Experimental study on mechanical behavior and countermeasures of mountain tunnels under strike-slip fault movement

Abstract

In the seismic mountainous regions such as western China, it is usuallly inevitable to construct tunnels near active fault zones. Those fault-crossing tunnel structures can be extremely vulnerable during earthquakes. Extensive experimental studies have been conducted on the response of continuous mountain tunnels under reverse and normal fault movements, limited experimental investigations are available in the literatures on mountain tunnels with special structural measures crossing strike-slip faults. In this study, a new experimental facility for simulating the movement of strike-slip fault was developed, accounting for the spatial deformation characteristics of large active fault zones. Two groups of sandbox experiment were performed on the scaled tunnel models to investigate the evolution of ground deformation and surface rupture subjected to strike-slip fault motion and its impact on a water conveyance tunnel. The nonlinear response and damage mechanism of continuous tunnels and tunnels incorporated with specially designed articulated system were examined. The test results show that most of slip between stationary block and moving block occurred within the fault core, and significant surface ruptures are observed along the fault strike direction at the fault damage zone. The continuous tunnel undergoes significant shrinkage deformation and diagonal-shear failure near the slip surface and resulted in localized collapse of tunnel lining. The segments of articulated system tunnel suffer a significant horizontal deflection of about 5, which results in opening and misalignment at the flexible joint. The width of the damaged zone of the articulated system tunnel is about 0.44 to 0.57 times that of the continuous tunnel. Compared to continuous tunnels, the articulated design significantly reduces the axial strain response of the tunnel lining, but increases the circumferential tensile strain at the tunnel crown and invert. It is concluded that articulated design provides an effective measure to reduce the extent of damage in mountain tunnel.

Headnote

Abstract

In the seismic mountainous regions such as western China, it is usuallly inevitable to construct tunnels near active fault zones. Those fault-crossing tunnel structures can be extremely vulnerable during earthquakes. Extensive experimental studies have been conducted on the response of continuous mountain tunnels under reverse and normal fault movements, limited experimental investigations are available in the literatures on mountain tunnels with special structural measures crossing strike-slip faults. In this study, a new experimental facility for simulating the movement of strike-slip fault was developed, accounting for the spatial deformation characteristics of large active fault zones. Two groups of sandbox experiment were performed on the scaled tunnel models to investigate the evolution of ground deformation and surface rupture subjected to strike-slip fault motion and its impact on a water conveyance tunnel. The nonlinear response and damage mechanism of continuous tunnels and tunnels incorporated with specially designed articulated system were examined. The test results show that most of slip between stationary block and moving block occurred within the fault core, and significant surface ruptures are observed along the fault strike direction at the fault damage zone. The continuous tunnel undergoes significant shrinkage deformation and diagonal-shear failure near the slip surface and resulted in localized collapse of tunnel lining. The segments of articulated system tunnel suffer a significant horizontal deflection of about 5, which results in opening and misalignment at the flexible joint. The width of the damaged zone of the articulated system tunnel is about 0.44 to 0.57 times that of the continuous tunnel. Compared to continuous tunnels, the articulated design significantly reduces the axial strain response of the tunnel lining, but increases the circumferential tensile strain at the tunnel crown and invert. It is concluded that articulated design provides an effective measure to reduce the extent of damage in mountain tunnel.

Keywords: Tunnel engineering; Strike-slip fault; Model test; Articulated design; Damage mechanism

1 Introduction

Long-extended highway, railway and water delivery tunnels, as critical underground structures, have incomparable advantages over other aboveground engineering structures in overcoming terrain obstacles, shortening distances and protecting ecological environment. In the seismic active zones, such as southwestern China, the wide-spread distribution of deep and large active faults as well as associated seismic and geological hazards become inevitable challenges during the route planning, design, construction and operations of mountain tunnels (Zhang et al., 2022). Four catastrophic earthquakes, 1999 Chi-Chi Earthquake (Wang et al., 2021), 2008 Wenchuan Earthquake (Li, 2012), 2016 Kumamoto Earthquake (Zhang et al., 2018) and 2022 Menyuan Earthquake (Chen et al., 2023; Li et al., 2022), which were induced by fault ruptures, causing severe damage to structures especially long extended mountain tunnels close to the fault damage zones (Jaramillo, 2017; Lai et al., 2017; Roy & Sarkar, 2017; Yu et al., 2017). Seismic ground shaking and fault tectonic movements are the two main reasons of severe seismic damage to underground structures (Dowding & Rozen, 1978; Gao et al., 2021; Huang et al., 2017; Liu et al., 2021; Qiao et al., 2022). The transient propagation of ground motion causes wide-spread slight to medium structural damages to the mountain tunnels, which are usually repairable after the earthquakes, as shown in Fig. 1(a). However, fault tectonic movements can induce locally concentrated devastating structural failure of underground tunnels (usually within 100 m), as shown in Fig. 1(b).

In view of the serious threat of tectonic fault rupture to underground lifeline structures, Burridge et al. (1989) conducted a series of centrifugal tests using earthquake modeling apparatus at California Institute of Technology to investigate the response characteristics of a tunnel under ground shaking and fault movement. The test results showed that concrete tunnels would fail even under small fault displacements, thus continuous steel lining was recommended as a feasible measure. Recently, several centrifuge tests were performed to study the effect of dip-slip fault rupture propagation through soil on the deformation of continuous and shield tunnels. It was found that continuous tunnels are irreparably damaged by large ground displacements induced by normal faulting (Cai et al., 2019; Sabagh & Ghalandarzadeh, 2020a). The shield tunnel exhibits obvious deformation of the rings under fault movement, and the soil pours into the tunnel through the separation between rings (Kiani et al., 2016a, 2016b). As the case of centrifuge testing, sandbox tests were also dedicated to exploring the effects of faulting (Ahmadi et al., 2018). Recently, Liu et al. (2015b) conducted studies on the effects of normal fault movements on continuous mountain tunnels based on scaled 1g physical model tests, and concluded that the tunnels were susceptible to bending or shearing failures due to large tectonic deformations. Cui et al. (2022) adopted small-scale model tests to investigate the characteristics of a mountain tunnel under strike-slip fault movement and concluded that circular and longitudinal cracks induced by fault movement are the main damage modes of the structure. Numerical simulations can carry out parametric studies in a much shorter period of time than laboratory experiments, and are therefore widely used in studies investigating the effects of fault-tunnel interactions. Ma et al. (2019) proposed a discrete-continuum coupling approach for investigating the interaction between normal fault and mountain tunnels, and found that the affected region of the tunnel was not correlated with the magnitude of fault displacement. Sabagh and Ghalandarzadeh (2020b) established three-dimensional finite element model to analyze the effects of fault angle and tunnel design parameters on the structural internal force subjected to reverse fault movement, and concluded that the fault angle of 60 is the most unfavorable to the tunnel response. Qiao et al. (2022) used ABAQUS to evaluate the longitudinal response of tunnels under normal fault movement and discussed the results of parametric studies of four critical factors.

