Study of Mechanical Response of Tunnels Crossing Active Faults in Different Burial Depths

: There are numerous tunnels worldwide that cross active fault zones. These tunnels are situated in complex geological environments and are subjected to intense seismic activities. When active fault zones experience displacement, tunnels are susceptible to varying degrees of damage. Over the past few decades, many scholars have researched tunnels crossing active fault zones using numerical simulation methods, including ﬁnite element analysis, discrete element analysis, and ﬁnite difference methods. However, certain aspects have been overlooked, such as the inﬂuence of burial depth on tunnels crossing active fault zones. Most prior studies have primarily omitted consideration of tunnel depth and high-stress effects, resulting in disparities between research ﬁndings and practical engineering outcomes. In light of these issues, this paper analyzes the impact of ground stress ﬁelds at different burial depths on tunnels crossing active fault zones. It compares the mechanical response characteristics of deep-buried and shallow-buried tunnels after experiencing fault displacement, elucidating variations in displacement patterns, stress, and strain at different burial depths. The results indicate that: (1) Deep-buried and shallow-buried tunnels exhibit an “S”-shaped deformation pattern. (2) Regarding the strain distribution within the tunnel, the affected regions are predominantly concentrated within the fault zone. (3) Regarding the stress distribution within the tunnel, deep-buried tunnels experience a broader range of stress variations distributed across the fault zone. In contrast, shallow-buried tunnels predominantly exhibit stress concentration at the fault slip plane. (4) By analyzing the patterns of tunnel damage at different burial depths, it is observed that burial-depth effects notably inﬂuence tunnels with a burial depth less than 200 m. In comparison, tunnels exceeding 300 m gradually reduce the impact of burial depth. These ﬁndings can be essential theoretical references for studying tunnels crossing active fault zones in deep-buried environments.


Introduction
As the global economy develops rapidly, China continues to expand its transport infrastructure, marked by the extensive development of highway and high-speed railway construction throughout the country [1,2].These massive constructions of highways and railways have also accompanied the emergence of many underground pipeline projects, especially in western China, where the massive construction of highways and railways has generated many highway tunnels, railway tunnels, and water-diversion tunnels.However, China's geology is unique in that active faults are widely distributed, which poses a significant challenge to underground engineering construction.In order to mitigate structural damage caused by active faults to underground pipeline projects, efforts are typically made to avoid crossing active faults wherever possible.Nevertheless, tunnel crossings of active faults may become unavoidable in practical engineering scenarios due to geological and construction constraints, among other factors.Consequently, the investigation of tunnel depths.Therefore, researching deep-buried tunnels crossing active fault zones has become a crucial scientific issue that must be addressed in underground engineering construction.
This paper utilizes Abaqus CAE/2022 finite element analysis software to establish a three-dimensional nonlinear model to address the current research gap in studying deep-buried tunnels crossing active fault zones.It compares the distinctions in the failure mechanisms between deep-buried and shallow-buried tunnels when subjected to fault displacement.Additionally, it analyzes the variations in displacement patterns, stress, and strain resulting from fault displacement under different burial conditions.Finally, the paper recommends fault mitigation measures for deep-buried and shallow-buried tunnels.

Engineering Background and Finite Element Model 2.1. Project Overview
The Xianglushan Tunnel is located in Yunnan Province, China, and is a crucial structure in the first section of the Dianzhong Water Diversion Project, traversing the Ma'er Mountains.As shown in Figure 1, the Xianglushan Tunnel crosses multiple Holocene active fault zones and encounters a complex geological environment, which results in a higher risk profile.This study focuses on the Xianglushan Tunnel within the context of the Dianzhong Water Diversion Project.The tunnel crosses the Longpan-Qiaohou (F10-1) fault zone prototype, which has experienced cumulative horizontal displacement of up to 0.4 m over the past century.The tunnel features a circular cross-section with a radius of 5.65 m, and its initial lining is constructed using C25 concrete, while the secondary lining is made of C30 concrete.
practical engineering, the impact of in situ stress conditions on rock displacement is a significant factor, especially in areas with more complex geological conditions at greater depths.Therefore, researching deep-buried tunnels crossing active fault zones has become a crucial scientific issue that must be addressed in underground engineering construction.
This paper utilizes Abaqus CAE/2022 finite element analysis software to establish a three-dimensional nonlinear model to address the current research gap in studying deepburied tunnels crossing active fault zones.It compares the distinctions in the failure mechanisms between deep-buried and shallow-buried tunnels when subjected to fault displacement.Additionally, it analyzes the variations in displacement patterns, stress, and strain resulting from fault displacement under different burial conditions.Finally, the paper recommends fault mitigation measures for deep-buried and shallow-buried tunnels.

