Study on Torsional Shear Deformation Characteristics of Segment Joints Under the Torque Induced by Tunnel Boring Machine Construction

Abstract

During the excavation process of a Tunnel Boring Machine (TBM), the cutterhead exerts significant torque on the tunnel structure, which potentially causes torsional shear deformation at segment ring joints. Thus, examining the characteristics of torsional shear deformation and the shear-bearing performance of segment joints under construction torque is crucial for the design and safety of segment structures and the construction of TBM tunnels. To achieve this, a refined finite element model of the segment joints was developed to study their torsional shear resistance under varying axial forces and with or without mortise and tenon. Furthermore, the failure modes of bolts and the damage characteristics of segment concrete during torsional shear deformation are analyzed. The results show that the load-bearing process of torsional shear deformation in segment joints consists of three stages: development of the friction at the segment interface (Stage I), development of the bolt force (Stage II), and development of the mortise and tenon force (Stage III). It is noteworthy that axial force is the primary factor in enhancing the torsional shear resistance of the segmental joints. Moreover, as the torsional shear deformation increases, the contact and compression occur between the bolts and the segment bolt holes as well as between the mortise and tenon, leading to the yielding of the bolts and the failure of the concrete at the joints. Consequently, the segment concrete around the mortise and tenon and the bolt hole is prone to cracking and crushing. To prevent shear failure of the bolts, it is recommended that the rotational angle of segment be maintained at less than 0.045°.

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. Hasanpour, established a refined numerical model, revealing the deformation of surrounding rock and the force characteristics of segments during TBM tunnel construction [2]. Chaipanna and Jongpradist 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. Zhang 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. Liu 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]. Liu 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]. Zhang 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]. Zhang 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]. Teachavorasinskun 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]. Ranjbar 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. The results show that increasing the rotational stiffness of the joints leads to an increase in bending moment, with significant changes for lower values of rotational stiffness. In contrast, changes in axial force were minimal. Additionally, increasing the axial and shear stiffness of the segment joints resulted in negligible changes in both bending moment and axial force in the segmental lining [15]. Zhang et al. derived the bending moment capacity curve based on the calculation method for segmental joint bending capacity proposed by previous researchers, as well as joint parameters obtained from numerous real-world engineering projects. They quantitatively analyzed the influence of segment joint parameters on the bending capacity of the segment joints [16]. Zhang et al. proposed a theoretical model regarding the compression-bending capacity of non-bolted segmental joints and verified by full-scale failure tests. The influence of the segment thickness and length of the core pressure zone on the compression–bending capacity of non-bolted joints were analyzed based on the proposed theoretical model and joint parameters from six segmental joints with different segment thicknesses, and the basic characteristic compression–bending capacity curves of non-bolted joints were obtained [17]. Liu et al. experimentally studied the ultimate bearing capacity of longitudinal joints under different loading conditions and investigated the failure mechanisms of the segments. They developed a corresponding analytical model to calculate the bearing capacity of the longitudinal joints throughout the entire loading process [18]. Yang et al. established a three-dimensional numerical model of segment joints based on a specific tunnel project. The study showed that the rotational stiffness of the joints exhibits complex and nonlinear characteristics. While the segmental joints have little impact on the axial force of the lining, the bending stiffness of the segmental lining corresponding to the joint locations is reduced, leading to discontinuous stress distribution, a decrease in bending moment, and an increase in deformation [19]. Wu et al. conducted full-scale experiments and numerical simulations on the bending behavior of oblique bolt connections, revealing the typical bending behavior and failure characteristics of a single oblique bolt node, and then studied the influence of different oblique bolt arrangements (i.e., number and direction) on the bending behavior of the node under different axial forces [20]. Zhang et al. combined the deformation characteristics of segment joints under compressive bending loads, using the concrete yield of the joint surface as the criterion for the ultimate bearing capacity of segment joints. Based on this, they established a theoretical model for calculating the bending capacity of segment joints [21]. Cheng conducted a series of bending tests to study the bending behavior of segments and developed an analytical model for the bearing capacity of the segments [22]. Feng et al. conducted a series of full-scale tests on segment joints of underwater shield tunnels and compared the results with numerical simulations. The results show that the bending stiffness of the joints can be divided into three stages based on the inflection points of “visible concrete cracking” and “bolt yielding”. The axial force has a significant impact on retention [23]. Han et al. designed a finite element model that can be used to evaluate the shear stiffness of circumferential joints during the relative displacement between rings facing the same circumferential joint, and, based on this model, analyzed the influence of bolts on the shear stiffness of the joints [24].

