Effects of Reverse Fault Dislocation Application Method for Tunnelling Through Active Faults

Active faults seriously threaten the structural integrity of mountain tunnels in seismic zones, and reverse faults are the most hazardous. A tunnel project in the western region was used as a reference to analyze the damage mechanism of tunnels under different modes of reverse fault displacement. The ABAQUS finite element analysis software was employed for the numerical simulation, and a quasi-static method was adopted to analyze the displacement and stress response patterns of the tunnel structure traversing the fault under three typical modes of reverse fault displacement. This led to deriving the tunnel structure’s longitudinal damage modes and impact zones based on reverse fault displacement. The study revealed that the damage modes of the tunnel under different fault displacement modes varied, which was reflected in the different degrees of shear and compression. Regardless of the fault displacement mode, the tunnel structure located within the fault fracture zone was severely damaged, with the most severe damage occurring at the interface between the fixed plate and the fault displacement section. Therefore, in the design, special attention should be paid to the displacement resistance performance of the dangerous sections of the tunnel. The research results provide significant reference and guidance for similar projects.


Introduction
Active faults, also known as active faults and ruptures, are important influencing factors in the preparation of ground vibration parameter maps, selection of major engineering sites, and safety evaluation of lifeline projects [1,2] , refer to faults that have been active during the recent geological period, are still active today, and are likely to become active again.China's western region is mostly in the high-intensity seismic zone, with a high frequency of plate activity, dense active fractures, and strong tectonic geological effects; deep-buried long tunnels face a significant risk of crossing the active fracture zones or being constructed near the faults.
Active faults can be classified into normal, reverse, and strike-slip faults according to the direction of the fault movement and the characteristics of the ground stress field.Different types of faults produce different stress-field distributions, and previous studies have shown that reverse faults are more destructive than normal and strike-slip faults [3,4] .Mao et al. [15] found that a tunnel under a reverse fault dislocation experienced greater damage than that under a strike-slip fault under the same cover thickness and earthquake magnitude.Using a finite element model, Wang and Guo [16] compared the degree of tunnel damage under reverse, normal, and strike-slip faults and concluded that the reverse fault case leads to the greatest damage to the tunnel.Existing studies on the simulation of 1334 (2024) 012026 IOP Publishing doi:10.1088/1755-1315/1334/1/012026 2 reverse faults are mainly based on the displacement of the hanging wall parallel to the fault plane.Li et al. [5] simulated the existence of a fault zone below the tunnel with a fault dip angle of 75°, applied the displacement boundary condition of the hanging wall of the soil parallel to the fault plane in the existence of the fault zone, and then compared the damage of the tunnel when the number of dislocations was 5, 10, and 15 cm.Wang et al. [6] considered that the fault zone has a certain range; thus, the fault plane is divided into the fault zone and fault core.At the same time, the author considered the effect of the magnitude 5.0 to 6.7 far-field earthquakes, so the maximum dislocation was set to 1m.The dislocation of 1m along the fault dip was divided into two components, horizontal and vertical, and applied to the boundary of the hanging wall in the numerical model.Chermahini and Tahghighi [7] developed a two-dimensional numerical model with homogeneous stratigraphy using the Sabzkouh tunnel as an example and empirically applied a fault dislocation of 4m to the footwall boundary of the tunnel.Existing studies have mainly set the direction of the dislocation of the hanging wall parallel to the fault plane when simulating the reverse fault displacement [5][6][7][8][9][10] .However, the displacement pattern of reverse fault dislocation is not caused by the occurrence of dislocation of the hanging wall parallel to the fault plane but is coupled with the extrusion of the footwall by the peripheral rocks and the uplift of the hanging wall and its absolute displacement angle is not necessarily strictly parallel to the fault plane [11] .However, there is a lack of sufficient research on the displacement mode of reverse faults, and engineering design in the case of unclear identification of the displacement mode will lead to design basis and target ambiguity, operational safety cannot be guaranteed, and other practical problems.Therefore, it is important to study the failure mechanism of cross-fault tunnels under reverse dislocation further to improve the seismic design of tunnels.
Most existing studies adopt a simplified 2D section model for the numerical model of tunnels through faults, which considers the fracture zone as a single line.A normal 3D geological model simplifies the fault fracture zone into a 2D interface, as shown in Figure 1.