Project Overview
The Xianglushan Tunnel is located in Yunnan Province, China, and is a crucial structure in the first section of the Dianzhong Water Diversion Project, traversing the Ma'er Mountains.As shown in Figure 1, the Xianglushan Tunnel crosses multiple Holocene active fault zones and encounters a complex geological environment, which results in a higher risk profile.This study focuses on the Xianglushan Tunnel within the context of the Dianzhong Water Diversion Project.The tunnel crosses the Longpan-Qiaohou (F10-1) fault zone prototype, which has experienced cumulative horizontal displacement of up to 0.4 m over the past century.The tunnel features a circular cross-section with a radius of 5.65 m, and its initial lining is constructed using C25 concrete, while the secondary lining is made of C30 concrete.

Finite Element Model Analysis
A three-dimensional numerical model was established using Abaqus software, and numerical simulations were conducted.As shown in Figure 2, after a comprehensive analysis of various structural factors related to real-world engineering faults, the parameters for this calculation were determined as follows: fault dip angle of 90 • , fault width of 200 m, tunnel depth of 100 to 1200 m, and the dimensions of the three-dimensional numerical model were set at 200 × 200 × 600 m.As shown in Figure 3, the tunnel lining has a circular cross-section consisting of an initial support with a thickness of 25 cm and a secondary lining with a thickness of 80 cm.In the numerical simulation, the Geological Structure Method is employed, and special attention is paid to the response characteristics of the tunnel lining when analyzing the interaction between the faults and the tunnel.At the same time, to ensure the accuracy and efficiency of the calculations, a finer mesh has been employed for the rock mass within the fault zone and in the vicinity of the tunnel.The remaining rock mass employs a relatively coarse grid.The tunnel lining employs a refined grid in the sections where the tunnel intersects fault zones and their perimeters.

Finite Element Model Analysis
A three-dimensional numerical model was established using Abaqus software, and numerical simulations were conducted.As shown in Figure 2, after a comprehensive anal ysis of various structural factors related to real-world engineering faults, the parameter for this calculation were determined as follows: fault dip angle of 90°, fault width of 200 m, tunnel depth of 100 to 1200 m, and the dimensions of the three-dimensional numerica model were set at 200 × 200 × 600 m.As shown in Figure 3, the tunnel lining has a circula cross-section consisting of an initial support with a thickness of 25 cm and a secondary lining with a thickness of 80 cm.In the numerical simulation, the Geological Structure Method is employed, and special attention is paid to the response characteristics of the tunnel lining when analyzing the interaction between the faults and the tunnel.At the same time, to ensure the accuracy and efficiency of the calculations, a finer mesh has been employed for the rock mass within the fault zone and in the vicinity of the tunnel.The remaining rock mass employs a relatively coarse grid.The tunnel lining employs a refined grid in the sections where the tunnel intersects fault zones and their perimeters.The numerical model represented the rock mass and the lining using C3D8R hexahedral elements.The rock mass was assumed to exhibit elastoplastic behavior, and the elastoplastic constitutive model for the rock mass followed the Mohr-Coulomb yield criterion.Considering the potential separation between the surrounding rock and the lining due to fault movement, a separable approach was employed in the average direction.It means that when the contact pressure becomes zero or negative, the two contact surfaces separate, removing the contact constraint between them.In the tangential direction, the shear behavior of the interface can be modeled by the Coulomb friction law, which can be expressed as:   In this study, it is assumed that the friction coefficient µ between the surrounding rock and the lining is 0.6 [29].Where τ crit is the critical value of the contact shear stress, µ is the friction coefficient, and p is the contact compressive stress.The slip in the tangential direction remains zero until the contact shear stress reaches the critical value τ crit .
Because the permanent deformation of the surrounding rock induced by fault displacement is the primary cause of tunnel lining damage, a pseudo-static method was employed to apply fault displacement in the X-direction when calculating the response of the tunnel lining under the influence of active fault displacement.Tunnel excavation and support are taken into account during the construction process.In the analysis, the top boundary was defined as a stress boundary to simulate the gravitational effects of the overlying rock strata, while the remaining boundaries were considered displacement boundaries.Stress magnitudes were determined based on the overlying deep-seated rock and soil self-weight.The fault-tunnel 3D numerical model analysis involves three main steps: (1) Initial Ground Stress Equilibrium: The initial step establishes the equilibrium of ground stresses in the model.(2) Tunnel Excavation: This step simulates the tunnel excavation and is often simplified as instantaneous excavation from one side to the other.(3) Application of Fault Displacement: In this step, fault displacement is applied to the model to simulate the fault's movement (movement process).
In the numerical model, the rock body is assumed to be elastic-plastic material, and the lining is assumed to be elastic material; the mechanical parameters in this numerical model refer to the values of the parameters in the actual engineering report, and the specific physical and mechanical parameters are shown in Table 1.

