Optimization of rock bolt support parameters for TBM tunnels in high in situ stress soft rock based on deformation and stress evolution analysis

1 Introduction

With the ongoing advancement of railway and major underground engineering construction in China, Tunnel Boring Machines (TBMs) have been widely adopted in deep buried long tunnels due to their advantages of high construction efficiency and excellent tunnel quality. However, under high in situ stress and soft rock formations characterized by low strength, high stress levels, and complex structures, TBM construction often faces challenges such as large deformation of the surrounding rock, support failure, and equipment jamming. These issues severely impact construction safety and progress, presenting significant engineering obstacles that hinder the further application and promotion of TBM technology.

The deformation mechanism of surrounding rock in high in situ stress soft rock tunnels has long been a key research focus in the field of underground engineering. Existing studies indicate that the occurrence and development of surrounding rock deformation are controlled by multiple factors, including the in situ stress level, the mechanical properties of the rock mass, and its structural characteristics. Recent studies have also emphasized the coupled response of geomaterials under high stress conditions, highlighting the importance of stress driven deformation mechanisms and material behavior under extreme loading. Chen Fei et al. conducted a quantitative classification of soft rock deformation features under high in situ stress using the strength stress ratio, noting that significant plastic deformation is prone to occur when this ratio falls below a certain threshold (Chen et al., 2015). Based on extensive engineering cases, Chen Ziquan established a large deformation prediction model, further validating the dominant role of the matching relationship between in situ stress and rock mass strength on the degree of deformation (Chen et al., 2018). For stratified and fractured soft rock, relevant studies point out that under high in situ stress, surrounding rock is susceptible to shear slip and asymmetric failure, with the tunnel crown and sidewalls becoming the primary zones of concentrated deformation (Guo et al., 2017; Guo et al., 2008).

In addition to in situ stress, water rock interactions and excavation disturbance effects also significantly influence deformation in soft rock tunnels. Research shows that the elastic modulus and strength parameters of soft rock decrease markedly upon contact with water, leading to enhanced long term rheological effects in the surrounding rock and consequently exacerbating tunnel deformation (Zhou et al., 2022a; Liu et al., 2005; Yu et al., 2022; Wei et al., 2017). Simultaneously, the stress release path during excavation and the construction disturbance methods significantly affect the stress redistribution and plastic zone evolution in the surrounding rock. Improper sequencing of excavation and support can potentially trigger instability or even structural failure of the surrounding rock (Zhao et al., 2024; He et al., 2023; Yan, 2012; Hasanpour et al., 2018). The aforementioned studies reveal the complex mechanical nature of deformation in high in situ stress soft rock tunnels from various perspectives. Advanced numerical techniques, including lattice element modeling, have further improved the understanding of deformation and failure mechanisms in geomaterials under complex stress conditions by providing a useful framework for capturing crack initiation and propagation processes (Gao, 2021).

Regarding support technologies, methods such as prestressed rock bolts, shotcrete, steel arches, and yielding support systems are extensively used in high in situ stress soft rock tunnel engineering. Numerous studies demonstrate that rationally configuring parameters such as bolt length, spacing, and prestress levels can effectively improve the stress state of the surrounding rock and inhibit the expansion of plastic zones (Rizvi et al., 2020; Hu, 2019; Li, 2018; He et al., 2014; Tao et al., 2023; Oreste and Cravero, 2008; Lei et al., 2024; Wang, 2018; Zhou et al., 2022b). In addition, staged yielding support for open TBM excavation in soft rock has been shown to improve the coupling between the surrounding rock and the support system, reduce bolt stress concentration, decrease surrounding rock deformation, and narrow the loose zone under low strength, high stress, and water bearing conditions (Kang et al., 2024). Concurrently, the thickness of shotcrete and the stiffness of the support structure also play a crucial role in controlling surrounding rock deformation (Song et al., 2026; Song et al., 2021; Zuo et al., 2011; Song et al., 2025; Wang et al., 2018; Cao et al., 2018; Huang et al., 2024; Li et al., 2014; Ahmad et al., 2021; Lu et al., 2025). In recent years, the concepts of combined support systems and dynamic adjustment have gained increasing attention. These approaches emphasize optimizing support parameters during construction based on the response characteristics of the surrounding rock, aiming to achieve a balance between deformation control and project economy (Zhang et al., 2015; Wang et al., 2023; Wang, 2013; Zhou et al., 2023; Hasanpour et al., 2018).