The literature review indicates that most of the previous studies focus on the transverse deformation characteristics of the lining rings and the bending resistance performance of circumferential joints. However, during TBM excavation, the cutterhead applies a significant torque to the segment structure. A shield tunnel is an assembled underground structure composed of segments and connecting bolts, so that the overall structural system of a shield tunnel behaves differently from the torsional characteristics of reinforced concrete components. Under torque, the primary deformation occurs at the joints between adjacent lining segments, as these joints represent the weakest points of the shield tunnel. Therefore, this paper aims to study the shear resistance performance of segment joints under TBM construction torque. The structure of this paper is as follows: First, a three-dimensional refined finite element model of the segment is established based on a specific shield tunnel engineering project. Then, the numerical model is validated by comparing it with the load curve from the literature. Finally, numerical tests are conducted under various loading conditions, and the stress and strain of each part of the segment under different conditions is presented and the torsional shear deformation characteristics of the segment joints are analyzed.

2. Engineering Background

The Shenjiang Railway Tunnel spans a total length of 11,886.56 m. The primary construction methods employed include mining, TBM, and open–cut techniques. The tunnel, constructed using the TBM method, has a total length of 7989 m. The burial depth of the tunnel varies between 30 and 75 m, with the predominant rock type in the surrounding strata being gneiss. The stratigraphic distribution is shown in Figure 1. For excavation, the project employs a composite TBM equipped with 18 uniformly arranged double-cylinder jacks (36 jacks in total). In terms of performance, the TBM can achieve a maximum propulsion speed of 80 mm/min, a maximum rotational speed of 5 rpm, a maximum thrust of 174.56 MN, and a maximum torque of 27,691 kN·m.

The tunnel structure in this project has an outer diameter of 12.8 m, a thickness of 0.55 m, and a width of 2 m. Each tunnel ring consists of nine prefabricated concrete segments, including one key block (K), two adjacent blocks (L1 and L2), and six standard blocks (B1, B2, B3, B4, B5, and B6), with each segment having a central angle of 40°. The segment partitioning is shown in Figure 2. The segments are connected using high-strength inclined bolts, with 3 bolts positioned at each circumferential joint, resulting in a total of 27 connection bolts per tunnel ring. For the longitudinal joints between the lining rings, a bolt is placed at every 10° interval, yielding a total of 36 connection bolts.

3. Establishment and Validation of Finite Element Model

3.1. Equation Solving Techniques

The finite element software ABAQUS 2021 was used to solve the problem [25]. In ABAQUS, the nonlinear contact problem is solved using a direct solver and the Full Newton method, which is known for its high accuracy and stability. The direct solver performs a full decomposition of the stiffness matrix (e.g., LU decomposition) to obtain an accurate solution. Although the computational cost is higher, this method is suitable for handling the high degree of nonlinearity and stiff contact stiffness that can arise in contact problems. In the Full Newton method, the system stiffness matrix is reassembled in each iteration to accurately capture the contact and geometric nonlinearities. The nonlinear contact problem is solved incrementally, with each load increment being decomposed into several sub-steps, and each sub-step is solved using the Full Newton iterative method. In each incremental loading step, the following three primary convergence criteria are used to ensure the accuracy and stability of the computational results: displacement convergence criterion (Inequality (1)), residual force convergence (Inequality (2)) criterion, and contact pressure convergence criterion (Inequality (3) and (4)).

$$‖\Delta u‖=\sqrt{{\displaystyle \sum _i^n{\left(\Delta u_i\right)}^2}}<{\kappa }_{\mathrm{u}}$$

(1)

$$‖R‖<{\kappa }_{\mathrm{r}}$$

(2)

$$P_{\mathrm{n}}<{\kappa }_{\mathrm{p}}$$

(3)

$$T_{\mathrm{t}}<{\kappa }_{\mathrm{t}}$$

(4)

where Δu is the displacement increment and the displacement convergence tolerance; n is the total number of degrees of freedom; Δu_i is the displacement increment for each degree of freedom; R and κ_r are the residual force and the force convergence tolerance; P_n is the change in the normal contact pressure on the contact surface; κ_p is the normal contact pressure convergence tolerance; T_t is the changes in friction force on the contact surface; and κ_t is the friction force convergence tolerance.

