2.1 Field investigations

The seismic damage investigation, which does not need to account for the scale effect, is generally the most straightforward approach to recognizing dynamic deformation and failure characteristics of tunnels under earthquake forces. Numerous experts and scholars have collected and collated the compiled data of underground structures across or near faults caused by previous major earthquakes. Table 3 lists tunnel damages across/near faults under strong seismic events from 1906 to 2023. Figure 4 illustrates seven forms of seismic damage characteristics shown by tunnels situated across or in proximity to faults. These historical records indicate that the seismic damages to tunnels across or near faults are mainly manifested as minor restorable damages, such as lining cracking, water leakage, and so on, to non-restorable damages such as structure dislocation and large-scale collapse. The degree of damage hinges on fault characteristics such as movement displacement, thickness, inclination degree, seismic waves, and the conditions of both lined structures and the rock mass strength (Dowding & Rozen, 1978; Jiang et al., 2010; Sharma & Judd, 1991). Figure 5 shows the four main factors affecting the extent of damage to tunnels within fault ground: tunnel structure, fault parameters, seismic waves, and stratum properties.

In addition, the spatial characteristics of seismic damage are determined, namely, the hanging wall effect. In the 1999 Chi-Chi earthquake investigation, much of the most and often serious damage occurred in the hanging wall, with less damage to the footwall (Wang et al., 2001). Likewise, Huang and Li (2008) also pointed out that geological disasters that occurred in the hanging wall were more intense through observation of geohazards triggered by the 2008 Wenchuan earthquake. It is thus recommended that more attention should be paid to the fortification of tunnels in areas where the hanging wall effect is prevalent.

2.2 Possible damage mechanisms

It can be expected that the damage in the portion of a fault-crossing tunnel subjected to seismic loading is more severe in the whole structure. However, this is not universally applicable, and the specific type of fault influences the damage response (Zhang et al., 2020). Tectonic earthquakes are characterized by two primary failure modes: first, ground shaking triggered by seismic waves, and second, permanent strata deformations induced by fault dislocation (Liu et al., 2015). The fault dislocation generally brings about catastrophic damage to tunnel structures, including vault collapse and lining dislocation, among other effects (Shen et al., 2014; Wang et al., 2022; Yu et al., 2016). Notably, it is crucial to distinguish the type of faults based on the fault dislocation for a while or induced seismic event potential, namely, active faults and inactive faults (Wu, 2019). Active faults are further classified as normal, reverse, and strike–slip faults based on the form of movement and stress regime (Amadei & Stephansson, 1997). Furthermore, the effects of active faults on stratigraphic stability also include the redistribution of the original stress field and the form of fault movement (Gao et al., 2020; Kiani, Akhlaghi, et al., 2016). Figure 6 displays the four categories of active faults.

During earthquakes, active faults generate considerable shear forces during the misalignment process, which may result in the tunnel being sheared off and collapsing on the misaligned surface. Without a doubt, the forced displacement destructive effect of the active fault is much greater than seismic waves (Wang et al., 2001). Additionally, the axial bending deformation of the tunnel can result in stress concentrations on both the internal and external surfaces of the tunnel lining on either side of the fault plane, along with the formation of tension and compression cracks (Figure 7a). In contrast, the inactive fault is described as a fault that is not expected to result in dislocation or seismic activity in the long term. The impact of inactive faults on the damage response of the lining structure is reduced, with the effect being comparable to that observed in fracture zones (Zhang et al., 2020). Figure 7b illustrates the damage mechanisms of tunnel lining in fault fracture zones. The loose earth pressure acting on the lining after an earthquake increases, and thus, minor damage arises, such as cracking, spalling, etc. Moreover, it should be noted that fault slippage may also emerge due to inconsistent movement of the surrounding rock in the fault fracture zone and hanging wall and footwall under seismic conditions. Meanwhile, collapse of weak regions of the lining can still take place, which is caused by the penetration of cracks and the plastic yielding of the fault. Overall, damage to tunnels caused by active faults is mainly attributed to the permanent displacement of the strata, while damage caused by inactive faults is due to the violent vibration of the surrounding strata. Consequently, fault zone and their movement characteristics are the focus of active fault investigations. The incident seismic wave propagation properties in poor geological conditions are the focus of investigations into inactive faults.

3.1 Simplified equivalent static analysis

The simplified analytical method enables the direct calculation of formulae for determining the internal forces and deformations of tunnels subjected to seismic action. Cross-fault tunnels are frequently subject to changes in their spatial configuration as a linear lifeline project, making assessment of their longitudinal mechanical response necessary. Two simplified analytical approaches to studying the longitudinal seismic response (Hashash et al., 2001) include the free-field deformation and ground–structure interaction methods. For the free-field deformation method, ground deformations in the absence of structure are chosen to impose on the structure. Indeed, this method may over- or underestimate structure deformation induced by seismic waves (Hashash et al., 2001). Instead, the ground–structure interaction method can consider the interplay between a structure and the surrounding ground based on the underground structure response controlled by site deformation, which is more widely applied in seismic analysis and design. The tunnel structure, whose axial length is much larger than its cross-sectional dimension, is usually treated as a long continuous elastic beam (Euler–Bernoulli or Timoshenko beam) acting on a linear elastic foundation (surrounding rock or soil). Various stiffness springs (i.e., transverse, axial, and vertical springs) represent the interaction between the tunnel and the foundation. During earthquakes, the damage caused by fault slip when underground structures cross active faults is much greater than seismic loading. Next, the forced displacement of the active fault is expressed as imposed spring displacements, including uniform fault displacements and nonuniform fault displacements. This simplified model typically assumes linear elasticity in tunnel lining and foundation while neglecting gravity, initial stress, and inertial forces.

