Analysis of the Combined Load-Bearing Mechanical Characteristics of the Combined Structure of “Inner Tensioned Steel Ring–Segment–Surrounding Rock” in a TBM Pressurized Water Conveyance Tunnel

Abstract

To explore the stress-bearing characteristics of the “inner tensioned steel ring–segment–surrounding rock” composite structure in TBM (Tunnel Boring Machine) pressurized water conveyance tunnels, a 3D refined finite element model for this composite structure was established, with the Class V surrounding rock section of the TBM pressurized water conveyance tunnel in the Rongjiang-Guanbu water diversion project selected as the research subject. The effects of the internal water pressure, surrounding rock type and tunnel burial depth on the mechanical properties of the composite structures are studied. The findings demonstrate that reinforcing the tunnel structure with an inner tensile steel ring can effectively constrain tunnel deformation, diminish the tensile stress of segments and the extent of tensile zones, and enhance the bearing capacity of the composite structure. Under the effect of internal water pressure, the compressive stress of segments, vertical deformation, joint opening degree, stress of connecting bolts, stress of the inner tension ring, and stress of anchor rods all exhibit a reduction compared to the scenario without internal water pressure. Under the combined action of external water–soil pressure and internal water pressure, variations in surrounding rock types lead to respective increases of 37.16%, 15.75%, and 15.12% in the stress of connecting bolts, segment joint misalignment, and anchor bolt stress. As the tunnel burial depth increases, the stress of connecting bolts and the vertical deformation of segment and the joint misalignment of the pipe segment increase by 140%, 107% and 60.61%, respectively. In addition, under the combined action of external water and soil pressure and internal water pressure, the load-sharing ratios of the surrounding rock, pipe segment, inner tension ring and anchor rod are 34.87%, 34.59%, 21.59% and 8.95%, respectively, and the load-sharing ratio of the inner tensioned ring is 85.80% higher than that observed in the absence of internal water pressure, indicating that internal water pressure effectively enhances the load-sharing performance of the inner tensioned steel ring. In the composite structure, the load-sharing ratio of surrounding rock decreases as the surrounding rock class increases (from Class III to Class V). Under the same load condition, the load-sharing ratio of Class III surrounding rock is 7.14% higher than that of Class V. As the tunnel burial depth increases, the inner tensioned steel ring and anchor rods function more prominently as reserve-bearing components. When the tunnel burial depth reaches 71 m, the load-sharing ratio of the inner tension steel ring and anchor rod increases by 19.91% and 55.72%, respectively, compared with that of the buried depth of 31 m. The research results can provide a theoretical reference for the lining design and late reinforcement measures of similar tunnel projects.

1. Introduction

In recent years, with the intensive development of water diversion tunnel engineering, complex geological conditions encountered in tunnel engineering, such as fault fracture zones and karst geology, have frequently occurred [1,2,3,4]. These factors impact engineering construction and even affect the safe operation of projects. Composite lining, which is a new type of lining that has emerged in recent years, is widely used in underground engineering due to its advantages of providing two consecutive supports that fully utilize the self-bearing capacity of the surrounding rock and absorbing lining stress [5,6,7,8,9].

Scholars worldwide have conducted extensive research on tunnel composite linings, which can be synthesized into two main research streams that address different aspects of lining performance [10,11,12,13,14].

The first stream focuses on enhancing the performance and durability of the lining structures themselves under various challenging conditions. Researchers have employed diverse methodologies—including field monitoring, model testing, and numerical simulation—to address specific failure modes. For instance, studies have investigated dynamic loads such as aerodynamic fatigue and seismic performance, as well as cracking mechanisms in complex geological settings like weak surrounding rock and loess foundations [15,16,17,18]. Advancements in reinforcement techniques are another key focus, encompassing novel support systems, the application of advanced materials like fiber-reinforced concrete, and analytical methods for specific defects such as insufficient lining thickness or interface slip. Collectively, these works provide a comprehensive, method-driven understanding of how to improve the mechanical behavior and durability of tunnel linings.

The second research stream delves into the load-transfer mechanism within composite support systems, particularly analyzing the load-sharing ratios among components in conventional “surrounding rock-lining” systems. Scholars have employed analytical methods, field monitoring, model tests, and numerical simulations to elucidate how external loads are distributed. These studies have established a fundamental framework for understanding synergistic interactions in traditional composite linings.

However, a significant research gap emerges at the intersection of these two streams when applied to novel structural configurations. While the aforementioned studies provide a solid foundation, their focus has largely remained on conventional, fully circumferential lining systems or traditional composite linings. The combined bearing mechanical characteristics, and critically, the detailed load-sharing mechanism among all constituents (specifically the surrounding rock, segment, inner tensioned steel ring, and anchor bolts) of a semi-ring reinforced “inner tensioned steel ring–segment–surrounding rock” composite structure—a specific configuration used in pressurized water conveyance tunnels—under the action of internal water pressure remain inadequately explored. This represents a transition from studying the performance of linings or conventional composite systems to understanding the integrated mechanics of a unique, partially reinforced composite system involving multiple, actively interacting components.

Therefore, this study aims to bridge this identified gap. We focus specifically on this semi-ring reinforced composite structure and employ a 3D refined finite element model to systematically investigate its combined bearing characteristics under internal water pressure, varying surrounding rock types, and different tunnel burial depths. A key objective is to quantitatively determine the load-sharing ratios of each component (surrounding rock, segment, inner steel ring, and anchor bolts), which has not been addressed in previous investigations. The findings are expected to provide a targeted theoretical basis for the design and safety assessment of such specialized TBM pressurized water conveyance tunnels.

Researchers worldwide have carried out investigations into the load-sharing ratios of composite structures and composite lining systems. For example, Zhou et al. (2021) calculated and analyzed the load-sharing ratio of the composite lining of a deep tunnel and its important influencing factors based on the Hoek–Brown strength criterion combined with the measured data [19,20]. Du et al. (2023) studied the influence of the ground stress field on the fracture evolution process of secondary linings under soft rock conditions by using static analysis, similar model tests and numerical simulation [21]. Trunda V et al. (2020) studied the load sharing of the secondary lining considering the deterioration of the initial support through field monitoring and numerical simulation methods [22]. Zhou et al. (2023) examined the load ratio of composite linings via on-site monitoring and theoretical analysis, revealing that weak rock masses, improper installation timing of secondary linings [23], and insufficient secondary lining thickness can result in a substantial rise in the load ratio of secondary linings. Zhou et al. (2023) studied the influence of different surrounding rock grades and secondary lining installation time on the load-sharing ratio of each component of the composite lining by a model test [23]. Liu et al. (2023) used the complex variable method to derive the analytical solutions of the stress and displacement of the surrounding rock, main support and secondary lining under the action of far-field stresses that meet the interface continuity and boundary conditions [24]. Previous studies have primarily focused on the load-sharing ratios of individual components or all components, as well as their influencing factors, in composite linings and combined structures such as the “surrounding rock-lining” system. Nevertheless, the load-sharing ratios of each component in the semi-ring reinforced “inner tensioned steel ring–segment–surrounding rock” combined structure have not been addressed in these investigations.

In this study, a section of the Class V TBM tunnel with pressure in the surrounding rock in the Rongjiang-Guanbu diversion project was taken as the research object, and a 3D fine finite element model of the “inner tensioned steel ring–segment–surrounding rock” combined structure was established to explore the influence of internal water pressure, surrounding rock type and tunnel burial depth on the mechanical characteristics of the combined structure. The load-sharing ratios of individual components within the composite structure under varying conditions of internal water pressure, surrounding rock types, and tunnel burial depths were calculated and analyzed in this study. The research findings are capable of providing a theoretical reference for the operational safety assessment of analogous hydraulic transmission tunnels.