Compared to drill and blast tunnels, TBM tunnels in high in situ stress soft rock formations are characterized by continuous excavation and a concentrated disturbance range, leading to distinctive features in surrounding rock deformation and support response. Existing research indicates that during TBM excavation, deformation of the surrounding rock ahead of the tunnel face accounts for a relatively high proportion of the total deformation, which highlights the importance of deformation control at this stage (Xu, 2018; Dong, 2016; Liu et al., 2024; Alsabhan et al., 2021; Zhang et al., 2022).

Current research still largely focuses on qualitative or single parameter analysis, with a systematic comparison of the quantitative impact and engineering sensitivity of different support parameters in high in situ stress soft rock TBM tunnels being insufficient. To address this gap, this paper takes a deep buried tunnel in southwestern China as a case study. It employs numerical simulation methods to analyze the deformation patterns of the surrounding rock under these specific geological conditions and further investigates the rational selection of rock bolt support parameters.

2 Project overview

This study is based on a deep buried long tunnel project located in southwestern China. The total tunnel length is approximately 62.6 km, with a maximum overburden depth of 1450 m. Sections with overburden depths exceeding 600 m account for more than two-thirds of the alignment, indicating a pronounced deep buried characteristic.

The tunnel adopts a circular cross section and was constructed using a combination of drill and blast and tunnel boring machine (TBM) excavation methods, as shown in Figure 1. The total length of the TBM excavated sections is 35.52 km. In these sections, the post lining internal diameter is 8.5 m for Type III surrounding rock and 8.4 m for Type IV and V surrounding rock.

Geologically, the project area is characterized by poor tectonic stability. The TBM sections are mainly located at overburden depths ranging from 600 m to 1300 m and are affected by multiple adverse geological conditions, including high in situ stress, rockburst, large deformation in soft rock, high external water pressure, water inrush, and faulted or densely jointed fractured zones. The tunnel alignment intersects several major faults, including active fault zones.

In the TBM excavated sections, poor surrounding rock conditions are dominant, with Type IV and Type V surrounding rock accounting for approximately 67% of the total length. Under such conditions, surrounding rock properties exhibit strong spatial variability and abrupt transitions, posing significant challenges to stable excavation and deformation control during TBM tunneling.

During TBM excavation in the deep buried soft rock section, obvious squeezing deformation of the surrounding rock was observed under high in situ stress conditions. The crown area experienced significant settlement and compression, accompanied by noticeable convergence of the surrounding rock. As excavation progressed, the deformation of the surrounding rock gradually transferred to the support system, resulting in bending and compression of the steel arches. In some sections, the deformation exceeded the allowable range of the initial support, which required on site treatment measures to restore the structural capacity of the support system. As shown in Figure 2, hydraulic jacks were used to correct the deformed steel arches and recover the tunnel profile. In addition, Figure 3 presents a close up view of the crown deformation of the surrounding rock during construction. These field phenomena indicate that the squeezing characteristics of the surrounding rock in this tunnel section are significant, posing considerable challenges to deformation control and support stability during TBM excavation.

3 Model establishment for TBM tunnel excavation

3.1 Constitutive model setup for the excavation numerical simulation

ABAQUS was employed to establish a three dimensional finite element model of the TBM tunnel in a deep buried soft rock stratum. The excavation process was simulated using the element activation and deactivation technique. The model dimensions were 100 m in the transverse direction, 50 m in the longitudinal excavation direction, and 100 m in the vertical direction. The tunnel axis was buried at a depth of 1200 m. The tunnel had an inner diameter of 8.4 m and an outer diameter of 9.0 m, with a shotcrete thickness of 0.30 m. The model size was selected with reference to previous studies, which indicate that boundary effects can be effectively reduced when the ratio of the model dimension to the tunnel diameter is greater than 5.