Computational Approach
Referring to the simulation environment established by Zhou et al. [30], horizontal tectonic stress was applied at the model's level, while vertical stress represented the overlying rock layers' gravitational force.The ratio of simulated horizontal stress to vertical stress was set at 0.8.In motion and time, a constant velocity displacement was imparted to the active fault to simulate creep-style fault movement.The calculated period covered a 100-year engineering service life.Eight distinct simulation scenarios were designed to investigate the impact of fault rupture on tunnels crossing at various burial depths, as outlined in Table 2. Figure 4 illustrates a schematic representation of the deformation of the surrounding rock and lining for tunnel displacement in response to these different burial depths.

Analysis of the Effects of Fault Displacement on Deep-Buried and Shallow-Buried Tunnels
In order to comprehensively investigate the differences in the mechanical responses of deep-buried and shallow-buried tunnels subjected to strike-slip fault displacement, an analysis was conducted on the displacements, stresses, and strains of the tunnel secondary lining under different fault displacements for Cases 1 and 8.

The Influence of Different Displacement Amounts on Tunnel Deformation
Figure 5 illustrates the deformation curves for shallow-buried and deep-buried tunnels under different fault displacement levels for Cases 1 and 8. From the deformation patterns, it can be observed that the secondary lining on the fixed side experiences minimal influence from fault displacement, and no displacement deformation is evident.The inner tunnel exhibits a curved deformation pattern within the fault zone interval, with relatively minor variations near the fixed side and more significant variations near the free side.Moreover, the leftmost section of the fault zone closely approaches the applied fault displacement value.Additionally, on the free side, the secondary lining displacements under different fault displacement conditions show consistency with the fault displacement values, with minimal variation along the longitudinal direction of the lining.

Analysis of the Effects of Fault Displacement on Deep-Buried and Shallow-Buried Tunnels
In order to comprehensively investigate the differences in the mechanical responses of deep-buried and shallow-buried tunnels subjected to strike-slip fault displacement, an analysis was conducted on the displacements, stresses, and strains of the tunnel secondary lining under different fault displacements for Cases 1 and 8.

The Influence of Different Displacement Amounts on Tunnel Deformation
Figure 5 illustrates the deformation curves for shallow-buried and deep-buried tunnels under different fault displacement levels for Cases 1 and 8. From the deformation patterns, it can be observed that the secondary lining on the fixed side experiences minimal influence from fault displacement, and no displacement deformation is evident.The inner tunnel exhibits a curved deformation pattern within the fault zone interval, with relatively minor variations near the fixed side and more significant variations near the free side.Moreover, the leftmost section of the fault zone closely approaches the applied fault displacement value.Additionally, on the free side, the secondary lining displacements under different fault displacement conditions show consistency with the fault displacement values, with minimal variation along the longitudinal direction of the lining.Figure 6 displays displacement contour plots for deep-buried and shallow-buried tunnels.A comparative analysis reveals that both types exhibit an "S"-shaped deformation pattern, with localized bending occurring at the deformation zone.Notably, shallow-buried tunnels exhibit significantly larger bending angles than their deep-buried counterparts.Regarding deformation trends, it becomes apparent that shallow-buried tunnels experience more pronounced deformation, albeit to a smaller extent.In contrast, deep-buried tunnels display a broader range of deformation distribution, resulting in a more considerable overall extent of damage.When the tunnel is affected by strike-slip dislocation, the left wall of the lining on the free side is dominated by compressive strain, the right wall is dominated by tensile strain, the left wall of the lining on the fixed side is dominated by tensile strain, and the right wall is dominated by compressive strain.

