# Study on the Fracture Resistance of Mixed Fiber Concrete Lining in a Reverse Fault Tunnel
## 7 Discussion  
### Influences of Fibers Compound  
The properties of the materials are compared by considering single fiber, mixed fiber, and no fiber. Figure 16 gives the variation of maximum principal stress and longitudinal strain extremes at the arch crown, shear strains at the arch sidewall and arch springing, and compressive and tensile damage variables in the invert arch for different conditions. The maximum principal stress extreme value at the arch crown is obviously larger than that of plain concrete after mixed fiber concrete, and the size of the extreme value always meets mixed fiber \(>\) single fiber \(>\) plain concrete, i.e., there is a synergistic effect of the two kinds of fibers in the matrix concrete, and it is more beneficial to improve the load-bearing capacity of the matrix concrete. The effect of the two single-doped fibers is related to the \(\lambda_{\text{sf}}\), and when the \(\lambda_{\text{sf}}<0.15\), the maximum value of the single polypropylene fiber is larger than single steel fiber. But when \(\lambda_{\text{sf}}\) further increase, the maximum value of single steel fiber is greater than that of single polypropylene fiber, and with continuous growth of \(\lambda_{\text{sf}}\), the difference between the two single-doped effect is significant. This is because the steel fiber characteristics are not obvious, polypropylene fiber plays a major bridging role, and  
Figure 15: Calculation results in individual fiber incorporation. reaches a certain value, the steel fiber plays a stronger role, from which we can put forward a limit of the characteristics of the value of \(\lambda_{\text{sf-1}}\). In this case, the boundary eigenvalue \(\lambda_{\text{sf-1}}\) for distinguishing between single steel fiber and single polypropylene fiber for the strength of the stress effect is 0.15. Due to the enhanced performance of mixed fiber, the extreme value of the longitudinal strain at the arch crown of fiber-enhanced concrete is much smaller than that of plain concrete, and the strain of mixed fiber is also smaller than that of single fiber, which indicates that the mixed fiber will inhibit the longitudinal deformation at the arch crown under the fault fracture misalignment, and the effect of compound admixture is better than that of single admixture. For the comparison of the effects of the two single-doped fiber strain suppressions, when \(\lambda_{\text{sf}}<0.36\), the single polypropylene fiber effect is better, with the increase in \(\lambda_{\text{sf}}\), the single steel fiber effect is gradually better. That is, for the inhibition effect of longitudinal strain, the boundary eigenvalue \(\lambda_{\text{sf-1}}\) of the two single-doped fibers is 0.36. The shear strain of arch springing and invert arch is obviously smaller than that of plain concrete after mixed fiber, and the inhibition effect of mixed doped will be better than single doped, for the comparison of two single doped fibers, arch springing in \(\lambda_{\text{sf}}\leq 0.36\), single steel fiber inhibition effect is not better than single polypropylene fiber, and invert arch in \(\lambda_{\text{sf}}>0.15\), the effect of single steel fiber inhibition of shear strain will be better than single polypropylene fiber gradually, i.e., for shear strain, arch springing and invert arch exist different boundary characteristic value \(\lambda_{\text{sf-1}}\), it can be obtained that invert arch has a higher requirement for \(\lambda_{\text{sf}}\), so it is more sensitive than other parts. At the invert arch, there are different boundary characteristic value of \(\lambda_{\text{sf-1}}\), it can be obtained that invert arch for \(\lambda_{\text{sf}}\) requirements are higher, so more sensitive than other parts. Considering the economic effect, different part can be designed with different ratios. After analyzing, it can be obtained that the relationship between fiber parameters and shear strain at the invert arch and arch springing is not much different in mixed fiber and single fiber.