# A Simulation Study of FRP-PCM Reinforcement for Tunnel Liniings with Void Defects
## 2 Research Methods and Evaluation Criteria  
### Simulation Methods for Research  
(1) Selecting the mechanical model of surrounding rock  
The finite element program ABAQUS 2020 was used to establish a plane model. ABAQUS 2020 software is generally applied for simulating the behavior of tunnel lining structure. The cases of voids behind the tunnel lining were considered and then compared after changing the range, position, and number of voids [21; 30]. In this study, when we  
Figure 1: A case of a tunnel lining void problem. Figure 2: The location of the tunnel void. conducted numerical simulation analysis, the properties of the surrounding rock were determined using an elastic-plastic mechanics model. At present, in the field of geotechnical engineering, people generally choose the ideal elastoplastic model calculation, mainly because (1) the modeling is relatively simple and (2) it allows one to easily obtain numerical simulation parameters using the most common simulation experiments. In this study, the geological structure method model, also known as the composite integral model, a type of modern rock mechanics calculation model, was used for tunnel structure calculation. This model regards the support structure and surrounding rock as one unit, and the support structure and surrounding rock can simultaneously bear the force. The surrounding rock is the most direct and main force unit, and the function of the support structure is to constrain and control the deformation of the surrounding rock towards the interior of the tunnel. When using the geological structure model for finite element method calculations, the surrounding rock and lining structure are discretized into elements that are only connected to each other at nodes, and the load is shifted to act on the nodes. In order to calculate the stress and displacement fields of the rock and soil medium and the lining structure, interpolation functions are used to consider the boundary conditions of the surrounding rock, and matrix force method or matrix displacement method equations are used to solve the unknowns of the nodes. The tunnel geometries are shown in Figure 3.  
2. Simulating the earth stress field  
The biggest advantage of highway tunnels is that they have a large cross-section and a flat shape. As the \"long axis\" direction of the tunnel structure is horizontal and orthogonal to the direction of the self-weight stress field, the most unfavorable stress field for the structures of highway tunnels is the self-weight stress field. Therefore, this calculation only considers the initial geostress field generated by self-weight. (3) Determining boundary conditions  
The size range of the calculation model and its boundary conditions were selected according to the analytical requirements of tunnel mechanics. Based on engineering practice experience, the impact of underground engineering is \"sufficiently small\" in areas outside 3-5 times the tunnel diameter from the center of the tunnel. The calculation range of the tunnel model was taken to be four times the tunnel's diameter of 48 m, so the height and width of the model are both 100 m, and the longitudinal length of the model was taken to be 30 m. The boundary conditions for the computational model are as follows: X direction constraints were applied to the left and right sides of the model in the X direction, no  
Figure 3: Tunnel geometry in numerical simulations. constraints were applied to the upper boundary in the Y direction, Y direction constraints were applied to the lower boundary in the Y direction, and Z direction constraints were applied to the longitudinal Z direction of the tunnel. The boundary conditions are shown in Figure 4.  
The height of the void behind the lining was set to 0.45 m, consistent with the thickness of the tunnel lining.