# Study on the Fracture Resistance of Mixed Fiber Concrete Lining in a Reverse Fault Tunnel
## 6 Parametric Study
### Influences of L/D Ratio of Steel Fiber (\(l_{\rm sf}/d_{\rm sf}\))  
Figure 11 shows the results of the monitoring points, computed with \(l_{\rm sf}/d_{\rm sf}\) increased from 30 to 80 under different \(\rho_{\rm sf}\) and \(\rho_{\rm pf}\).  
The analysis shows that as \(l_{\rm sf}/d_{\rm sf}\) increases, the maximum principal stress at the arch crown increases, but the magnitude of the increase is different; the longitudinal strain decreases; the extreme shear strain at arch springing decreases with the increase in \(l_{\rm sf}/d_{\rm sf}\); the extreme compressive damage variable at arch springing decreases gradually; and the extreme tensile damage variable decreases gradually. Further, Figure 12 shows the magnitude of change in each dependent variable as influenced by the independent variables.  
Figure 10: Magnitude of result changes caused by \(l_{\rm sf}/d_{\rm sf}\).  
Figure 11a shows that the stress increase caused by the increase in \(\rm l_{sf}/d_{sf}\) is greater when \(\rm\rho_{sf}\) is larger, and \(\rm\rho_{sf}\) increases from 0.05% to 0.1% when the growth rate of enhancement is larger, and with the further increase in \(\rm\rho_{sf}\), the enhancement is gradually weakened. That is, although the increase in \(\rm l_{sf}/d_{sf}\) will improve the bearing capacity of concrete, but the corresponding \(\rm\rho_{sf}\) is too small will affect the improvement effect, too large may produce side effects, and is not conducive to the actual construction operation, so it is necessary to take a reasonable value; and with the increase in \(\rm\rho_{pf}\), the corresponding increase in the magnitude of the slight weakening, that is, there is also an interaction between \(\rm\rho_{pf}\) and \(\rm l_{sf}/d_{sf}\), it is not appropriate to take a larger value at the same time.  
Figure 11b shows that the reduction of longitudinal and shear strain increases with the increase in \(\rm\rho_{sf}\). For longitudinal strain, the trend of its reduction is basically uniform when \(\rm\rho_{sf}\) is 0.5% and \(\rm l_{sf}/d_{sf}\) is increased from 30 to 60. When \(\rm\rho_{sf}\) is increased, its reduction increases significantly when \(\rm l_{sf}/d_{sf}\) is increased in the small value range (30-60), and then decreases when it is increased in the large value range (60-80), which is similar to the magnitude of maximum principal stress. For shear strain, the reduction is more pronounced at larger \(\rm\rho_{sf}\) and this pattern is largely independent of \(\rm\rho_{pf}\). In terms of the magnitude change from Figure 12c, when \(\rm\rho_{sf}\) increases from 0.5% to 1.2%, the role of \(\rm l_{sf}/d_{sf}\) changes significantly, and the difference in the effect of \(\rm l_{sf}/d_{sf}\) becomes weaker with the further increase in \(\rm\rho_{sf}\), i.e., when \(\rm\rho_{sf}\) varies in a low range, the increase in \(\rm l_{sf}/d_{sf}\) has a more significant shear strain suppression effect, i.e., for the suppression of shear strain deformation, the two main parameters of the steel fibers still have an interaction.  
Figure 12d,e show that the reduction of damage variables is relatively insignificant when \(\rm\rho_{sf}\) is low, and when \(\rm\rho_{sf}\) increases from 0.5% to 1.2%, the damage suppression effect is significant after increasing \(\rm l_{sf}/d_{sf}\), and at this time, there are significant changes in the reduction of damage variables at tunnel crown when \(\rm l_{sf}/d_{sf}\) is increased in a low range interval (30-60). When \(\rm l_{sf}/d_{sf}\) is increased again, the reduction gets weaker, even causing negative effects, which means steel fiber parameters \(\rm\rho_{sf}\) and \(\rm l_{sf}/d_{sf}\) are also unfavorable for the suppression effect of compression damage when they are too large.