To computationally replicate the unloading redistribution plastic zone expansion process induced by TBM excavation, this study employs a three dimensional finite element model established in ABAQUS. Regarding the element system: the overburden, bedrock, and shotcrete are modeled using C3D8R 8 node linear hexahedral reduced integration elements; the shield is simulated with S4R shell elements; and the rock bolts are represented by two node 3D truss elements. This setup allows for the simultaneous characterization of the continuum response of the surrounding rock, the structural effect of the shield, and the constraining action of the bolt support. The physical meaning and engineering applicability of parameters, including cohesion c and internal friction angle θ, were explicitly defined.

3.2 Construction process simulation

To improve the reproducibility of the numerical simulation, the key modelling procedures are clarified in this section. The surrounding rock was assumed to be an isotropic homogeneous elastoplastic medium, and the Mohr–Coulomb constitutive model was adopted to describe the yielding behaviour of the soft rock under high in situ stress conditions. The yield criterion was defined by the cohesion and internal friction angle of the rock mass. The mechanical parameters were determined according to the geological investigation data of the studied tunnel section and previous engineering experience. The shotcrete was modelled as a linear elastic material, while the TBM shield and support structures were simplified using equivalent structural elements.

The three dimensional finite element model was established in ABAQUS. The model dimensions were 100 m in the transverse direction, 50 m in the longitudinal excavation direction, and 100 m in the vertical direction. The tunnel axis was buried at a depth of 1200 m. The tunnel had an inner diameter of 8.4 m and an outer diameter of 9.0 m, with a shotcrete thickness of 0.30 m. The model size was selected to reduce boundary effects, since the ratio between the model dimension and the tunnel diameter was greater than 5.

In the finite element model, the overburden, bedrock, and shotcrete were discretized using C3D8R eight node linear hexahedral reduced integration elements. The TBM shield was simulated using S4R shell elements, and the rock bolts were represented by T3D2 two node three dimensional truss elements. The mesh was locally refined around the tunnel excavation boundary, the tunnel face, and the support zone to capture the stress redistribution and deformation gradient induced by excavation. A locally refined mesh was adopted around the tunnel excavation boundary, the tunnel face, and the support zone to capture the stress redistribution and deformation gradient induced by excavation, while a relatively coarse mesh was adopted near the external boundaries to improve computational efficiency. To reduce the influence of mesh density on the numerical results, the mesh scheme was checked by comparing the deformation trend and crown settlement under different mesh densities. The adopted mesh produced stable displacement results and was therefore used for the subsequent parametric analysis.

The interaction between the rock bolts and the surrounding rock was simulated using the embedded region constraint in ABAQUS. In this method, the bolt elements were embedded in the host rock elements, and the displacement of the bolt nodes was constrained by the displacement field of the surrounding rock. This treatment represents a fully bonded condition between the bolts and the rock mass. Therefore, relative slip, grout failure, and bolt rock interface debonding were not explicitly considered. This simplification is suitable for comparing the relative influence of bolt length, spacing, and prestress under the same modelling framework, although it may overestimate the support effect under severely fractured or poorly bonded conditions.

Bolt prestress was applied by introducing an initial axial force into the truss elements before the subsequent excavation step. The investigated prestress levels were 0, 50, 100, 150, and 200 kN. After the prestress was applied, an equilibrium step was conducted to ensure that the axial force was transferred to the surrounding rock support system before further excavation.

The excavation process was simulated using the element activation and deactivation technique to represent the sequential process of progressive excavation followed by support installation. In this method, the excavated rock elements were deactivated step by step, and the corresponding support elements were activated according to the construction sequence. All excavation and support elements were generated in the initial model so that their activation or deactivation states could be controlled during the calculation.