2. Basic Theory

The basic function expression of the Mohr–Coulomb elastoplastic calculation model is described as follows:

$$\tau -\sigma \tan \phi -c=0$$

(1)

As shown in Figure 1, the failure envelope $f\left({\sigma }_1,{\sigma }_3\right)=0$ is defined by the Mohr–Coulomb failure criterion $f^s=0$ from Point A to Point B as follows:

$$f^s=-{\sigma }_1+{\sigma }_3{N}_{\phi }-2c\sqrt{N_{\phi }}$$

(2)

From Point B to Point C, the tensile failure criterion $f^t=0$ is present and can be represented as follows:

$$f^t={\sigma }_3-{\sigma }^t$$

(3)

Shear-plastic flow and stretching-plastic flow are defined by the potential functions $g^s$ and $g^t$, respectively.

$$g^s=-{\sigma }_1+{\sigma }_3{N}_{\psi }$$

(4)

$$g^t={\sigma }_3$$

(5)

In these functions, $\sigma$, ${\sigma }_1$ and ${\sigma }_3$ are the normal stress, maximum principal stress and minimum principal stress of the shear plane, respectively. $\tau$ is shear stress; ${\sigma }^t$ is the tensile strength; and $c$ is the cohesion.

$\phi$ and $\psi$ are the internal friction angle and the expansion angle, respectively.

$$N_{\phi }={\displaystyle \frac{1+\sin \left(\phi \right)}{1-\sin \left(\phi \right)}}, N_{\psi }={\displaystyle \frac{1+\sin \left(\psi \right)}{1-\sin \left(\psi \right)}}$$

(6)

In the Mohr–Coulomb strength criterion, assuming that the change in stress is ${\sigma }^N$ and the change in elasticity is ${\sigma }^t$, for shear plasticity correction, the following expression can be obtained:

$$\left\{\begin{array}{c}{\sigma }_1^N={\sigma }_1^I+{\lambda }^s\left({\alpha }_1-{\alpha }_2{N}_{\psi }\right)\\ {\sigma }_2^N={\sigma }_2^I+{\lambda }^s{\alpha }_2\left(1-N_{\psi }\right)\\ {\sigma }_3^N={\sigma }_3^I+{\lambda }^s\left(-{\alpha }_1{N}_{\psi }+{\alpha }_2\right)\end{array}\right.$$

(7)

$${\lambda }^s={\displaystyle \frac{f^s\left({\sigma }_1^I,{\sigma }_3^I\right)}{\left({\alpha }_1-{\alpha }_2{N}_{\psi }\right)-\left(-{\alpha }_1{N}_{\psi }+{\alpha }_2\right)N_{\psi }}}$$

(8)

Regarding the correction of the tensile plasticity, the following can be obtained:

$${\sigma }_1^N={\sigma }_2^N={\sigma }_3^N={\sigma }^t$$

(9)

where ${\sigma }_1^N$, ${\sigma }_2^N$ and ${\sigma }_3^N$ are the changes in the first principal stress, the second principal stress and the third principal stress, respectively.

The Mohr–Coulomb elastoplastic model, as described above, is adopted in this study to characterize the mechanical behavior of the surrounding rock and the consolidated grout layer in the finite element simulation. This constitutive model is particularly suitable for simulating the shear failure and yielding of geomaterials under complex stress states, which is essential for accurately analyzing the load transfer and stress redistribution within the ‘inner tensioned steel ring–segment–surrounding rock’ composite structure subjected to combined external geostatic pressure and internal water pressure. Its application provides a fundamental theoretical basis for investigating the load-sharing mechanism among the components, which is the core objective of this research.

3. Establishment of the Tunnel Structure Simulation Model

The 3D refined finite element model was established and analyzed using the commercial finite element software ABAQUS (version 2022).

Numerical simulation technology was used to explore the influence of changes in internal water pressure, surrounding rock type, and tunnel burial depth on the mechanical characteristics of the “internally tensioned steel ring pipe–segment–surrounding rock” composite structure under certain external water pressure conditions, and to reveal its bearing deformation mechanism [24]. The external water pressure was held constant as it represents the steady-state hydrostatic pressure from the groundwater table, which is determined by the in situ geological and hydrological conditions. In contrast, the internal water pressure was varied to simulate the operational fluctuations within a pressurized water conveyance tunnel, allowing for the investigation of its specific influence on the mechanical response and load-sharing behavior of the composite structure, which is a primary focus of this study.

3.1. Finite Element Model and Boundary Conditions

Taking the section of the Type V surrounding rock TBM pressurized water delivery tunnel in a diversion project in the Guangdong area as the research object, a three-dimensional refined finite element model for the “inner tensioned steel ring–segment–surrounding rock” combined structure was constructed, with the corresponding diagram presented in Figure 2. The structure of the simulation model of the water transmission tunnel includes the surrounding rock, consolidated grouting layer, bean gravel layer, segments, epoxy resin layer, and inner steel ring in sequence from the outside to the inside. Meanwhile, the assembly effect of the segments and the presence of connecting bolts between the segments are considered. Among them, the surrounding rock, consolidated grouting layer, bean gravel layer, segments, epoxy resin layer, and inner steel ring all adopt three-dimensional solid units. The connecting bolt and anchor bolt between the segment and the segment are three-dimensional wire units, and the detailed structural dimensions are shown in Figure 3. The modified epoxy resin with a thickness of 10 mm was used to fill between the segments and the steel ring, while the bean gravel layer with a thickness of 0.18 m was adjacent to the outer layer of the segments. Moreover, the grouting layer extended 5 m along the periphery of the segments to the surrounding rock. Hollow grouting bolts with a length of 5.5 m and a row distance of 1.4 m were used for the anchor bolts (the holes were 5 m deep into the rock, with 8 pipes per ring). To ensure the validity of the calculation results, the model was established by taking the center point of the tunnel as the starting point to extend 5 times the tunnel diameter along the X-direction, Y-direction and Z-direction [25,26], where the upper boundary of Z was taken to the original ground line, and the tunnel excavation direction length was 14 m. The inner diameter and outer diameter of the tunnel segment lining are 4.3 m and 4.8 m, respectively. The steel ring width of the “steel cage type” inner tension ring is 600 mm, the thickness is 20 mm, and the row distance is 1.4 m (the half-ring reinforcement method is adopted: the track is set at the bottom, and the inner tension ring is not laid at the track). To mitigate stress concentration arising from force transmission during calculations, the model grid is primarily composed of regular hexahedral elements. The entire model is discretized into 65,344 elements (including overlapping elements such as the excavation body and grouting layer) and 77,853 element nodes. The model’s boundary conditions are defined as follows: the left and right boundaries are restricted in X-direction displacement, the front and back boundaries are constrained in Y-direction displacement, and the bottom boundary is fully fixed.

3.2. Material Parameters and Contact Relationship

In the established model, the Mohr–Coulomb yield criterion constitutive model is adopted for the surrounding rock and consolidated grout layer, while the linear elastic constitutive model is applied to the segments, gravel layer, inner tensioned steel ring, and anchor rods. The segment material is C55 concrete. The strength of the bean gravel layer is not less than that of C10 concrete, so C10 concrete material is used. The inner tensile steel ring is made of Q235 steel. Resin using epoxy resin. The anchor bolt is a Φ32 hollow grouting bolt. The key parameters of the materials are presented in

Table 1. Physical and mechanical parameters of the main materials.

