## 5 Results and Discussion
### Mechanical Behavior of Caisson before and after Void Filling Using Foamed Polymer  
As a consequence of the extreme condition of void formation, the primary impact on the mechanical behavior of the caisson is the removal of soil support at the void location, leading to an uneven distribution of loads around the caisson wall. Empirical evidence suggests that the depth of the void has a relatively minor effect on the mechanical behavior of the caisson, so it is uniformly set at 0.5 m for analysis. To investigate the influence of void location and size on the structural behavior of the caisson, the middle part of the caisson was selected as the path for void lengths of 2.0 m, 3.0 m, and 4.0 m. A comparison chart of the caisson's mechanical behavior before and after void formation is shown in Figure 13. From Figure 13a, it can be observed that the further the caisson wall from the bottom, the greater the displacement variation, with the maximum displacement located at the crown of the wall. For the void lengths of 2.0 m, 3.0 m, and 4.0 m, the horizontal displacements at the crown of the caisson wall are 0.46 mm, 0.52 mm, and 0.65 mm, respectively. This indicates that within a certain range, a larger void size leads to a greater curvature of the caisson wall from the support layer to the upper part of the void area, resulting in a more severe impact on the stability of the caisson. The curvature decreases in the shallow soil layers, but the deflection continues to increase, and even soil separation may occur. After the occurrence of void formation behind the wall, the stress distribution in the soil layer changes, leading to alterations in the stress experienced by the caisson wall. As shown in Figure 13b, after significant deformation occurs in the upper part of the caisson wall, the wall in the void area is directly affected by the lack of soil constraint, resulting in increased tensile stresses of 0.07 MPa, 0.12 MPa, and 0.34 MPa compared to the intact soil. Figure 14 presents a comparison of the mechanical behavior of the caisson at different void positions with a void length of 2.0 m in the scenario where void formation occurs at the interface between the jacking pipes and the caisson. As shown in Figure 14a, the maximum displacement at the crown of the caisson wall reaches 1.23 mm, which is 2.4 times that observed for the void located in the middle. It demonstrated that with the same void length, voiding at lower positions, results in more severe damage to the caisson. Furthermore, as illustrated in Figure 14b, an increasing burial depth results in the gradual compression of the caisson. This phenomenon arises because the lower void position contributes to a rise in the self-weight of the soil above the void, subjecting the caisson to lateral soil pressure greater than the tensile stress during deformation. Additionally, the caisson wall in the void area, lacking soil constraint, undergoes tension with a stress of approximately 0.30 MPa. Figure 12: Comparison of mechanical behavior of caisson structures before and after reinforcement. The foamed polymer grouting material was designed to expand and fill the void. Given the relatively shallow void position in the middle of the caisson, its impact on the mechanical behavior of the caisson wall is less significant. To prevent polymer expansion from exerting pressure on the caisson wall, a low-density foam-type polymer material was employed to fill this void. Conversely, the void near the jacking pipes is deeper, necessitating a higher-strength filling material to resist soil pressure. Additionally, to minimize leakage, the void area near the jacking pipes was filled using low-exothermic polymer grouting material, thereby reducing the chemical impact of polymer reactions on the caisson and jacking pipes. The density, elastic modulus, and Poisson's ratio of the low-density polymers are 0.15 g\(\cdot\)cm\({}^{-3}\), 50.0 MPa, and 0.2, and those of the low exothermic polymers are 0.30 g\(\cdot\)cm\({}^{-3}\), 130.0 MPa, and 0.17, respectively.