For the boundary conditions, a normal constraint approach was adopted. The left and right boundaries of the model were constrained in the X direction, the front and rear boundaries were constrained in the Z direction, and the bottom boundary was constrained in the Y direction, while the top boundary remained unconstrained. To represent the deep burial condition, a vertical load corresponding to the weight of the overlying rock mass was applied to the top surface.

Before excavation, the initial stress field was established through a geostatic equilibrium procedure. First, the complete model was calculated under self weight to obtain the initial internal stress state. Then, the calculated stress field was introduced into the excavation model as the initial stress field. Finally, gravity loading was applied again to achieve equilibrium before tunnel excavation. In the present model, the initial in situ stress field was simplified as a gravity dominated stress field, and the vertical stress was calculated as:where ρ is the rock density, g is the gravitational acceleration, and h is the burial depth. Horizontal tectonic stress, the lateral stress coefficient, and seepage pressure were not explicitly considered. Therefore, the model is mainly used for comparative analysis of support parameters under the same loading framework rather than exact prediction of absolute deformation values in a specific tunnel section.

σ v = ρ g h

The calculation was considered convergent when the residual force satisfied the default convergence tolerance of ABAQUS and the displacement increment after support installation became negligible. The same convergence criterion was used for all simulation cases to ensure comparability among different support parameter combinations. Although direct field monitoring data were not available for strict quantitative validation, the reliability of the numerical model was assessed from the perspective of engineering consistency. The adopted constitutive model, mechanical parameters, and excavation and support sequence were selected according to the geological conditions of the studied tunnel and previous studies on deep soft rock tunnels under high in situ stress. In addition, the simulated dominant deformation characteristics are consistent with the field phenomena observed in the project, including crown squeezing, surrounding rock convergence, and deformation of the initial support structure. A schematic diagram of the numerical model is shown in Figure 4.

The present numerical model involves several simplifications. The surrounding rock was assumed to be an isotropic homogeneous continuous medium, while actual soft rock formations may contain bedding planes, joints, fractures, or weak interlayers. Groundwater and seepage effects were not explicitly considered, although water rock interaction may weaken soft rock strength and increase deformation. In addition, rock bolts were simulated using truss elements, which mainly reflect axial tensile resistance, while shear resistance, bending behaviour, and bolt rock interface slip were not considered. Therefore, the proposed support parameters should be regarded as a reference for comparative optimization under similar high in situ stress soft rock TBM tunnel conditions rather than a universal design standard. For practical application, the parameters should be further calibrated using field monitoring and construction feedback.

4 Mechanical behavior of soft rock under high in situ stress

4.1 Analysis of surrounding rock displacement

In high in situ soft rock formations, TBM excavation induces large deformation and significant stress release, risking equipment jamming and support failure. Studying the evolution of displacement and stress is key to optimizing support design. This study uses numerical simulation, based on a tunnel project in southwestern China, to analyze the displacement and stress fields after excavation. The model parameters are: elastic modulus 1.5 GPa, overburden depth 1200 m, internal friction angle 35°, cohesion 200 kPa, and Poisson’s ratio 0.35.

Given that boundary effects can influence the calculation results to a certain extent, a cross section located 30 m away from the model boundary was selected for analysis. The contour plots of the vertical and horizontal displacements of the surrounding rock after initial tunnel excavation and support are shown in Figure 5.

As can be seen from the figure, the maximum crown settlement is 96.46 mm, and the maximum horizontal displacement at the tunnel arch is 31.2 mm. The predicted deformation pattern is dominated by crown settlement, while the lateral deformation is relatively smaller and mainly concentrated near the arch. This result is qualitatively consistent with the field observations in the studied tunnel section, where obvious crown deformation and surrounding rock convergence were observed during TBM excavation.

The relationship curves between surrounding rock deformation and the distance to the tunnel face are shown in Figure 6.

As shown in the Figure 6, when the distance from the monitoring cross section (tunnel face) exceeds 12 m, the crown settlement rate of the surrounding rock is relatively slow. At a distance of 12 m ahead of the monitoring cross section, the crown settlement is 7.12 mm. Within the 12 m range ahead of the monitoring cross section, the settlement rate increases significantly. Upon excavation reaching the monitoring cross section, the crown settlement reaches 68.49 mm. As the shield advances past the section, the settlement rate behind the monitoring cross section noticeably decelerates. Following subsequent support installation, the crown settlement stabilizes approximately 8 m after the face excavation.