The ground–structure interaction method has been widely put into practice in the structural response of underground pipelines subjected to fault movements. In 1975, Newmark and Hall (1975) accounted for a pipeline as a cable and first established a mechanical model to discuss the resistant capacity of the structure under strike–slip faulting. Thereafter, their pioneer's studies were extended by Kennedy et al. (1977, 1979). Wang and Yeh (1985) retrofitted the existing results by accounting for the bending rigidity of the structure, where the pipeline near the sliding surface and far from the sliding surface is simplified as constant curved beams and an elastic foundation beam, respectively (Figure 8). Based on the aforementioned elastic models, the applicability and reliability of analytical solutions were refined (Karamitros et al., 2007, 2011; Talebi & Kiyono, 2020, 2021; Trifonov & Cherniy, 2010, 2012). These results serve as a significant reference for the longitudinal response and failure mechanism of fault-crossing tunnels.

Table 4 summarizes a simplified equivalent static analysis for the mechanical response of fault-crossing tunnels. These analytical methods are principally predicated on various beam–spring models, whereby the tunnel is regarded as a beam model on a range of elastic foundation models, and they can be solved either directly or by using numerical methods such as the finite difference method (FDM) or Green's function. While the conventional Winkler foundation model assumes that foundation springs are independent of each other, it is still extensively used in existing studies. Based on the Timoshenko–Winkler model, Zhao et al. (2023) examined the structure–stratum interface tangential interaction by inflicting equivalent bending moments on the beam under the fault creeping. Their analysis was limited to tangential interactions within the fault zone rather than the whole tunnel model, constraining the analytical solution's applicability. In recent work, Xu et al. (2025) proposed a generalized solution for the longitudinal response of a tunnel inclined across a strike–slip fault, which takes into account the bending, tensile, and compressive deformation along the tunnel axis and the tangential contact conditions. Li, Li, et al. (2023) modeled longitudinal shear effects in shield tunnels under normal fault using horizontal subgrade springs, with circumferential joint plasticity, using the double broken line model.

Unlike Winkler's approach, the Pasternak model assumes the presence of a shear layer between the foundation spring and the long beam to address the nonlinear interaction between adjacent springs. It is capable of vertical shear deformation while remaining incompressible (Pasternak, 1954). Liu et al. (2020) divided the tunnel into three areas in the longitudinal direction, including the dislocation-affected zone, the transient zone, and the noninfluence zone. The double-parameter Pasternak elastic foundation beam was used for the calculation of deformation and stress (Figure 9). The longitudinal deflection of the tunnel structure resembles the dislocation, while it has a reverse deflection close to interfaces between the fault zone and the foot or hanging wall. Tao et al. (2022, 2023) expanded the previous study by combining the complementary error function to simulate free deformation of the ground surface when the tunnel structure across the overlying soil is under faulting. Figure 10 illustrates the mechanical response of the tunnels to faulting at different dip angles. The affected area and the peak value of the bending moment and shearing force are closely related to the inclination of the fault.

The above analytical solutions fail to reveal the frictional interactive stress and gap between the structure and the ground. Recently, Zeng et al. (2024) revisited previous research and proposed a new analytical method to focus on compressive and frictional behavior together. Meanwhile, Zeng also demonstrated that soil spring stiffness shows various distributions along the tunnel length rather than a constant value, necessitating further investigation to obtain a reasonable spring stiffness value.

Existing research has also been dedicated to special mechanical response issues, including the nonlinear displacement of a stratum (Yu et al., 2023; Zhang et al., 2024a), a tunnel with segmental flexible joints (Yan et al., 2022; Yu & Wei, 2023), a rectangular tunnel (Liu et al., 2025; Wang et al., 2023), nonlinear tunnel–stratum interaction (Zhang et al., 2024b), and a viscoelastic foundation (Yan & Zhao, 2023). Tang et al. (2024b) adopted a refined elastic beam model considering different tangential contact conditions to investigate the longitudinal response of the inactive fault-crossing tunnel under seismic waves. The transmissions and reflections of shear waves in the interfaces between the fault zone and intact rock were derived using the transfer matrix method effectively. The treatment of the tunnel–rock interface tangential interaction is similar to Zhao's work (Zhao et al., 2023).

Overall, the internal forces and displacements in the longitudinal direction of the tunnel by faulting are significantly influenced by several factors, including the shear stiffness of the foundations, the width and dip angle of faults, and the lining conditions. However, the elasticity assumption in the ground–structure interaction method may cause excessive calculation errors. Meanwhile, it is challenging to capture in detail the damage to the lining structure in the analytical solution. Elastic–plastic analysis can more realistically reflect the actual site conditions. The combination of numerical simulation and physical experiment allows the assumptions of the analytical solution to be overcome.

3.2 Analytic seismic analysis

Except for the fault dislocation, earthquake waves represent a critical factor in the seismic performance of the tunnel within an inactive fault ground. Decomposition and superposition of wave fields arise when seismic waves propagate to the interface of two media with different properties. Seismic waves repeatedly reflect and transmit within the fault fracture zone, forming standing waves, which amplify or reduce the response of an underground structure. This phenomenon is closely related to the parameters of frequency, angle, and type of incident wave, as well as the inherent properties of the fault itself. Since the rule of seismic wave propagation in inactive faults is quite complicated owing to multiple reflections and transmissions caused by medium variability, one may need to resort to wave propagation theory from the perspective of stress wave propagation (e.g., wave function expansion method, transfer matrix method, and time-domain recursive method).

In 1971, Mow and Pao initially introduced the wave function expansion method to study the diffraction of elastic waves and dynamic stress concentrations (Mow & Pao, 1971). This constitutes a significant foundation for the analysis of seismic response in underground structures. Chen and Yu (2023) recently presented a novel formula based on the wave function expansion technique and the Bessel–Fourier series transformation to determine the dynamic response of deeply buried tunnels passing in parallel with a fault zone under P- and SV-wave excitations (Figure 11). The ground, the fault, and the liner are supposed to be a homogeneous, isotropic, and linear elastic medium. In particular, the influence of the fault on the wave diffraction caused by the tunnel is considered to be irrelevant. The period and the width of the fault where the stress reaches a maximum are provided (Figure 12). For the P/SV wave with a 0° incidence angle, the peak value and the trough value appear at $$ and $$ , respectively, where $$ is the wavelength of the P/SV wave, k = 0, 1 …. In contrast, for the P/SV wave with a 180° incidence angle, the peak position and the valley position switch. Recently, the dynamic behavior of deep-buried tunnels close to a fault zone under SH waves has also been discussed (Yu et al., 2024). Generally, these solutions ignore the contact slippage between the ground and the fault.

