# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 4 Conclusions  
In this study, numerical simulation methods were used to compare the existence of different voids and repair effects, and the safety factor was used as a safety evaluation index to provide ideas on improving design around the void behind a tunnel.  
Different void positions (such as at the crown, spandrel, and springline) and their impacts on the tunnel lining's mechanical behavior were analyzed. The simulation results show that voids at the crown (top) are particularly critical, leading to higher stress concentrations and a greater need for reinforcement.  
This study demonstrates that FRP-PCM reinforcement significantly improves the mechanical behavior of tunnel linings. The following safety factor improvements were noted: The safety factor increased significantly after reinforcement, especially when higher-grade FRP grids such as CR8 were used. In some cases, the safety factor even surpassed that in the pre-void condition, indicating that FRP-PCM can restore and exceed the original structural integrity. FRP provides high tensile strength, significantly reinforcing areas prone to stress, such as the arch crown, sidewalls, and regions with existing defects (e.g., hollow areas). This reinforcement helps distribute loads more evenly and reduces the likelihood of structural failure or large deformations. PCM, on the other hand, improves the compressive strength and adhesion of the lining, especially in areas where traditional materials might crack or deteriorate over time. The time-dependent deformation (creep) of tunnel lining is an essential factor in assessing the long-term effectiveness of FRP-PCM. Over a period of 5 to 10 years, the simulations show that FRP-PCM significantly mitigates the negative effects of creep, ensuring the tunnel lining remains structurally sound over extended periods. Over time, the stress state in the surrounding rock stabilizes as the construction-induced displacements reduce in severity. FRP-PCM reinforcement plays a crucial role in helping the tunnel lining maintain its shape and structural integrity during this stabilization phase. As shown in the displacement results, the tunnel moves toward a stable equilibrium faster when reinforced with FRP-PCM, reducing long-term maintenance needs.  
To prevent future issues, a combination of regular monitoring, proactive maintenance, effective drainage, and localized strengthening should be adopted to ensure the ongoing safety and durability of tunnel structures reinforced with FRP-PCM.  
Data curation, Q.L.; formal analysis, Q.L.; methodology, Y.J.; resources, Y.J. and S.S.; software, J.W.; writing--original draft, Q.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by JST SPRING, Japan, under grant number JPMJSP2172.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the laboratory's privacy restrictions.  
Author [PERSON] was employed by the company MCC Wukan Engineering Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.