3.2. Establishment of Finite Element Model

This study investigates the structural response of segmental joints under torsion shear interactions from the perspective of segmental structure. It analyzes the patterns of rotational deformation and structural failure of the segments, without considering the interaction between the segmental structure and the soil. This study first establishes a refined numerical model of segment joints based on the actual design specifications of the circumferential joints, taking into account factors such as joint construction, connecting bolts, and reinforcement. To counteract the torque generated by the TBM cutterhead during excavation, mortise and tenon are incorporated into the circumferential joints, with each segment equipped with two sets of these structures. In the actual segmental structure design, a 7 mm gap is provided between the tenon and the mortise to facilitate assembly during construction, while a 3 mm gap is designed between the bolts and the bolt holes. To enhance computational efficiency, a half-model is constructed, leveraging the symmetry of the segment. The refined segment joint model is illustrated in Figure 3. Due to the structural complexity of the joint configuration, the segments were meshed using a combination of integration eight-node hexahedral linear elements (C3D8R) and ten-node modified quadratic tetrahedron elements (C3D10M). The bolts are simulated using C3D8R elements The rebars are simulated using two-node linear three-dimensional truss elements (T3D2). The joint model with mortise and tenon features consists of 188,451 nodes and 145,075 elements, while the joint model without mortise and tenon features consists of 183,295 nodes and 140,784 elements.

3.3. Constitutive Model and Parameters for Material

The stress–strain relationship of concrete can be determined according to the Code for Design of Concrete Structures (GB50010-2010) [26].

For concrete under uniaxial compression,

$${\sigma }_{\mathrm{c}}=\left(1-d_{\mathrm{c}}\right)E_{\mathrm{c}}{\epsilon }_{\mathrm{c}}$$

(5)

$$d_{\mathrm{c}}=\left\{\begin{array}{l}1-{\displaystyle \frac{{\rho }_{\mathrm{c}}m}{m-1+x}}\hspace{1em}\left(x\le 1\right)\\ 1-{\displaystyle \frac{{\rho }_{\mathrm{c}}}{{\alpha }_{\mathrm{c}}{\left(x-1\right)}^2+x}}\hspace{1em}\left(x>1\right)\end{array}\right.$$

(6)

$${\rho }_{\mathrm{c}}={\displaystyle \frac{f_{\mathrm{c},\mathrm{r}}}{E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}}}$$

(7)

$$m={\displaystyle \frac{E_{\mathrm{c}}{\epsilon }_{\mathrm{c},\mathrm{r}}}{E_0{\epsilon }_{\mathrm{c},\mathrm{r}}-f_{\mathrm{c},\mathrm{r}}}}$$

(8)

$$x={\displaystyle \frac{{\epsilon }_{\mathrm{c}}}{{\epsilon }_{\mathrm{c},\mathrm{r}}}}$$

(9)

where σ_c is the compressive stress of the concrete; ε_c is the compressive strain of the concrete; E_c is the elastic modulus of the concrete; α_c is the parameter value for the descending segment of the uniaxial compressive stress–strain curve of the concrete, determined according to ${\alpha }_{\mathrm{c}}=0.157f_{\mathrm{c}}^{0.785}-0.905$; f_c,r is the representative value of the uniaxial compressive strength of the concrete, taken as f_c = 38.5 MPa; ε_c,r is the peak strain corresponding to the representative value of uniaxial compressive strength f_c,r, determined according to ${\epsilon }_{\mathrm{c},\mathrm{r}}=\left(700+172\sqrt{f_{\mathrm{c}}}\right)\times {10}^{-6}$; and d_c is the damage evolution parameter for concrete under uniaxial compression.

For concrete under uniaxial tension,

$${\sigma }_{\mathrm{t}}=\left(1-d_{\mathrm{t}}\right)E_{\mathrm{t}}{\epsilon }_{\mathrm{t}}$$

(10)

$$d_{\mathrm{t}}=\left\{\begin{array}{l}1-{\rho }_{\mathrm{t}}\left(1.2-0.2x^5\right)\hspace{1em}\left(x\le 1\right)\\ 1-{\displaystyle \frac{{\rho }_{\mathrm{t}}}{{\alpha }_{\mathrm{t}}{\left(x-1\right)}^{1.7}+x}}\hspace{0.5em}\left(x>1\right)\end{array}\right.$$

(11)

$${\rho }_{\mathrm{t}}={\displaystyle \frac{f_{\mathrm{t},r}}{E_{\mathrm{t}}{\epsilon }_{\mathrm{t},\mathrm{r}}}}$$

(12)

$$x={\displaystyle \frac{{\epsilon }_{\mathrm{t}}}{{\epsilon }_{\mathrm{t},\mathrm{r}}}}$$

