# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 3 Results and Analysis
### The Influence of the Creep Phenomenon
#### 3.2.2 Creep Calculation  
Since creep is a time-dependent process, it is crucial to explicitly consider time in the analysis. Creep develops gradually under a sustained load, and its effects become more pronounced as time progresses, influencing the long-term performance and stability of materials. However, unlike dynamic processes, creep is characterized by slow deformation over time rather than rapid changes, meaning that inertia effects, such as those associated with the acceleration of the structure, are negligible [37]. This fact simplifies the analysis because the forces resulting from changes in velocity or acceleration do not need to be considered. Instead, the focus is on the gradual strain accumulation due to constant stress over an extended period, making it a quasi-static problem. By understanding and accounting for this, the long-term safety and serviceability of structures can be accurately assessed without the complexities of dynamic analysis. To handle these characteristics, ABAQUS provides specific analysis steps designed for this type of process. Constitutive model identification includes the determination of the model's structure and parameters, the principle for which is derived from control theory. Selecting an appropriate creep model and determining the corresponding parameters constitute an important part of creep research. The safety performance of a tunnel must be judged not only by the stress condition after excavation but also by the stress condition of the tunnel under the influence of time factors. In fact, as the deformation of a material increases with time, its stress also changes. Therefore, creep broadly refers to change of the stress and deformation under the action of a constant external force over time. The characteristic of this phenomenon is that deformation, stress, and external force no longer maintain a one-to-one correspondence relationship; even when the stress is less than the yield limit, the deformation still has the property of irreversible deformation. We conducted a deformation analysis of the lining structure. In order to fully grasp the FRP-PCM reinforcing performance of the lining structure, the figure below shows the vertical safety factor of the lining structure under the influence of creep  
Figure 11: Creep time curve (Under different stress conditions). action on the lining void. As can be seen from the figure, the deformation of the lining structure progressively decreases with the increase in FRP-PCM grade at the reinforcing and strengthening parts. Due to the relatively small values of creep strain, the change in the safety factor over a 10-year period was selected as the main focus of analysis in this study. Based on the calculation examples of three different reinforcement types, void positions, and creep times, the decrease in the safety factor was taken as the focus of the analysis. In reference to Figure 12, by comparing the effects over time, it can be observed that as the reinforcement model improves, the impact of creep on reinforcement diminishes. Simultaneously, the reinforcement is influenced by gravity. At the crown of the arch, the creep effect is most pronounced, while at the springline, the height is lower. Additionally, the direction of the reinforcement support force differs from that at the crown, resulting in a reduced time-dependent impact on reinforcement at the springline. Furthermore, even at the crown, where the creep effect is most evident, the maximum deterioration rate does not exceed 8%. After reinforcement, the safety factor significantly improves. Compared to the section repair rate of 40-60%, creep causes only an 8% deterioration over an extended period when the reinforcement is effective, and this value is acceptable. In reference to Figure 13, for the case \"Void at Crown\", without FRP, the safety factor declines significantly, reaching a 7.35% decrease after 10 years.