Material Parameter	Density kg/m3	Modulus of Elasticity GPa	Poisson’s Ratio $\mu$	Cohesive Force MPa	Angle of Internal Friction ${\phi }^{(°)}$
Material Name
Class V surrounding rock	2550	1.75	0.33	0.075	27.5
Consolidated grout layer	2610	4.50	0.30	0.20	32.5
Bean gravel grout layer	2360	17.50	0.30	——	——
Segment (C55 concrete)	2500	35.50	0.20	——	——
Epoxy resin	2000	1.00	0.38	——	——
Inner tensile steel ring	7850	206	0.30	——	——
Connecting bolt	7850	206	0.30	——	——
Anchor bolt	7850	206	0.30	——	——

. In the model, surface-to-surface contact is used to simulate the interaction between the segments, between the segments and the gravel layer, and between the gravel layer and surrounding rock, which is defined as hard contact in the normal direction and allows separation between contact surfaces. The tangential upward direction is subject to Coulomb’s friction law. When the tangential stress reaches the critical value, slip is allowed to occur, and the friction coefficient is 0.5 [27,28]. In this numerical model, the surrounding rock and the consolidated grout layer are simulated as elastoplastic materials following the Mohr–Coulomb yield criterion, which was introduced in Section 2. This constitutive model governs their stress–strain relationship and failure behavior under the complex loading conditions imposed by the tunnel excavation, internal water pressure, and overburden stress. The specific material parameters used in the Mohr–Coulomb model, including the cohesion (c), internal friction angle (φ), and dilation angle (ψ), are assigned based on the geotechnical investigation report of the project and are listed in Table 1. This theoretical framework is critical for accurately capturing the plastic deformation and potential shear failure zones in the surrounding medium, which directly influences the load transfer to and the stress distribution within the ‘inner steel ring–segment’ composite lining system—the primary focus of this study.

3.3. Loading Mode

To ensure the correctness of the initial ground stress state of the surrounding rock structure, the initial ground stress field of the surrounding rock structure is simulated by the ground stress balance. The hollow grouting bolt was used for consolidation grouting, and the grouting pressure was 0.50 MPa~1.00 MPa. The uneven distribution of external water pressure is applied to the outer surface of the segment structure along the height direction, and the external water pressure is 0.27 MPa. An unevenly distributed internal water pressure is applied to the inner surface along the height direction, with an increment set to 0.05 MPa per step and a maximum internal pressure specified as 0.30 MPa. The detailed calculation conditions are summarized in

Table 2. Working conditions.

Condition Number	Calculated Load
	External Water Pressure/MPa	Internal Water Pressure/MPa
1	0.27	——
2	0.27	0.05
3	0.27	0.10
4	0.27	0.15
5	0.27	0.20
6	0.27	0.25
7	0.27	0.30

.

4. Analysis of the Influence of Internal Water Pressure on the Mechanical Properties of Composite Structures

4.1. Effects of Internal Water Pressure on the Mechanical Properties of Tunnel Segments

To investigate the mechanical properties of the pipe segment structure under the combined loading of “inner tensioned steel ring–segment–surrounding rock” under internal water pressure, and the influence of different internal water pressures on the mechanical properties of the pipe segment structure, the stress and displacement of the internal surface of the pipe segment structure with internal tensioned steel ring reinforcement and the position without the internal tensioned steel ring and only connected to the steel plate were extracted. Regarding the analysis of the results of this study, only the stress and displacement of the middle two rings of the tunnel model were extracted to eliminate the influence of the boundary effect (the same as below). A schematic diagram of the typical measuring points is shown in Figure 4.

At an internal water pressure of 0.30 MPa, the distribution of the maximum circumferential principal stress on the inner surface of the two middle ring segments is presented in Figure 5, covering both the section reinforced with the inner tensioned steel ring and the steel plate-connected section without this steel ring reinforcement. As seen from the figure, the maximum principal stress at the inner surface and joints of the top and left and right pipe segments, as well as at the arch waist of the left and right pipe segments, has decreased by 177%, 63%, and 28%, respectively. Additionally, the range of the tensile zone of the segments also decreases, indicating that the reinforcement of the inner tension ring plays a significant role in reducing the maximum principal stress on the segments. Nevertheless, due to the half-ring reinforcement structure of the inner tensioned ring, a certain abrupt stress phenomenon will occur at the bottom track where there is no inner tension ring reinforcement and the maximum principal stress of this part should be monitored during tunnel operations.

The relationship curve between the maximum tensile stress and internal water pressure of the two ring segments in the middle of the tunnel under the combined load of the “inner tensioned steel ring–segment–surrounding rock” composite structure under different internal water pressures is shown in Figure 6. It can be observed from the figure that the maximum tensile stress in the segment increases gradually with the increase in internal water pressure. The maximum tensile stresses of the fifth ring segment under various internal water pressures are 0.986 MPa, 1.046 MPa, 1.085 MPa, 1.123 MPa, 1.161 MPa, 1.254 MPa, and 1.407 MPa, which are 42.70% higher than those without internal water pressure. The maximum tensile stresses of the sixth ring segment are 1.004 MPa, 1.069 MPa, 1.131 MPa, 1.183 MPa, 1.221 MPa, 1.28 MPa, and 1.408 MPa, which are 40.24% higher than those without internal water pressure. The maximum tensile stress of the segment increased by approximately 41.47% overall. When the internal water pressure is 0.30 MPa, the maximum tensile stress on the pipe segment is 1.408 MPa, which is 51.39% of the standard tensile strength value of 2.740 MPa for C55 concrete, meeting the requirements of the normal use limit state. Therefore, in practical engineering, it is necessary to focus on monitoring the tensile stress of pipe segments in environments with high internal water pressure.

When the internal water pressure is 0.30 MPa, the distribution of circumferential compressive stress on the inner surface of the two ring segments in the middle of the tunnel, including the reinforcement of the inner tensioned steel rings and the connection of the steel plates without the inner tensioned steel rings, is shown in Figure 7. As seen from the figure, the compressive stress of the top segment at the reinforcement of the inner steel ring and a small part of the upper segment at the left and right sides of the inner steel ring is greater than that at the place where only the steel plate is connected. Moreover, the compressive stress increased by approximately 12.05%, indicating that the upper segment is supported by the reinforcement effect of the inner steel ring, preventing the deformation of the upper segment. The upper segment produces greater compressive stress under the combined action of the inner tension steel ring, external water and soil pressure and internal water pressure.

The compressive stress on the bottom section of the inner tensioned steel ring reinforcement and most of the left and right sections is reduced compared to the compressive stress only at the connection steel plate. A large compressive stress is generated at the junction of the bottom section connection steel plate and the track, which may be related to the semi-ring reinforcement structure of the inner tensioned steel ring. No inner tension steel ring is reinforced at the bottom track. Moreover, a certain sudden stress phenomenon will occur in this area, and the compressive stress in this part should be monitored during the operation of the tunnel.

The relationship curve between maximum compressive stress and internal water pressure between the two ring segments in the middle of the tunnel under the combined load of the “inner tensioned steel ring–segment–surrounding rock” composite structure is shown in Figure 8. As illustrated in the figure, the compressive stress on the segment exhibits a linear decreasing trend with the increase in internal water pressure. The maximum compressive stresses on the fifth ring segment under different internal water pressures are 9.100 MPa, 8.924 MPa, 8.747 MPa, 8.569 MPa, 8.392 MPa, 8.214 MPa, and 8.034 MPa, representing a reduction of 11.71% compared with the condition without internal water pressure. The maximum compressive stresses on the sixth ring segment are 9.116 MPa, 8.938 MPa, 8.758 MPa, 8.579 MPa, 8.401 MPa, 8.221 MPa, and 8.040 MPa, corresponding to a decrease of 11.80% relative to the case without internal water pressure. On the whole, the maximum compressive stress of the segment is reduced by about 11.76%. The application of internal water pressure counteracts part of the external surrounding rock pressure and the influence of external water pressure on the segment.

When there is no internal water pressure, the maximum compressive stress of the segment structure is 9.116 MPa, which is 25.68% of the standard compressive strength value of 35.500 MPa for C55 concrete, meeting the requirements of the normal service limit state. Concrete materials exhibit a gradually decreasing trend due to their compressive and non-tensile properties, as well as the compressive stress on the segments as the internal water pressure increases. Therefore, appropriate monitoring of the compressive stress on the segments during tunnel engineering operations is sufficient.