Strain Distribution in Tunnels under Varying Displacement Levels
Although the strain law of shallow-buried tunnels is the same as that of deep-buried tunnels, the strain distribution range of both is different.The strain distribution of shallow-buried tunnels is more concentrated, while that of deep-buried tunnels is more dispersed.Figure 6 displays displacement contour plots for deep-buried and shallow-buried tunnels.A comparative analysis reveals that both types exhibit an "S"-shaped deformation pattern, with localized bending occurring at the deformation zone.Notably, shallow-buried tunnels exhibit significantly larger bending angles than their deep-buried counterparts.Regarding deformation trends, it becomes apparent that shallow-buried tunnels experience more pronounced deformation, albeit to a smaller extent.In contrast, deep-buried tunnels display a broader range of deformation distribution, resulting in a more considerable overall extent of damage.Figure 6 displays displacement contour plots for deep-buried and shallow-buried tunnels.A comparative analysis reveals that both types exhibit an "S"-shaped deformation pattern, with localized bending occurring at the deformation zone.Notably, shallow-buried tunnels exhibit significantly larger bending angles than their deep-buried counterparts.Regarding deformation trends, it becomes apparent that shallow-buried tunnels experience more pronounced deformation, albeit to a smaller extent.In contrast, deep-buried tunnels display a broader range of deformation distribution, resulting in a more considerable overall extent of damage.When the tunnel is affected by strike-slip dislocation, the left wall of the lining on the free side is dominated by compressive strain, the right wall is dominated by tensile strain, the left wall of the lining on the fixed side is dominated by tensile strain, and the right wall is dominated by compressive strain.

Strain Distribution in Tunnels under Varying Displacement Levels
Although the strain law of shallow-buried tunnels is the same as that of deep-buried tunnels, the strain distribution range of both is different.The strain distribution of shallow-buried tunnels is more concentrated, while that of deep-buried tunnels is more dispersed.In order to further analyze the strain distribution patterns during the fault displacement process, Figure 8 compares strain patterns in the tunnel lining at the fault zone after a 0.4 m displacement.It highlights differences in the damaged areas of the lining influenced by different in situ stress conditions for tunnels at varying burial depths.In shallowburied tunnels, strain primarily concentrates around the fault dislocation surface, whereas in deep-buried tunnels, strain distribution is more extensive, with fewer occurrences near the fault dislocation surface.Consequently, deep-buried tunnels experience less influence from fault displacement.As the burial depth increases, the in situ stress within the surrounding rock mass also rises.Higher in situ stress results in more significant constraints on tunnel lining deformation, making it less prone to deformation.Although the strain law of shallow-buried tunnels is the same as that of deep-buried tunnels, the strain distribution range of both is different.The strain distribution of shallowburied tunnels is more concentrated, while that of deep-buried tunnels is more dispersed.

Strain Distribution in Tunnels under Varying Displacement Levels
In order to further analyze the strain distribution patterns during the fault displacement process, Figure 8 compares strain patterns in the tunnel lining at the fault zone after a 0.4 m displacement.It highlights differences in the damaged areas of the lining influenced by different in situ stress conditions for tunnels at varying burial depths.In shallow-buried tunnels, strain primarily concentrates around the fault dislocation surface, whereas in deep-buried tunnels, strain distribution is more extensive, with fewer occurrences near the fault dislocation surface.Consequently, deep-buried tunnels experience less influence from fault displacement.As the burial depth increases, the in situ stress within the surrounding rock mass also rises.Higher in situ stress results in more significant constraints on tunnel lining deformation, making it less prone to deformation.By considering the displacement patterns of tunnels, we can deduce that tunn age tends to be more severe in shallow-buried environments, primarily concentra the fault-dislocated surface.In contrast, the damage extends over a wider area f buried tunnels.Based on these distinct damage patterns, it becomes evident that, tical engineering, it is necessary to establish longer fault-resistant zones for dee tunnels.

The Impact of Varying Fault Displacement on Tunnel Stress
Figures 9 and 10 illustrate the longitudinal distribution curves of the p stresses on the left and right tunnel walls under deep-buried and shallow-burie tions, with tensile stress considered positive and compressive stress as unfavora to the weaker rock properties near the fault zone, most of the stress variations occu the fault zone.When the tunnel is buried at a depth of 100 m, the minimum and m principal stresses are 27.6 MPa and 37.1 MPa, respectively.However, at a tunnel 1200 m, the minimum and maximum principal stresses are 4.17 MPa and 4.23 spectively.When the maximum principal stress in the tunnel exceeds the ultimat strength of C30 concrete, and the minimum principal stress surpasses the ultim pressive-tensile strength of C30 concrete, the tunnel lining undergoes damage.A to the Chinese Code for Design of concrete structures (GB 50010-2010) [31], C30 has an ultimate tensile strength of 2.01 MPa and an ultimate compressive strengt MPa.By monitoring the stress variations within the tunnel, it is evident that both buried and deep-buried tunnels experience lining damage when the fault slip rea m, at which point the tunnel lining has reached the ultimate tensile strength of C crete, indicating structural failure.
Via the above numerical simulation, the damaged form of the tunnel linin identified as shear tensile damage.The tunnel lining resisted the movement of th ble disc during the slip movement, and the lining of the left and right walls in direction produced significant tensile and compressive stresses.When the ten compressive stresses exceed the lining strength, the lining produces shear tensile This type of damage is lining damage, the more common form of damage in t deformation stage, and the faults are minor.In the early deformation stage, the am fault misalignment and the tunnel force are small.This stage is mainly the positio By considering the displacement patterns of tunnels, we can deduce that tunnel damage tends to be more severe in shallow-buried environments, primarily concentrated near the fault-dislocated surface.In contrast, the damage extends over a wider area for deep-buried tunnels.Based on these distinct damage patterns, it becomes evident that, in practical engineering, it is necessary to establish longer fault-resistant zones for deepburied tunnels.

