Introduction

With the rapid development of infrastructure construction in China, a large number of transportation projects are advancing into the western "Third Pole"—the Qinghai-Tibet Plateau region [1, 2]. This region is characterized by high seismic intensity, active plate tectonics, and densely distributed active faults, making it a prominent strong earthquake and tectonic zone [3, 4]. Consequently, numerous tunnel projects in this high-intensity seismic area are constrained by route selection and must cross active faults. Such fault-crossing tunnels face severe threats from near-field strong ground motion, large fault displacement deformation, and their synergistic coupling effects throughout their long construction and operational periods [5, 6]. The severe damage to the Daliang Tunnel on the Lanzhou-Xinjiang high-speed railway caused by the M6.9 earthquake in Menyuan County, Qinghai Province, on January 8, 2022, exemplifies this problem [7]. To ensure the safe construction and stable operation of strategic transportation tunnel projects, a clear understanding of the dynamic response characteristics and seismic damage mechanisms of fault-crossing tunnels under "strong shaking–fault movement" coupling effects is an urgent requirement for supporting major national strategic layouts.

Shaking table model testing serves as a crucial research method for investigating seismic dynamic responses in tunnel engineering, capable of revealing seismic dynamic response mechanisms and reproducing seismic damage characteristics. Numerous scholars have conducted extensive studies on tunnel dynamic response features through shaking table model tests. Since tunnel engineering is often constructed in various site conditions, researchers have investigated the seismic dynamic response characteristics of tunnel structures under different surrounding rock environments, including soft soil [8–10], sand [11], compacted clay [12], loess [13], and bedrock [14, 15]. Scholars such as Zhang Jing [16], Cui Guangyao [17], Fan Kaixiang [18], and Lu Yaobo [19] have analyzed the influence of sudden changes in surrounding rock stiffness on tunnel structural dynamic response characteristics when tunnels pass through soft-hard rock transitions. Research has also examined the interaction mechanisms and seismic dynamic response patterns among different structural systems, including tunnel-surrounding rock/lining structure systems [20], tunnel-surface building systems [21], tunnel-foundation systems [22], and tunnel-soil-adjacent pile systems [23]. For the critical portal sections of tunnel engineering, shaking table tests have been employed to investigate dynamic response patterns from multiple perspectives, including biased topography [24, 25], ground motion input direction [26], ground elevation [27], and interaction between portal slopes and tunnels [28, 29]. Additionally, detailed studies have been conducted on the seismic dynamic response characteristics of special complex tunnel structures, such as large-section tunnels [30], orthogonal tunnels [31], oblique tunnels [32], three-dimensional crossing tunnels [33], complex connecting passage structures [34, 35], and ultra-small clearance tunnels [32, 36], while also considering factors such as different burial depths [37], progressive damage states [38, 39], and existing damage in tunnel linings [40]. Building upon extensive research on seismic dynamic response characteristics, scholars have investigated the damping performance of various measures through shaking table tests, including deep grouting reinforcement [41], polypropylene fiber concrete lining structures [42], and buffer layers of foam, damping materials, and rubber installed between surrounding rock and lining [43–46], as well as buffer layer structures in different directions.

In recent years, shaking table tests investigating the seismic dynamic response of fault-crossing tunnels have gradually attracted widespread attention. However, most existing research results treat the fault fracture zone as a geological condition by altering the similar materials of the corresponding range of surrounding rock [47–50], without considering the permanent displacement and large deformation issues induced by active fault rupture. Zhang Zhichao et al. [51, 52] simulated the dynamic response characteristics of fault-crossing underground pipelines by dividing both sides of the active fault into two model boxes fixed on the ground and shaking table, respectively. Other scholars have simulated non-uniform seismic excitation using multiple sub-shaking tables to analyze the seismic dynamic response characteristics of underground engineering [53–55]. Xin Chunlei et al. [56, 57] placed the entire model box on a single shaking table and installed a fault displacement device inside the model box to analyze the seismic performance of different aseismic measures for active fault-crossing tunnels. Shen et al. [58] placed the entire model box on a shaking table and controlled the movement of one side of the model box using a jack to simulate normal fault movement, thereby investigating the dynamic response characteristics of tunnels crossing normal active faults. However, all the aforementioned shaking table model tests on the dynamic response characteristics of active fault-crossing tunnels treat high-frequency strong ground motion and low-frequency fault permanent displacement as two independent events, without considering their synchronous non-uniformity and coupling effects, which is insufficient to realistically simulate the "strong shaking–fault movement" coupling effect on fault-crossing tunnels. Table 1 [TABLE:1] summarizes how various shaking table test methods consider the "strong shaking–fault movement" coupling effect.