To cope with the threat of seismic faults to tunnel structures adjacent to them, special structural measures are usually adopted. Articulated design has been proven an effective strategy for mitigating faulting-hazard. The articulated design is to separate the tunnel lining within the active fault zone and its influence area into several segments through flexible joints, which can increase the flexibility of the tunnel and thus accommodate the fault movement in a ductile manner. Under the effect of fault stick–slip or long-term creep-slip, the deformation of the flexible joint limits the damage to tunnel lining to a localized extent, avoiding the development of irreversible structural damage and thus reducing the cost of post-disaster recovery. 1g physical model tests are the most commonly used methods to investigate the mitigation effect and mechanism of the articulated design. Based on sandbox tests, Liu et al. (2015a) investigated the damage pattern and mechanism of mountain tunnels with articulated design subjected to reverse fault movement, and the test results showed that the damage of tunnels with articulated design was concentrated at the joints, while the damage suffered by local segments of tunnel lining was relatively minor. Wang et al. (2018) performed several sandbox tests to investigate the response characteristics of tunnels with different systems under normal fault movement, and concluded that the combined measures of dislocation reducing layer with flexible joints can effectively reduce the structural damage risk of the tunnel lining subjected to fault movement. Shen et al. (2020) and Yan et al. (2020) evaluate the damage mechanism of sectional tunnels with the flexible joint subjected to normal fault movement and seismic motion using shaking tables and commercial program ABAQUS, and concluded that tunnels was more susceptible when subjected to fault movement than seismic shaking. Wang et al. (2022) conducted a large-scale model test to explore the ground displacement and failure mechanism of articulated system tunnel under normal fault rupture, and found that the sectional tunnel lining exhibited an S-shaped displacement mode along the longitudinal direction. Xia et al. (2022) proposed a quantitative calculation method for the articulated design in fault-crossing tunnels subjected to reverse fault movement, and verified it using 1g physical model test and numerical analysis.

Remarkable achievements have been made to facilitate the understanding of mechanical response of tunnels under different types of faulting. Besides, different seismic damage mitigation strategies have been proposed in those studies to provide guidance for the design and construction of underground tunnels. It can be noticed that most of the experimental studies so far have focused on dip-slip faulting, while the experimental studies on the response of tunnels under strike-slip faulting are still insufficient. The design of the sandbox in experiment to reshape the fault zone architecture is a shortcoming in the current study. Basically, faults are composed of a fault core and the surrounding damage zone. Fault cores are generally composed of slip surfaces as well as faulted rock formed by intense shearing. The surrounding damage zones are tectonic structures that contain subsidiary minor faults, fractured rock masses and deformation bands (Torabi & Berg, 2011). A three-dimensional system of damage zone-fault core should be constructed in the experimental study. During fault propagation, not only does slip occur in the fault core but also deformation exists in the surrounding damage zone. Thus, this deformation pattern needs to be realized by special design of the fault region in the sandbox with larger scales. Another shortcoming is that the nonlinear behaviors of the mountain tunnels with articulated design in the mitigation of structural damage, including shear deformation, horizontal rotation and failure, are still unclear under strike-slip fault movement.

To bridge the obvious gaps in previous research, this paper focuses on the nonlinear behavior of a typical mountain tunnel under strike-slip fault movement. The Xianglu Mountain Tunnel in central Yunnan Province, which is threatened by active seismic fault in the western region of China, was selected as the tunnel prototype. A 1∶40 reduced scaled test model was designed to simulate strike-slip fault movement. Two sets of 1g physical model tests with different tunnel configurations (i.e., continuous and articulated system tunnels) were conducted to investigate the ground deformation pattern and nonlinear behavior of the embedded mountain tunnels induced by strike-slip fault movement. The results of two scaled tests on continuous and articulated system tunnels under strike-slip fault movement are compared to evaluate the faulting-hazard mitigation effect of the articulated design on tunnel lining.

2 Case study

The Xianglu Mountain Tunnel is a hydraulic tunnel with a length of 63.426 km located in southwestern China, central Yunnan region. Many deep and large active faults present along the route of the Xianglu mountain tunnel, posing a serious threat to the safety of the structure (CISPDR, 2015). For example, F10 Longpan-Qiaohou fault (Fig. 2), F11 Lijiang-Jianchuan fault and F12 Heqing-Eryuan fault are three regional active faults of the Holocene, showing moderate to strong seismicity. In Fig. 2, P represents Permian system and b stands for basalt. Table 1 shows the characteristic parameters of active fault zones near the route of engineering project. The dip angles of active fault zones are distributed between 50 and 90, and are mostly between 70 and 90. The thicknesses of fault damage zone measured at different locations on the ground surface varying from several to and several kilometers, of which the most common ones are within 10–100 m. The tectonic rocks in active fault zones along the Xianglu Mountain Tunnel are primarily composed of fault breccia, limestone, mudstone, sandstone and cataclasite, as shown in Fig. 3. The fault breccias in the Longpan-Qiaohou fault zone and Lijiang-Jianchuan fault zone has poor cementation, as shown in Fig. 3(a) and (b). The grayish-white cataclasite in the Heqing-Eryuan fault zone exhibits poor overall integrity and softens after absorbing water, as shown in Fig. 3(c).

The potential fault movements are the primary threats to the tunnel during the construction and later operation. The drilling-blasting method was used in the construction of the tunnel portions crossing the fault damage zone. For the portions of tunnel located outside the fault damage zone, the tunnel boring machine (TBM) was employed to accelerate the construction process. The tunnel supporting system near the active fault zones contains both the primary and secondary linings. The primary lining includes shotcrete with a thickness of 0.25 m and the secondary lining consists of cast-in place concrete linings with a thickness of 0.60 m. The schematic of tunnel supporting system constructed by drilling-blasting method is shown in Fig. 4. The concrete used for the primary lining and secondary lining of the support are C25 and C30 respectively (the grade is consistent with GB 50010-2010: Code for design of concrete structures (MOHURD, 2010).