Although analytical investigations require fulfilling manifold hypotheses before the solution of equations, they are approved by many tunnel engineers in the preliminary design phase due to higher computational efficiency and lower cost. However, more attention has been devoted to the mechanical behavior of tunnels in terms of the effects of faulting or seismic waves, with less consideration of seismic mitigation measures. The provision of reasonable seismic design criteria based on analytical investigations is a topic for future research.

4.1 1g-Shaking tables

To conduct a shaking table test, a unidirectional or multidirectional real or artificially synthetic or sinusoidal seismic wave acceleration time history is inputted into the shaking table surface. This activates the upper dynamic model box to achieve the dynamic response of the underground structure. Here, the model box can be classified as either a rigid, flexible, or laminar shear box. In the specific case of cross-fault tunnels, the rigid model box is typically used, incorporating flexible materials (e.g., foam boards, rubber, and sponge) within the model box itself to mitigate the impact of boundary effects. Thus, the thickness of the flexible material must be carefully determined as a critical design parameter.

For underground tunnels across faults, the shaking table is mainly used for the following two aspects: (1) the influence of the azimuthal relationship between faults and wave propagation direction on the seismic response of tunnels, which is a reference to proposed shock absorption measures; and (2) the feasible verification of vibration damping measures, as discussed in Section 6. Fang et al. (2011) carried out a large-scale shaking table test to capture the dynamic response of the tunnel across a fault. Figure 13 illustrates the triaxial shaking table system, including one fixed station and another mobile station. This study was completed using the fixed station through input artificial waves fitted to the tunnel engineering site. A gravel layer at the model box base enhances interfacial friction resistance, preventing soil-base slippage during excitation. Polystyrene foam boards stuck on the walls simulate the deformation and elastic recovery of the soil in a semi-infinite domain during an earthquake, with their thickness optimized according to boundary stiffness and damping characteristics. The experimental results indicated that the direction of seismic waves, with respect to a fault's inclination and strike, is an essential factor influencing the seismic response characteristics of structures. The influence of the dip angle and strike of the fault on the dynamic response characteristics of the tunnel was further studied in their work (Liu et al., 2017; Liu et al., 2019; Zhang et al., 2023; Zhu et al., 2021).

The above studies focused on clarifying the seismic response of tunnels have already played a substantial role, but they have some challenges in replicating fault movement effects in strong seismic excitation. With this in mind, Xin et al. (2014) proposed a new simulation approach based on a single conventional rigid model box. The rollers are positioned beneath a layer of a steel plate on the surrounding rock of the fault zone side. Sponges are then placed inside the box in the same direction as the excitation. During the test, the sliding of the surrounding rock is facilitated, and rebound is induced due to the presence of the sponge. This better simulates the fault displacement, thus enabling the nonuniform seismic excitation of the model system.

In high seismic activity regions, mountain tunnels across faults are often subjected to both fault dislocation and earthquakes. Recently, Fan et al. (2020) developed a special model box to consider the normal faulting and earthquake motion together. First, the fault movement was achieved by raising jacks installed in one half of the model box, and seismic excitation was generated by the shaking table. Furthermore, the bottom of the model box on the movable side was placed on round steel balls for horizontal sliding under seismic excitation. This can realize three-dimensional fault sliding during an earthquake. In addition, the boundary effect of the model box was also examined by the Pearson product–moment correlation coefficient.

The hanging wall effect in the fault sites has also been documented (Li, Li, et al., 2023; Li, Yuan, et al. 2024; Li, Zhao, et al. 2024; Xu et al., 2015). Li, Li, et al. (2023) conducted a shaking table test of the fault site effect and demonstrated that the hanging wall effect is due to the geometric effect induced by the asymmetric distribution of inclined faults. Meanwhile, the transfer function is introduced to represent the dynamic characteristics of a site in the frequency domain. However, the experimental results are based on a single seismic wave, which may be controversial, and more convincing results need to be discussed for different kinds of waves.

Generally, the shaking table is viewed as a popular test equipment among engineers and researchers to investigate the damage mechanisms of tunnels across inactive faults during earthquakes. However, the efficacy of shaking table tests is also contingent upon the rational design of the model box. Therefore, before experiments, efforts must be made to analyze the dynamic boundary effect and the resonance of the box.

4.2 Ng-centrifuges

Although the scale of the model in the centrifuge is relatively limited in comparison to that of the 1g-shaking table, the geotechnical centrifuge could effectively make up for the reduced-scale model stress loss by subjecting it to Ng-centrifugal acceleration. As early as 1980, centrifuge modeling of an unlined tunnel was first performed by Schofield (1980). In recent times, geotechnical dynamic centrifugal model tests have attracted considerable attention in the study of the mechanical behaviors of underground facilities (Li et al., 2014). Figure 14 shows the fault-crossing tunnel model installed within the centrifuge basket.

Based on location relationships between the fault rupture plane and the tunnel axis, centrifugal model tests focused on transverse cross-sectional deformation behavior and longitudinal deformation behavior of underground structures, respectively. In the analysis of the transverse response of the tunnel, Baziar et al. (2014) launched a succession of 80-g centrifuge tests to investigate the effect of the tunnel position, soil relative density, and tunnel stiffness on the fault–tunnel interaction under 60° reverse faulting. The soil was crafted using quartz sand, and the tunnels were treated as aluminum alloy tubes. The findings of this study highlighted that a deeper tunnel could diffuse a wider shear deformation area with an unsmooth surface displacement, which may induce substantial damage to the ground structure. Similarly, Nabizadeh and Seghateh Mojtahedi (2021) studied the interaction between the fault and tunnel with its longitudinal parallel to the normal fault in the dry soil layer. The experimental results showed that both rigid and flexible tunnels tested create an additional rupture plane on the left side of the structures, and they show visible displacement and rotation. Moreover, this rotation is even more violent with an increase in the burial depth.

