\text{/}\text{d}_{\text{sf}}\), respectively, which are strongly correlated. In the compressive damage variable, \(\text{l}_{\text{sf}}\)/d\({}_{\text{sf}}\) and \(\rho_{\text{pf}}\) showed weak correlation, \(\rho_{\text{sf}}\) and \(\rho_{\text{pf}}\text{-}\text{l}_{\text{sf}}\)/d\({}_{\text{sf}}\) showed moderate correlation, which also indicates that steel-polypropylene mixed fiber is more effective in resisting compressive damage. In the tensile damage variable, \(\text{l}_{\text{sf}}\)/d\({}_{\text{sf}}\), \(\rho_{\text{sf}}\), \(\rho_{\text{pf}}\text{-}\text{l}_{\text{sf}}\)/d\({}_{\text{sf}}\) and \(\rho_{\text{sf}}\)-\(\rho_{\text{pf}}\) are all medium correlation, while \(\rho_{\text{pf}}\)-\(\rho_{\text{sf}}\)-\(\text{l}_{\text{sf}}\)/d\({}_{\text{sf}}\) correlation is only the second one, which explains that in the tensile damage, the steel fibers are more important than polypropylene fibers, and in order to inhibit the tensile damage, it is necessary to reasonably select the steel fiber parameters.