At an internal water pressure of 0.30 MPa, the vertical deformation distribution on the inner surface of the two middle ring segments is presented in Figure 9, which covers the region reinforced by the inner tensioned steel ring and the region connected by steel plates without such a ring. This figure shows that the vertical deformation of the top segment and the inner surface of the left and right sides of the segment is negative, indicating that the vertical deformation direction of this part of the segment is downward and results in settlement deformation. The vertical deformation of the inner surface of the bottom pipe segment is positive, that is, the vertical deformation direction of this part of the pipe segment is upward, resulting in bottom uplift deformation. As there is no reinforcement from inner tensioned steel rings and connecting steel plates at the bottom track, the uplift deformation at this location is slightly larger than that at other parts of the bottom segment. The vertical deformation of the inner surface at the reinforcement positions of the fifth and sixth ring segments with inner tensioned steel rings is reduced by approximately 6.14% compared with that at the reinforcement positions without inner tensioned steel rings (only equipped with connecting steel plates). This demonstrates that the reinforcement of inner tensioned steel rings can restrict the deformation of the segment structure to a certain extent and ensure the safety and stability of the segment structure.

Schematic diagram of maximum settlement and uplift deformations results of the pipe segment in the middle of the tunnel under different internal water pressures is shown in Figure 10. The figure shows that the settlement deformation at the top of the segment structure is greater than the uplift deformation at the bottom, and is approximately 3.47 times that of the uplift deformation at the bottom. This indicates that most of the load on the segment structure is borne by the top segment. Therefore, during tunnel operations, the settlement deformation of the top segment should be closely monitored. Under the combined action of the external surrounding rock pressure and external water pressure, the pipe segment exhibits a deformation pattern similar to that of a “horizontal duck egg”. As the internal water pressure increases, the overall trend indicates a gradual outward expansion, which indicates that the vertical deformation decreases. When the internal water pressure is 0.30 MPa, the settlement deformation decreases by 4.93%, and the uplift deformation decreases by 30.37% compared to that without internal water pressure. An analysis shows that the occurrence of internal water pressure resists the influences of some external surrounding rock pressures and external water pressures on the pipe structure. However, the top pipe segment is less affected by internal water pressures due to bearing a large external load.

The opening and misalignment of segment joints are common problems in TBM tunnel engineering. For pressurized water delivery tunnels, it may affect the hydraulic characteristics of the tunnel’s flow section, reduce the flow capacity, cause internal and external water seepage, and even pose a threat to the structure of the water delivery tunnel, affecting the safe and stable operation of the entire project. Therefore, for hydraulic tunnels with segment linings, joint opening and displacement deformation need to be thoroughly considered [29,30,31].

The deformation of the joint on the inner surface of the middle section of the tunnel under different internal water pressures is shown in Figure 11. Figure 11a shows that the opening of the joints at L2-B and B-L1 at the bottom of the tunnel arch is significantly larger than that at L1-F and F-L2 at the top of the arch. The opening degree of the segment joint continuously decreases with an increasing internal water pressure. The opening degree of the joints at L1-F and F-L2 of the tunnel arch crown changes more significantly, with an internal water pressure of 0.30 MPa, which is reduced by approximately 11.93% compared to the state without an internal water pressure. The opening changes of the joints at L2-B and B-L1 at the arch bottom are relatively small, with an internal water pressure of 0.30 MPa, which is reduced by approximately 6.86% compared to the state without internal water pressure. The maximum opening of the segment joint is 0.01647 mm, which is far less than the joint opening limit of 4 mm and meets the limit state of normal use.

Figure 11b shows that the misalignment of the L2-B and B-L1 joints at the tunnel arch bottom is significantly greater than that of the L1-F and F-L2 joints at the arch top. Compared with the L1-F and F-L2 joints of the tunnel arch without internal water pressure, the displacement of the joints at the L1-F and F-L2 joints increased by approximately 64.27% when the internal water pressure was 0.30 MPa. The deformation of the L2-B and B-L1 joints at the arch bottom increased by approximately 6.85% due to misalignment. The joint displacement and deformation of the segment continue to rise with the increase in internal water pressure, which is consistent with the overall outward expansion trend of the segment under internal water pressure as described above.

4.2. Influence of the Internal Water Pressure on the Mechanical Properties of the Connection Bolts

The stress curve of the connecting bolts between the two ring segments in the middle of the tunnel as a function of internal water pressure is shown in Figure 12. This figure shows that connecting bolts S1, S2, Z1, and Y1 are subjected to relatively high stress levels, while the remaining connecting bolts located at the bottom are subjected to significantly lower stress levels. The settlement displacement of the top segment is much greater than the uplift displacement of the bottom segment; that is, the top segment produces a large settlement displacement, and the top bolt acts as a constraint on the segment to resist its displacement, bearing a greater load. The uplift displacement of the bottom segment is relatively small, and the stress on the bottom bolt is also relatively small. The stress on the bottom bolt is approximately 85% higher than that on the top bolt.

Thus, the bolt has not yet yielded. When the internal water pressure is 0.30 MPa, the stress of the bolt is 62.04 MPa. As the internal water pressure increases, the bolt stress continues to decrease. However, the change in stress is not significant. The occurrence of internal water pressure resists a portion of the external surrounding rock pressure and external water pressure. As the internal water pressure increases, the pipe segment shows a gradual outward expansion trend, and the constraint effect of the connecting bolts decreases, allowing the connecting bolts to bear more external loads.

4.3. The Effect of the Internal Water Pressure on the Mechanical Properties of the Inner Tensioned Steel Rings

The internal water pressure is 0.30 MPa, and the Mises stress cloud diagram of the internally tensioned steel ring is shown in Figure 13. This figure shows that there is significant stress generated at the hollow position where the edge of the inner tension steel ring is not connected to the steel plate welding, and the stress level is significantly lower at the bottom track and other positions where the connecting steel plates are reinforced.

The von Mises stress diagram of the tensioned steel ring in the middle of the tunnel is shown in Figure 14. According to the von Mises stress at the edge of the inner tensioned steel ring in Figure 14a, there is an uneven force distribution at the edge of the inner tensioned steel ring. The stress at the hollow position of the steel ring edge differs by 51.66% from the stress at the welding position of the connecting steel plate. The connecting steel plate has a certain reinforcement effect on the steel ring, bearing some of the load. According to the von Mises stress in the middle of the inner tensioned steel ring in Figure 14b, it can be seen that the stress carried by the middle of the inner tensioned steel ring is also affected by the hollow position at the edge of the steel ring, and a certain degree of uneven stress occurs. Moreover, the stress difference between the hollow position at the corresponding edge of the steel ring and the welding position of the corresponding edge connecting the steel plate is 45.00%, which significantly reduces the uneven stress phenomenon at the edge of the steel ring.

As shown in Figure 14c, when there is no internal water pressure, the maximum von Mises stress on the internally tensioned steel ring is 52.97 MPa. When the internal water pressure is 0.30 MPa, the maximum von Mises stress on the internally tensioned steel ring is 45.61 MPa, and the stress on the internally tensioned steel ring is 19.41%~22.54% of the allowable stress value of 235.000 MPa on Q235 steel. The internally tensioned steel ring has not yet yielded, and as the internal water pressure increases, the stress on the internally tensioned steel ring decreases, indicating that the occurrence of internal water pressure resists a part of the external surrounding rock pressure and external water pressure, which is conducive to the safety and stability of the internally tensioned steel ring. Therefore, appropriate monitoring of the stress of the internally tensioned steel ring during tunnel operation is sufficient.

4.4. Influence of the Internal Water Pressure on the Mechanical Characteristics of the Bolt

The von Mises stress cloud diagram of the anchor rod when the internal water pressure is 0.30 MPa is shown in Figure 15. The stress distribution of the anchor rod is symmetrical on both sides, and the larger stress values of the anchor rod are mainly concentrated in the first half of the anchor rods on both sides. The von Mises stress of the anchor rod in the middle section of the tunnel is extracted when the internal water pressure is 0.30 MPa for analysis. The stress distribution comparison diagram of the anchor rods is shown in Figure 16. It can be seen from the figure that the stress on the anchor rods Z1, Z2, Y1, and Y2 is relatively large and shows a trend of first increasing and then decreasing with an increasing depth into the rock mass. The maximum von Mises stress appears at a depth of 1.1 m. The stress on anchor rods S1 and S2 also shows a trend of first increasing and then decreasing with an increasing distance into the rock mass. The pipe segment undergoes significant settlement and deformation under external soil and water loads. The anchor rods at the top, left and right sides prevent settlement and displacement of the pipe segment, causing bending deformation at the intersection of the pea gravel layer and the consolidation grouting layer, resulting in a higher stress level in that area. This is also related to the significant difference in the material stiffness between the pea gravel layer and the consolidation grouting layer. The stress on the anchor rods D1 and D2 shows a gradually decreasing trend as the distance to the rock mass increases. The displacement of the bottom segment is relatively small, and the stress on the anchor rod is relatively small. Therefore, the stress on the bottom anchor rod follows a general law.