3 Experimental program

3.1 Generalized model of fault zone architecture

Two main categories of fault geo-mechanical models are available in the literatures (Stearns, 1978) in the simulation of the interaction between active faults and underground structures, as shown in Fig. 5. For the first case, the material properties in fault damage zone are roughly the same, and the thickness of the fault damage zone is small, which is usually simplified as a single rupture plane. The critical parameters affecting this type of fault geo-mechanical model include the normal stress across the surface and friction coefficient between layers. However, for most large fault zones that induce strong earthquakes, the thickness of the fault damage zone is usually larger than the diameter of the tunnel. Based on geological surveys, several scholars (Pei et al., 2015; Torabi & Berg, 2011) found that the fault damage zone consists of two parts, the fault core and surrounding damage zone, as shown in Fig. 5(b). In the fault core and damage zone model, most of the slips occur in the fault core during faulting. Furthermore, the surrounding damage zone also suffers considerable shear deformation during faulting. In this study, detailed geological investigations indicated that the active fault zones in the vicinity of the Xianglu Mountain Tunnel are fault core and damage zone model.

3.2 Design of strike-slip fault simulation facility

For the investigation of the interaction between underground tunnels and active faults, a fault simulation facility that reproduces the movement of active strike-slip fault was developed in this study. To better reflect the geological condition and interactions between underground structure and stratum as realistically as possible, the fault simulation facility was designed with full consideration of the deformation of rock masses in the fault zone during faulting. It should be pointed out that the fault simulation facility developed in this study mainly focuses on the design of fault region and the simulation of high geostress was not considered.

Figure 6 shows the strike-slip fault simulation facility, which consists of a sandbox with central movable frames, a quasi-static loading system and a data acquisition system. The loading system is composed of a reaction frame and a long-stroke hydraulic actuator. The data acquisition system consists of a computer, a data logger and a voltage regulator, as shown in Fig. 6(a). The sandbox is composed of a moveable box and a fixed box, a series of prefabricated rectangular frames with rollers at bottoms, a rigid lateraldisplacement constraint device and a rigid base plate, as shown in Fig. 6(b). The overall geometries of the sandbox are 311 cm in length, 160 cm in height, and 175 cm in width, as shown in Fig. 6(c). Figure 7 demonstrates the working mechanism of the sandbox. A detailed introduction is as follows.

The moveable box consists of a steel box and several steel rods at bottom. The dimensions of the steel box are 1.0 m (length) 1.6 m (height) 1.75 m (width). A series of steel rods with a diameter of 50 mm were arranged at the bottom of steel box, as shown in Fig. 6 (d). Meanwhile, these steels were placed on the rigid base plate. A loading plate was welded to the front side of the moveable box and lateral force can be applied to the moveable box by hydraulic jack. The bottom of the moveable box is designed to be moveable horizontally along the fault strike direction. During the test, the steel moveable box drives the rock mass inside it to follow the rolling of the solid round steel, thus achieving the simulation of the strike-slip fault movement. The tunnel scaled model inside the moveable box also moves with the deformation of the surrounding rock masses. The maximum displacement of the moveable box along the fault strike direction is approximately 10 cm.

The fixed box is made of steel plate and angles. The dimensions of the fixed box are the same as those of the moveable box. The bottom of fixed steel box is welded to the rigid base plate. Under strike-slip faulting scenario, the steel fixed box is restrained and remains stationary. Meanwhile, the rock mass and tunnel scaled model inside the steel fixed box also remain stationary.

A series of rectangular frames with the same geometries were designed and installed between the moveable and fixed sand box to simulate the shear deformation of the fault damage zone under strike-slip faulting. Each rectangular frame has two wheels at the bottom to achieve horizontal movement. By installing different numbers of rectangular frames, the thickness of fault damage zone model can be varied within the range of 0.25–1.25 m.

3.3 Design of reduced-scale fault-tunnel interaction models

Two scaled models of a mountain tunnel and rock masses in the strike-slip fault zones were designed and fabricated according to the law of similarity to reproduce similar structural response as the prototype. Considering the actual dimensions of the test model, the geometric similarity ratio CL is equal to 1/40. The width of fault damage zone is designed to be 0.25 m. The actual dimensions of the test model are 3.11 m (length) 1.6 m (height) 1.75 m (width). The similarity ratio of elasticity modulus CE is 1/60. To ensure that the strain characteristics and response of the scaled model are consistent with those of the prototype tunnel, the similarity ratio of strain Ce should be 1. Similarity ratios for other critical material properties, as listed in Table 2, are derived by dimensional analysis.

Composite lining, including the primary and secondary linings, was used in areas where prototype tunnel cross fault damage zones. During the test, if the primary and secondary linings were designed and manufactured separately, the thickness of the primary lining in the scaled model was 6.25 mm, which would make it difficult to ensure the quality and accuracy of model manufacturing. Therefore, combining the effects of primary and secondary linings and simplifying the composite lining to a single-layer lining in the test design is a commonly used approach adopted by scholars in similar research of fault-tunnel interactions (Cui et al., 2022; Shen et al., 2020; Wang et al., 2023). In this study, the composite lining was designed as a singlelayer lining of 0.021 m thickness based on the geometric similarity ratio of 1/40. The outer diameter of the tunnel lining was 0.25 m.

Post-earthquake reconnaissance showed that underground tunnels intersecting active fault zones are susceptible to structural damage. In this study, the tunnel lining structure model were made of non-linear materials that reflect the damage evolution and reproduce the damage mechanism of the tunnel structure under fault dislocation. The mix proportion of the tunnel lining materials was designed based on the similarity theorem. Gypsum, cement, barite powder, river sand, quartz sand, fly ash and lime are some of the commonly used materials in the proportioning scheme of tunnel lining structure in the research of fault-tunnel interaction (Cui et al., 2022; Liu et al., 2015b, 2022).

In this study, the barite powder and fine sand were used as the aggregate and the gypsum as cementing material to manufacture the scaled model of concrete lining, as shown in Fig. 8. The main function of barite powder is to increase the density of mixed materials. As a brittle material, gypsum is similar in texture to concrete, and its strength can be adjusted by adding different admixtures. Based on the similarity ratios for test model as listed in Table 2, the mix design of the tunnel lining material was carried out by orthogonal experiment, using barite powder, fine sand, high-strength gypsum, low-strength gypsum and water as the raw materials, and analyzed the effect of different proportion of raw materials on the mechanical properties of tunnel lining scaled model. Based on the laboratory test, the one that most conforms to the similarity ratio design is selected from different mix proportions. The weight ratio of river sand, high-strength gypsum, low-strength gypsum, barite powder and water is 12∶5∶5∶19∶23 for the tunnel lining scaled model. The physical and mechanical parameters of the tunnel lining scaled model are shown in Table 3. It should be noted that the theoretical value is calculated by dividing the prototype value by the similarity ratio of the corresponding physical quantity in Table 2. Error is calculated by dividing theoretical value by actual value and represents matching degree of model manufacture and theoretical design.