The Impact of Varying Fault Displacement on Tunnel Stress
Figures 9 and 10 illustrate the longitudinal distribution curves of the principal stresses on the left and right tunnel walls under deep-buried and shallow-buried conditions, with tensile stress considered positive and compressive stress as unfavorable.Due to the weaker rock properties near the fault zone, most of the stress variations occur within the fault zone.When the tunnel is buried at a depth of 100 m, the minimum and maximum principal stresses are 27.6 MPa and 37.1 MPa, respectively.However, at a tunnel depth of 1200 m, the minimum and maximum principal stresses are 4.17 Mpa and 4.23 MPa, respectively.When the maximum principal stress in the tunnel exceeds the ultimate tensile strength of C30 concrete, and the minimum principal stress surpasses the ultimate compressivetensile strength of C30 concrete, the tunnel lining undergoes damage.According to the Chinese Code for Design of concrete structures (GB 50010-2010) [31], C30 concrete has an ultimate tensile strength of 2.01 MPa and an ultimate compressive strength of 20.1 MPa.By monitoring the stress variations within the tunnel, it is evident that both shallow-buried and deep-buried tunnels experience lining damage when the fault slip reaches 0.2 m, at which point the tunnel lining has reached the ultimate tensile strength of C30 concrete, indicating structural failure.
Via the above numerical simulation, the damaged form of the tunnel lining can be identified as shear tensile damage.The tunnel lining resisted the movement of the movable disc during the slip movement, and the lining of the left and right walls in the axial direction produced significant tensile and compressive stresses.When the tensile and compressive stresses exceed the lining strength, the lining produces shear tensile damage.This type of damage is lining damage, the more common form of damage in the early deformation stage, and the faults are minor.In the early deformation stage, the amount of fault misalignment and the tunnel force are small.This stage is mainly the position of the misalignment surface lining damage, with the increase in the amount of misalignment of shear tensile damage gradually expanding.This section delves into the variations in displacement patterns, stress, and strain for deep-buried and shallow-buried tunnels under the influence of fault displacement.As the fault displacement increases, shallow-buried tunnels experience a rapid surge in stress near the fault zone, while the stress variations in deep-buried tunnels stabilize.However, the damage extent of the tunnels gradually expands.Consequently, it can be inferred that the depth effect significantly impacts the range of tunnel damage during fault displacement.Greater burial depths result in a broader damage extent.This section delves into the variations in displacement patterns, stress, and strain for deep-buried and shallow-buried tunnels under the influence of fault displacement.As the fault displacement increases, shallow-buried tunnels experience a rapid surge in stress near the fault zone, while the stress variations in deep-buried tunnels stabilize.However, the damage extent of the tunnels gradually expands.Consequently, it can be inferred that the depth effect significantly impacts the range of tunnel damage during fault displacement.Greater burial depths result in a broader damage extent.