According to the comparison of the von Mises stress distribution of anchor rods in the middle of the tunnel, the maximum stress on the anchor rods appears at a depth of 1.1 m into the rock. The von Mises stresses of the anchor rods at the tunnel midpoint, which are 1.1 m deep into the rock mass under various internal water pressures, are extracted and illustrated in Figure 17. It can be seen from the figure that the stress acting on the anchor rod presents a continuous decreasing trend as the internal water pressure increases. The maximum von Mises stress on the anchor rod under different internal water pressures is 23.499 MPa, 23.165 MPa, 22.832 MPa, 22.507 MPa, 22.180 MPa, 21.850 MPa, and 21.513 MPa, respectively. The occurrence of the internal water pressure resists a portion of the external surrounding rock pressure and the effect of external water pressure on the tunnel structure, making the tunnel structure safer and reducing the anchoring effect of anchor rods on the segment components, allowing it to withstand more external loads.

5. Analysis of the Influence of Surrounding Rock Type on the Load-Bearing Mechanical Properties of Composite Structures

Since the TBM construction method is highly sensitive to geological engineering conditions and is accompanied by the intensive development of pressurized water conveyance tunnel engineering, complex geological conditions in tunnel engineering frequently occur. These conditions impact engineering constructions and even threaten the safe operations of projects. Therefore, analysis and research are conducted on the load-bearing and deformation characteristics of the “inner tensioned steel ring–segment–surrounding rock” composite structure under different geological conditions. Based on the on-site engineering geological survey data, three types of surrounding rock, namely, Class III, Class IV, and Class V, were selected as the numerical calculation parameters, as shown in

Table 3. Physical and mechanical parameters of the surrounding rock.

Material Parameter	Density kg/m3	Modulus of Elasticity GPa	Poisson’s Ratio $\mu$	Cohesive Force MPa	Angle of Internal Friction ${\phi }^{(°)}$
Type of Surrounding Rock
III	2640	10	0.25	0.95	37.5
IV	2610	4.5	0.3	0.2	32.5
V	2550	1.75	0.33	0.075	27.5

.

5.1. The Influence of the Surrounding Rock Types on the Mechanical Properties of Segments

Under the combined action of external surrounding rock pressure, external water pressure, and internal water pressure, the mechanical parameters of the segments at the tunnel midsection under various surrounding rock conditions were extracted for analysis, so as to investigate the influence of surrounding rock type on the mechanical behavior of the segment structure under the joint bearing of the “inner tensioned steel ring–segment–surrounding rock” composite system. The maximum tensile stress of the segment in the middle of the tunnel under different surrounding rock conditions is shown in

Table 4. Table of the maximum tensile stress of the segment under different surrounding rock conditions (MPa).

Surrounding Rock Type	Internal Water Pressure
	0.00	0.05	0.10	0.15	0.20	0.25	0.30
Class III surrounding rock	1.002	1.033	1.100	1.166	1.229	1.292	1.355
Class IV surrounding rock	1.039	1.069	1.131	1.183	1.221	1.258	1.397
Class V surrounding rock	1.043	1.086	1.150	1.212	1.275	1.337	1.408

. The table shows that the maximum tensile stress on the pipe segment under different surrounding rock conditions will increase with an increasing internal water pressure. Under different internal water pressures, the maximum tensile stress on the segment structure under Class III surrounding rock is reduced by approximately 3.96% compared to Class V surrounding rock, while under Class IV surrounding rock, it is reduced by approximately 2.42% compared to Class V. The tensile stress on the segment structure decreases with the improvement of the physical and mechanical properties of the surrounding rock. The better the physical and mechanical properties of the surrounding rock are, the more significant the impact of the surrounding rock quality on the segment structure. “The observed increase in maximum tensile stress with greater tunnel burial depth can be attributed to the corresponding increase in the initial in situ stress field, primarily due to the heightened overburden pressure from the surrounding rock mass. As the burial depth increases, the vertical stress (σv = γH, where γ is the unit weight of the overburden and H is the burial depth) and the consequent horizontal stress acting on the tunnel lining increase proportionally. This elevated external pressure induces greater compressive forces on the segment ring. According to the principle of bending in a compressed ring structure, these increased compressive forces lead to a higher bending moment within the segments. Consequently, the tensile stress on the inner surface of the segments, which results from this bending, also increases. This mechanistic explanation aligns with the fundamental behavior of buried pressure conduits and deep tunnel linings, where structural loads are directly governed by the overburden and lateral earth pressures”.

The maximum compressive stress of the segment at the tunnel midsection under various surrounding rock conditions is presented in

Table 5. Table of the maximum compressive stress of the segment under different surrounding rock conditions (MPa).

Surrounding Rock Type	Internal Water Pressure
	0.00	0.05	0.10	0.15	0.20	0.25	0.30
Class III surrounding rock	9.116	9.080	8.955	8.284	8.242	8.152	8.061
Class IV surrounding rock	9.319	9.23	9.145	8.938	8.758	8.579	8.401
Class V surrounding rock	9.914	9.808	9.233	9.070	8.901	8.759	8.656

. It can be seen from the table that the maximum compressive stress on the segment decreases with the increase in internal water pressure under different surrounding rock conditions. Under different internal water pressures, the maximum compressive stress on the segment structure under Class III surrounding rock is reduced by approximately 6.91% compared to Class V surrounding rock, and the maximum compressive stress on the segment structure under Class IV surrounding rock is reduced by approximately 2.99% compared to Class V. The maximum compressive stress on the segment structure decreases with the improvement of the physical and mechanical properties of the surrounding rock, and the better the physical and mechanical properties of the surrounding rock are, the more significant the impact of the surrounding rock quality on the segment structure.

The development curve and overall deformation diagram of the vertical convergence of the middle segment of the tunnel with internal pressure under three types of surrounding rock conditions are shown in Figure 18. Under the combined action of the external water and soil pressures and the internal water pressure, the pipe lining under the three types of surrounding rock shows a “horizontal duck egg” deformation with the arch top and arch bottom converging inward. As the internal water pressure increases, the overall trend depicts a gradual outward expansion, that is, the vertical diameter deformation of the pipe segment decreases. Under the same internal water pressure, the vertical deformation trend of the segment structure under Class IV surrounding rock is slightly smaller than that under Class V surrounding rock. The vertical deformation trend of the segment structure under Class III surrounding rock is significantly lower than that under Class V surrounding rock, decreasing by approximately 12.92%. As the mechanical properties of the surrounding rock improve, the vertical deformation of the pipe segment structure decreases. Moreover, the better the quality of the surrounding rock is, the more obvious the effect of reducing the deformation of the pipe segment structure.

The opening degree and staggered deformation of the segment joints at the tunnel midsection under various surrounding rock conditions are illustrated in Figure 19. Figure 19a depicts the variation curve of segment joint opening degree with internal water pressure under different surrounding rock conditions. At an internal water pressure of 0.30 MPa, the maximum opening degree of the segment under Class V surrounding rock is 0.0171 mm, and the maximum opening degree of the segment under Class III surrounding rock is 0.0155 mm. As the mechanical properties of the surrounding rock improve, the deformation of the opening of the pipe joint decreases, and the opening deformation of the pipe under Class III surrounding rock decreases by approximately 9.36% compared to Class V surrounding rock. Figure 19b shows the variation curve of segment joint misalignment with internal water pressure under different surrounding rock conditions. When the internal water pressure is 0.30 MPa, the maximum value of segment misalignment under Class V surrounding rock is 0.1022 mm, and the maximum value of segment misalignment under Class III surrounding rock is 0.0861 mm. As the mechanical properties of the surrounding rock improve, the deformation of segment joint misalignment gradually decreases, and the deformation of segment misalignment under Class III surrounding rock is reduced by approximately 15.75% compared to that under Class V surrounding rock.