The longitudinal response of the tunnel was also the focus of centrifuge tests. Kiani, Akhlaghi, et al. (2016) assessed the failure modes, joint damage, and change in the cross-section of segmental shallow tunnel linings in addition to sinkhole formation at the surface under normal faulting. Their results indicated that the separation of segmental rings results in major failure and soil collapse into the tunnel, and then a massive sinkhole arises that destroys the surface infrastructure. Subsequently, a novel vulnerability evaluation approach of segmental tunnels across active normal faults based on centrifuge experiments was presented (Kiani, Ghalandarzadeh, et al., 2016). Figure 15 illustrates five categories of fragility curves of segmental tunnel linings under permanent ground displacement. It is important to acknowledge the limitations of this study, which is primarily supported by a modest number of test cases. The type of tunnel explored is a shield tunnel in soil. This may lead to limited scope for application of this result, and the next stage should focus on the established fragility curves of mountain tunnels under faulting. Recently, Sabagh and Ghalandarzadeh (2020) and Cai et al. (2019) further extended Kiani, Akhlaghi, et al. (2016), Kiani, Ghalandarzadeh, et al. (2016)'s work into continuous shallow tunnels.

However, many of the above-examined centrifuge tests did not examine in detail the effects of a large vertical pressure. A few research teams have discussed the behavior of soils at a significant depth under a substantial overburden pressure. Recently, a fault simulator to consider a large overburden pressure was developed at the Tokyo Institute of Technology (Takemura et al., 2020), as shown in Figure 16. A rubber bag was installed on top of soil to exert vertical pressure. The study found that higher stress levels resulted in accelerated propagation and narrower fault zones. Making use of the new installation, Yao et al. (2021) studied active lengths of concrete tunnels subjected to the action of a reverse fault by using both centrifuge testing and numerical modeling.

Finally, the deflections and stresses experienced by a tunnel across a fault induced by fault movement and ground motion were quantified by Burridge et al. (1989) using a centrifuge. The momentum triggered by the model earthquake was found to be considerably smaller in magnitude than that produced by the fault-based mechanism.

Generally, the centrifuge is an effective tool for modeling active fault–tunnel interaction and understanding the failure and damage mechanisms of underground structures under faulting. However, centrifuges are primarily useful for the characterization of damage in tunnels across normal or reverse faults, with less frequent instances of utilization in in-depth explorations of strike–slip faults. Moreover, the centrifuge model is relatively small, and its integration with numerical simulation tools can facilitate a more in-depth understanding of the response and damage mechanisms.

4.3 Self-designed devices

The rock masses adjacent to an active fault demonstrate a degree of misalignment in response to seismic activity. Many self-designed equipment have been developed to simulate the misalignment properties of active faults in a quasi-static way (Lin et al., 2007). Such devices simulate fault movement by the one-dimensional relative sliding of the fixed and movable box, disregarding the dynamic effect of faulting. Table 5 lists the application of self-designed devices to investigate damage mechanisms to underground structures under active faults. Recently, Liu et al. (2015) designed a small-scale normal fault rupture simulation device to discuss the influence of different dip angles on mountain tunnels. The fault dislocation can be accompanied by oil jack expansion and contraction at the hanging wall. The bearing is placed between the loading system and the hanging wall base plate so that the fault inclination can change from 30° to 90°. The geometric similarity ratio is 1:50. The results showed that failure modes of tunnel linings are closely related to the inclination of the fault. When the dip angle is 75°, the flexure failure with the circumferential cracks predominantly appears in the footwall (Figure 17a). When the dip angles are 45° and 60°, failures result from the binding of flexure and shear, both in the shear and footwall zones, with vast circumferential and inclined cracks (Figure 17b,c).

Table 5. Summary of self-designed device application to investigate seismic damages to underground structures under faulting.

Reference	Testing apparatus	Active fault	Installation performance		Main findings
			Model box dimension L × W × H (m)	Fault simulator
Liu et al. (2015)		Normal fault	2.0 × 0.8 × 1.1	Oil jack	The failure patterns of tunnel linings depend on fault dip angles. With a decrease of the fault dip angle, the extent of the inverted triangular rupture shear zone increases.
Wang et al. (2022, 2023)		Normal fault	3.0 × 1.5 × 1.5	An angle-adjustable and speed-controlled hydraulic jack.	An S-shaped deformation of the axis direction of the tunnel is observed.
Zhou et al. (2022)		Strike-slip fault	0.72 × 0.50 × 0.40	A slide rail and thrust loading system	The flexible jointed tunnel shows an S-shaped deformation with segmental rotation and dislocation damage to the lining.
Liu et al. (2022)		Strike-slip fault	1.5 × 0.6 × 0.6	Jack and gas spring	The damage range is between 3.5 and 4.0 times the diameter of the tunnel. The tunnel lining failure is highly related to the S-shaped displacement and its hill-shaped displacement.
Sun et al. (2019)		Normal fault	5.0 × 2.5 × 2.5	High-power electric servo screw.	The inside of the invert and outside of the wall on both sides of the fault experience significant eccentric stresses.
Erami et al. (2015)		Reserve fault	15.0 × 0.8 × 1.2	Split-box container	The influence of connected joints on pipes is investigated, and a new equation for the pipe–soil interaction is proposed.
Jalali et al. (2016)		Reserve fault	8.5 × 1.7 × 2.0	Hydraulic jack	Pipes present S-shaped deformation with two local failure sections.
O'Rourke et al. (2016)		Strike-slip fault	12.0 × 3.2 × 2.3	Actuator	The maximum downward interaction force between the pipe and soil is approximately one-third of the value recommended in the current guideline.
Hui et al. (2018)		Normal/Reserve fault	6.0 × 1.0 × 1.0	Jack and Spring	The test setup can simulate the autonomous generation of earthquakes on active faults.