(13)

where σ_t is the compressive stress of the concrete; ε_t is the compressive strain of the concrete; E_t is the elastic modulus of the concrete; α_t is the parameter value for the descending segment of the uniaxial compressive stress–strain curve of the concrete, determined according to ${\alpha }_{\mathrm{t}}=0.312f_{\mathrm{t},\mathrm{r}}^2$; f_t,r is the representative value of the uniaxial compressive strength of the concrete, taken as f_t = 2.85 MPa; ε_t,r is the peak strain corresponding to the representative value of uniaxial compressive strength f_t,r, determined according to be ${\epsilon }_{\mathrm{t},\mathrm{r}}=f_{\mathrm{t},\mathrm{r}}^{0.54}\times 65\times {10}^{-6}$; and d_t is the damage evolution parameter for concrete under uniaxial tension.

In this study, the mechanical behavior of concrete is represented using the Concrete Damage Plasticity (CDP) model. This model incorporates a continuum plasticity-based damage mechanism for concrete, assuming that isotropic damage and cracking occur under both compressive and tensile stresses. The strength grade of the precast segment concrete is C60. According to the Code for Design of Concrete Structures (GB50010-2010), the compressive strength of the concrete is (f_c = 38.5 MPa) and the tensile strength is (f_t = 2.85 MPa). The damage factors for the CDP Model are calculated using the energy equivalence principle proposed by Sidoroff [27].

Table 1. Parameters of C60 concrete damage plastic model.

Parameters	Numerical	Parameters	Numerical
ρ (kg/m3)	2400	fb0/fc0	1.16
Ec (GPa)	36.5	e	0.1
ν	0.18	σcu (MPa)	38.5
ψ (°)	38	εcu	0.0018
Kc	0.6667	σt0 (MPa)	2.85
μ	0.0005	εt0	0.00011

Note: ρ is mass density; E_c is the elastic modulus; ν is Poisson’s ratio; ψ is the dilatancy angle; K_c is the stress invariant ratio; μ is the viscosity coefficient; f_b0/f_c0 is the ratio of biaxial to uniaxial compressive strength; e is the flow potential offset; σ_cu and ε_cu are the axial compressive strength and the corresponding strain (the peak compressive strain); σ_t0 and ε_t0 are the axial tensile strength and the corresponding strain (the peak tensile strain), respectively.

lists the parameters for the C60 concrete damage plasticity model, and Figure 4 illustrates the damage characteristics of concrete under both compression and tension.

The mechanical behavior of the rebars and bolts is modeled using a bilinear elastic–plastic constitutive model, while the bolt washers are simulated with a linear elastic constitutive model. The elastic modulus and Poisson’s ratio for both bolts and washers are set at 210,000 MPa and 0.22, respectively. The bolts used are high-strength grade 10.9 bolts, featuring a yield strength of 900 MPa and an ultimate strength of 1000 MPa. Additionally, the elastic modulus and Poisson’s ratio for the reinforcement bars are 200,000 MPa and 0.28, respectively. The reinforcement bars are classified as HRB335, with a yield strength of 335 MPa and an ultimate strength of 455 MPa.

3.4. Contact Interaction

Surface-to-surface contact interactions refer to the contact between two deformable surfaces or between a deformable and a rigid surface [25]. Methods for surface-to-surface contact include contact discretization and tracking techniques. The finite sliding tracking method is the most commonly used, as it accommodates arbitrary separation, sliding, and rotation between contact surfaces, making it suitable for scenarios involving large relative sliding or rotation. Compared with node-to-surface discretization, surface-to-surface discretization better prevents the nodes of the master surface from penetrating the slave surface. Therefore, this study employs finite sliding tracking and surface-to-surface discretization methods for simulation. The tangential and normal mechanical properties of the contact follow the penalty function and hard contact, respectively. Surface-to-surface contact is used to simulate the interactions between adjacent segments, between the bolt contact section and segment concrete, between the bolt washer and segment concrete, and between the bolts and bolt washers [28]. The tangential and normal mechanical properties of the contact between the segments follow the penalty function and hard contact, with a friction coefficient of 0.55. Similarly, the tangential and normal mechanical properties of the contact between the bolt contact section and the segment concrete, as well as between the bolt washer and the segment concrete, also adhere to the penalty function and hard contact, with a friction coefficient of 0.15. The friction coefficient between the bolts and bolt washers is set to 0.2 [13]. The interactions between the bolt anchoring section and the segment and between the reinforcement and the segment are simulated using the embedded region. Ties are applied to constrain the nuts and bolt washers, the bolt washers and the concrete, and the bolt sleeves and the concrete bolt hole walls [29,30]. The specific contact relationships are depicted in Figure 5.

