# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 1 Introduction  
Numerous mountain tunnels in Japan were constructed expeditiously during the era of robust economic expansion, and these structures have now been operational for periods ranging from 30 to 50 years [1]. The conditions of many of these tunnels are not promising, with varying degrees of structural deficiencies manifesting. Many researchers have concentrated their studies on voids situated behind the lining structures of tunnels. The determinants influencing these voids encompass the location, depth, and dimensions of the voids themselves [2]. The effects of these factors on the mechanical behavior of the lining have been extensively examined through a multitude of methodologies. Numerous studies have concentrated on analyzing the mechanical behavior of tunnel linings, particularly under the influence of void defects [3]. Theoretical analyses of tunnel lining behavior have been extensively conducted using approaches such as the Hoek-Brown failure criterion and classical calculus of variations techniques to assess stress and failure conditions [4]. These analyses confirm correlations from a theoretical perspective, and derive three-dimensional elastic solutions for a deep cylindrical tunnel with a void subjected to obliquely incident seismic waves [5]. Furthermore, empirical field investigations have provided crucial insights. These studies have been performed utilizing methods such as microthermor analysis to assess tunnel health conditions [6], along with risk assessment techniques that incorporate statistical models to evaluate the probability and consequences of failure [7]. Complementing these approaches, scaled-model testing has offered valuable data on tunnel performance under stress, such as through small-scale (1:30) model tests [7], shaking table tests where scaled tunnel models were subjected to varying seismic intensities to study the effects of voids [8; 9; 10; 11], and experimental investigations conducted to examine the effect of twin voids behind tunnel linings on their progressive failure process [12]. Moreover, computational numerical analyses such as the extended finite element method (XFEM) have been employed to model the development of cracking patterns and distribution in tunnel linings affected by defects such as local cavities and insufficient lining thickness [13; 14], and numerical models of tunnels' dynamic responses have been optimized using improved inversion results [15; 16]. These studies provide valuable references for preventing and repairing lining cracks influenced by voids behind tunnel linings. Fiber-reinforced polymer (GFRP) reinforcement and fiber-reinforced concrete (FRC) have also been frequently used in studies on tunnel lining reinforcement [17; 18; 19]. In contrast, fiber-reinforced plastic with polymer cement mortar (FRP-PCM) represents an efficacious method for tunnel reinforcement, offering benefits such as ease of application, consistent reinforcement outcomes, lightweight characteristics, and high tensile strength [20]. In this study, we aimed to enhance the sensitivity analysis of the reinforcement method by evaluating the impact of voids through an analysis of bending moments and axial forces within the tunnel lining [21]. In hydraulic structures where moisture and aggressive environmental conditions are prevalent, FRP grids help improve the durability and longevity of the concrete. Proper adhesion ensures that the FRP grid can effectively transfer stress and reinforce the structure. The surface texture and resin properties of FRP grids play significant roles in enhancing this bond. This study involved simulating tunnel linings that had been reinforced with FRP and assessing the effects of such reinforcement in tunnels afflicted with various structural problems. The reinforcement effect of the fiber-reinforced polymer and phase change material (FRP-PCM) method on tunnel lining has been discussed in previous work [22; 23]. [PERSON] et al.