This study pioneers physical simulation research on the "strong shaking–fault movement" coupling effect for tunnels crossing active faults. First, a novel physical simulation system for fault-crossing tunnels under coupled "strong shaking–fault movement" conditions was developed, consisting of a twin shaking table array, a non-uniform loading model box capable of applying combined "seismic motion–permanent displacement," and a co-moving sliding support module. Additionally, an artificial ground motion synthesis method was proposed to realize synchronous and non-uniform inputs of "seismic motion–permanent displacement," establishing a hybrid input framework for "strong shaking–fault movement" coupling. This enables the physical simulation of the mutual interaction between the seismic wave field and the deformation–displacement field on both sides of the fault zone. Taking the severely damaged Daliang Tunnel during the Menyuan earthquake as a case study, a demonstration test was carried out to reproduce the observed damage phenomena. Comparative analyses of the shaking table response characteristics, model box responses, and the surrounding rock and lining structure responses of the fault-crossing tunnel confirmed the validity and reliability of the proposed experimental system and methodology. This study provides an innovative physical simulation approach for investigating the coupled mechanism of "strong ground motion–fault displacement" effects on fault-crossing tunnels and is expected to promote the advancement of seismic design practices for tunnels intersecting active faults.

2.1 Research Background and Problem Description

The Daliang Tunnel is located in Menyuan County, Haibei Prefecture, Qinghai Province, and serves as a key control project on the national strategic Lanzhou-Xinjiang passenger dedicated line. The tunnel entrance is at mileage K1965+525.24, the exit at K1972+093.06, with a total length of 6,576.82 m, maximum burial depth of approximately 800 m, and maximum elevation of approximately 4,430 m. The tunnel traverses the middle-high mountain region of the Qilian Mountains. The tunnel adopts a double-track layout with a horseshoe-shaped cross-section. During the M6.9 earthquake that occurred in Menyuan County, Qinghai Province, on January 8, 2022, the epicenter was approximately 4.5 km from the Daliang Tunnel, with a focal depth of 10 km. The seismogenic fault was the Lenglongling Fault (F5) in the middle-western segment of the Qilian-Haiyuan Fault on the northeastern margin of the Qinghai-Tibet Plateau, characterized by left-lateral strike-slip movement, with the epicenter located approximately 3–4 km south of the F5 fault.

The F5 fault is a Holocene active fault with an average left-lateral slip rate of 3.5–6.6 mm/a. The strata on both sides consist of Ordovician crystalline limestone interbedded with striped slate (hanging wall) and Permian light white to gray-white sandstone (footwall). Post-earthquake surface investigations revealed a main fracture approximately 21.5 km long crossing the tunnel exit, extending roughly east-west. The tunnel section crossing the active fault zone exhibited severe fiber offset, sidewall extrusion and dislocation, secondary lining crushing, track bed uplift, drainage system blockage, and damage to power and communication equipment. Post-earthasurement scanning of the tunnel cross-section indicated that structural dislocation was concentrated within approximately 21 m near the main rupture plane in the active fault zone (K1971+390.4–K1971+411.7). The tunnel structure experienced obvious compression and dislocation near the main rupture plane of the F5 fault zone (approximately 21 m), with severe deformation and a relative dislocation of 2.8 m. In other sections, the tunnel structure showed overall offset, with a maximum internal contour offset of approximately 1.92 m, though the structure itself did not exhibit obvious dislocation.

The seismic damage to the Daliang Tunnel during the Menyuan earthquake transcends the scope of traditional underground engineering seismic research. The damage demonstrates that the coupling effect between strong seismic ground motion and fault displacement is the core cause of catastrophic structural failure [59], as shown by the purple segment in Figure 1 [FIGURE:1]. The key to realizing the "strong shaking–fault movement" coupling effect lies in creating an extremely special loading environment that incorporates both strong seismic forces causing structural inertia and fatigue damage, and fault displacement causing large deformation and geometric instability.

2.2 Technical Approach and Implementation Process

To address the key scientific issues concerning the dynamic response characteristics and seismic damage mechanisms of fault-crossing tunnels under "strong shaking–fault movement" coupling effects, this study conducts relevant shaking table physical simulation tests based on the Menyuan earthquake Daliang Tunnel damage, which reveals that fault-crossing tunnels are simultaneously subjected to high-frequency strong shaking from external seismic sources and low-frequency large displacement (as shown in Figure 2 [FIGURE:2]), aiming to reveal the dynamic response characteristics of fault-crossing tunnels under this combined action.

