# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 1 Introduction
[24] used fiber reinforcement to construct primary (initial) tunnel linings and secondary (final) tunnel linings of metro projects and conducted an analysis in terms of project duration. [PERSON] et al. [25] showed it was possible to replace traditional steel reinforcement with glass-fiber-reinforced polymer (GFRP) cages in precast concrete tunnel segmental lining. [PERSON] et al. [26] analyzed and evaluated the structural safety of the Jiao Xiling Tunnel through determining the influence of voids on the tunnel lining structure. [PERSON] et al. [27] studied the influence of a void behind a side wall and another void on the stress of tunnel lining under different lateral pressure coefficients. [PERSON] et al. [28] analyzed the existence of voids behind the lining from the perspective of design, construction, and operation and studied the influence law of the position and size of the voids with respect to the structure. In this study, we endeavored to furnish insights into the alterations observed in both rock and liner attributable to the presence of voids between these structures. We present a quantitative discussion on the impacts of such voids on the stress and deformation responses of the liner and surrounding rock formations. As shown in Figures 1 and 2[29], the formation of voids behind a tunnel can also lead to issues such as insufficient lining thickness and exposure of internal reinforcement. In traditional approaches, sensitivity analyses are often limited by the simplified assumptions made regarding the mechanical properties of materials and the interaction between tunnel lining and voids. Previous studies have shown that FRP reinforcement can improve the tensile capacity of tunnel linings and reduce crack propagation, thus enhancing structural integrity. Despite the extensive use of FRP in tunnel reinforcement, there is limited knowledge on the combined effects of FRP grids and polymer cement mortar (PCM), particularly in the context of void defects in tunnel linings. The long-term behavior of tunnel linings reinforced with FRP-PCM under time-dependent factors, such as creep, has not been fully explored. Most studies do not account for time-dependent degradation or how FRP-PCM systems perform under long-term loading conditions. Current sensitivity analyses lack the precision to capture the full range of structural responses to small changes in void characteristics, leaving gaps in our understanding of how FRP-PCM reinforcement performs under varying void conditions and sizes. In this study, we mainly used the numerical simulation method to carry out the research work on the influence of FRP on structural safety in the case of the investigated tunnel's surrounding rock behind the void. The main stress in the model is the deadweight stress of the soil. The influence of the stress, deformation, and failure of the tunnel under the condition of a void behind the lining was studied. In order to consider the reinforcing effect of FRP, it was compared with the effect of stress, deformation, and failure of the FRP reinforced tunnel. In this study, we improved sensitivity analysis by using different numerical simulation cases that incorporate a more detailed and accurate representation of void variability, FRP-PCM characteristics, and time-dependent effects (creep). This study enhances the precision of sensitivity analysis, leading to more-accurate predictions of the mechanical behavior of tunnel linings and the effectiveness of FRP-PCM reinforcement under varying conditions. The safety factor of the specification is referred to in judging the reinforcement effects of different FRP grades on the tunnel under the influence of time. Cases of a void behind tunnel lining were considered and then compared after changing the range, position, and number of voids.