Then, Wang et al. (2022, 2023) specially designed a model box to study the longitudinal deformation of tunnel structures. A hydraulic jack, equipped with angle adjustment and rate-control capabilities, is installed beneath the steel plate of the hanging wall. It automatically applies a low velocity of 0.01 mm/s, which simulates faulting dislocation. They concluded that the longitudinal axis of the tunnel experiences an S-shaped deformation under normal fault movement. Coincidentally, Zhou et al. (2022) also pointed out that the flexible joint tunnel shows an S-shaped deformation under strike–slip fault dislocation through indoor small-scale model tests with a 0.125 mm/s loading rate. Based on the creep slip movement, deep in situ stress conditions, and rock mass characteristics within the active fault zone, a new experimental setup was developed by Liu et al. (2022). A 3D load function, a slip mechanism with changeable angles, and a flexible loading device with airbags and air springs are mounted in this test system. Zhang et al. (2024) invented a new device to study the effect of high in situ stress conditions on a deep-buried tunnel under a strike–slip fault. The in situ stress is loaded by confining pressure-loading jacks in five directions.

To improve the boundary effect (longitudinal dimension) and time effect (loading rate), Su et al. (2019) originally designed a 1:25 large-scale and wide-controlled rate device to simulate the stick–slip of a 60° normal fault. A high-power electric servo screw is installed in the lower plate of the device, and the stick–slip dislocation is modeled by lifting of the screws. Subsequently, the test shear dislocation rate is then set as 5 mm/min. It was observed that the lining damage zone of the hanging wall is 4.2 times the tunnel span and that of the footwall is 2.4 times the tunnel span. The damage to the hanging wall is more severe than that of the footwall. Recently, a novel house-made mechanical equipment that can simulate the three-way motion of a fault was developed (Gao, Wang, Ma, et al., 2024; Gao, Wang, Wang, et al., 2024) that is comprised of several key components, including a strike–slip box, a dip–slip box, intermediate connecting parts, reverse thrust driving devices, etc. In their work, a comparative study was conducted to analyze the failure mode of a railway tunnel subjected to strike–slip fault and oblique-slip fault dislocations. In addition, a few full-scale test facilities were established to observe the soil–pipe interaction under fault rupture (Erami et al., 2015; Jalali et al., 2016; O'Rourke, 2010; O'Rourke et al., 2016). Generally, a self-designed device with excellent power train and control systems can focus on more factors, including the rupture rate, in situ stress, and the simultaneous consideration of fault misalignment and earthquake waves, thus providing a more comprehensive understanding of the stratum–structure interaction mechanism under active faults.

In short, a variety of experimental devices have been invented to study the seismic response of cross-fault tunnels, allowing more targeted countermeasures to be proposed. However, there is still a lack of research into the simulation of the fault misalignment of seismicity. In instances where fault misalignment and seismic loading must be considered concurrently, the test procedure typically commences with the imposition of dislocation upon the model box, followed by application of earthquake loadings via a shaking table. This approach is appropriate for nonseismogenic faults, but whether the two processes are coupled remains unresolved for seismogenic faults. It is clear, therefore, that further efforts are needed to develop multifunctional home-made test devices.

5.1 Continuous medium methods

The continuous medium methods consider tunnels, surrounding rock, and fault zones as a continuum to solve elastoplastic civil engineering problems. The analysis of nonlinearities in geotechnical materials is of paramount importance for the comprehension of tunnel–fault interactions under the influence of fault misalignment or earthquake forces. Table 6 lists continuous medium methods for nonlinear seismic analysis of fault-crossing tunnels.

It has been demonstrated that a structural element model can lead to a substantial enhancement in computational efficiency when compared with a solid element model. A few studies have used structural elements to simulate the tunnel–ground interaction under fault action, such as the beam–spring model (Anastasopoulos et al., 2008; Cheng et al., 2025; Joshi et al., 2011), the shell–solid model (Cai et al., 2019), the beam-solid model (Zeng et al., 2024), and the shell–spring model (Xie et al., 2011). However, certain details on the response of structures and ground in these models may be obscured.

The continuous medium methods are also widely used to investigate seismic response mechanisms of tunnels under oblique incident waves. It balances the fact that a 1g-shaking table can only input ground motion in one direction at a time. One of the key issues in modeling wave propagation in a semi-infinite or infinite domain is the absorption of the scattered wave at the truncated boundaries. So far, various local artificial boundaries have been created, such as viscous boundary conditions, viscous–spring boundary conditions, perfectly matched layer conditions, infinite element boundary conditions, etc. Among them, the viscous–spring boundary is commonly used in numerical calculations, since it can efficiently simulate elastic recovery and radiation-damping energy dissipation of the medium at artificial boundaries. The scattered seismic waves can be absorbed by springs and viscous dampers at the artificial boundary nodes. Recently, Huang, Zhao, et al. (2017) applied ABAQUS software to explore the nonlinear dynamic behavior of tunnels situated in normal fault ground subjected to the excitation of a P wave at oblique incidence. Falling back on the viscous–spring artificial boundary, the ground motions are transformed into the equivalent nodal forces that act upon the truncated boundary of the finite element model. The numerical results revealed that the tunnels across the fault sustain the most significant plastic deformation, followed by those located within the hanging wall. Furthermore, when the tunnel crosses the fault and is in the hanging wall, the structural seismic response manifests more noticeably as the incidence angle increases, but it is the opposite at the footwall. Jiao et al. (2021) further extended Huang, Zhao, et al. (2017)'s work to three-dimensional space, discussing the influence of oblique incident P wave on the longitudinal response of a tunnel across a fault. Moreover, Liu et al. (2021) adopted the indirect boundary element method (IBEM) to investigate how a noncausative fault affects the dynamic behavior of an adjacent lined tunnel exposed to incident plane SV waves. The free wave field and scattered wave fields were considered to be virtual loads imposed on the medium boundaries. In addition, for the BE method, it is not necessary to introduce artificial boundaries to meet the infinite radiation boundary, which is simple and easy to consider for researchers.