To achieve true physical simulation testing of fault-crossing tunnels under "strong shaking–fault movement" coupling effects, the research approach consists of five steps: (1) Synthesize permanent-displacement-containing ground motions based on an equivalent velocity pulse model [60], enabling the seismic input loaded on the shaking table to simultaneously reflect both high-frequency components of seismic energy and low-frequency components of large deformation, thereby realizing the special loading environment; (2) Conduct shaking table physical simulation tests using a twin shaking table array combined with a self-developed "seismic motion–permanent displacement" non-uniform loading model box, which achieves non-uniform seismic input on both sides of the model box through the twin shaking tables and enables non-uniform response of both model box sides through a displacement frame connecting the boxes fixed on the shaking table surfaces; (3) Determine the model test similarity ratios and surrounding rock-lining similar material mix proportions by establishing appropriate length similarity ratios based on test conditions, model box dimensions, and prototype engineering parameters, then deriving similarity ratios for different dimensional parameters, and determining suitable surrounding rock-lining similar material mix proportions through laboratory mechanical property tests; (4) Implement comprehensive multi-target and multi-parameter monitoring using multiple monitoring devices to measure shaking table acceleration, velocity, and displacement, model box displacement, surrounding rock acceleration, stress, and surface rupture, as well as lining structure acceleration, stress, deformation, and damage characteristics, with appropriate monitoring schemes arranged according to tunnel-surrounding rock and lining structural features; (5) Upon completion of the aforementioned research and design preparations, conduct the "strong shaking–fault movement" coupling effect simulation test.

3 Physical Simulation Test System

The test apparatus system employed in this study primarily consists of three modules: a twin shaking table array, a "seismic motion–permanent displacement" non-uniform loading model box, and a co-moving sliding support bracket. The twin shaking table array comprises two sub-tables from the nine-subarray, three-direction, six-degree-of-freedom high-performance shaking table test system at Beijing University of Technology. The "seismic motion–permanent displacement" non-uniform loading model box and the co-moving sliding model box support bracket were jointly developed by the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, and the Institute of Geotechnical and Underground Engineering at Beijing University of Technology. Figure 3 [FIGURE:3] illustrates the physical model test system for the "shaking–dislocation" coupling effect on fault-crossing tunnels.

The shaking table system operates in a twin-subarray configuration, with the two sub-tables spaced 80 cm apart, as shown in Figure 3(a) and 5(b). The main technical parameters of the two sub-tables are consistent, with each sub-table featuring a table dimension of 1 m × 1 m, maximum load capacity of 5 t, maximum displacement of ±7.5 cm, maximum velocity of 50 cm/s, full-load acceleration of 1.5 g in the horizontal direction and 0.8 g in the vertical direction, frequency range of 0.1–50 Hz, and acceleration and displacement control modes.

The "seismic motion–permanent displacement" non-uniform loading model box has internal net dimensions of 2.8 m × 1.4 m × 1.0 m (length × width × height), with each rigid side box measuring 1.0 m in length. The middle section comprises six displacement frames (totaling 0.8 m) connected to each other and to the side boxes via four rows of bolts, as shown in Figure 3(c). The relative displacement within the fault zone is achieved by controlling the pretightening degree of the bolts. Three openings with a diameter of 20 cm are provided at both ends of the model box to facilitate post-test internal monitoring access. During testing, 10 cm-thick polyethylene foam boards are installed around the interior of the model box as flexible boundary conditions to absorb vibration energy propagating to the boundaries.

A co-moving sliding support bracket is designed in the space between the twin shaking table surfaces beneath the model box to enhance the load-bearing capacity of the twin shaking tables and prevent the displacement frames from falling down after bolt release, as shown in Figure 3(d). The six displacement frames are placed on three rows of 30 universal rollers fixed on the support bracket, thereby reducing friction between the displacement frames and support bracket and ensuring effective displacement response of the surrounding rock-lining within the fault fracture zone range.

