# Study on the Fracture Resistance of Mixed Fiber Concrete Lining in a Reverse Fault Tunnel
## 6 Parametric Study
### Influences of Polypropylene Fiber (\(\rho_{\text{pf}}\))  
Figure 9 shows the results of the monitoring points under the condition of different additions of steel fiber (\(\rho_{\text{pf}}\)) and L/D ratios of steel fiber (\(\text{l}_{\text{sf}}\)/\(\text{d}_{\text{sf}}\)), and with the gradual increase in the addition of polypropylene fiber (\(\rho_{\text{pf}}\)) from 0.05%, 0.10%, to 0.15%. The analysis shows that as \(\rho_{\text{pf}}\) increases, the maximum principal stress at the arch crown increases uniformly in the extreme value, and this law does not change with the change of \(\rho_{\text{sf}}\) and \(\text{l}_{\text{sf}}\)/\(\text{d}_{\text{sf}}\), i.e., the increase in \(\rho_{\text{pf}}\) in this range helps to improve the bearing capacity of the concrete. At the same time, shear strain at arch springing, the extreme value of the compressive damage variable at arch springing, and the extreme value of the tensile damage variable at arch springing all decrease accordingly. Further, Figure 10 shows the magnitude of change in each dependent variable as influenced by the independent variables. As shown in Figure 10a, as \(\rho_{\text{sf}}\) or \(\text{l}_{\text{sf}}\)/\(\text{d}_{\text{sf}}\) grows, the increase in \(\rho_{\text{pf}}\) causes a gradual decrease in the increase in the extreme value of the maximum principal stress at the arch crown, i.e., the effect of \(\rho_{\text{pf}}\) on the stress is related to \(\lambda_{\text{sf}}\). When \(\lambda_{\text{sf}}\) is 0.15, the maximum principal stress increases by 30.8% when \(\rho_{\text{pf}}\) is increased from 0.05% to 0.15%, while when \(\lambda_{\text{sf}}\) is increased to 1.52, the increase in the extreme value of the principal stress caused by the same change in \(\rho_{\text{pf}}\) is 9%, and the former is about three times as much as the latter, i.e., when \(\lambda_{\text{sf}}\) is lower, \(\rho_{\text{pf}}\) plays a role in increasing the principal stresses, and when \(\lambda_{\text{sf}}\) is increased, the effect is gradually weakened. This is because when \(\lambda_{\text{sf}}\) is less than 0.15, the influence of steel fibers is weaker; at this time, polypropylene fibers play a major role in stress enhancement, and with the increase in \(\lambda_{\text{sf}}\), the enhancement effect of steel fibers is stronger than that of polypropylene fibers, and therefore the influence of \(\rho_{\text{pf}}\) diminishes, from which it can be deduced that when \(\lambda_{\text{sf}}\) reaches a certain value, the stress change caused by the continued increase in \(\rho_{\text{pf}}\) is weak and even produces a negative effect. Similarly, when \(\lambda_{\text{sf}}\) is small, the effect of \(\rho_{\text{pf}}\) on longitudinal and shear strain does not vary significantly with \(\lambda_{\text{sf}}\), while \(\lambda_{\text{sf}}\) at larger scales, the magnitude of the reduction diminishes with further increase. For longitudinal strains, when \(\lambda_{\text{sf}}\) reaches 0.57, the strain reduction corresponding to the increase in \(\rho_{\text{pf}}\) from 0.05% to 0.15% is 14.9%, whereas when \(\lambda_{\text{sf}}\) is increased to 1.52, the strain reduction for the same change in \(\rho_{\text{pf}}\) is 11.6%. This is because the polypropylene fibers act as the main toughening role when the steel fiber characteristics are not obvious, so the structural deformation is significantly affected by \(\rho_{\text{pf}}\), while the growth role of the polypropylene fibers gradually assumes a secondary role as the characteristics of the steel fibers become apparent, so the magnitude of the change is reduced. However, at this time, the interaction of the two fibers is weakly reflected in the strain relative to the stress.