Overall, the continuous medium method is robust for addressing the deformation, stress state, and plastic yielding of tunnel lining and wave incidence conditions. Furthermore, the incorporation of damage indices serves to enhance the precision of the assessment of damage levels in tunnel linings.

5.2 Discontinuous medium methods

Under long-term geological action, geotechnical soils show structural discontinuities, inhomogeneities, and anisotropies. The discontinuous medium methods regard geomaterials as units or particles to define such natures. Over 50 years ago, Cundall first proposed the discrete element method to represent the rock matrix as a collection of encapsulated blocks (Cundall, 1971). Subsequently, commercial software UDEC and 3DEC are widely used in the field of geotechnical earthquake engineering. Especially, the fault is regarded as a large geological structural plane where faults are treated as zero-thickness interfaces. Taking three main fractures in the Longmenshan region as an example in the Wenchuan earthquake, Zhou et al. (2011) validated the shock isolation effects and the hanging wall effects of the large-scale fracture using a universal distinct element code (UDEC). Yang et al. (2013) identified that the nonlinear dynamic failure process of the tunnel–fault system subjected to Wenchuan earthquake can qualitatively consist of five main stages on the basis of its stress, strain, and rupturing behaviors based on 3DEC software: (1) strain localization, (2) rupture initiation, (3) rupture acceleration, (4) spontaneous rupture growth, and (5) stabilization. Cui et al. (2016, 2018) created a 3D discrete element model (3DEC model) to study the impact of a controlling geological discontinuity on the stability and safety of a hydropower chamber under earthquakes.

The interior of the fault has been subjected to a process of geological reshaping, resulting in the formation of a variety of distinctive shapes. The findings of the investigation, as presented by Zhang et al. (2020), highlighted that the geometric features of rock mass structures within the fault core are analogous to Voronoi polygonal clusters. Thus, a plan-strain model considering the structural properties of the rock block and joint within the fault is established to study the distribution rules of rock mass displacement in deep-buried regions caused by the fault creep slip from the perspective of the engineering scale. Figure 20 displays the flowchart of the establishment of the discrete element numerical model under an active fault. It was noted that nearly 70% of the creep slip displacement seems to occur within the fault core subjected to creep slip for 100 years, regardless of whether the fault is in a normal, reverse, or strike–slip configuration.

The initiation, extension, and propagation of fractures occur within the geotechnical body during fault misalignment, and granular media rotate. These processes can be better represented using a particle flow-based discrete element method. Garcia and Bray (2022) used the open-source DEM software LIGGGHTS to study the impact of soil inhomogeneity on earthquake surface fault rupture. Chang et al. (2013) conducted centrifuge experiments and numerical simulations (Particle Flow Code-PFC 2D) to imitate reverse fault slip at 1g, 40g, and 80g centrifugal acceleration. In addition, the seismic failure laws of deeply buried tunnels near a fault of a high-seismic region by shaking table tests and PFC 2D were reported (Zhang et al., 2023).

Overall, the discontinuous medium method is an appropriate method when faults are considered as geological discontinuities or when the internal structural features of faults are to be examined. In addition, it is feasible to document instances of cracking and destruction phenomena of the rock mass and the lining.

5.3 Other methods

Taking advantage of all kinds of numerical methods, hybrid FDM(FEM)–DEM(BEM) modeling has been gradually incorporated into the seismic performance of tunnel structures. In a recent publication, Liu et al. (2024) presented a 2D hybrid indirect boundary element-finite element numerical method (IBE-FEM) for modeling the seismic phenomenon throughout the complete process, from the near-seismogenic fault to the underground structures. In this study, the seismic wave field of a strike–slip fault with different source parameters is generated by the IBE method, and the finite element method (Abaqus software) is then used to assess the seismic performance of an underground station. However, the substantial computational cost of this method poses a challenge to its application in large-scale three-dimensional engineering models. The domain reduction method (DRM) provides a novel approach for solving the problem of source-to-structure seismic engineering (Bielak et al., 2003). The main advantage of this method is that it allows the re-simulation of an effective simplified model without re-simulating a large computational model involving seismic faults (Korres et al., 2023). Several modified DRMs have accordingly been proposed to address the seismic performance of long tunnels, complex site conditions, and near-fault ground motion effects, and stochastic assessment of underground engineering (Banjare & Avatar, 2024; Banjare et al., 2025; Veeraraghavan & Banjare, 2025).

To model the discontinuous medium, the hybrid finite difference–discrete element code CA2 (continuum analysis 2-dimensional) was applied to understand the fault layout control on the seismic design of large-scale chambers (Ardeshiri-Lajimi et al., 2015). Recently, Wang et al. (2020) established a nonlinear thin-layer element model to elucidate the complex mechanical properties of the fault in ABAQUS. Besides, Yang et al. (2020) developed a dynamic contact force method focusing on the discontinuous deformation between linings and surrounding rock and calculated the seismic stability of an underground tunnel across a fault in the Lawa Hydropower Station Project. Cui, Li, et al. (2022) constructed a discrete–continuous hybrid numerical model for the analysis of a tunnel under strike–slip fault rupture. The tunnel lining is modeled by FLAC3D with a new Mohr-T model, which is capable of accurately manifesting the brittleness and the subsequent cracking in the tunnel lining. The rock mass model is represented by means of PFC 3D balls.

Compared with the hybrid continuous–discontinuous method, which uses a nonuniform theory to solve the problem, the Peridynamics method uses a uniform model to solve the continuous–discontinuous problem, avoiding the complexity of information transfer at different scales. This also enables better handling of fracture and damage. Liao et al. (2023) utilized Peridynamics to reveal brittle damage of buried pipes under diverse dip–slip faults. In this approach, pipes are represented as Peridynamics shell structures, while the soil is expressed as Winkler springs. Overall, if the problem to be studied for fault-crossing tunnels requires attention in terms of both continuity and discontinuity, the hybrid method or PD would be a better choice.

