## 1 Introduction  
With the gradual improvements in tunnel construction standards, highly mechanized and automated Tunnel Boring Machines (TBMs) have been widely applied in the construction of railway and highway tunnels. The lining structure for the tunnels built by TBMs consists of prefabricated reinforced concrete segments, which form an assembled structure. The load-bearing performance of this structure is directly related to the safety and durability of the tunnel [1]. In recent years, many scholars have conducted research on this structure. [PERSON], established a refined numerical model, revealing the deformation of surrounding rock and the force characteristics of segments during TBM tunnel construction [2]. [PERSON] and [PERSON] proposed a nonlinear ground spring model that takes into account yield pressure and applied it in numerical analysis [3]. The model considers all relevant components of the shield tunnel construction process, including the TBM, jack thrust, shield tail wire brush, segment lining, key segments, and ring and segment joints, as well as the appropriate interactions. The torque and thrust of the boring machine are the two main design parameters of the shield TBM. [PERSON] et al. extends the traditional block theory to analyze the life-cycle behavioristics (morphology, mechanics, kinematics, and stability) of rock blocks during TBM tunneling considering TBM-block interactions [4]. The segmental tunnel is a cylinder structure composed of precast segments connected by bolts in longitudinal and circumferential directions. The segment joint is composed of concrete blocks, bolts, and washers, and is the weakest part of the shield tunnel lining structure [5; 6; 7; 8]. Due to the differential stiffness between joints and segments, the tunnel stiffness is significantly weakened at the joints. Thus, the segmental tunnels subjected to asymmetric loads often suffer from differential settlement and cross-sectional torsion [9]. The study of the longitudinal differential settlement, bending, and torsion of tunnels has drawn wide attention, and plentiful calculation methods and experiment have been proposed. In contrast, little attention has been paid to the effect of shearing action on tunnel structure. [PERSON] et al. proposed a bending-shear-torsion-resistant beam foundation model to explore the effects of cross-sectional torsion on tunnel performance and compared it with the Finite Element program and other published methods based on two case studies. It was found that longitudinal torsional stiffness is greatly affected by the number of bolts and segment size [10]. [PERSON] et al. explored the structural responses of an existing DOT tunnel caused by shield under-crossing in close proximity in soft ground, where the torsional deformation and torsion-induced bolt stress are significant [11]. [PERSON] et al. proposes a new analytical method to better investigate the longitudinal bending-shear-torsion behavior of shield tunnels under asymmetric external loads, and derives the formula for the stiffness of joint springs [12]. [PERSON] et al. established a three-dimensional refined numerical model of the segment and conducted scaled tests to verify the accuracy of the model. The characteristic equations for calculating the compression-bending stiffness of segmental joints with different thicknesses are determined [13]. [PERSON] et al. proposed a simplified method for evaluating the bending moment capacity of segmental tunnel linings through FEM analysis, where the parameters were calibrated based on tests conducted on a real-scale model. Based on this, they further studied the effects of the segmental joint, number of segments, and soil subgrade modulus on the bending moment capacity characteristics of the tunnel [14]. [PERSON] et al. used finite element software to study the influence of rotational stiffness, shear stiffness, and axial stiffness of segmental lining joints on internal forces (bending moment and axial force) under static conditions.