To reproduce the permanent ground deformation under the movement of strike-slip fault, the developed materials need to reasonably reflect the properties of prototype rock masses. Considering the factors such as raw material properties, manufacture craft and cost, river sand was selected as aggregate, and high-strength gypsum and lime were used as cementing materials to prepare the rock mass. The weight ratio of river sand, lime, high-strength gypsum and water was 30∶4∶6∶4 for the intact rock mass. The weight ratio of river sand, lime, high-strength gypsum and water was 120∶7∶3∶13 for the fault damage zone. The physical and mechanical parameters of rock masses are shown in Table 4.

3.4 Design of articulated system tunnel

Underground tunnels are particularly vulnerable to large tectonic deformations induced by seismic fault movement. Table 5 summarizes the mitigation methods that are generally considered effective for underground tunnels. The over-excavation and articulated design are two of the most commonly used methods in engineering practice. The overexcavation method will significantly reduce the seismic risk to the structure, but the costs of the project may significantly increase, especially when the fault damage zone traversed by the tunnel is comparatively long. The principle for the articulated design of tunnel lining is to mitigate the hazards of fault movement without significantly increasing the cost of the project. Therefore, an articulated design was selected in this study as a countermeasure for the Xianglu Mountain Tunnel.

The articulated underground tunnels accommodate the fault displacement by providing a series of ductile joints between adjacent linings. The length of tunnel lining segment has a significant influence on the faulting-hazard mitigation. From a theoretical point of view, smaller distance between ductile joints generally lead to better performance (Hashash et al., 2001). However, the integrity and waterproofing requirements of the tunnel lining during construction and operation should be also considered. The articulated system tunnel is arranged in the fault damage zone, and the region close to the boundary between fault damage zone and intact rock. Furthermore, in areas significantly affected by active faulting, the length of tunnel lining segment should be smaller. The arrangement of lining segments of the articulated design method during the test is shown in Fig. 9. The length of lining segments in the articulated design are approximately 0.3–2.0 times the outer diameter of the tunnel (Shahidi & Vafaeian, 2005; Wang et al., 2022; Zaheri et al., 2020). In this study, the length of lining segments of prototype tunnel with articulated design in the fault damage zone was 4.0 m, i.e., 0.4 times the tunnel outer diameter. The length of corresponding 1∶40 scaled model of tunnel lining segments for the test was 0.1 m. For the regions close to the fault damage zone, the length of lining segments of prototype tunnel with articulated design was 8.0 m and the length of corresponding scaled model of tunnel lining segment was 0.2 m. In the region far from the fault damage zone, the continuous tunnel lining model was employed.

In the articulated system model, a T-shaped elasticity rubber belt was used to connect adjacent lining segments. The rubber belt has an inner diameter of 0.25 m and a thickness of 0.01 m, as shown in Fig. 9. The mechanical parameters of lining articulated materials are listed in Table 6.

3.5 Boundary effects on the model test

In order to investigate the influence of boundary effects on the tunnel response under strike-slip fault movement, models 1 and 2 were established by using finite element program ABAQUS. Model 1 has dimensions of 3.11 m (length) 1.75 m (width) 1.6 m (height), which is the same as the actual geometry of the model in the test, as shown in Fig. 10. The dimensions of model 2 are increased by 2 m along the length, with overall dimensions of 5.11 m (length) 1.75 m (width) 1.6 m (height). The width of the fault damage zone is 0.25 m. The angle between the fault strike direction and tunnel axis is 70. The elasticperfectly plastic Mohr–Coulomb model was employed for the intact rock and fault damage zone. The tunnel lining is simulated using the elastic constitutive model. The material parameters in the numerical model are consistent with the actual parameters of the material in the test. Binding constraints were used between the outer surface of tunnel lining and surrounding rock mass to simulate their synergistic movements during faulting. To simulate the movement of strike-slip fault, a horizontal displacement along the fault strike direction is applied to the external surfaces of the moving block.

Figure 11 shows the displacement and principal stress response of the tunnel lining for models 1 and 2. A comparison of the tunnel response between model 1 and model 2 shows that the displacement pattern and internal force distribution of the tunnel lining are basically the same for different model sizes. It can be concluded that the length of the sand box could eliminate the influence of boundary effects on the test results. It should be noted that the developed numerical model was also used in the verification of the reliability of test results in the following sections.

3.6 Model preparation and test setup

In the preparation of the similarity materials for the rock masses, a concrete blender was adopted to mix raw materials such as the fine sand, lime, gypsum, water and retarder. Figure 12 shows the model casting process of rock masses and the installation of the tunnel lining model. The casting of rock masses can be summarized as the following two steps. (1) A tarpaulin was firstly laid inside the sandbox, and the fault damage zone was separated from the intact rock mass by two wooden boards, as shown in Fig. 12(a) and (b). The intact rock mass was cast layerby-layer with a thickness of 5.0 cm. Each layer was manually compacted throughout the sandbox. (2) The previously installed wooden boards in the fault damage zone were removed when the model for the intact rock masses were fully compacted to a height of 20 cm. Next, the fault damage zone was cast into the box layer by layer, and a 10 mm thick wooden board was arranged in the middle of the fault damage zone to represent fault core, as shown in Fig. 12(c). The fault core was made by thoroughly mixing fine sand with sawdust in a mass ratio of 5∶1. The cohesion of the fault core was 0. The continuous and articulated system tunnel models were installed at a height of 50 cm from the base of the sandbox, as shown in Fig. 12(d).

Six displacement transducers are mounted on the front of the sandbox and orientated to measure the permanent ground deformation developed in the fault damage zone during strike-slip fault movement, as shown in Fig. 13(a). The displacement transducers used in the test were made by Miran Technology Co., Ltd. (product model: KTR11150 mm), with a measurement range of 150 mm and accuracy of 0.01 mm. To measure the axial and circumferential strains of the tunnel lining, 12 strain gauges were attached to the vault, crown, springing line, knee and shoulder of each critical cross-section for the tunnel specimen, as shown in Fig. 13(b). The spacing of those critical cross-sections along the tunnel axial is 8–30 cm, as shown in Fig. 13(c) and (d). The strain gauge used in the test is made by China Academy of Building Research (product model: BE1205AA), with a nominal resistance of (120.6 ± 0.1) X and strain gauge sensitivity modulus of 2.20 ± 1%.

The lateral displacements were applied to the moveable box to simulate the strike-slip faulting scenario. The magnitude of lateral displacement was applied using a longstroke hydraulic actuator. The hydraulic actuator was connected to the reaction frame, which was fixed to the strong floor through two post-tensioned anchors with a diameter of 70 mm. The lateral loading was incrementally applied in a series of steps during the experiment. The maximum horizontal movement of the moveable box was equal to 50 mm, achieved in a sequence of 10 steps. A quasi-static loading protocol was adopted in the experiments with a relatively low loading rate of 0.5 mm/min to remove the dynamic effects. The horizontal displacement of the moveable box was monitored by displacement transducers during lateral loading. The intermediate time between each loading step is 15–20 min to take photos of the surface rupture and tunnel lining interior.

