# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 3 Results and Analysis
### The Influence of Void Location and FRP Reinforcement  
The material properties of FRP are very different from those of traditional structural materials such as steel and concrete, and their forms are varied. Fiber is the main mechanical material in FRP, and it can be divided into long fiber and short fiber. The reinforcement in the FRP used in engineering structure is mainly long fiber. Continuous fibers can range from several meters to over 100 m in length depending on how they are laid out in the structure (e.g., in unidirectional or woven format). In most applications, such as in structural reinforcements or load-bearing components, fiber lengths are designed to match or exceed the dimensions of the component being reinforced to maximize strength. The long fibers used in FRP reinforcement for engineering structures are generally continuous fibers, which can be several meters long or even much longer, depending on the specific design and application. Apart from the specific strength and specific modulus with respect to the size of the actual engineering result, the material application effect of carbon fiber is the best, but the elongation of carbon fiber material is very low, so it sometimes needs to be mixed with other fibers to achieve better performance. Carbon fiber FRP has become a very important structural reinforcement material, and it has been widely used and developed in the renovation and reinforcement of various civil and industrial buildings. The FRP-PCM method should be used to ensure the required performance of a repaired or reinforced concrete structure in regard to aspects such as safety, fatigue durability, usability, and environmental impact durability. Therefore, it is necessary to fully investigate and understand the environment in which the existing concrete structure to be repaired or reinforced is situated, along with the damage it has sustained, before construction and implement the measures before and after construction according to the specific needs of the project [31; 32; 33]. According to the current research, the void behind the lining was determined to be a common problem, and after analyzing the effect of different void toroidal ranges and locations on the tunnel lining, the distribution characteristics of tunnel lining structure problems were obtained. Based on the specific parameters of tunnel problems in the literature, a tunnel model was established using the numerical simulation method in order to analyze reinforcement behavior. The effect of reinforcement needed to be considered, and an indicator needed to be introduced to facilitate the comparison of the repair effect and time impact. So, here, we introduce the concept of the sectional repair rate [34]. \[R=\frac{K}{K_{0}}-1\times 100\% \tag{6}\]  
In the formula above, R is the sectional repair rate, K represents the safety factor of the lining with FRP reinforcement, and \(K_{0}\) is the safety factor in the initial state. The FRP construction example refers to the crack repair work of NEXCO West Japan's lining reinforcement project in the Nagasaki do Hidake Tunnel [35]. The bending moment, axial force, and safety factor were calculated using Formulas (3) and (5). The stress and strain of the tunnel structure were analyzed by simulating the voids in different positions and ranges behind the lining, and the safety of the structure was evaluated. The evaluation indexes of tunnel lining damage in the current code were sorted out to provide data support for the subsequent research on the effect of a void behind tunnel lining and the evaluation of tunnel lining health. Stress is generally concentrated at the edge of the void, significantly increasing the compressive force. Concrete structures have much less tensile strength than compressive strength, so the safety factor of such structures is significantly reduced, but reinforcing the lining can effectively improve the soundness in the void range. The bending moment, axial force, and safety factor after reinforcement are shown in Figures 6-10.