4.1 Artificial Ground Motion Synthesis Considering Synchronous Non-Uniform "Seismic Motion–Permanent Displacement"

When determining the shaking table loading scheme, it is necessary to input synchronous non-uniform seismic motion time histories containing "seismic motion–permanent displacement" into each of the two shaking table sub-platforms. Since no real ground motion records currently meet this requirement, the research team proposed a method involving the artificial synthesis of baseline ground motion (without permanent displacement) and the subsequent synthesis of permanent-displacement-containing ground motion based on this baseline to provide input loads for the physical simulation tests.

This study generates baseline ground motion based on the ground motion attenuation relationship provided in the site seismic safety evaluation report for the prototype project (the Daliang Tunnel in the Menyuan earthquake), as shown in Equation (1), combined with the site seismic geological parameters to obtain a peak ground acceleration of 460 gal. According to the site response spectrum shape (in this case, the Code for Seismic Design of Railway Engineering (GB50111-2006) (2009 edition) [61] with a characteristic period of 0.4 s), the baseline ground motion is generated, as shown in Figure 4 FIGURE:4.

where represents the peak ground acceleration amplitude (in gal), is the magnitude (taken as 6.9), and is the fault distance (km, taken as 10).

Based on the baseline ground motion, the ground motion is divided into low-frequency and high-frequency components using the reciprocal of the ground motion design response spectrum characteristic period (1/Tp) as the boundary. The two components are simulated through different forms to reflect their respective ground motion characteristics, then translated, amplitude-modulated, and superimposed to generate a permanent-displacement-containing ground motion that reflects the seismic geological condition characteristics of the engineering site. The low-frequency velocity pulse parameters are determined based on the seismic geological parameters of the project site and an equivalent velocity pulse model, while the high-frequency component is based on the aforementioned baseline ground motion with Fourier spectral bandwidth limited above 1/Tp. The specific artificial synthesis method has been disclosed as an invention patent [60] and will not be elaborated here. Using this method, this study artificially synthesized two ground motion time histories with permanent displacements of 3.6 m and 2.2 m, with specific time histories shown in Figures 4(b) and 4(c).

4.2 Similarity Ratios and Similar Materials

This test was conducted using a scaled model based on similarity relationships. Using the Buckingham π theorem and dimensional analysis, with geometric dimensions, density, and acceleration as fundamental physical quantities, and considering both test equipment dimensions and the requirement to ensure similarity between model and prototype values in primary mechanical properties, a geometric dimension similarity ratio (CL) of 70, density similarity ratio of 2, and acceleration similarity ratio of 1 were designed. Other parameter similarity ratios were derived through dimensional analysis. Table 2 [TABLE:2] provides the specific similarity ratio values for various physical quantities, including material characteristics and dynamic features.

Based on the actual geological investigation report of the prototype project, the surrounding rock within the fault zone crossed by the tunnel is considered as Class V, the rock on both sides as Class IV, and the tunnel lining structure strength grade as C30 concrete. Combining the geological investigation report data with China's Standard for Engineering Classification of Rock Masses (GB/T50218-2014) [62] and Code for Design of Concrete Structures (GB50010-2010) [63], the prototype values for surrounding rock and lining structure are taken as shown in Table 3 [TABLE:3]. According to China's Standard for Test Methods of Engineering Rock Mass (GB/T50266-2013) [64] and Standard for Geotechnical Testing Method (GB/T50123-2019) [65], standard specimens of surrounding rock and lining similar materials were prepared. Through orthogonal testing, uniaxial compression, triaxial compression, and direct shear tests were conducted on specimens of various mix proportions to measure multiple mechanical parameters.

Considering fabrication feasibility, mechanical parameter similarity ratios, and material stiffness differences, the final mix proportions were determined as follows: barite powder, low-strength gypsum, and water at a mass ratio of 3.5:1:2 to simulate the C30 concrete lining structure; fly ash, yellow sand, engine oil, and diatomite at a mass ratio of 1:1.5:0.25:0.47 to simulate Class IV surrounding rock on both sides; and fly ash, yellow sand, engine oil, diatomite, and sawdust at a mass ratio of 1:0.74:0.35:0.2:0.47 to simulate Class V surrounding rock in the fault zone. The specific mechanical parameters of the surrounding rock and lining similar materials are shown in Table 3.