4 Experimental results

4.1 Surface rupture of rock mass

Figure 14 shows the rupture characteristics of rock mass surface under different magnitudes of fault displacement, Df. Before loading, there were no visible cracks on the ground surface of rock mass, including the fault damage zone and the intact rock mass, as shown in Fig. 14(a). When Df = 15 mm, the fault rupture induced by strikeslip fault movement can be observed on the surface of rock mass, as shown in Fig. 14(b). The rupture trace extended from the left side of the sandbox, i.e., the side where the load was applied, to the middle of the sandbox along the fault core. The rupture length at the ground surface was approximately 65–80 cm. When Df sequentially increased to 25 mm, as shown in Fig. 14(c), the first rupture continued to develop towards the right side of sandbox along the fault core and the length increased to 95–110 cm. The collapse of rock mass occurred in adjacent to the fault core. When Df further increased to a target magnitude of 50 mm, the rupture trace extended from the left to the right side of the sandbox along the fault core, as shown in Fig. 14(d). Significant ground deformation was observed between the rock masses on both sides of the fault core. In addition, during the whole test process, all the observable surface fractures concentrated in the fault damage zone and the rock mass outside the fault damage zone remained almost intact.

4.2 Displacement response of rock mass

Figure 15 shows the results of displacement response at different locations monitored by the external displacement transducers with the increase of the fault displacement. Constraining frames No. 1 and No. 2 are on the right side of the fault core, adjacent to the fixed box. Constraining frames No. 3 and No. 4 are on the left side of the fault core, near the moving box. A clear gradient change of rock lateral displacement at the fault core can be obviously seen from Fig. 15. The rock displacement propagates from the moving box to the constraining frame No. 3 in a linearly decreasing form, while it decreases rapidly when passing from the constraining frame No. 3 to the constraining frame No. 2 and tends to zero when passing to the constraining frame No. 1. Overall, the rock mass inside the moveable box, constraining frames No. 3 and No. 4 undergoes significant horizontal movement, yet the rock mass inside the fixed box and constraining frame No. 1 remains in place during the test.

Figure 16 plots the ratio of relative displacement between adjacent components of the box to the total fault displacement for the cases of Df = 25 mm and Df = 45 mm, respectively. The area enclosed by the solid yellow line represents the ratio of horizontal fault displacement regulated by the fault damage zone. The relative displacement occurring at the fault core (between constraining frames No. 2 and No. 3) account for more than 70% of the total fault displacement, while the relative displacement at other position account for less than 30%, which indicates that the closer the tunnel lining to the fault core, the higher the threat of fault movement. The displacement of rock mass inside the fault damage zone accounts for more than 85% of the total fault slip, indicating that most of the fault slip are accommodated in the fault damage zone. In addition, the relative displacement at the interface between the moveable part and the fault damage zone (between the moveable box and the constraining frame No. 4) is greater than that at the interface between the fixed part and the fault damage zone (between the fixed box and the constraining frame No. 1).

In summary, under strike-slip fault movement, most of the rock slip occurs in the fault core. The thickness of fault core is commonly smaller than that of the surrounding damage zone, and thus it exhibits the largest magnitude of deformation. A small portion of the rock slip is distributed in the fault damage zone that surrounds the fault core. In addition, slip of the rock mass are likewise observed at the interface of intact rock mass and fault damage zone.

4.3 Comparative analysis of response of tunnels with different system

4.3.1 Comparative of macroscopic damage phenomena of tunnel structure

Figure 17 compares the evolution of macroscopic damage inside the lining of continuous tunnel and articulated system tunnel with the increase of fault displacement Df. Before loading, i.e., Df = 0 mm, there were no visible cracks occurred in the tunnel linings of either of these systems, indicating that the designed test model can bear the initial in-situ stress of the surrounding rock mass. When Df = 5 mm, circumferential cracks first formed and extended from the left knee to the vault inside the continuous tunnel. Under the same test case, there were no visible cracks inside the lining of the articulated system tunnel. When Df sequentially increased to 15 mm, the damaged area on the left side of the continuous tunnel was further enlarged, and the lining surface was uplifted. In the articulated system tunnel, a tiny crack appears at the left knee of segment A5. When Df further increased to 30 mm, concrete collapse occurred on the left sidewall of the continuous tunnel accompanied by the exposure of the iron wire. In the articulated system tunnel, the length of the cracks formed earlier at the left knee of segment A5 of the tunnel lining increased. Meanwhile, new micro-cracks formed at the left springing line of segment A4 of the tunnel lining, and slight concrete spalling appeared at the right shoulder of the lining internal surface. When Df increased to target displacement of 50 mm, excessive fault movement led to large-scale collapse of continuous tunnel on the left side of the lining. The width of severe damaged zone along the tunnel axis direction exceeds 20 cm. In the articulated system tunnel, segment A4 of the tunnel lining suffered a partial fall of the concrete material at its right shoulder. In addition, there is an obvious dislocation of the flexible joint between segments A4 and A5, and segments A5 and A6 of the tunnel lining.

Figure 18 shows the deformation and damage patterns of continuous tunnel lining. At the ending of faulting, the continuous tunnel model shows significant tensile cracks at the right of lining on the movable side and the left of lining on the fixed side, as shown in Fig. 18(a). Tensile damage caused partial collapse of the interior of tunnel lining. Furthermore, both numerical simulations and test results show that in the area where the tunnel crosses the fault damage zone, the lining is subjected to horizontal compression resulting in shrinkage deformation and significant diagonal-shear failure at the tunnel vault. For the articulated system tunnels, segment A5 shows a horizontal deflection of about 5, which results in opening and misalignment at the flexible joint, as shown in Fig. 19(a). From the numerical simulation as shown in Fig. 19(b), significant rotation of the tunnel lining occurs in segments A4, A5 and A6 and caused deformation at the joints, which is the same as the damage patterns of the tunnel lining obtained by the scaled model test. Overall, the results of the numerical simulation are basically consistent with those of the scaled model test, which verifies the reliability of the test results.