Regarding the horizontal displacement at the tunnel arch, it remains essentially unchanged at distances greater than 8 m from the monitoring cross section. The growth rate of horizontal displacement accelerates markedly within the range from 4 m ahead to 2 m behind the monitoring cross section. The displacement value is 20.37 mm at the monitoring cross section (0 m) and 26.45 mm at 2 m behind it. Beyond 2 m from the tunnel face, the increase in horizontal displacement at the arch slows considerably.

Within the deformation of the surrounding rock ahead of the tunnel face, the crown settlement accounts for 71% of the total settlement, while the horizontal displacement at the arch at the tunnel face accounts for 64.4% of the total horizontal displacement. The results indicate that the deformation ahead of the tunnel face constitutes a dominant proportion of the total surrounding rock deformation. Therefore, when considering measures to control surrounding rock deformation, the primary focus should be on mitigating the deformation ahead of the tunnel face. Furthermore, in high in situ stress soft rock formations during TBM excavation, the vertical crown settlement is significantly greater than the horizontal displacement at the arch. Consequently, greater emphasis should be placed on crown support during TBM tunnel construction and support operations.

4.2 Analysis of spatial stress state characteristics

Figure 7 illustrates the evolution of vertical stress at the crown and horizontal stress at the arch during tunnel excavation as the tunnel face advances.

As excavation approaches the monitoring section, the vertical stress at the crown begins to increase gradually at approximately 20 m ahead of the section and accelerates as the tunnel face approaches, reaching a peak value of 26.20 MPa at about 10 m ahead. Within the last 10 m before the tunnel face, the vertical stress decreases sharply due to excavation induced stress release, reaching a minimum value of 5.26 MPa at the tunnel face. After the shield passes, the vertical stress at the crown increases slightly and stabilizes following the installation of the initial support.

In contrast, the horizontal stress at the arch shows a similar but less pronounced trend. It starts to increase at approximately 14 m ahead of the monitoring section, reaches a peak of 14.51 MPa at around 6 m ahead, and then decreases rapidly toward the tunnel face, with a minimum value of 3.21 MPa. After shield passage, the horizontal stress gradually recovers and stabilizes at approximately 4.20 MPa with the completion of initial support.

Overall, tunnel excavation induces a wider disturbance range and more significant stress redistribution at the crown than at the arch. The crown is the primary zone for vertical in situ stress release and stress concentration, resulting in larger deformation and a higher risk of instability under high in situ stress conditions. This interpretation is also consistent with the field phenomena observed in the studied tunnel section, where obvious crown squeezing and support deformation were concentrated in the crown area during TBM excavation. Therefore, although direct quantitative monitoring data were not available for one to one validation, the model results still provide a reasonable basis for comparative assessment of support parameters. These results also highlight the necessity of timely support installation and continuous monitoring of stress evolution in the crown area during TBM excavation.

5 Optimization of initial support parameters for TBM tunnels in high stress soft rock

5.1 Effect of bolt length on surrounding rock displacement

As shown in Figure 8, and Table 1, increasing bolt length significantly reduces surrounding rock displacement in high in situ stress soft rock tunnels. Vertical displacement is most pronounced at the crown, where settlement decreases from 101.31 mm to 95.08 mm as bolt length increases from 3 m to 11 m, corresponding to a reduction of 6.15%. Similar decreasing trends are observed at the shoulder, arch, and waist, indicating an overall enhancement in deformation control.

TABLE 1. Summary of monitoring point displacements for different bolt lengths.

Horizontal displacement is most sensitive at the arch, decreasing from 34.27 mm to 30.58 mm with increasing bolt length, which demonstrates improved lateral stability. Reductions in horizontal displacement are also observed at the shoulder, crown, and invert, although with smaller magnitudes.