Figure 1. Schematic representation of two typical models.
There are only a small number of fault zones with only one type of fractured rock, and some larger fault zones have all three types of fractured rock [12] , which leads to a relatively large difference in rock and soil properties within the fault fracture zones.For example, the fracture zone of the FI9 fault zone in the Gaoshiti-Muoxi area in the central part of the Sichuan Basin developed tail, linear, diagonal, and stacked tectonics, which have apparent segmentation characteristics [13] .Some scholars have proposed that the reason for this is that, owing to the interaction of shear expansion and strain hardening of the rock, the displacement transmitted from the active disc to the fracture zone has obvious nonlinear characteristics, and the displacements in different areas within the fracture zone have obvious gradient effects; fluid in the crust is transported downward along the fracture zone, increasing pore pressures and reducing positive stresses in the fracture, further reducing the friction angles and compressive strengths of the soft enclosing rocks within the fault properties [14] .Therefore, it is necessary to consider the multi-segmentation of the fault fracture zone region in the model.In this study, a method for dividing the fault fracture zone region into a fault influence zone and fault core is proposed, which is closer to actual engineering to obtain more accurate numerical simulation results, which will be the future trend of the refined model.

Brief introduction of the Project
A tunnel through an active fault zone in western China as a study object, the tunnel design form for the single-hole two-lane, cross-section form is shown in Figure 2; the tunnel cross-section span of 15.84 m, headroom of about 12.32 m, and the tunnel initial support is 33 cm thick, using C30 early highstrength fiber concrete.The second lining was 65 cm thick, using C35 reinforced concrete.According to the construction design, a reserved space of 50 cm was set for potential fault slip.

Overview of the model
The finite element software ABAQUS was used to model and analyze the rock and mountain tunnel structure.The dimensions of the computational model were 200 × 1540 × 400 m (corresponding to the x, y, and z directions, respectively), and the burial depth of the tunnel was taken as 40 to 350 m.
The surrounding rock of the tunnel is divided into five sections along the longitudinal direction: the hanging wall, the fault influence zone①, the fault core, the fault influence zone②, and the footwall.The total width of the fracture zone was 420 m, the width of the fractured core was 100 m, width of the fault influence zone was 160 m, dip of the fracture zone was assumed to be 30°, and dip angle of the fracture zone was assumed to be 50°.The model has 3652730 units, as shown in Figure 3.

Modelling the Surrounding Rock and Lining Properties
The Mohr-Coulomb principal model was used for the surrounding rock, and an elastic model was used for the lining.The specific values of the surrounding rock and lining parameters are presented in Tables 1 and 2, respectively

Friction surface properties
For the tunnel structure existing in the peripheral rock medium itself, the tunnel structure plays a supporting role for the surrounding geotechnical body when fault dislocation occurs.The surrounding geotechnical body, in turn, transfers the contact pressure to the tunnel structure through the contact surface.To solve the fault dislocation problem, researchers and scientists have studied establishing a suitable contact method.The relationship between the tunnel and surrounding rock medium is considered to be a frictional relationship, and there are contact behaviors in the tangential and normal directions.Currently, the most fundamental model in finite element software is the Coulomb friction model, which relates the maximum allowable frictional (shear) stresses across the contact surface to the contact pressure.It was possible to obtain a certain amount of shear stress before the two objects slipped relative to each other.A relative slip begins if the shear stress exceeds this value [9] .Usually, the coefficient of friction takes the value µ = tanφ, which is about 0.2 (φ is the angle of internal friction in the surrounding rock) [10] .
In this case, owing to the problem of inconsistent deformation of faults and tunnels, the existence of hollowed areas is verified by tests; therefore, when analyzing, the contact between the tunnel and structure is ticked to allow the option of separation after contact [11] .

Simulation Process
The numerical calculation was divided into two main steps: restoration of the initial geostatic stress field and fault dislocation.
First, in the analysis step of the restoration of the initial geostatic stress, the bottom was completely fixed, and the normal displacement was restricted on each side to achieve the initial geostress equilibrium and obtain the initial stress field.
In the fault dislocation analysis step, the boundary conditions of the footwall were fixed, and the remaining part was lifted.Considering the different methods of applying the reverse fault, the total amount of control dislocations was 50 cm; the three types of reverse fault dislocation cases were designed with different fault dislocation angles.

Analytical cases
Table 3. Summary of the case conditions.3.6.2.Cross-section's monitoring point.According to the investigations of the damage of crossingfault tunnels, such as the Kizawa tunnel [17] in Japan and the Longxi tunnel [18] in China, the most damaged parts of the tunnels are at the interface of different lithologies.Three sections of the lithology interface (shown in Figure 5) were selected as the object of investigation; eight monitoring points were selected for each section, and the positions of the corresponding lithology of monitoring points No. 1 to No. 8 are the crown, left shoulder, left spring line, left foot, invert, right foot, right spring line, and right shoulder, as shown in Figure 6.