Based on the comparison of macroscopic damage of tunnels in different systems, it can be found that the damage extent of the continuous tunnel is more serious than that of the articulated system tunnel. Under strike-slip faulting, the continuous tunnel suffered a severe collapse, causing the tunnel to completely lose its function and closed to traffic. The articulated system tunnel accommodates part of the ground displacement through the misalignment of flexible joints, thereby mitigating damage to the tunnel lining. Besides, the damage of articulated system tunnel model was distributed in segments A4 and A5 with a total length of 20 cm. The width of the damaged zone in continuous tunnel model was 35–45 cm. It can be seen that the width of the damaged zone of the articulated system tunnel is about 0.44–0.57 times that of the continuous tunnel.

4.3.2 Comparative of strain response

Figure 20 shows the comparison of axial strain responses of the continuous tunnel and articulated system tunnel at the crown, invert, and left and right springing lines with five different magnitude of fault displacements (Df = 5, 10, 15, 20 and 25 mm). The black and red lines represent continuous and articulated system tunnels respectively. The positive and negative values denote tensile and compressive strains respectively.

For the continuous tunnel, the axial strain fluctuates violently within a width of about 20 cm from both sides of the fault core under strike-slip fault movement. The tensile strain exceeds the design strength of the material, and it can be seen that tensile damage occurs at the tunnel crown. At the tunnel springing line, the axial strain is distributed anti-symmetrically on both sides of the fault core. Significant tensile damage zones are formed at the left and right springing lines of tunnel lining. For the articulated system tunnel, the axial strain induced by the strike-slip fault movement is concentrated in tunnel invert of segment A5 with a length of 10 cm that intersects the fault core.

Comparisons between the peak axial strains of continuous tunnel and articulated system tunnel under different magnitude of fault displacements are illustrated in Fig. 21 to further evaluate the influences of flexible design on the underground tunnel-rock mass interaction effects. As anticipated, compared with the continuous tunnel, the peak axial strains at the tunnel crown and springing line of the articulated system tunnel are significantly reduced. The peak axial strains at tunnel crown and springing line are 97 and 246 le, respectively, in the articulated system tunnel model. Those in the continuous tunnel model are 1740 and 1531 le, respectively, which are more than 5 times larger.

Figure 22 illustrates the distribution of the induced axial strain at two springing lines of tunnel lining model under strike-slip fault movement. The black and red shadings represent the axial strain induced in the continuous and articulated system tunnel models, respectively. X represents the horizontal distance from the tunnel cross-section to the fault core. The effect of strike-slip fault movement on the strain response of tunnel lining is minimal at distances greater than 40 cm from the fault core. At the movable side, when the cross-section of continuous tunnel lining is close to the fault damage zone, the right springing line is subjected to tension while the left springing line is subjected to compression. At the fixed side, the distribution of the axial strain exhibits compression of the right springing line and tension of the left springing line when getting close to the fault damage zone. In practice, the continuous tunnel lining is vulnerable to damage undergo excessive axial tensile strain. When the articulated design is adopted, the axial strain distribution is significantly different from that of the continuous tunnel model, with only axial tensile strain occurring in the cross-section close to the fault damage zone. Comparison of the strain induced at the springing line of tunnel lining along the longitudinal direction suggest that the articulated design can improve the tensile properties of tunnel lining and avoid tensile cracking damage under strike-slip fault movement.

Figure 23 presents the distribution of circumferential strain along the tunnel axial direction for different systems of tunnel lining. The black lines represent the continuous tunnel, while the red lines stand for the articulated system tunnel. As can be observed from Fig. 23, significant circumferential strain is induced near fault damage zones at -15 cm < X < 15 cm under strike-slip faulting. The circumferential compressive strain is induced at two springing lines of continuous tunnel, while significant circumferential tensile strain is induced at the crown of articulated system tunnel. As the monitoring location moves away from the fault damage zone, the circumferential strain of the tunnel lining in both the stationary and moving blocks gradually converges to zero.

The monitoring location within the fault damage zone are selected for the analysis of circumferential strain distribution of tunnel lining cross-section, as shown in Figs. 24 and 25. The positions of the red dot in Figs. 24 and 25 represent the different regions at tunnel cross-section. Based on the arrangement scheme of the strain sensors (see Fig. 13), sections X = 0.05 m and X = -0.05 m are selected for the continuous tunnel model and section X = 0 for the articulated system tunnel model. The magnitude of fault displacement is 25 cm. It can be seen from Fig. 24 that strike-slip fault movement induces significant circumferential compressive strain at the springing line and knee in continuous tunnel model. Furthermore, circumferential tensile strain is generated at the crown and invert in continuous tunnel model. However, the magnitude of circumferential tensile strain is significantly smaller than the compressive strain. For the articulated system tunnel, circumferential compressive strain is observed from the shoulder to the knee, as shown in Fig. 25. While at the tunnel crown and invert, circumferential tensile strain is observed, and the induced circumferential tensile strain at the tunnel crown is substantially higher than in other areas of the tunnel lining model.

Figure 26 compares the peak circumferential strain of the continuous and articulated system tunnels under different magnitude of fault displacements. The peak circumferential compressive strain of the continuous tunnel model is 1033 le, which is larger than 478 le that induced in articulated system tunnel model. However, the peak circumferential tensile strain at the crown of articulated system tunnel model is equal to 2056 le, which is approximately 10 times the strain in continuous tunnel model of 199 le. It is evident that the significant reduction in the longitudinal length of the tunnel lining with the articulated design would result in an increase in local stiffness. At the crown and invert of the tunnel with articulated system, the shear force induced by the horizontal displacement of strikeslip fault movement leads to a significant increase in the circumferential strain, indicating that the structure of articulated system would suffer more pronounced tension-shear damage with circumferential cracking at tunnel crown and invert.

5 Conclusions

This study presents three-dimensional sandbox experiments to examine the deformation of rock masses under strike-slip fault movement and its impacts on a typical mountain tunnel. A strike-slip fault simulation facility consisting of a sandbox with movable central frames, a quasistatic loading system and a data acquisition system was designed to reproduce the fault movement mechanism with explicit consideration of the width of fault damage zone.

Two reduced-scaled models of the fault and tunnels was manufactured consideration of nonlinearity of fault rupture and fault-tunnel interaction. The continuous and articulated tunnel-fault-rock system were constructed in the sandbox. The performance of those two systems subjected to strike-slip fault movement were systematically assessed to validate the proposed faulting-hazard mitigation measure of articulated design for fault-crossing tunnel. Moreover, the surface rupture and deformation gradient of rock mass are used to define the fault-affected zone. The nonlinear response and damage mechanism of the tunnel structures are investigated to facilitate the understanding of the interaction mechanism between the ground deformation and the embedded tunnel. The primary conclusions of this study are summarized as follows.

(1) The ground deformation induced by the strike-slip fault movement is propagated from the moveable box to the fixed box via the fault damage zone, and produces an obvious surface rupture at the weak stratigraphic unit (i.e., fault core) inside the fault damage zone. The final surface rupture direction is consistent with the fault strike direction.