5.2. The Influence of the Surrounding Rock Type on the Mechanical Properties of Connecting Bolts

The schematic diagram of the maximum von Mises stress results for the connecting bolts between the two middle tunnel rings under various surrounding rock conditions is displayed in Figure 20. As can be seen from the figure, the bolt stress gradually decreases with the increase in internal water pressure. However, the change in the bolt stress is not significant. The load on the bolt mostly comes from the external surrounding rock pressure and external water pressure, and the effect of the internal water pressure is much smaller than that of the external surrounding rock pressure and external water pressure. When there is no internal water pressure, the maximum von Mises stress values of the bolts under Class III, IV, and V surrounding rocks are 39.29 MPa, 53.77 MPa, and 62.32 MPa, respectively, which are less than the allowable stress value of 345.00 MPa. The bolts have not yet yielded and are in a normal service limit state. The maximum von Mises stress on the bolts under Class III surrounding rock is reduced by approximately 37.16% compared with that under Class V surrounding rock. With the improvement of the mechanical properties of surrounding rock, the stress on the bolts gradually decreases, leading to enhanced stability of the tunnel structure.

5.3. The Influence of the Surrounding Rock Types on the Mechanical Properties of Internally Tensioned Steel Rings

The circumferential von Mises stress distribution of the inner tensioned steel ring at the tunnel midsection is presented in Figure 21. As can be observed from the figure, the maximum von Mises stresses at the edge of the inner tensioned steel ring under Class III, IV, and V surrounding rocks are 41.62 MPa, 45.60 MPa, and 46.70 MPa, respectively. The maximum von Mises stress at the edge of the inner tensioned steel ring under Class III surrounding rock is reduced by 10.88% compared with that under Class V surrounding rock and by 8.73% compared with that under Class IV surrounding rock. The maximum von Mises stresses in the middle of the inner tensioned steel ring and steel ring under Class III, IV, and V surrounding rocks are 26.15 MPa, 29.27 MPa, and 29.45 MPa, respectively.

The maximum von Mises stress in the middle of the inner tensioned steel ring and steel ring under Class III surrounding rocks is 11.21% less than that under Class V surrounding rocks and 0.61% less than that under Class IV surrounding rocks. Analysis results show that with the improvement of the physical and mechanical properties of the surrounding rock, the stress on the internally tensioned steel ring gradually decreases. Moreover, the stronger the surrounding rock is, the better the mechanical properties, and the more obvious the changes. However, the change in the mechanical properties of the surrounding rock has a greater impact on the edge of the inner tensioned steel ring than on the inside of the steel ring, and the uneven force distribution of the inner tensioned steel ring still exists under different types of surrounding rock. This may be due to the “steel cage” semi-ring reinforcement structure of the inner tensioned steel ring itself.

5.4. The Influence of Surrounding Rock Type on the Mechanical Properties of Bolts

The maximum von Mises stress of the anchor rod in the middle of the tunnel under different surrounding rock conditions varies with the internal water pressure, as shown in Figure 22. Additionally, the figure shows that under different surrounding rock conditions, the stress on the anchor rod continues to decrease with an increasing internal water pressure. The stress on the anchor rod under Class III surrounding rock is reduced by approximately 15.12% compared to Class V surrounding rock. As the physical and mechanical properties of the surrounding rock improve, the stress on the anchor rod decreases, indicating that the stronger the surrounding rock is, the better the geological conditions, and the safer the structure. As a reserve-bearing component, the anchor rod can bear more loads.

6. Analysis of the Influence of Tunnel Buried Depth on Composite Structures

In this section, the influence of the tunnel burial depth on the combined bearing mechanical characteristics of the “inner tensioned steel ring–segment–surrounding rock” composite structure is investigated. Tunnels with burial depths of 31 m, 41 m, 51 m, 61 m, and 71 m were selected for conducting calculations and analyses. The working conditions of the tunnel burial depth are shown in

Table 6. The depth of the tunnel.

Condition Number	The Depth of the Tunnel/MPa	Surrounding Rock Type
1	31	Category V
2	41	Category V
3	51	Category V
4	61	Category V
5	71	Category V

.

6.1. Influence of the Tunnel Buried Depth on the Mechanical Properties of the Segments

Under the combined action of external surrounding rock pressure, external water pressure, and internal water pressure, the mechanical parameters of the segments at the tunnel midsection under different surrounding rock conditions were extracted for analysis, so as to explore the influence of tunnel burial depth on the mechanical characteristics of the segment structure under the joint bearing of the “internally tensioned steel ring–segment–surrounding rock” composite structure.

The maximum tensile stress of the segment in the middle of the tunnel under different burial depths is shown in

Table 7. Maximum tensile stress table of tubes with different tunnel burial depths (MPa).

Internal Water Pressure	The Depth of the Tunnel
	31 m	41 m	51 m	61 m	71 m
0	0.980	0.989	1.043	1.102	1.249
0.05	1.032	1.040	1.086	1.115	1.263
0.10	1.044	1.092	1.150	1.166	1.277
0.15	1.074	1.156	1.212	1.226	1.308
0.20	1.091	1.200	1.275	1.292	1.366
0.25	1.194	1.243	1.337	1.341	1.426
0.30	1.231	1.374	1.408	1.442	1.485

. This table shows that the maximum tensile stress on the segment under different tunnel burial depths increases with an increasing internal water pressure. Under different internal water pressures, the maximum tensile stress on a segment buried at a depth of 71 m in a tunnel increased by approximately 22.64% compared to a depth of 31 m, and the maximum tensile stress on a segment buried at a depth of 51 m increased by 11.12% compared to a depth of 31 m. The tensile stress on the segment structure increases with the depth of the tunnel, and the greater the depth of the tunnel, the greater the impact on the tensile stress borne by the segment structure.

The maximum compressive stress of the segment in the middle part of the tunnel under different burial depths is shown in

Table 8. Maximum compression stress table of tubes with different tunnel burial depths (MPa).

Internal Water Pressure	The Depth of the Tunnel
	31 m	41 m	51 m	61 m	71 m
0	7.187	8.212	9.914	10.186	11.246
0.05	7.058	8.083	9.808	10.082	11.086
0.10	6.997	8.075	9.233	10.008	11.069
0.15	6.864	7.959	9.070	9.955	10.956
0.20	6.815	7.894	8.901	9.829	10.891
0.25	6.634	7.714	8.759	9.651	10.713
0.30	6.486	7.535	8.656	9.472	10.534

. This table shows that the maximum compressive stress on the segments decreases with an increasing internal water pressure under different tunnel burial depths. Under the action of different internal water pressures, the maximum compressive stress of the pipe segment that is placed 71 m underground increases by 59.29% compared with the buried depth of 31 m and 33.87% compared with the buried depth of 51 m. The compressive stress of the pipe segment structure increases with an increasing burial depth.

The development curve of the vertical convergence of the middle segment of the tunnel with internal pressure under different burial depths is shown in Figure 23. The figure shows that under different tunnel burial depths, the vertical deformation of the pipe segment gradually decreases with an increasing internal water pressure. Under different internal water pressures, the vertical deformation of the tunnel segment buried at a depth of 71 m increased by 1.07 times compared to the buried depth of 31 m, and that of the tunnel segment buried at a depth of 51 m increased by 50.68% compared to that buried at a depth of 31 m. The greater the burial depth of the tunnel is, the greater the external load borne by the segment structure, and the greater the vertical deformation of the segment structure.