Analysis of Mechanical Response Characteristics of Cross-Fault Tunnels at Different Burial Depths
To investigate the mechanical response characteristics of tunnels crossing active faults at varying burial depths, we conducted a comparative analysis of displacement patterns, stress, and strain responses for tunnel depths ranging from 100 m to 1200 m.It allowed us to summarize the damage patterns of tunnels under the influence of fault displacement at different burial depths.
As depicted in Figure 11, displacement data at the tunnel lining's crown were collected for all eight scenarios, and longitudinal distribution curves were plotted using this data.When examining the tunnel lining displacement under different conditions, it is evident that the deformations of tunnels at different burial depths still exhibit an "S"-shaped pattern.However, as the burial depth increases, the influence of the overlying stress field imposes more significant constraints on the rock mass's deformation concerning the lining.When the burial depth is 100 m or 200 m, the tunnel experiences significant bending deformation, whereas, for depths exceeding 300 m, the variation in tunnel displacement becomes less pronounced.Analysis of the displacement curves reveals that the degree of bending deformation at the tunnel deformation location gradually diminishes with increasing burial depth.Consequently, it can be inferred that as the tunnel's burial depth increases, the rock mass exerts a more significant constraint on the tunnel lining, resulting in reduced bending deformation.
Buildings 2023, 13, x FOR PEER REVIEW pattern.However, as the burial depth increases, the influence of the overlying stre imposes more significant constraints on the rock mass's deformation concerning ing.When the burial depth is 100 m or 200 m, the tunnel experiences significant b deformation, whereas, for depths exceeding 300 m, the variation in tunnel displa becomes less pronounced.Analysis of the displacement curves reveals that the d bending deformation at the tunnel deformation location gradually diminishes w creasing burial depth.Consequently, it can be inferred that as the tunnel's buria increases, the rock mass exerts a more significant constraint on the tunnel lining, re in reduced bending deformation.Figure 12 shows the longitudinal distribution of the left and right wall strain eight cases after 0.4 m of slippage.It can be seen from the figure that the peak st the tunnel lining all appear in the fault zone.The peak strains of the tunnels with burial depths are bigger.In contrast, the peak strains of the tunnels with large depths are smaller.From the point of view of the strain characteristics of the tunn deeply buried tunnels are less affected by the misalignment effect.However, the s the misalignment effect is more extensive.The reason is that the environmenta Figure 12 shows the longitudinal distribution of the left and right wall strains in the eight cases after 0.4 m of slippage.It can be seen from the figure that the peak strains of the tunnel lining all appear in the fault zone.The peak strains of the tunnels with smaller burial depths are bigger.In contrast, the peak strains of the tunnels with larger burial depths are smaller.From the point of view of the strain characteristics of the tunnels, the deeply buried tunnels are less affected by the misalignment effect.However, the scope of the misalignment effect is more extensive.The reason is that the environmental stress value of deeply buried tunnels is bigger, and the deformation constraint of the rock body on the tunnel lining is bigger, so the strain value of the tunnel lining is smaller when it is forced to be displaced by the rock body.In the actual project, the tunnel length should be reasonably increased for deeply buried tunnels to resist misalignment.For shallowburied tunnels, where damage is more intensive, the number of annular reinforcement bars near the junction of the tunnel lining and the misalignment surface can be increased appropriately to resist the effects of misalignment.Figure 13 illustrates the stress distribution on the left and right tunnel walls un the influence of fault displacement in all eight scenarios.The peak stress values are highest for shallow-buried tunnels among all conditions.As the burial depth of the tun increases, the peak stress values gradually decrease.Notably, the stress variations indu by fault displacement are more significant when the tunnel is buried at depths of 100 and 200 m.However, for depths exceeding 300 m, the stress peak values gradually crease.In deep-burial environments, the influence of fault displacement on tunnel str is relatively consistent, with stress peak locations nearly identical.In contrast, stress c centrations primarily occur at the fault plane in shallow-buried environments.Figure 13 illustrates the stress distribution on the left and right tunnel walls under the influence of fault displacement in all eight scenarios.The peak stress values are the highest for shallow-buried tunnels among all conditions.As the burial depth of the tunnel increases, the peak stress values gradually decrease.Notably, the stress variations induced by fault displacement are more significant when the tunnel is buried at depths of 100 m and 200 m.However, for depths exceeding 300 m, the stress peak values gradually decrease.In deep-burial environments, the influence of fault displacement on tunnel stress is relatively consistent, with stress peak locations nearly identical.In contrast, stress concentrations primarily occur at the fault plane in shallow-buried environments.
By examining the deformation patterns of tunnels at different burial depths, it is evident that tunnel linings exhibit an "S"-shaped deformation pattern, with the maximum deformation closely matching the fault displacement.
Notably, substantial differences in tunnel deformation are observed at 100 m and 200 m burial depths.However, as the burial depth exceeds 300 m, the influence of burial depth gradually diminishes, and the deformation pattern remains nearly constant.Similarly, tunnels' stress and strain characteristics are significantly affected by burial depth at depths of 100 m and 200 m.Nonetheless, as the burial depth surpasses 300 m, the impact of burial depth progressively decreases, resulting in a relatively stable stress and strain pattern.By examining the deformation patterns of tunnels at different burial depths, it is evident that tunnel linings exhibit an "S"-shaped deformation pattern, with the maximum deformation closely matching the fault displacement.
Notably, substantial differences in tunnel deformation are observed at 100 m and 200 m burial depths.However, as the burial depth exceeds 300 m, the influence of burial depth gradually diminishes, and the deformation pattern remains nearly constant.Similarly, tunnels' stress and strain characteristics are significantly affected by burial depth at depths of 100 m and 200 m.Nonetheless, as the burial depth surpasses 300 m, the impact of burial depth progressively decreases, resulting in a relatively stable stress and strain pattern.