4.3 Test Loading and Monitoring Scheme

This physical simulation test employed the artificially synthesized permanent-displacement-containing ground motion described above, with specific time histories shown in Figure 4. The designed test loading scheme is presented in Table 4 [TABLE:4]. The permanent-displacement-containing ground motions A1 and B1, synthesized from the same baseline ground motion, were input to the shaking table sub-platforms on the hanging wall and footwall sides of the model test box, respectively, enabling the two independent shaking table sub-platforms to simulate strong ground motion effects while simultaneously achieving relative permanent displacement from post-earthquake active fault dislocation, thereby realizing the simulation of "strong shaking–fault movement" coupling effects on active fault-crossing tunnels. The test also included a white noise test case with a peak acceleration of 0.1 g and duration of 40 s to reduce interference from偶然因素 and transient effects. The specific test case settings are shown in Table 5 [TABLE:5].

This test employed multiple monitoring devices to measure various dynamic physical quantities, including shaking table surfaces, model boxes, surrounding rock mass, and lining structures, thereby establishing a comprehensive multi-target and multi-parameter monitoring scheme. Table 6 [TABLE:6] lists the test monitoring equipment.

A total of seven monitoring sections were arranged, as the test focused on the response characteristics of the surrounding rock structure within the fracture zone. Sections 1# and 7# were positioned at the middle of the two side model boxes, sections 2# and 6# near the joints between the side boxes and displacement frames, sections 3# and 5# at the interfaces between the fracture zone and surrounding rock on both sides, and section 4# at the middle of the fracture zone. Each monitoring section was equipped with accelerometers and strain gauges. Accelerometers were installed above the lining at each monitoring section, with additional accelerometers at the surface, middle, and bottom positions of the surrounding rock mass at sections 1#, 4#, and 7#, totaling 16 accelerometers. Circumferential and longitudinal strain gauges were installed at the left and right arch waists and arch feet of the lining structure at each monitoring section, with circumferential strain gauges at the arch crown and invert, totaling 70 strain gauge positions. Cable displacement meters were installed at sections 2#, 3#, 5#, and 6# to monitor lining structure displacement responses. Earth pressure cells were installed at the arch waist at the lining-surrounding rock contact at sections 1#, 3#, 5#, and 7#. Laser displacement meters were installed on the six displacement frames within the fracture zone and at the middle positions of the side boxes. The specific monitoring layout is shown in Figure 5 [FIGURE:5].

Due to the large number of sensors, two types of dynamic data acquisition instruments were used—nine units with 114 channels total—to meet the monitoring requirements. After completing the shaking tests, an industrial endoscope (Dellon-VT) and laser point cloud scanner (FX-S70(A)) were used to collect data on internal damage and overall offset of the tunnel lining structure. Table 6 provides information on the monitoring equipment and specific measured physical quantities.

4.4 Model Fabrication and Test Procedures

Based on the similarity ratios designed for this test and considering the prototype tunnel structural parameters and model box size limitations, a three-centered circular tunnel cross-section lining mold was fabricated with a maximum inner height of 196.5 mm, maximum width of 200 mm, and thickness of 20 mm. The lining model was cast using the aforementioned lining similar material proportion, followed by demolding and curing upon material solidification to complete the lining similar model fabrication. Subsequently, surrounding rock and fault zone similar materials were prepared according to the determined mix proportions and backfilled within ranges of 1.2 m width for side rock and 0.2 m width for the fracture zone. To ensure integrity and similarity of the surrounding rock mass similar material, layered backfilling was employed, with each layer compacted and allowed to stabilize before the next layer was placed. Compaction effectiveness was controlled through compaction thickness and material quantity.

During backfilling, when the height reached the predetermined position for the tunnel lining model, the lining model was installed, various sensors were attached, and subsequent overburden material backfilling and compaction were completed. Grid lines were drawn on the surface to facilitate observation of post-earthquake surface rupture characteristics. After completing the surrounding rock-lining model fabrication and sensor installation, numerous monitoring device cables were carefully connected to the dynamic data acquisition instruments and signal validity was verified. Upon completion of all preparations, the shaking table oil valve was opened to begin the non-uniform shaking test. The test procedures are illustrated in Figure 6 [FIGURE:6].

5 Validation of Shaking–Dislocation Coupling Test Results

To verify the rationality and effectiveness of the physical simulation test scheme design, this study analyzes and discusses the results from three aspects: shaking table response, model test box response, and dynamic response characteristics of the surrounding rock mass and lining structure.

5.1 Shaking Table Response Characteristics

Shaking table surface response results directly reflect equipment reliability. Therefore, monitored acceleration and displacement responses on the shaking table surface were compared with input ground motion acceleration and displacement time histories, as shown in Figure 7 [FIGURE:7] and Figure 8 [FIGURE:8].