In essence, numerical simulation is not contingent on the nature of the geotechnical material, the scale of the model, or the boundary conditions. Apart from validating the results of field investigations, physical tests, and analytical solutions, the tunnel–stratum interaction can be explored in a more refined way, including nonlinear materials, internal features of faults, and the structural failure damage process. However, there is still scope for improvement by modeling of different types of fault rupture and seismic wave generation, to linking this to the mechanical response of the tunnel structure. On the other hand, the computational efficiency needs to be improved further and time consumption needs to be reduced. Table 7 compares the characteristics and adaptability of different seismic analysis methods for tunnels within fault sites.

6.1 Grouting

Within an inactive fault fracture zone, the strength of the rock mass is frequently observed to be inferior to that of the hanging wall or footwall. Therefore, asynchronous and uneven deformation occurs in a tunnel under earthquakes, causing additional displacements and stress concentrations of the structure at the fault. It can be seen, therefore, that the reduction of the difference between strata is the foundation of seismic mitigation. Grouting reinforcement technology is an effective method to strengthen the seismic performance of tunnels by increasing the tensile strength and ductility of the faulted zones (Wang et al., 2012).

Grouting reinforcement technology consists of whole-chain touch grouting, whole-chain alternative grouting, and partial grouting (Gao et al., 2009), as depicted in Figure 23. Zhao et al. (2022) performed a range of large-scale shaking table experiments to understand the influence of grouting in a tunnel across an inactive fault and to investigate the seismic mitigation mechanism behind it. The grouting process was simulated by a lightweight plaster with a mass ratio of gypsum to water of 1:2. The relative stiffness of the grouting zone and the fault fracture zone is close to 100:1 by shaking table tests, with the seismic damping effect being more significant. In addition, the interval grouting prereinforcement schemes possess certain advantages over the other two methods (Shen et al., 2011). It is a shift from the rock–tunnel mode to the rock-reinforcement zone–rock–tunnel mode, which can significantly dissipate the energy of earthquake waves and lessen the degree of damage to the tunnel lining. Especially, Liang et al. (2020) reported that grouting with an interval of 1 m and 4 m in thickness at the fault zone is reasonable for a super-large span tunnel. Overall, the stress concentration and violent deformation on the tunnel lining structure can be reduced by grouting reinforcement to mitigate the severity of disasters such as circumferential and inclined cracks, or even complete collapse, produced by tunnels in fault fracture zones during earthquakes. Nevertheless, grouting is only possible for tunnels across inactive faults, as it fails to control the large displacement caused by fault movement. Additionally, the question of how the distance of grouting along the axis of a tunnel should be determined remains unanswered.

6.2 Fiber-reinforced concrete

The practical applications of plain concrete have considerable limitations due to the low tensile strength, poor impact resistance, susceptibility to cracking, and poor corrosion resistance of ordinary concrete. To address these shortcomings, fiber concrete materials, due to their high strength and durability (Nehdi et al., 2015), are often used to enhance the seismic capability of tunnel linings. It is noteworthy that steel fiber (Avanaki, Hoseini, Vahdani, de la Fuente, 2018, Avanaki, Hoseini, Vahdani, de Santos, et al., 2018), polypropylene fiber (Xin et al., 2019), basalt fiber (Zeng et al., 2021), polyethylene terephthalate fiber-reinforced polymer (Ma et al., 2023), and hybrid fiber (Li et al., 2019) are generally used for reinforcing concrete in underground engineering in earthquake-prone zones. Xin et al. (2019) carried out numerous shaking table tests to determine the seismic performance of polypropylene fiber-reinforced concrete tunnel lining. Zeng et al. (2021) found that the length and width of tunnel cracks induced by stick–slip faulting are reduced by over 30% when applying the 0.5% basalt fiber-reinforced concrete articulated design. Particularly, hybrid fiber-reinforced concrete, that is, steel–basalt and steel–polypropylene hybrid fiber, offers better damage resistance (An et al., 2020; Cui et al., 2020). Overall, fiber-reinforced concrete is one of the indispensable options for fault resistance in tunnels. However, as a passive fortification strategy, fiber-reinforced concrete cannot possibly bring down shear force under fault movement or soil pressure caused by stratum deformation (Zhang et al., 2020). In addition, it is always important to choose suitable materials to put into full use for the seismic performance of tunnel linings according to actual project seismic requirements and prudent consideration of economic feasibility.

6.3 Isolation layer

The subsurface structure is subject to deformation in response to the stress exerted on it by the surrounding rock during seismic activity. This, in turn, results in an increase in extra stress on tunnel linings, which can ultimately lead to structural failure of the lining. Hence, covering a tunnel with a flexible medium will be a feasible measure to reduce tunnel damage (Kim & Konagai 2000; Konagai & Kim 2001). The isolation layer transforms the traditional strata-lining structural system into a strata (lining)-isolation layer-lining structural system. Note that isolation layer materials mainly incorporate silicone-based material (Chen & Shen, 2014), geofoam (Xu et al., 2016), rubber (Chen et al., 2018), foamed concrete (Ma et al., 2019; Zhao et al., 2018), asphalt (Yang et al., 2022), and aluminum foam (Anato et al., 2022; Su et al., 2019). Xin et al. (2022) designed a casing-shaped composite tunnel lining. The tunnel lining comprises both an internal and an external lining, with a buffer layer situated between them. Recently, Peng, Liu, et al. (2023), Peng, Zeng, et al. (2023) observed a rubber–sand isolation layer that is an appropriate countermeasure to mitigate the potential damage of small creep slip faults and subsequent seismic shaking. Especially, Cui et al. (2017) recommended that an isolation layer with a 10 cm thickness for a stick–slip fracture tunnel is optimal. As materials with high damping and malleability, rubber and foamed concrete are generally well-suited for absorbing displacements caused by seismic waves. However, they are prone to aging and loss of bearing capacity in humid, confined spaces. Therefore, it is necessary to select materials with approximate strength and include supplementary measures to prevent premature aging during the construction stage. Meanwhile, the isolation layer is more favorable in inactive fault conditions due to these materials with weak stiffness.