3.5. Model Validation

To validate the reliability of the numerical simulation method, a finite element model was established based on existing segment joint tests. The loading and boundary conditions were set according to the experimental parameters, and the accuracy of the simulation was evaluated by comparing the test results with those from the numerical simulation. Zhang et al. conducted a bending performance loading test on shield segment joints [13]. The joint configuration of these test segments is similar to that of the TBM shield segment joints used in the Shenjiang Railway project, with both featuring a segment thickness of 550 mm and high-strength inclined bolts for connection, allowing for a comparative analysis with the numerical simulation in this study. The dimensions of the segment joint model in this study match those from the test, and the numerical model for the segment joint bending performance test is illustrated in Figure 6. The loading scheme for the numerical simulation was designed to replicate the test method used in the segment joint bending performance test. The boundary conditions are that one end of the loading device is a fixed support, and the other end is a sliding support. Horizontal axial forces and vertical two-point loading were applied to induce bending moments. In the numerical model, the preload is applied to the bolt based on the load type “Bolt load” in ABAQUS, in which the direction, magnitude, and applied section of the bolt preload should be determined [25]. The direction of the preload is along the length direction of the bolt, and the bolt preload was determined based on joint tests, with a value of 95.96 kN. The loading method and boundary conditions are shown in Figure 7.

The segment joint test examined the bending performance of the joints under varying axial force conditions and under both positive and negative bending moments. To enable a comprehensive comparison between the test and numerical simulation results, vertical displacement and joint opening were chosen as key comparison parameters.

As shown in Figure 8, the comparison between the vertical displacement results from both the test and the numerical simulation is presented for various bending moments and axial forces. Figure 9 compares the joint opening results under similar conditions. From Figure 8 and Figure 9, it is evident that the overall trend in the numerical simulation results is consistent with that in the test results, although some numerical discrepancies exist. In the segment joint test, the nonlinear mechanical behavior of concrete becomes more prominent under larger bending moments due to its significant nonlinear properties. The constitutive material model and contact definitions in the numerical simulation are less effective in capturing the complex force and deformation characteristics at this stage, leading to a gradual accumulation of numerical errors. As the bending moment increases, the relative error between the numerical simulation and the test results grows. However, within a certain range in bending moments, the relative error remains small, and the numerical model closely approximates the actual force and deformation behavior of the segment joints. Changes in vertical displacement and joint opening also follow the same trends observed in the tests. Therefore, the numerical simulation method demonstrates a reasonable degree of reliability and can serve as a solid foundation for further research.

4. Torsional Shear Deformation Characteristics of Segment Joints

4.1. Computational Cases

To evaluate the shear resistance performance of ring joints under torsional shear, a fixed segment and a movable segment were employed to induce torsional deformation along the tangential direction at the joints. The numerical simulation was carried out in three main stages: first, bolt pretension was applied; second, an axial force (N) was applied; and third, a tangential force (T) was applied in the circumferential direction to the movable segment, simulating torque and inducing torsional shear deformation at the joint. The loading method and boundary conditions are depicted in Figure 10. This study primarily investigates the effects of the mortise and tenon, as well as the axial force, on the shear resistance of ring joints. The detailed calculation conditions are provided in

Table 2. Computational cases.

Case	Joint Configuration	Pretightening Force on Bolt (kN)	Axial Force (kN)
C1	Non-mortise and tenon (NMT)	95.96	0
C2			1000
C3			2000
C4			3000
C5			4000
C6	Mortise and tenon (MT)	95.96	0
C7			1000
C8			2000
C9			3000
C10			4000

.

4.2. Load-Bearing Performance of the Segment Joints

Figure 11 presents the distribution of the rotational angle at the segmental joint (C10), where θ represents the rotational angle about the center of the segment. A counterclockwise rotation is considered positive. The boundary conditions and loading methods established in this study are designed to simulate the torsional–shear deformation of the segmental joint, thereby enabling an analysis of its torsional–shear bearing capacity. As shown in Figure 11, the rotational deformation of the segmental joint is predominantly concentrated in the movable segment, which undergoes uniform rotation. In contrast, the fixed segment exhibits no rotational deformation. The anchoring section of the bolts, however, experiences rotational deformation in unison with the movable segment. Upon significant rotational deformation of the bolt, the contact region between the bolt and the bolt hole is activated. This contact is constrained by the fixed segment, inducing torsional shear deformation in the bolt. As the rotation of the movable segment increases, the mortise and tenon joint also comes into contact, leading to torsional shear deformation of the tenon.