Further analysis shows that displacement decreases markedly as bolt length increases from 3 m to 9 m, whereas extending bolt length beyond 9 m provides only marginal additional benefit. Quantitatively, increasing the bolt length from 3 m to 9 m reduced the crown settlement from 101.31 mm to 95.50 mm, corresponding to a reduction of approximately 5.74%. However, further increasing the bolt length from 9 m to 11 m only reduced the crown settlement by 0.44%, indicating that the deformation control effect gradually reached a saturation state beyond 9 m. This indicates diminishing returns in deformation control for longer bolts. Therefore, considering both deformation mitigation and economic efficiency, a bolt length of 9 m is recommended.

As shown in Figure 9, the principal stress results further confirm the mechanical effectiveness of increasing bolt length. As bolt length increases, the absolute values of both the maximum and minimum principal stresses generally decrease at all monitoring points, indicating alleviated stress concentration and improved stress redistribution.

For the maximum principal stress, representative reductions are observed at the crown (from 6.39 MPa to 6.15 MPa) and the shoulder (from 7.62 MPa to 7.35 MPa), suggesting that longer bolts effectively restrain vertical compression and suppress shear related stress concentration. Similar decreasing trends at the arch and waist indicate weakened lateral squeezing and a more stable stress field.

For the minimum principal stress, the absolute values also show a decreasing trend with increasing bolt length, with the most pronounced reduction occurring at the arch (from 37.23 MPa to 36.63 MPa). This reflects enhanced confinement of the surrounding rock and improved overall stress conditions, consistent with the observed reduction in deformation.

5.2 Effect of bolt longitudinal row spacing variation on surrounding rock displacement

After the installation of steel arches with fixed bolt spacing, different longitudinal bolt row spacings of 60, 80, 100, 120, and 140 cm were applied. Following the simulated tunnel excavation, the displacement at each monitoring point was recorded, as summarized in Table 2.

TABLE 2. Displacement summary under different longitudinal bolt spacing.

Based on the displacement data summarized in Table 2, the corresponding displacement curves are shown in Figure 10. As shown in Figure 10 and Table 2, bolt longitudinal row spacing has a significant influence on surrounding rock displacement in high in situ stress soft rock tunnels.

Overall, both vertical and horizontal displacements increase with increasing bolt row spacing, indicating reduced support effectiveness at larger spacings. Vertical displacement is most sensitive at the crown, where settlement increases from 93.28 mm at 60 cm spacing to 103.08 mm at 140 cm spacing. Similar increasing trends are observed at the shoulder and waist, whereas the arch shows only a minor change in vertical displacement.

For horizontal displacement, the most pronounced increase occurs at the arch, rising from 29.58 mm to 37.16 mm as spacing increases from 60 cm to 140 cm, indicating weakened resistance to horizontal stress and shear deformation. Horizontal displacements at the shoulder also increase markedly, while those at the crown and waist show relatively smaller changes.

Further analysis indicates that displacement growth accelerates when the longitudinal bolt row spacing exceeds 80 cm, whereas reducing spacing below 80 cm provides diminishing additional benefit. When the longitudinal bolt spacing increased from 80 cm to 140 cm, the crown settlement increased by approximately 9.57%, while the horizontal displacement at the arch increased by 23.01%. This indicates that excessive longitudinal spacing significantly weakens the confinement effect of the bolt system, especially for controlling lateral deformation at the arch. Therefore, considering both deformation control effectiveness and economic efficiency, a longitudinal bolt row spacing of 80 cm is recommended, particularly for deformation sensitive areas such as the crown and arch.

As shown in Figure 11, the principal stress results further demonstrate the mechanical response to variations in longitudinal bolt row spacing. With increasing spacing, the absolute values of both maximum and minimum principal stresses exhibit an overall increasing trend at all monitoring points, indicating intensified compressive stress concentration due to reduced support density.