Lining stress analysis
According to the lining displacement cloud diagram, the maximum stress value is 70 MPa, as shown in Figure 7.By extracting the location where the maximum stress occurred, the lining produced a stress concentration in the displacement-loaded section; the maximum stress occurred at the bottom of the lining.In Figure 8, the distribution trend of the maximum principal stresses of Case 1 and Case 2 is the same, with Case 2 having slightly larger than values than Case 1; the maximum principal stresses of the two cases change abruptly and reach the peaks at the junction of the hangingwall and fracture zone and at the junction of the influence zone and the core, which are about 20 and -23 MPa respectively; the maximum principal stresses of the section 1 and 2 are higher than those of section 3.This is because section 1 is a staggered interface, while Section 2 is very close to the interface; therefore, sections 1 and 2 bear the main stress and deformation, and when the stress is transferred to Section 3, it is greatly attenuated.
For Case 3, the trend of the maximum principal stress distribution of the invert is different from those of Cases 1 and 2, primarily because the force in Case 3 is dominated by the axial pressure, which is distributed in the longitudinal direction of the extended tunnel and changed abruptly at the fault interface.Although there is a larger distribution of stresses at the front and rear ends of the tunnel owing to the influence of the received boundary effect, this influence is negligible according to the St. Venant principle.
In reverse faults, tunnel structures are primarily subjected to compressive and shear stresses.Owing to the differences in Young's modulus and Poisson's ratio of the surrounding rock along the different longitudinal segments (hanging wall-influence zone-fault core-influence zone-foot wall), the deformation and compression force of the surrounding rock are transmitted to the tunnel structure with an obvious regional characteristic.Therefore, the region affected by fault slip and dislocation can be subdivided according to the longitudinal distribution of shear force at the key monitoring points of the tunnel structure.The variation in the compressive stresses along the longitudinal direction at the locations of the tunnel invert is shown in Figure 8. Figure 9 shows that, unlike the maximum principal stress distribution, the peak axial force in Cases 1 and 2 does not occur at the fault boundary but at the fault core, mainly because it has the lowest modulus compared with the surrounding rock on both sides and because the lining produces an S-shaped deformation at the junction of the hanging and foot walls (Figure 15).A greater deformation occurs at the fault core during compression, increasing compressive stresses on the lining in this area.The peak shear stresses of the inverts in Cases 1 and 2 occur at the interface between the hanging wall and foot wall.The dislocation shear stresses suffered by the tunnel structure at a location farther from the fault interface were lower and smoother, respectively (Figure 10).The peak shear stresses in the lining invert are approximately -16 and 15 MPa, respectively, while the peak shear stress in Case 3 and superelevation vault occurs near section 4 and at section 1, respectively, which is similar to that of Cases 1 and 2. Sections 1 and 4 are subject to greater shear stresses, which belong to the weak lining shear parts.Flexible joints and other methods should be considered for defense.
From the previous stress distribution law along the length of the tunnel, it can be observed that the lining is subjected to the maximum stress at the fault interface, which is a critical section of the lining.Therefore, further data should be extracted and analyzed for critical sections to investigate the lining's failure mechanism under reverse fault displacement.In section 1, the lining in Case 3 receives the largest axial force, approximately 5.7×10 4 kN, followed by Case 2 and Case 1, as shown in Figure 11(b).The pressure on both sides of the arch waist of the lining is higher than that on the crown and invert.Figure 11(c) shows that the lining of the right foot receives a higher shear stress in Cases 1 and 2, which is due to the relationship between the fault direction and the tendency, causing the lining to experience a larger relative displacement in the direction of 45°.In contrast, the fault direction of Case 3 is parallel to the direction of the tunnel; hence, the shear stress is lower than that of Cases 1 and 2. As seen from Figures 12 and 13, in Case 3, the axial forces in sections 2 and 3 are smaller than those in Cases 1 and 2 because the lining in Case 3 is mainly under pressure, and there is a larger distribution along the length of the lining.In Cases 1 and 2, owing to the presence of vertical dislocation, there is a sudden change in the interface between the fault intersection and the fault core; therefore, a stress concentration is generated, and the distribution of shear stresses for the three cases in Section 2 is relatively similar.In Section 3, the shear stresses of Cases 1 and 2 are larger than those of Case 3, and the reason is similar to that in Section 1.
In summary, the reversed fault on the hanging wall, when there is a large vertical displacement, will damage the lining, and in the hanging and footwall junction with the fault core of the most serious, in the design of anti-fault should focus on considering the performance of shear; when the hanging wall along the tunnel direction of the extrusion of the main tunnel, it will make the tunnel more prone to compression damage, and in the tunnel opening and the hanging wall inside the junction between soft and hard rock owing to the larger compressive stresses in the design of the tunnel must focus on considering the performance of compressive resistance.The design should focus on the compressive performance.