Figure 12 illustrates the load–displacement relationships for the segment joints. As shown in the figure, the force transmission process during torsional shear deformation of the segment circumferential joints occurs in three distinct stages: development of the segment interface friction (Stage I), development of the bolt force (Stage II), and development of the mortise and tenon force (Stage III). Notably, during the segment interface friction and bolt force stages, the load-bearing performance is similar for joints with and without the mortise and tenon. However, in the final stage, the presence of the mortise and tenon significantly enhances shear resistance. The first stage (Stage I) corresponds to the segment interface friction force stage (0° < θ < 0.03°). During this stage, neither the bolts nor the mortise and tenon participate in force transmission due to gaps between the bolts and their holes, as well as gaps within the mortise and tenon. Therefore, the primary source of torsional shear resistance is the friction at the segment interface. An increase in the applied axial force during this stage enhances the segments’ resistance to torsional shear. For instance, in the absence of axial force, the maximum tangential force is 20.58 kN. In comparison, axial forces of 1000 kN, 2000 kN, 3000 kN, and 4000 kN result in an increase in the tangential force by 487.85%, 962.88%, 1416.38%, and 1940.62%, respectively. This highlights the crucial role of axial force in improving the initial frictional resistance. The second stage is the bolt force stage (0.03° < θ < 0.09°). Once the rotational angle exceeds 0.03°, contact is established between the bolts and the bolt holes, enabling the bolts to begin resisting shear forces. The effectiveness of the bolts in resisting shear is more pronounced under lower axial forces. As the axial force increases, the relative contribution of the bolts diminishes. Specifically, under axial forces of 0 kN, 1000 kN, 2000 kN, 3000 kN, and 4000 kN, the maximum tangential forces increase by 354.73%, 47.87%, 22.58%, 13.23%, and 8.12%, respectively. This indicates that while the bolts are more influential under lower axial force conditions, their overall effect diminishes as the system becomes increasingly dominated by other force mechanisms at higher axial forces. The third stage is the mortise and tenon force stage (θ > 0.09°). When the rotational angle exceeds 0.09°, contact between the mortise and tenon begins, thereby constraining the torsional shear deformation of the segment. The presence of the mortise and tenon greatly enhances torsional shear resistance, particularly at lower axial force levels. However, as the axial force increases, the relative effect of the mortise and tenon decreases. Compared to the conditions without the mortise and tenon, the maximum tangential forces under axial forces of 0 kN, 1000 kN, 2000 kN, 3000 kN, and 4000 kN increase by 70.22%, 22.17%, 14.27%, 8.49%, and 6.12%, respectively. This diminishing improvement suggests that higher axial forces tend to saturate the system’s shear resistance, reducing the additional benefit provided by the mortise and tenon. The conclusions are as follows: The shear resistance increases significantly with higher normal forces in all stages. The presence of the mortise and tenon provides a substantial advantage in the third stage, although its relative impact diminishes at higher axial forces. The system transitions from being dominated by frictional forces to bolt engagement and, finally, to mortise and tenon contact, as the tangential displacement progresses.

It found that the role of bolts and mortise and tenon in resisting torsional shear in segment joints is relatively small, while axial force is the primary factor influencing the torsional shear performance of segment joints. Therefore, improving the torsional shear resistance of segment joints can be achieved by enhancing the interface friction coefficient. The gap between the mortise and tenon directly affects the torsional shear resistance of the segment joint. An excessively large gap may prevent the mortise and tenon from functioning during rotational deformation. However, an overly large gap also increases the difficulty of segment assembly. Therefore, the design of the gap between the mortise and tenon should be considered comprehensively based on practical conditions. Appropriately reducing the gap can effectively control the twisting deformation of the segment.