(2) After strike-slip fault movement, ground deformation occurring in the fault damage zone accounts for more than 85% of total fault displacement, with more than 70% being attributed to the deformation of fault core. While the proportion of ground deformation at the interface between the intact rock mass and fault damage zone is less than 15% of the total fault displacements. The ground deformation gradients are greatest at the fault core and decreases monotonically with increasing distance from the fault core, indicating that there is the highest damage risk of the tunnel at fault core.

(3) The movement of strike-slip fault leads to cracking and spalling of continuous tunnel from the knee to the shoulder. The extent of damage along the longitudinal direction of continuous tunnel is about 3545 cm. Heavy tensile damage leads to loss of functionality and structural failure of the tunnel. However, with an articulated design, the deformation at the flexible joints can accommodate large lateral displacements, thus effectively reducing the extent of damage to the structure, allowing the tunnel capacity to undergo only a modest reduction.

(4) For continuous tunnel, the movement of strike-slip fault with a crossing angle of 70 leads to large axial strains in the vicinity of the fault damage zone for about 40 cm in length. The axial strain is characterized by an antisymmetric distribution at the tunnel springing line and bending strain state plays a dominant role. For articulated system tunnel, large circumferential strains are induced at tunnel crown and invert of the two lining sections with a total length of 20 cm near the fault core, while the axial strains are insignificant. The articulated system tunnel primarily suffers a local shear failure under strike-slip fault movement.

(5) Arranging the tunnel articulated system near the fault core can better accommodate the fault movement and is an effective strategy for disaster mitigation. To avoid the shear damage that occurs in lining segments in articulated systems, consideration should be given to improving the stiffness of tunnel lining in the prototype project. In addition, considering that the flexible joint would suffer significant misalignment during fault movement, special designs need to be carried out, such as the installation of water stop belts that can be adapted to large deformations.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

CRediT authorship contribution statement

Zhen Wang: Writing – original draft, Validation, Methodology, Data curation. Zilan Zhong: Writing – review & editing, Methodology, Investigation. Mi Zhao: Writing – review & editing, Methodology, Investigation, Conceptualization. Xiuli Du: Visualization, Conceptualization. Jingqi Huang: Writing – review & editing, Validation, Methodology. Hongru Wang: Software, Data curation.

Declaration of competing interest

Mi Zhao is an early career editorial board member for Underground Space and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

Acknowledgement

The authors would like to thank the National Key R&D Program of China (Grant No. 2022YFC3004300) and the National Natural Science Foundation of China (Grant No. 52220105011) for their financial support of the present research. Also, the authors would like to thank the Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology for providing the facilities.

Sidebar

Received 4 February 2024; received in revised form 2 July 2024; accepted 11 July 2024

Available online 3 October 2024

Footnote

* Corresponding author.

E-mail address: [email protected] (M. Zhao).

Peer review under the responsibility of Tongji University

References

References

Ahmadi, M., Moosavi, M., & Jafari, M. K. (2018). Experimental investigation of reverse fault rupture propagation through wet granular soil. Engineering Geology, 239, 229–240.

Burridge, P. B., Scott, R. F., & Hall, J. F. (1989). Centrifuge study of faulting effects on tunnel. Journal of Geotechnical Engineering, 115(7), 949–967.

Cai, Q. P., Peng, J. M., Ng, C. W. W., Shi, J. W., & Chen, X. X. (2019). Centrifuge and numerical modelling of tunnel intersected by normal fault rupture in sand. Computers and Geotechnics, 111, 137–146.

Chen, P. L., Geng, P., Chen, J. B., & Gu, W. Q. (2023). The seismic damage mechanism of Daliang tunnel by fault dislocation during the 2022 Menyuan Ms 6.9 earthquake based on unidirectional velocity pulse input. Engineering Failure Analysis, 145, 107047.

CISPDR (Changjiang Institute of Survey, Planning, Design and Research). (2015). Feasibility study report of the Xianglu Mountain Tunnel of water diversion project in central Yunnan Province. (in Chinese).

Cui, Z., Li, J. H., Fu, X. W., Shen, Q., Zhou, G. X., Ma, Y. L. N., & Wang, T. Q. (2022). Evaluating the response of a tunnel subjected to strike-slip fault rupture in conjunction with model test and hybrid discrete-continuous numerical modeling. Rock Mechanics and Rock Engineering, 55, 4743–4764.

Dowding, C. H., & Rozen, A. (1978). Damage to rock tunnels from earthquake shaking. Journal of the Geotechnical Engineering Division, 104(2), 175–191.

Gao, Z. D., Zhao, M., Huang, J. Q., Du, X. L., & Wu, L. H. (2021). Three-dimensional nonlinear seismic response analysis of subway station crossing longitudinally inhomogeneous geology under obliquely incident P waves. Engineering Geology, 293, 106341.

Hashash, Y. M., Hook, J. J., Schmidt, B., John, I., & Yao, C. (2001). Seismic design and analysis of underground structures. Tunnelling and Underground Space Technology, 16(4), 247–293.

Huang, J. Q., Du, X. L., Zhao, M., & Zhao, X. (2017). Impact of incident angles of earthquake shear (S) waves on 3-D non-linear seismic responses of long lined tunnels. Engineering Geology, 222, 168–185.

Jalali, M. (2018). Tunnel rehabilitation in fault zone using sequential joints method-case study: Karaj water conveyance tunnel. International Journal of Mining and Geo-Engineering, 52(no. 1), 87–94. Jaramillo, C. A. (2017). Impact of seismic design on tunnels in rock-Case histories. Underground Space, 2(2), 106–114.

Kiani, M., Akhlaghi, T., & Ghalandarzadeh, A. (2016a). Experimental modeling of segmental shallow tunnels in alluvial affected by normal faults. Tunnelling and Underground Space Technology, 51, 108–119.

Kiani, M., Ghalandarzadeh, A., Akhlaghi, T., & Ahmadi, M. (2016b). Experimental evaluation of vulnerability for urban segmental tunnels subjected to normal surface faulting. Soil Dynamics and Earthquake Engineering, 89, 28–37

Lai, J. X., He, S. Y., Qiu, J. L., Chen, J. X., Wang, L. X., Wang, K., & Wang, J. B. (2017). Characteristics of seismic disasters and aseismic measures of tunnels in Wenchuan earthquake. Environmental Earth Sciences, 76(2), 76–94.

Liang, W. H., & Li, G. L. (2004). Tentative project of Wushaoling tunnel. Modern Tunnelling Technology., 41(2), 1–7 (in Chinese). Li, T. B. (2012). Damage to mountain tunnels related to the Wenchuan earthquake and some suggestions for aseismic tunnel construction. Bulletin of Engineering Geology and the Environment, 71(2), 297–308.