Conclusions
This paper presents a systematic study of deep-buried tunnels crossing active fault zones, employing numerical simulation methods to compare and analyze the differences in mechanical response characteristics between deep-buried and shallow-buried tunnels under the influence of fault displacement.Numerical simulations allow us to compare the mechanical response of deep-buried and shallow-buried tunnels under the influence of fault displacements.The study also investigates the changes in displacement patterns, stresses, and strains in tunnels at different depths, thus addressing a gap in the study of

Conclusions
This paper presents a systematic study of deep-buried tunnels crossing active fault zones, employing numerical simulation methods to compare and analyze the differences in mechanical response characteristics between deep-buried and shallow-buried tunnels under the influence of fault displacement.Numerical simulations allow us to compare the mechanical response of deep-buried and shallow-buried tunnels under the influence of fault displacements.The study also investigates the changes in displacement patterns, stresses, and strains in tunnels at different depths, thus addressing a gap in the study of deep-buried tunnels crossing active fault zones.The main conclusions of this study are summarized below.
(1) Regarding deformation patterns, deep-buried and shallow-buried tunnels exhibit an "S"-shaped deformation characterized by bending near the fault slip surface.However, in shallow-buried tunnels, the degree of bending is more pronounced than in deep-buried tunnels.Specifically, shallow-buried tunnels experience significant deformation, albeit within a narrower distribution range, while deep-buried tunnels display a broader distribution of deformation and more extensive damage.(2) In terms of strain distribution, the damage of the tunnel is mainly concentrated near the middle of the fault zone.After the tunnels experienced strike-slip fault movement, the shallow-buried tunnels showed similar strain patterns to the deep-buried tunnels, but their strain peaks' locations differed.However, the damage in the shallow-buried tunnels mainly concentrates near the fault-dislocated surface, whereas the damage in the deep-buried tunnels spreads more widely throughout the fault zone.(3) Analyzing the stress distribution within tunnels, the intense stress changes occur within the weak rock layers of the fault zone.Both shallow-buried and deep-buried tunnels experience lining failure, reaching their ultimate tensile strength when displacement reaches 0.2 m.The stress analysis confirms shear and tensile failure in the tunnel linings.(4) When examining the damage patterns of tunnels at different burial depths, it is evident that tunnel linings are more sensitive to burial-depth effects when buried at depths of 100 m and 200 m.However, as the burial depth exceeds 300 m, the influence of burial depth on tunnel response gradually diminishes.At this point, only minimal changes occur in tunnel displacement, and there is only a slight reduction in tunnel lining stress and strain peak values with increasing burial depth.(5) Based on the findings, practical engineering applications should involve reasonable extensions of the anti-fault protection length for deep-buried tunnels.For shallowburied tunnels with concentrated damage, an appropriate increase in the number of circumferential steel bars near the tunnel lining and fault interface is recommended to withstand the effects of fault movement.

Figure 5 .
Figure 5. Displacement characteristics of deep-buried and shallow-buried tunnels.(a) Tunnel depth of 100 m.(b) Tunnel depth of 1200 m.

Figure 6 .
Figure 6.Displacement contour maps for deep-buried and shallow-buried tunnels.

Figure 7
Figure 7 illustrates the variations in strain along the left and right walls of shallowburied and deep-buried tunnels at different fault displacement levels.Positive values represent tensile strains, while negative values indicate compressive strains.As the fault displacement increases, the strain on the left and right tunnel walls continues to rise, with the most significantly affected areas primarily concentrated in the middle of the fault zone.When the tunnel is affected by strike-slip dislocation, the left wall of the lining on the free side is dominated by compressive strain, the right wall is dominated by tensile strain, the left wall of the lining on the fixed side is dominated by tensile strain, and the right wall is dominated by compressive strain.Although the strain law of shallow-buried tunnels is the same as that of deep-buried tunnels, the strain distribution range of both is different.The strain distribution of shallow-buried tunnels is more concentrated, while that of deep-buried tunnels is more dispersed.

