# 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
With the expansion in the void range at the top, the overall axial force on the tunnel lining decreases, the axial force on the top and shoulder decreases significantly, and there is a sudden change in axial force between the shoulder and the waist. Moreover, the internal force adjustment of the lining brought about by stress redistribution causes the load in the shoulder area to transfer to the waist, so the axial force suddenly increases in the waist position. Figure 7: The inner force of the tunnel with different void ranges: (**a**) bending moment; (**b**) axial force; (**c**) safety factor. Regarding the bending moment trend, when the void range is small (30\({}^{\circ}\)), the bending moment at the center of the void is positive because the lining is under pressure from the transformation of the weight of the overlying soil. At this time, the soil load slightly increases compared with that in the condition without a void because there is an obvious stress concentration phenomenon on both sides of the void, and the center of the void is relatively close to the stress concentration point, so the bending moment increases, and the safety factor decreases compared with the condition without void; that is, the safety of the lining decreases. Figures 8 and 9 display the bending moment (Mz) and axial force (Nx) distribution around the tunnel lining under different conditions. These diagrams show how voids and FRP reinforcement influence the internal forces acting on the tunnel lining. When the void range is large (60\({}^{\circ}\)), the soil load within the void range can no longer be transferred, so the load size is 0. At this point, the force on both sides of the void and lining shoulder generates a bending moment at the center of the void, and the bending moment is negative. It is subject to great tensile force because the tensile performance of concrete is poor, amounting to approximately one tenth of its compressive strength. Therefore, in the case of a large void, the lining safety factor is much lower and close to the limit value; thus, the corresponding safety factor is so poor that the lining can be very easily damaged. In Figure 9, we can observe the impacts of different void positions on the internal forces of the tunnel lining. When the void range is 45 degrees, the bending moment at the center of the void significantly increases in the tensile direction, with the tensile increase at the shoulder void being the most prominent. Table 5 and Figure 10 shows the distribution of the safety factor and bending moment at different void locations. Using eight symmetrically arranged monitoring points along the cross-section of the tunnel lining, we can see the distribution of internal forces, with point A at the top of the tunnel serving as the center of symmetry. The bar graph represents the bending moment distribution, wherein the vertical axis on the right shows positive and negative values, while the line graph represents the safety factor, with its vertical axis on the left showing only positive values. The safety factor limit was set at 2.0, indicating that monitoring points where the safety factor approaches 2 are more prone to structural imbalance or imminent failure. The safety factor at point E of the inverted arch remained consistently high due to its lower position, where gravitational influence is minimal, and it is under vehicle load in actual operation. Therefore, its static structural stability is not the focus of this study. By comparing the safety factors at points A, B, and C under three different void conditions, it is evident that the safety factor decreases most significantly at the monitoring point located at the center of the void.