For the maximum principal stress, representative increases are observed at the crown (from 5.98 MPa to 6.87 MPa) and the shoulder (from 6.94 MPa to 8.27 MPa), suggesting weakened restraint on vertical deformation and enhanced stress concentration in complex stress zones. A more pronounced increase at the arch (from 9.93 MPa to 12.16 MPa) indicates reduced resistance to lateral squeezing under larger bolt spacing, while the waist shows a moderate increase, reflecting deterioration of the stress distribution.

Similarly, the absolute values of the minimum principal stress increase consistently with spacing, with the most significant rise occurring at the arch (from 35.07 MPa to 42.64 MPa). This trend implies weakened confinement and aggravated compressive stress concentration at larger bolt spacings, which is consistent with the observed increase in deformation.

5.3 Effect of bolt circumferential spacing on surrounding rock displacement

After steel arch installation, with the longitudinal bolt spacing held constant, circumferential bolt spacings of 40, 60, 80, 100, and 120 cm were applied. Following the simulated tunnel excavation, the displacement at each monitoring point was recorded, as summarized in Table 3.

TABLE 3. Displacement summary under different circumferential bolt spacing.

Based on the displacement data at each monitoring point, the corresponding curves for different bolt circumferential spacings are shown in Figure 12.

As shown in Figure 12 and Table 3, bolt circumferential spacing has a significant influence on surrounding rock displacement under high in situ stress conditions. Both vertical and horizontal displacements generally exhibit a non monotonic trend, decreasing initially and then increasing as circumferential spacing increases.

For vertical displacement, the crown shows the most pronounced response, with settlement decreasing from 95.43 mm at 40 cm spacing to a minimum of 93.22 mm at 60 cm, followed by a sharp increase to 104.87 mm at 120 cm. Similar increasing trends are observed at the shoulder, arch, and waist as spacing increases, indicating progressively weakened control of vertical deformation and floor heave at larger spacings.

For horizontal displacement, the arch is the most sensitive location. Displacement decreases slightly from 31.17 mm at 40 cm to 30.36 mm at 60 cm, but then increases markedly to 35.77 mm at 120 cm, indicating reduced resistance to horizontal stress and aggravated lateral deformation. Horizontal displacements at the shoulder also increase significantly with spacing, whereas those at the crown and waist show relatively smaller changes.

Overall, both vertical and horizontal displacements reach minimum values at a circumferential spacing of approximately 60 cm. Compared with the circumferential spacing of 60 cm, increasing the spacing to 120 cm increased the crown settlement by approximately 12.50% and the horizontal displacement at the arch by 17.82%. This further confirms that 60 cm provides a more effective balance between deformation control and support efficiency. A smaller spacing of 40 cm does not provide additional benefit and may induce local stress concentration, while spacing larger than 60 cm leads to rapidly increasing deformation. Therefore, a circumferential bolt spacing of 60 cm is recommended as the optimal choice considering both deformation control and support efficiency. The corresponding principal stress distributions under different circumferential bolt spacings are shown in Figure 13.

5.4 Effect of bolt prestress variation on surrounding rock displacement

After steel arch installation with fixed bolt spacing, bolt prestress levels of 0, 50, 100, 150, and 200 kN were applied. Following the simulated tunnel excavation, the displacement at each monitoring point was recorded, as summarized in Table 4.

TABLE 4. Displacement summary under different bolt prestress levels.

Based on the displacement data at each monitoring point under different bolt prestress levels, Figure 14 is presented.

Data from Figure 14 and Table 4 indicate that bolt prestress plays a decisive role in controlling surrounding rock deformation in high in situ stress soft rock tunnels. Both vertical and horizontal displacements decrease monotonically with increasing prestress at all monitoring points, with the crown and arch exhibiting the most pronounced responses. Crown settlement is reduced from 100.62 mm at 0 kN to 94.87 mm at 200 kN, while arch horizontal displacement decreases from 35.98 mm to 29.12 mm, reflecting enhanced confinement and lateral stability provided by prestressed bolts. Deformation at the shoulder and waist also shows consistent reductions, indicating an overall improvement in rock mass integrity and suppression of shear slip and floor heave.