4.3. Bolt Stress Response

A node on each bolt where the stress first reaches 900 MPa is selected as the characteristic point for the bolt stress. The stress variation at this characteristic point is then extracted for quantitative analysis. Figure 13 illustrates the relationship between bolt stress and the rotational angle, with Figure 13a,b corresponding to the cases with and without the mortise and tenon at the segmental joint (C1–C5 and C6–C10, respectively). As observed in the figure, the relationship between bolt stress and rotation angle remains generally consistent across different joint configurations and axial forces. This suggests that, during torsional–shear deformation of the segmental joint, the bolt stress is predominantly governed by the rotation angle of the segment. The variation in bolt stress with respect to the rotation angle can be categorized into three distinct stages. In the rotational angel in a range from 0° to 0.03°, the bolt stress increases gradually, with the bolt primarily undergoing bending deformation. During this stage, the bolt does not make contact with the segmental bolt hole wall, and the rotation of the segment induces bending deformation in the bolt. In the rotational angel in a range from 0.03° to 0.045°, the bolt stress increases more rapidly, with the bolt predominantly experiencing shear deformation. Here, the bolt comes into contact with the segmental bolt hole wall, which causes the bolt to undergo shear deformation. Once the rotational angle exceeds 0.045°, the bolt stress reaches the yield strength, and the bolt is locally compressed by the segment’s bolt hole wall. This leads to the yielding and potential failure of the bolt at the segment joint. To prevent shear failure of the bolts, it is recommended that the segment’s rotation angle be maintained at less than 0.045° in practical engineering applications.

Figure 14a shows the bolt stress distribution under different rotational angles (N = 4000 kN). As observed, the stress distribution across the bolts remains generally consistent across different joint configurations. With an increase in the rotation angle, the bolt stress gradually rises. When θ < 0.03°, the bolt stress distribution is relatively uniform, and the stress levels are low. However, when θ > 0.045°, localized stress concentrations begin to occur in the bolts, with the maximum stress primarily concentrated at the joint. As the rotation angle exceeds θ > 0.09°, the stress at the contact section of the bolt reaches the yield strength, and the range in yielding progressively expands with further increases in rotation. Figure 14b shows the bolt stress distribution under different axial forces (θ = 0.135°). It can be observed that, once the rotation angle reaches 0.135° and the stress level approaches 900 MPa, the bolts have already yielded under all conditions. Notably, the stress distribution remains consistent across varying axial force conditions, indicating that the rotation angle is the dominant factor influencing the stress behavior, rather than the axial load. Additionally, the presence or absence of the mortise and tenon has a minimal impact on the overall stress distribution. Instead, the primary factor driving the stress is the interaction between the bolts and the bolt holes. This interaction induces shear deformation as the bolts come into direct contact with the bolt holes during torsional loading, resulting in concentrated stress at the contact points. The observed high stress levels, regardless of the joint configuration, underscore the risk of shear failure in the bolts under torsional deformation. Although the mortise and tenon may provide additional stability, it does not significantly reduce the shear stress on the bolts. This suggests that bolt–hole interactions under torsional shear play a more critical role in joint performance than the presence of the mortise and tenon.

4.4. Damage Characteristics of Concrete

In this study, the tensile damage factor of the concrete is used as an indicator to evaluate crack development, while the compressive damage factor is employed to assess crushing damage. Figure 15 presents the distribution of tensile damage in the segment concrete under torsional shear deformation at the circumferential joints. The results indicate that tensile damage is concentrated around the bolt holes and mortise and tenon. The distribution of this tensile damage appears to be consistent across varying axial force conditions. As torsional shear deformation progresses, one side of each bolt hole experiences compression due to the bolt, which induces tensile cracks on the opposite side of the hole. Furthermore, as illustrated in Figure 15a–d, with increasing torsional deformation, these cracks propagate outward from the bolt hole toward both the outer and inner arc surfaces of the segment. During this process, both the mortise and tenon experience compression, with distinct behaviors at each joint type. In particular, tenons are subjected to shear forces at the surface of the segment, leading to significant cracking near the compressed regions. In contrast, cracking in the mortise predominantly occurs on the non-compressed side, as the compressed side is in contact with the tenon. The formation of tensile cracks on the non-compressed side is a direct result of this contact during torsional shear.

Figure 16 illustrates the compressive damage distribution in segmental concrete structures under torsional shear deformation at circumferential joints. The compressive damage predominantly concentrates around the bolt holes and the mortise and tenon, where significant stress is generated. Under different axial force, a consistent damage pattern is observed, with the progression in damage intensifying as torsional deformation increases. Specifically, during high torsional shear, the bolts and mortise and tenon experience substantial compressive forces, leading to localized crushing of the concrete around these critical areas. Figure 16a–d further reveals that, under large deformations, the tenons undergo complete crushing, while the mortise exhibit damage primarily on the compressed side. This suggests that the mortise and tenon geometry and bolt positioning significantly influence the failure modes and shear resistance of the joints.