Figure 5 .
Figure 5. Displacement characteristics of deep-buried and shallow-buried tunnels.(a) Tunnel depth of 100 m.(b) Tunnel depth of 1200 m.

Figure 5 .
Figure 5. Displacement characteristics of deep-buried and shallow-buried tunnels.(a) Tunnel depth of 100 m.(b) Tunnel depth of 1200 m.

Figure 6 .
Figure 6.Displacement contour maps for deep-buried and shallow-buried tunnels.

Figure 7
Figure 7 illustrates the variations in strain along the left and right walls of shallowburied and deep-buried tunnels at different fault displacement levels.Positive values represent tensile strains, while negative values indicate compressive strains.As the fault displacement increases, the strain on the left and right tunnel walls continues to rise, with the most significantly affected areas primarily concentrated in the middle of the fault zone.When the tunnel is affected by strike-slip dislocation, the left wall of the lining on the free side is dominated by compressive strain, the right wall is dominated by tensile strain, the left wall of the lining on the fixed side is dominated by tensile strain, and the right wall is dominated by compressive strain.Although the strain law of shallow-buried tunnels is the same as that of deep-buried tunnels, the strain distribution range of both is different.The strain distribution of shallow-buried tunnels is more concentrated, while that of deep-buried tunnels is more dispersed.

Figure 6 .
Figure 6.Displacement contour maps for deep-buried and shallow-buried tunnels.

Figure 7 Figure 7 .
Figure 7 illustrates the variations in strain along the left and right walls of shallowburied and deep-buried tunnels at different fault displacement levels.Positive values represent tensile strains, while negative values indicate compressive strains.As the fault displacement increases, the strain on the left and right tunnel walls continues to rise, with the most significantly affected areas primarily concentrated in the middle of the fault zone.When the tunnel is affected by strike-slip dislocation, the left wall of the lining on the free side is dominated by compressive strain, the right wall is dominated by tensile strain, the left wall of the lining on the fixed side is dominated by tensile strain, and the right wall is dominated by compressive strain.

Figure 7 .
Figure 7. Strain characteristics of deep-buried and shallow-buried tunnels.(a) Left tunnel wall at a burial depth of 100 m, (b) right tunnel wall at a burial depth of 100 m, (c) left tunnel wall at a burial depth of 1200 m, (d) right tunnel wall at a burial depth of 1200 m.

Figure 8 .
Figure 8. Strain characteristics of deep-buried and shallow-buried tunnels.

Figure 9 .Figure 9 .Figure 10 .
Figure 9. Variations in the minimum principal stress.(a) Minimum principal stress on the left wall of the 100 m deep tunnel, (b) minimum principal stress on the right wall of the 100 m deep tunnel, (c) minimum principal stress on the left wall of the 1200 m deep tunnel, (d) minimum principal stress on the right wall of the 1200 m deep tunnel.

Figure 10 .
Figure 10.Variation in maximum principal stress characteristics.(a) Maximum principal stress on the left wall of the tunnel at a depth of 100 m, (b) maximum principal stress on the right wall of the tunnel at a depth of 100 m, (c) maximum principal stress on the left wall of the tunnel at a depth of 1200 m, (d) maximum principal stress on the right wall of the tunnel at a depth of 1200 m.

Figure 11 .
Figure 11.Displacement variation characteristics of tunnels crossing active faults at differen

Figure 11 .
Figure 11.Displacement variation characteristics of tunnels crossing active faults at different depths.

Figure 12 .
Figure 12.Strain characteristics of tunnels at different depths.(a) Strain on the left wall of the tun (b) strain on the right wall of the tunnel.

4 Figure 12 .
Figure 12.Strain characteristics of tunnels at different depths.(a) Strain on the left wall of the tunnel, (b) strain on the right wall of the tunnel.

Figure 13 .
Figure 13.Stress distribution characteristics in tunnels at different depths.(a) Minimum principal stress on the left tunnel wall, (b) minimum principal stress on the right tunnel wall, (c) maximum principal stress on the left tunnel wall, (d) maximum principal stress on the right tunnel wall.

Figure 13 .
Figure 13.Stress distribution characteristics in tunnels at different depths.(a) Minimum principal stress on the left tunnel wall, (b) minimum principal stress on the right tunnel wall, (c) maximum principal stress on the left tunnel wall, (d) maximum principal stress on the right tunnel wall.

Table 1 .
Mechanical parameters in the numerical model.