Li, Y. S., Jiang, W. L., Li, Y. J., Shen, W. H., He, Z. T., Li, B. Q., Li, Q., Jiao, Q. S., & Tian, Y. F. (2022). Coseismic rupture model and tectonic implications of the January 7 2022, Menyuan Mw 6.6 earthquake constraints from InSAR observations and field investigation. Remote Sensing, 14, 2111.

Liu, X. Y., Zhang, C. Q., Xiao, H. B., Zhou, H., & Chi, F. D. (2022). Deformation and failure characteristics of a deeply buried tunnel subjected to creep slip fault movement: Based on the engineering conditions of Yunnan water intake project. Bulletin of Engineering Geology and the Environment, 81, 322.

Liu, X. Z., Liu, J. D., Li, X. F., & Chen, G. F. (2015a). Experimental research on effect of anti-dislocation of highway tunnel lining with hinge joints in thrust fault. Chinese Journal of Rock Mechanics and Engineering, 34(10), 2083–2090 (in Chinese).

Liu, X. Z., Li, X. F., Sang, Y. L., & Lin, L. L. (2015b). Experimental study on normal fault rupture propagation in loose strata and its impact on mountain tunnels. Tunnelling and Underground Space Technology, 49, 417–425.

Liu, Z. X., Liu, J. Q., Pei, Q., Yu, H. T., Li, C. C., & Wu, C. Q. (2021). Seismic response of tunnel near fault fracture zone under incident SV waves. Underground Space, 6(6), 695–708.

Ma, Y. L. N., Sheng, Q., Zhang, G. M., & Cui, Z. (2019). A 3D discretecontinuum coupling approach for investigating the deformation and failure mechanism of tunnels across an active fault: A case study of Xianglushan tunnel. Applied Sciences, 9(11), 1–17.

MOHURD (Ministry of Housing and Urban-Rural Development of the People's Republic of China). (2010). GB 50010-2010: Code for design of concrete structures. Beijing: China Architecture & Building Press (in Chinese).

Pei, Y. W., Paton, D. A., Knipe, R. J., & Wu, K. Y. (2015). A review of fault sealing behaviour and its evaluation in siliciclastic rocks. EarthScience Reviews, 150, 121–138.

Qiao, Y. F., Tang, J., Liu, G. Z., & He, M. C. (2022). Longitudinal mechanical response of tunnels under active normal faulting. Underground Space, 7(4), 662–679.

Russo, M., Germani, G., & Amberg, W. (2002). Design and construction of large tunnel through active faults: A recent application. In Proceedings of the International Conference of Tunnelling & Underground Space Use, Istanbul, Turkey (pp. 1–14). Lombardi Engineering Ltd.

Sabagh, M., & Ghalandarzadeh, A. (2020a). Centrifugal modeling of continuous shallow tunnels at active normal faults intersection. Transportation Geotechnics, 22, 100325.

Sabagh, M., & Ghalandarzadeh, A. (2020b). Numerical modelings of continuous shallow tunnels subject to reverse faulting and its verification through a centrifuge. Computers and Geotechnics, 128, 103813.

Shahidi, A. R., & Vafaeian, M. (2005). Analysis of longitudinal profile of the tunnels in the active faulted zone and designing the flexible lining (for Koohrang-III tunnel). Tunnelling and Underground Space Technology, 20(3), 213–221.

Shen, Y. S., Wang, Z. Z., Yu, J., Zhang, X., & Gao, B. (2020). Shaking table test on flexible joints of mountain tunnels passing through normal fault. Tunnelling and Underground Space Technology, 98, 103299.

Stearns, D. W. (1978). Faulting and forced folding in the rocky mountain foreland. Geological Society of America, 151, 1–38.

Stirbys, A. F., Radwanski, Z. R., Proctor, R. J., & Escandon, R. F. (1999). Los Angeles metro rail project-geologic and geotechnical design and construction constraints. Engineering Geology, 51(3), 203–224.

Torabi, A., & Berg, S. S. (2011). Scaling of fault attributes: A review. Marine and Petroleum Geology, 28(8), 1444–1460.

Wang, D. Y., Cui, G. Y., Yuan, J. X., Zhu, Y. Q., Zhu, Z. G., Li, D., & Wang, H. F. (2018). Model tests on effect of dislocation reducing measures of stick-slip fault of tunnels. Chinese Journal of Geotechnical Engineering, 40(8), 1515–1521 (in Chinese).

Wang, Q., Geng, P., Li, P. S., Wang, T. Q., & Sun, W. H. (2023). Failure analysis and dislocation-resistant design parameters of mining tunnel under normal faulting. Engineering Failure Analysis, 143, 106902.

Wang, T. Q., Geng, P., Li, P. S., Wang, Q., & Wang, L. J. (2022). Deformation and failure of overburden soil subjected to normal fault dislocation and its impact on tunnel. Engineering Failure Analysis, 142, 106747.

Wang, T.-T., Kwok, O.-L.-A., & Jeng, F.-S. (2021). Seismic response of tunnels revealed in two decades following the 1999 Chi-Chi Earthquake (Mw 7.6) in Taiwan: A review. Engineering Geology, 287(2), 106090.

Xia, C., Sun, F. B., Zhou, Z. Q., Liu, T., & Qi, C. Z. (2022). Quantitative design method for anti-dislocation joints for tunnels passing through active faults. Tunnelling and Underground Space Technology, 124, 104489.

Yan, G. M., Shen, Y. S., Gao, B., Zheng, Q., Fan, K. X., & Huang, H. F. (2020). Damage evolution of tunnel lining with steel reinforced rubber joints under normal faulting: An experimental and numerical investigation. Tunnelling and Underground Space Technology, 97, 103223.

Yu, H. T., Yuan, Y., & Bobet, A. (2017). Seismic analysis of long tunnels: A review of simplified and unified methods. Underground Space, 2(2), 73–87.

Zaheri, M., Ranjbarnia, M., Dias, D., & Oreste, P. (2020). Performance of segmental and shotcrete linings in shallow tunnels crossing a transverse strike-slip faulting. Transportation Geotechnics, 23, 100333.

Zhang, D. L., Sun, Z. Y., & Fang, Q. (2022). Scientific problems and research proposals for Sichuan-Tibet railway tunnel construction. Underground Space, 7(3), 419–439.

Zhang, X. P., Jiang, Y. J., & Sugimoto, S. (2018). Seismic damage assessment of mountain tunnel: A case study on the Tawarayama tunnel due to the 2016 Kumamoto Earthquake. Tunnelling and Underground Space Technology, 71, 138–148.