5. Conclusions

This study conducted a comprehensive numerical investigation on the torsional shear deformation characteristics of segment joints, which is induced by the excessive construction torque during TBM tunneling. To achieve this, a refined finite element model of the segment joints was developed using finite element simulation techniques, incorporating factors such as joint construction, mortise and tenon elements, connecting bolts, and reinforcement. The development process of the torsional shear resistance at the segment joints under varying axial forces, for both the structures with and without mortise and tenon, were revealed. In addition, the failure modes of bolts and the damage characteristics of the segment concrete under torsional shear deformation were analyzed. The main conclusions from this study are as follows:

(1)

The development of torsional shear deformation of segment circumferential joints consists of three stages: development of the friction at the segment interface (Stage I: 0° < θ < 0.03°), development of the bolt force (Stage II: 0.03° < θ < 0.09°), and development of the mortise and tenon force (Stage III: θ > 0.09°). Under low axial force conditions, the contributions of the bolts and the mortise and tenon to improving the torsional shear resistance are more significant, while at high axial forces, their contributions are relatively small. When the axial force is 0 kN, compared to the friction loading stage (Stage I), the torsional shear resistance of the segmental joint increases by 354.73% in the bolt force stage and 70.22% in the mortise and tenon force stage. When the axial force is 1000 kN, the corresponding increases are 47.87% and 22.17%, respectively. When the axial force is 2000 kN, they are 22.58% and 14.27%, respectively. When the axial force is 3000 kN, they are 13.23% and 8.49%, respectively. When the axial force is 4000 kN, they are 8.12% and 6.12%, respectively. It is noteworthy that axial force is the primary factor in enhancing the torsional shear resistance of the segmental joints.

(2)

During the development of torsional shear deformation of segment circumferential joints, the bolts come into contact and compress against the walls of the segment bolt holes, leading to the development of shear deformation. When the rotation angle exceeds 0.045°, the bolt stress reaches the yield strength. In the working condition, when the rotation angle increases from 0.04° to 0.045°, the bolt stress rapidly rises from approximately 850 MPa to 900 MPa. Subsequently, when the rotation angle is further increased, the bolts begin to yield and experience local failure. Therefore, to prevent shear failure of the bolts, it is recommended that the segment’s rotation angle be maintained at less than 0.045° in practical engineering applications.

(3)

Under the torsional shear deformation, concrete cracking tends to occur around the mortise and tenon and bolt holes. Specifically, cracks in the tenons are primarily distributed near the compression side, while cracks around the bolt holes and in the mortises are mainly located on the non-compressed side, extending toward both the outer and inner arc surfaces of the segment. And concrete crushing is concentrated around the bolt holes and mortise and tenon. Moreover, under significant torsional shear deformation, the tenons are completely crushed, while the mortises experience crushing only on the compressed side.

(4)

This study investigates the characteristics of large torque generation during TBM construction and explores the torsional shear deformation behavior of circumferential segment joints. The research takes into account the design considerations of segment joints in real-world shield tunnel projects. A comprehensive analysis is conducted to assess the impact of axial forces, bolts, and tongue-and-groove connections on the torsional–shear performance of segment joints. The findings offer valuable insights for the structural design of TBM tunnels. It is observed that the torsional shear performance of segment joints exhibits significant variation under different axial forces, highlighting the need to consider the pushing force during TBM tunneling when designing segment joints. In cases of substantial torsional deformation, the bolts and tongue-and-groove structures are identified as the primary locations of failure within segment joints. Consequently, the design of these components should incorporate considerations for the torsional deformation of the lining rings to enhance the structural integrity and reliability of the tunnel segments.

(5)

This study investigates the effects of torque on shield tunnels at the segment joint level, providing insights into the mechanical behavior and performance of segment joints under torsional loads. Recognizing that a shield tunnel operates as a structural system comprising segments and connecting bolts, future research could extend the scope to explore the influence of torque at the lining ring level. In terms of constitutive modeling, the Concrete Damage Plasticity (CDP) model employed in this study has demonstrated its effectiveness in simulating the mechanical behavior of concrete. For the bolts, a bilinear ideal elastic–plastic constitutive model was applied; however, this approach does not account for bolt fracture behavior under ultimate load conditions. Future investigations could enhance the constitutive model for bolts to better capture the failure mechanisms of segment joints under extreme torque. Additionally, this study compares the torsional–shear performance of segment joints with and without mortise and tenon structures, based on structural designs from actual projects. To further refine these findings, future research could examine the influence of mortise and tenon dimensions and geometric parameters on the torsional–shear performance of segment joints, thereby proposing optimized design strategies for improving the overall structural resilience of shield tunnels.