## 5 Conclusions  
This study successfully developed and validated a refined numerical model for shield tunnel lining structures with staggered joints, employing finite element software and full-scale model tests to ensure model reliability. By integrating the Boussinesq formula with advanced numerical simulations, this research innovatively calculates the impact of ground surcharge, offering new insights into the deformation characteristics of shield tunnels. These findings significantly contribute to the field by providing a comprehensive analysis of tunnel convergence, internal forces, joint dynamics, and stress responses in concrete and reinforcement, thereby enhancing design and monitoring strategies in tunnel engineering. The main conclusions are as follows:  
(1) This research established a numerical model for shield tunnel lining structures, meticulously comparing the convergence deformation of tunnel haunches against full-scale shield tunnel segment tests. The findings reveal an alignment in deformation trends between numerical simulations and physical tests across various loading phases, despite the presence of errors ranging from 5% in the elastic loading phase to 47% in the plastic unloading phase. These discrepancies highlight the complexity of accurately simulating structural plastic deformations. However, the consistent trend agreement underscores the model's validity and its potential as a basis for further investigation. This study not only validates the numerical model's utility in predicting the mechanical behavior of shield tunnel linings but also underscores the need for refining these models to enhance their predictive accuracy, particularly in the plastic deformation phases. Future research should aim to reduce simulation errors by exploring the impacts of different loading conditions. (2) This study has elucidated the deformation behaviors of shield tunnel lining structures under ground surcharge, revealing a distinctive pattern of horizontal elongation and vertical compression, resulting in an \"oval\"-shaped deformation. The investigation into joint deformations has highlighted a critical response mechanism: segment rotation, dependent on the orientation of joint deformation. Specifically, the rotation hinge's location varies with the deformation orientation, facilitating a predictive model for the deformation mode of lining structures in practical monitoring scenarios. This insight not only enhances our understanding of shield tunnel lining behavior under external loads but also lays the  
Figure 18: Development of concrete cracks (tension damage parameter \(D_{\text{t}}\)). (**a**) Case C1 (\(P_{0}\) = 140 kPa); (**b**) Case C2 (\(P_{0}\) = 240 kPa); (**c**) Case C3 (\(P_{0}\) = 360 kPa); (**d**) Case C4 (\(P_{0}\) = 480 kPa); (**e**) Case C5 (\(P_{0}\) = 600 kPa); (**f**) Case C6 (\(P_{0}\) = 720 kPa); (**g**) Case C7 (\(P_{0}\) = 840 kPa); (**h**) Case C8 (\(P_{0}\) = 960 kPa); (**i**) Case C9 (\(P_{0}\) = 1080 kPa); (**j**) Case C10 (\(P_{0}\) = 1200 kPa). groundwork for developing more accurate predictive tools and methodologies for tunnel design and monitoring. (3) This research delineates a direct correlation between joint deformation patterns and bolt stress within shield tunnel linings, identifying tension and compression dynamics based on the direction of joint opening. Our findings reveal that bolts experience increased stress, reaching the material's yield strength, particularly when joints open toward the inner arc. Upon the inner arc joints' opening reaching 4.9 mm, the stress exerted on the bolts escalates to the yield strength of 640 MPa, with a peak stress concentration observed near the nut. (4) Under the influence of ground surcharge, significant deformation is observed in the lining structure, with the maximum tensile stress in the segmental reinforcement being primarily located at the joints.