The deformation control effect of prestress is most significant within the low to moderate prestress range. When prestress increases from 0 to 100 kN, displacement at deformation sensitive zones such as the crown, shoulder, and arch decreases rapidly, whereas further increases beyond approximately 150 kN result in diminishing returns. Increasing bolt prestress from 0 to 150 kN reduced the crown settlement by approximately 5.10% and the horizontal displacement at the arch by 17.45%. However, further increasing the prestress from 150 kN to 200 kN only reduced the crown settlement by 0.65% and the horizontal arch displacement by 1.95%, indicating that the marginal benefit of prestress becomes limited beyond 150 kN. This saturation behavior suggests that once sufficient confinement is established, additional prestress contributes more to stress concentration than to deformation reduction. Correspondingly, as shown in Figure 15, the absolute values of principal stresses generally increase with prestress, particularly at the shoulder and waist, indicating strengthened confinement but also intensified compressive stress concentration. In contrast, stress at the waist slightly decreases, implying localized stress redistribution. Considering both deformation control efficiency and engineering economy, a prestress level of approximately 150 kN is identified as an effective and reasonable choice for high stress soft rock TBM tunnels.

The recommended support scheme of 9 m bolt length, 80 cm longitudinal spacing, 60 cm circumferential spacing, and 150 kN prestress is generally consistent with the support concept commonly adopted in deep buried high in situ stress soft rock tunnels, where longer bolts, denser spacing, and active prestress are required to enhance the confinement of the surrounding rock. Compared with ordinary surrounding rock conditions, the relatively long bolt length and dense bolt spacing recommended in this study indicate that the excavation disturbed zone is large and that short or sparsely arranged bolts may be insufficient to control crown settlement and arch convergence. However, the proposed parameters were obtained from comparative numerical simulations under simplified modelling assumptions. Therefore, they should be regarded as a reference for support optimization in similar TBM tunnels rather than a universal design standard, and further calibration using field monitoring and construction feedback is required in practical applications.

6 Conclusion

This study investigated the deformation and stress evolution of surrounding rock during TBM excavation in high in situ stress soft rock and evaluated the influence of rock bolt support parameters using a three dimensional numerical model. The main conclusions are as follows:

• A considerable proportion of the total surrounding rock deformation occurs ahead of the tunnel face, and crown settlement is the dominant deformation mode during TBM excavation. The crown area is also the main zone of stress redistribution and deformation concentration. Therefore, deformation control ahead of the tunnel face and timely crown support are particularly important for TBM tunnelling in high in situ stress soft rock.
• Bolt length has a clear influence on deformation control. Increasing the bolt length from 3 m to 9 m effectively reduces crown settlement and horizontal displacement at the arch. However, further increasing the bolt length from 9 m to 11 m provides only limited additional benefit, indicating that the deformation control effect gradually reaches a saturation state. Under the studied conditions, a bolt length of 9 m is recommended.
• Bolt spacing significantly affects support performance. Excessive longitudinal spacing weakens the confinement effect of the bolt system, especially for crown settlement and arch convergence. The longitudinal spacing should not exceed 80 cm. Circumferential spacing shows a non monotonic effect, and 60 cm provides the best overall deformation control effect under the studied conditions.
• Bolt prestress improves the confinement of the surrounding rock and reduces deformation, especially in the crown and arch areas. Increasing prestress from 0 to 150 kN produces a significant deformation reduction, while further increasing prestress beyond 150 kN provides only limited additional benefit. Therefore, a prestress level of 150 kN is recommended.
• Based on the parametric analysis, an effective rock bolt support scheme for similar high in situ stress soft rock TBM tunnels consists of a bolt length of 9 m, a longitudinal spacing of 80 cm, a circumferential spacing of 60 cm, and a prestress of 150 kN. These results can provide a reference for support parameter optimization and deformation control in similar deep buried TBM tunnel projects.

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Footnotes

Edited by: Zheng Yang, TU Bergakademie Freiberg, Germany

Reviewed by: Zhanping Song, Xi’an University of Architecture and Technology, China

Ke Deng, Henan University, China