Lining Displacement
The vertical displacement map of the tunnel (Figure 14) shows the vertical displacement of the lining from the hanging wall to the fracture zone and then to the footwall, which gradually increases, mainly because the foot wall produces an upward displacement with the surrounding rock.Moreover, the shear force and pressure of the surrounding rock on the lining, when transferring the lining to the hanging wall, is borne by the lining close to the hanging wall.The displacement is smaller within the hanging wall of the tunnel lining.In Figure 15, the three working conditions have a settlement of approximately 2-3 cm at the contact surface between the hanging and foot walls and the crushed zone, probably due to the combined effect of shear and compressive stress on the lining, and "S" type bending in the crushed zone area, resulting in downward displacement near the hanging wall.In the process of extension to the footwall, Cases 1 and 2, the lining experienced upward displacement due to the uplift effect of the reverse fault in the crushed zone, and produced a gradual increase in upward displacement; the maximum value is 37 cm, and the vertical boundary displacement is consistent with the application; Case 3 did not have a significant uplift at the back end, but only the region of the fault crushed zone was squeezed due to the existence of the fault dip angle producing a small vertical dislocation, which occurred in "S" type bending deformation.the presence of the fault dip angle when the fracture zone occurs in the reverse fault.The peripheral rock in the fracture zone is softer, and when subjected to compressive stress, it will produce a greater deformation than the two sides of the hard rock, which will cause the lining in the fracture zone, especially in the core, to be subjected to greater horizontal shear stress, producing horizontal displacement.The peak horizontal displacements of Cases 1 and 2 were approximately 6-8 cm, approximately 1.5 times that of Case 3, and the maximum horizontal displacement occurred in the core of the fracture zone.A larger vertical displacement makes the lining more prone to slipping on the extended fault plane, resulting in a corresponding increase in the horizontal displacement.Although it is much lower than the vertical displacement, it is large and should be considered in the design.

Conclusions
This study focuses on different loading modes to simulate the effects of reverse fault dislocations on tunnels.Considering the dig angle and direction of the fault surface, a 3D refined FE model was established, and three reverse fault dislocation application methods were introduced to study the internal force response and damage characteristics of tunnels under the reverse fault.The following major conclusions were drawn: (1) Owing to the uncertainty of fault dislocation patterns, the design of cross-fault tunnels must consider the possible effects of different dislocation patterns on the tunnels.(2) When applying inverse fault, a greater vertical displacement will make the lining more susceptible to shear damage, and the critical section is at the junction of the hanging and foot walls and the junction of soft and hard rock near the interface of the hanging and foot walls.In contrast, a greater horizontal displacement will cause the lining to receive greater compressive stress, and the distribution pattern is large at both ends and small in the middle.(3) When the reverse fault displacement slides along the fault surface, the maximum lining compressive stress occurs in the core of the fault; the value is smaller in the area away from the core.When reverse fault displacement is applied in the axial direction of the tunnel, the lining undergoes a sudden change and a larger distribution at the interface of the different lithologies.(4) Considering pressure and tensile lining in the area of the reverse fault fracture zone, the lining should be in the hanging and footwall interface with the fault core of the first key defense, followed by considering the soft and hard peripheral rock interface.(5) In this study, to simplify the calculation, the linear elasticity eigenstructure model was adopted for the lining, while the effect of concrete damage should be considered for the lining in actual engineering.The response and damage mechanism of the concrete damage plastic model under inverse fault displacement should be considered in future research.

Figure 3 .
Figure 3. Finite element model of fault-tunnel system.

Figure 4 .
Figure 4. Schematic of boundary conditions of three cases.3.6.Monitoring points arrangement 3.6.1.Longitudinally monitoring point.Along the lining arch and superelevation arch in the longitudinal direction of the tunnel every 40 m to arrange a monitoring point, used to measure and observe the lining longitudinal stress and strain distribution of the size and regularity.

Figure 6 .
Figure 6.Schematic layout of monitoring points on the critical sections.

Figure 8 .
Figure 8.Comparison of the distribution of maximum principal stresses of the three cases.

Figure 9 .
Figure 9.Comparison of the axial force distribution of the three cases.

Figure 10 .
Figure 10.Comparison of the shear stress distribution of the three cases.

Figure 11 .
Figure 11.Comparison of the stress distribution at section 1.

Figure 15 .
Figure 15.Vertical displacement of the lining.In Figure15, the three working conditions have a settlement of approximately 2-3 cm at the contact surface between the hanging and foot walls and the crushed zone, probably due to the combined effect of shear and compressive stress on the lining, and "S" type bending in the crushed zone area, resulting in downward displacement near the hanging wall.In the process of extension to the footwall, Cases 1 and 2, the lining experienced upward displacement due to the uplift effect of the reverse fault in the crushed zone, and produced a gradual increase in upward displacement; the maximum value is 37 cm, and the vertical boundary displacement is consistent with the application; Case 3 did not have a significant uplift at the back end, but only the region of the fault crushed zone was squeezed due to the existence of the fault dip angle producing a small vertical dislocation, which occurred in "S" type bending deformation.

Figure 16 .
Figure 16.Lateral Displacement of the Lining.