Under the combined action of external surrounding rock pressure, external water pressure, and internal water pressure, the mechanical parameters of the segments at the tunnel midsection under different tunnel burial depths were extracted for analysis, so as to explore the influence of tunnel burial depth on the mechanical characteristics of the segment structure under the joint bearing of the “internally tensioned steel ring–segment–surrounding rock” composite structure. The opening degree and staggered deformation of the segment joints at the tunnel midsection under different tunnel burial depths are illustrated in Figure 24. Figure 24a depicts the curve of segment joint opening degree varying with internal water pressure under different tunnel burial depths. At an internal water pressure of 0.30 MPa, the maximum opening degree of the segment at a burial depth of 71 m is 0.0186 mm, while that at a burial depth of 31 m is 0.0120 mm. With the increase in tunnel burial depth, the opening degree of the segment joint increases by approximately 55% at a burial depth of 71 m compared with that at 31 m. Figure 24b shows the variation curve of segment joint staggered deformation with internal water pressure under different tunnel burial depths. When the internal water pressure is 0.30 MPa, the maximum value of segment misalignment under the tunnel burial depth of 71 m is 0.1052 mm, and the maximum value of segment misalignment under the burial depth of 31 m is 0.0655 mm. As the tunnel burial depth increases, the segment joint misalignment increases, with the burial depth of 71 m increasing by approximately 60.61% compared to the burial depth of 31 m.

6.2. The Influence of Tunnel Burial Depth on the Mechanical Properties of Connecting Bolts

A schematic diagram of the maximum von Mises stress results of the connecting bolts between the two ring segments in the middle of the tunnel under different tunnel burial depths is shown in Figure 25. As shown in the figure, the bolt stress gradually decreases with an increasing internal water pressure. When there is no internal water pressure, the maximum values of the von Mises stresses on the bolts under tunnel burial depths of 31 m, 41 m, 51 m, 61 m, and 71 m are 38.48 MPa, 52.65 MPa, 62.32 MPa, 76.36 MPa, and 91.20 MPa, respectively, which are less than the allowable stress value of 345.00 MPa. The bolts have not yet yielded and are in a normal service limit state. The maximum von Mises stress on the bolt at a burial depth of 71 m increased by approximately 1.40 times compared to that at a burial depth of 31 m. As the tunnel burial depth increases, the stress on the bolt gradually increases, making the tunnel structure more prone to instability.

6.3. Influence of the Buried Depth of the Tunnel on the Mechanical Properties of the Inner Tensioned Steel Ring

The circumferential von Mises stress distribution diagram of the tensioning steel ring in the middle of the tunnel is shown in Figure 26. As shown in the figure, the maximum von Mises stresses on the edge of the inner tensioned steel ring at tunnel burial depths of 31 m, 41 m, 51 m, 61 m, and 71 m are 35.57 MPa, 40.44 MPa, 45.61 MPa, 50.71 MPa, and 56.12 MPa, respectively. Compared with the burial depth of 31 m, the maximum von Mises stress at the edge of the inner tensioned steel ring increases by 57.77% at 71 m and by 28.23% at 51 m, while the maximum von Mises stresses at the middle of the inner tensioned steel ring at the same burial depths are 22.75 MPa, 25.90 MPa, 29.27 MPa, 32.48 MPa, and 35.78 MPa, respectively, which increase by 57.27% at 71 m and by 28.66% at 51 m in comparison with that at 31 m. The maximum von Mises stress on the edge of the inner tensioned steel ring at a burial depth of 71 m increased by 57.77% compared to that at a burial depth of 31 m. Moreover, the maximum von Mises stress on the edge of the inner tensioned steel ring at a burial depth of 51 m increased by 28.23% compared to that at a burial depth of 31 m. When the tunnel is buried at depths of 31 m, 41 m, 51 m, 61 m, and 71 m, the maximum von Mises stresses on the middle of the inner tensioned steel ring steel ring are 22.75 MPa, 25.90 MPa, 29.27 MPa, 32.48 MPa, and 35.78 MPa, respectively. When the tunnel is buried at a depth of 71 m, the maximum von Mises stress on the edge of the inner tensioned steel ring increases by 57.27% compared to that at a buried depth of 31 m. Moreover, the maximum von Mises stress on the edge of the inner tensioned steel ring at a buried depth of 51 m increases by 28.66% compared to that at a buried depth of 31 m. Analysis results show that as the burial depth of the tunnel increases, the stress on the internally tensioned steel ring gradually increases, and the greater the burial depth of the tunnel is, the more obvious the change. Moreover, the phenomenon of uneven stress on the internally tensioned steel ring still exists at different tunnel depths.

6.4. The Influence of Tunnel Burial Depth on the Mechanical Properties of Anchor Rods

The maximum von Mises stress of the anchor rod in the middle of the tunnel with different burial depths varies with the internal water pressure, as shown in Figure 27. Moreover, this figure shows that under different tunnel depths, the stress on the anchor rod continues to decrease with an increasing internal water pressure. The stress of the anchor rod at a tunnel burial depth of 71 m is increased by 13.79% compared with that at 31 m. As the tunnel burial depth increased, the stress on the anchor rod also increased, indicating that as a reserve-bearing component, the anchor rod plays a more significant role as the tunnel burial depth increases.

7. Analysis of Load-Sharing Rate of Water Conveyance Tunnel Composite Structure

The determination of the load-sharing ratio of composite lining structures provides a certain theoretical basis for the design of tunnel engineering structures and the selection of support parameters and clarifies the joint bearing mechanism of composite lining structures more clearly. In addition, in tunnels subjected to internal water pressure, the lining structure not only bears external soil and water pressure but also the effect of internal water pressure. Therefore, it is of great significance to investigate the load-sharing ratio of composite lining structures under internal water pressure.

7.1. Calculation Method for the Load-Sharing Rate

To explore the load distribution mode of the “inner tensioned steel ring–segment–surrounding rock” combined structure in water conveyance tunnels, the average values of node forces at different positions of the surrounding rock, pipe segment, inner tensioned steel ring, and anchor rod in the middle of the tunnel are extracted as the load-sharing values of each component. The sum of the average load borne by each component in the composite structure of the “inner tensioned steel ring–segment–surrounding rock” is $P$, the average load shared by the surrounding rock is $P_1$, the average load shared by the pipe segments is $P_2$, the average load shared by the internally tensioned steel ring is $P_3$, and the average load shared by the anchor bolts is $P_4$. Therefore, the proportion of the load shared by each component is expressed as follows:

$$k_n={\displaystyle \frac{P_n}{P_1+P_2+P_3+P_4}}\times 100\%$$

(10)

In the formula, $k_n$ is the proportion of the load shared by each component, where n = 1, 2, 3, 4.

7.2. Analysis of the Influence of the Internal Water Pressure on the Load-Sharing Rate of the Composite Structures

Figure 28 illustrates how the load-sharing ratio of each component under Class V surrounding rock changes with internal water pressure. It can be observed that under the combined effects of external water and soil pressures and internal water pressure, the load-sharing ratios of the components in the “inner tensioned steel ring–segment–surrounding rock” composite structure follow a descending order: pipe segment, surrounding rock, inner tensioned steel ring, and anchor rod. As the internal water pressure increases, the proportion of load shared by the surrounding rock, pipe segments, and anchor rods gradually decreases. At an internal water pressure of 0.30 MPa, the corresponding load proportions decrease by around 11.68%, 4.99%, and 21.70%, respectively, relative to the zero internal water pressure condition. Meanwhile, the load-sharing ratio of the inner tensioned steel ring exhibits a gradual increase, rising by approximately 85.80% at 0.30 MPa compared with the case without internal water pressure, which reveals that the internal water pressure effectively enhances the load-sharing performance of the inner tensioned steel ring. The internal water pressure counteracts part of the external load effects on the composite structure, thus weakening the influence of external loads on the pipe segment, surrounding rock, and anchor rod. In contrast, the internal water pressure acts directly on the inner tensioned steel ring, causing it to carry most of the internal water load, which further improves the load-sharing performance of the inner tensioned steel ring.