6.4 Flexible articulation design

6.5 Other countermeasures

In this section, a few novel countermeasures for underground structures are introduced, along with insights into strategies for retrofitting buildings supported by shallow foundations or piles. Yao et al. (2020) invented a novel subway station that is composed of a rectangular cross-station and two rigid diaphragm walls. The diaphragm walls consist of reinforced concrete, located at the bottom corners of the structure. Moreover, two subsidiary protection structures for shield tunnels are explored under fault dislocation, namely, inclined rigid sliding walls and an anti-rotation shelf (Yao, Luo, et al., 2023; Yao, Zhang, et al., 2023). Figure 24 shows these two types of novel countermeasures. Recently, Tao et al. (2024) validated the function of the NPR anchor cable support system in the earthquake-resistant design of tunnels crossing faults. Overall, new aseismic measures are embodied in the incorporation of new accessory structures and the application of new materials.

6.6 Summary

As discussed above, each seismic mitigation measure offers effective seismic resistance, while different measures are suited to specific application scenarios. Table 8 summarizes the characteristics and application scenarios of various fault-crossing seismic measures. However, a single seismic mitigation measure is often inadequate to address complex geological conditions. Consequently, an optimal aseismic design should first assess the fault characteristics and accurately estimate potential displacements. It should then integrate the benefits of various aseismic strategies to implement composite mitigation measures at the tunnel–fault crossing section (Wang et al., 2020).

7.1 Hanging wall effect

The tunnels are highly vulnerable to seismic damage under strong earthquakes, seriously threatening the safe operation of underground structures. Minor to severe damage can be observed in tunnels within fault ground, and the extent of the damage is influenced by four key factors: tunnel structure, fault parameters, seismic waves, and stratum properties in the vicinity. This is what needs to be looked at in tunnel defense. In addition, seismic damage to tunnels tends to show spatial differentiation, that is, the hanging wall effect. The seismic damage to the hanging wall is worse than that to the footwall. This phenomenon has been reported in field investigations (Huang & Li, 2008; Wang et al., 2001), physical model tests (Cui et al., 2017; Li, Li, et al., 2023; Li, Yuan, et al., 2024; Li, Zhao, et al., 2024; Shen et al., 2020; Su et al., 2019; Xu et al., 2015; Zhao et al., 2022), and numerical simulations (Huang, Zhao, et al., 2017; Liu et al., 2021; Zhou et al., 2011). Taking the 1999 Chi-Chi earthquake as an example, Yu and Gao (2001) discussed the effects of the hanging wall and footwall on peak acceleration. In addition, the frequency content difference between the hanging wall and the footwall was highlighted (Lu et al., 2013; Xu & Xie, 2005). Therefore, identification of the fault rupture process, seismic wave characteristics (e.g., incident direction, spectral, etc.), and its propagation law will be highly valuable to gain an understanding of the mechanism of the hanging wall effect.

7.2 Deep tunnel in the high-intensity earthquake area

Research on the factors affecting seismic damage to underground structures focuses on shallow underground engineering. Only a few studies have paid attention to seismic response analysis of deep-buried underground facilities (Anastasopoulos et al., 2008; Ardeshiri-Lajimi et al., 2015; Chen & Yu, 2023; Cui et al., 2016, 2018; Liu et al., 2022; Takemura et al., 2020; Yao et al., 2021; Yu et al., 2024; Zhang et al., 2020, 2022, 2023; Zhu et al., 2021). Sharma and Judd (1991) recapitulated that damage in tunnels deeper than 50 m is much less frequent, and there is no serious damage below 300 m. This phenomenon was also validated in the 2008 Wenchuan earthquake. However, in weak rocks with faults or high situ stress, the relationship merits further discussion (Li, 2012). To illustrate, the Sichuan–Tibet Railway, a 1543 km long lifeline engineering project, traverses the Qinghai–Tibetan plateau area, which has significant tectonic deformation, extensive distribution of deep, large active fault zones, and frequent seismic activities (Cui, Ge, et al., 2022). All along the Sichuan–Tibet Railway, there are 12 active fault zones and 5 suture zones. This constitutes a significant and pervasive challenge to the field of railway engineering. Therefore, more research and analysis are required that integrates geological structure, high geostress environment, and characteristics of strong ground shaking. For a causative fault, fault misalignment and seismic wave disturbance occur simultaneously (Hui et al., 2018). Both can be considered together to more realistically reproduce the actual site conditions, thereby making the design of a fault-crossing tunnel more accurate and effective in terms of resistance and damping. Besides, seismic waves decay in energy as the distance traveled increases from the source. Due to their inherent continuity, tunnels are frequently subjected to nonuniform excitation. Such an analysis may prove invaluable in understanding the dynamic response of the tunnel across faults in this event. In addition, the incident direction of seismic waves is also a key concern (Fan et al., 2020; Gao et al., 2021; Huang, Du, et al., 2017).

7.3 Refined modeling of faults

With the advent of discrete–continuous hybrid simulation methods, the internal structural characteristics of rock mass can be considered at a more refined level. The surrounding rock within the fault fracture zone generally consists of rock blocks and joints (Gudmundsson et al., 2010; Zhang et al., 2020). The mechanical properties of rock and joints, taken together, exert control over the dynamic response of tunnels. The fundamental frequency of seismic waves is below 10 Hz, which is close to the natural frequency of the loose-jointed rock mass. The propagation of a seismic wave through a jointed rock mass will result in resonance, thereby increasing the seismic response (Xin et al., 2024). More effects are needed to reveal the seismic response mechanism of tunnels with complex 3D discrete fracture networks. Then, the effect of joint features (i.e., density, length, orientation, dip, set, etc.) and wave frequency on the dynamic response characteristic of the tunnel can be further clarified.

7.4 Gaps in existing design standards