7.3. Analysis of the Influence of the Surrounding Rock Types on the Load-Sharing Rate of Composite Structures

The load-sharing rate of each component under different surrounding rocks varies with the internal water pressure, as shown in Figure 29. This figure shows that the proportion of load shared by the surrounding rock under Class III rock increased by approximately 7.14% compared to that under Class V rock, while under Class IV rock, it has increased by approximately 4.62% compared to that under Class V rock. As the physical and mechanical properties of the surrounding rock improve, the proportion of load shared by the surrounding rock gradually increases. The proportion of pipe segments sharing the load under Class III surrounding rock is reduced by approximately 0.97% compared to that under Class V surrounding rock, and that under Class IV surrounding rock is reduced by approximately 0.67% compared to that under Class V.

With the improvement of the physical and mechanical properties of the surrounding rock, the load-sharing proportion of the pipe segments decreases gradually. The proportion of anchor bolts sharing load under Class III surrounding rock is reduced by approximately 11.28% compared to that under Class V surrounding rock, and that under Class IV surrounding rock is reduced by approximately 8.04% compared to that under Class V rock. As the physical and mechanical properties of the surrounding rock improve, the proportion of the sharing load of anchor bolts shows a gradually decreasing trend. The stronger the surrounding rock is, the stronger its ability to share the load, and the smaller the proportion of pipe segments and anchor rods sharing the load.

7.4. Analysis of the Influence of the Tunnel Burial Depth on the Load-Sharing Rate of Composite Structures

The load-sharing rate of each component under different tunnel burial depths when the internal water pressure is 0.30 MPa is shown in Figure 30. As shown in the figure, under the combined action of external water and soil pressure and internal water pressure, the proportion of load shared by the surrounding rock when the tunnel is buried at a depth of 71 m increases by 19.87% compared to that at a buried depth of 31 m. The larger the tunnel burial depth is, the higher the proportion of load shared by the surrounding rock. When the tunnel is buried at a depth of 71 m, the proportion of load borne by the inner tensioned steel ring and anchor rod increases by 19.91% and 55.72%, respectively, compared to that at a buried depth of 31 m. As the tunnel burial depth increases, the proportion of load borne by the internally tensioned steel ring and anchor rod increases. As the burial depth of the tunnel increases, the proportion of pipe segments sharing the load gradually decreases. When the burial depth of the tunnel is 71 m, the proportion of pipe segments sharing the load decreases by 34.02% compared to that at a burial depth of 31 m. As the burial depth of the tunnel increases, the external load borne by the composite structure gradually increases. As reserve load-bearing components, the proportion of load sharing gradually increases, and the role of the internal tension steel ring and anchor rod becomes more apparent.

8. Conclusions

By using numerical simulation methods, the influence of the internal water pressure, surrounding rock type and tunnel burial depth on the stress and deformation law of the “inner tensioned steel ring–segment–surrounding rock” composite structure of the TBM pressurized water conveyance tunnel was investigated. The load-sharing rate of each composite component under different internal water pressures, surrounding rock type and tunnel burial depth conditions was studied. The conclusions are as follows:

(1)

Under the combined action of external water–soil pressure and internal water pressure, the “inner tensioned steel ring–segment–surrounding rock” composite structure presents an inward-converging “horizontal oval” deformation mode. Compared with the section connected only by steel plates, the tensile stress and the range of the tensile zone in the reinforced section of the inner tensioned steel ring are both reduced, which effectively restrains surface cracking of the section. The compressive stress of the top segment increases by approximately 12.05%. The vertical deformation of the pipe segment decreases by approximately 6.14%, indicating that the internal tension steel ring reinforcement method improves the structural bearing capacity and makes tunnel engineering projects safer and more stable.

(2)

The emergence of internal water pressure gradually causes the composite structure to tend to expand outward. The compressive stress of the pipe segment, vertical deformation, joint opening, connecting bolt stress, internal tension steel ring stress, and anchor rod stress all decrease. However, when the internal water pressure is 0.30 MPa, compared to the state without internal water, the tensile stress of the pipe segment increases by 41.47%, and the joint misalignment increases by 64.27%. Therefore, during the water filling operation, the internal water pressure should be properly controlled to avoid pipe cracking and the further development of joint dislocation.

(3)

Under the combined action of the external water and soil pressures and the internal water pressure, the tensile stress, compressive stress, vertical deformation, joint opening, joint misalignment, connection bolt stress, internal tensile steel ring stress, and anchor bolt stress of Class V surrounding rock increased by 3.96%, 6.91%, 12.92%, 9.36%, 15.75%, 37.16%, 11.21%, and 15.12%, respectively, compared to those of Class III surrounding rock. The change in the surrounding rock type has the greatest impact on the stress of the connection bolts. The second is the deformation of the pipe segment joints and the stress of the anchor rods. Therefore, in the transition areas of different types of surrounding rocks, key monitoring should be carried out on the stress of connecting bolts, deformation of pipe joints, and stress of anchor bolts.

(4)

Under the combined action of external water and soil pressures and internal water pressure, the tensile stress, compressive stress, vertical deformation, joint opening, joint misalignment, connection bolt stress, internal tensile steel ring stress, and anchor rod stress of the tunnel segment at a depth of 71 m increased by 22.64%, 59.29%, 107%, 55%, 60.61%, 140%, 57.77%, and 13.79%, respectively, compared to those at a depth of 31 m. The change in the tunnel burial depth has the greatest impact on the stress of the connection bolt. The second is the vertical deformation of the pipe segment and the deformation of the joint misalignment. Therefore, when designing tunnels with different burial depths, special attention should be given to the stress of the connecting bolts, vertical deformation of pipe segments, and staggered deformation of the pipe segment joints.

(5)

Under the combined action of external water and soil pressure and internal water pressure, the load-sharing ratio of the inner tensioned steel ring increases by approximately 85.80% with the rise of internal water pressure. The effect of the internal water pressure improves the load-sharing effect of the internally tensioned steel ring. With the improvement of the physical and mechanical properties of the surrounding rock, the ability of the surrounding rock to share the load becomes stronger. The proportion of the surrounding rock to share the load under Class III surrounding rock increased by approximately 7.14% compared to that under Class V surrounding rock, and the proportion of the pipe segments and anchor rods to share the load decreased by approximately 0.97% and 11.28%, respectively. As the burial depth of the tunnel increases, the composite structure bears greater external loads, and the role of the internally tensioned steel ring and anchor rod as reserve-bearing components becomes increasingly apparent. When the burial depth of the tunnel is 71 m, the load-sharing rates of the internally tensioned steel ring and anchor rod increase by 19.91% and 55.72%, respectively, compared to those at a burial depth of 31 m.

(6)

Discussion and Inferences: Beyond the quantitative findings summarized above, this study provides further insights into the behavior of the semi-ring reinforced composite structure. The significant load redistribution caused by internal water pressure highlights its role as an active stabilizing mechanism. Furthermore, the strong dependence of bolt stress on burial depth underscores that for deep tunnels, connecting bolts become critical components requiring careful design. These inferences, drawn from the integrated analysis of internal pressure, rock type, and depth, offer practical guidance for optimizing the design and monitoring strategies of similar TBM-pressurized tunnels.

(7)

Limitations and Scope of the Study: This study has certain limitations that should be acknowledged. The numerical model is based on simplified assumptions, including the use of the Mohr–Coulomb constitutive model for the surrounding rock and ideal elastic behavior for other materials. The analysis focused on a specific composite structure (semi-ring reinforcement) under static loading conditions, and the effects of dynamic loads (e.g., seismic activity) or the time-dependent behavior (creep) of the surrounding rock were not considered. Additionally, the range of parameters investigated (e.g., internal water pressure up to 0.30 MPa, burial depths up to 71 m) is tied to the specific engineering case. Future research could extend this work by incorporating more complex material models, considering construction sequences, and exploring a wider range of geological and loading conditions.