Figure 7 shows that under both white noise and Input Method 1 (A1-B1 ground motions), the monitored acceleration waveforms on the shaking table surface maintain good consistency with the input ground motions. For white noise input with a peak acceleration of 0.1 g (Test Case 1), the monitored peak accelerations on the hanging wall and footwall sides were 0.16 g and 0.13 g, respectively, with root mean square errors (RMSE) of 0.0389 and 0.0403. For Input Method 1 with a peak acceleration of 0.46 g (Test Case 2), the monitored peak accelerations were 0.49 g and 0.48 g, respectively, with RMSE values of 0.0379 and 0.0262.

Figure 8 compares displacement responses under different ground motion inputs. The results show that under both white noise and Input Method 1, the monitored displacement time histories maintain high consistency with input ground motions. In Test Case 1, the input white noise displacement peak was 5.79 mm, while the monitored peaks were 5.73 mm (hanging wall) and 5.52 mm (footwall), with post-shaking residual displacements of 0.57 mm and 0.47 mm, respectively, essentially achieving repositioning after shaking. In Test Case 2, the target permanent displacements were 51.43 mm (hanging wall) and 31.43 mm (footwall), while the monitored values were 54.20 mm and 33.80 mm, achieving displacement realization accuracies of 94.6% and 92.5%, respectively.

These analyses demonstrate that from both acceleration and displacement response perspectives, the shaking table sub-platform outputs faithfully reproduce the input seismic data, achieving high-fidelity ground motion input.

5.2 Model Test Box Response Characteristics

Following verification of shaking table output reliability, model test box response characteristics become crucial for test success. Given monitoring limitations and the rigid nature of the side boxes, no acceleration monitoring scheme was designed for the model boxes. The key to successfully realizing "strong shaking–fault movement" coupling effects and achieving test objectives lies in the displacement response of the model boxes. Therefore, laser displacement meters 1# and 8# were installed at the middle positions of the hanging wall and footwall side boxes, respectively, while meters 2# through 7# were sequentially installed along the hanging wall-to-footwall direction at the middle positions of the six displacement frames connecting the side boxes.

Figure 9 [FIGURE:9] shows the displacement response curves of the model box monitored by laser displacement meters under two test cases. Under white noise input (Figure 9(a)), the displacement responses of both side boxes and the six middle displacement frames maintain high consistency with the input ground motion displacement time history, with monitored displacement peaks ranging from 4.4 mm to 6.61 mm across the eight points, achieving 76%–86% accuracy compared to the input white noise displacement peak. Under Test Case 2 (Figure 9(b)), the displacement response trends of the hanging wall box and the three displacement frames near it match the hanging wall input ground motion, while those of the footwall box and its adjacent three frames match the footwall input ground motion. This occurs because the middle column of bolts in the displacement frames was completely released before shaking to ensure relative permanent dislocation between hanging wall and footwall after shaking. Additionally, due to the enormous weight of the model boxes and displacement frames and the presence of gaps between frames, other bolts could not be fully pretightened, creating a flexible connection state between other frames during shaking.

Figure 10 [FIGURE:10] shows the post-shaking displacement distribution of the model test box under Test Case 2. A permanent relative dislocation of 77.65 mm occurred between the frames on either side of the fully released bolts. The displacement response pattern shows gradually increasing displacement between the displacement frames and side boxes on both sides, which forms the basis for successfully reproducing the fault zone dislocation mode rather than simplifying it as a single rupture surface. These results confirm that the research approach and model test box design can ensure permanent relative dislocation between the hanging wall and footwall under strong shaking while reproducing the fault zone dislocation mode.

5.3 Surface Rupture Distribution Characteristics

After verifying the rationality and effectiveness of the shaking table and model test box design, final validation of the test's ability to simulate "strong shaking–fault movement" coupling effects on fault-crossing tunnels requires comparison between model surrounding rock and lining response characteristics under Test Case 2 and actual seismic damage.

Figure 11 [FIGURE:11] compares the post-shaking shear rupture and propagation effects on the model surface with actual surface rupture photographs from the Menyuan earthquake. Multiple fractures developed on the model test surface, with two continuous main rupture surfaces appearing at the soft-hard interfaces between the fracture zone and surrounding rock on both sides. Numerous branches developed during main rupture propagation, effectively reproducing the actual rupture surface development characteristics during earthquakes.

5.4 Lining Damage Pattern Characteristics

This study validates the test's effectiveness in simulating "strong shaking–fault movement" coupling effects on fault-crossing tunnels by comparing overall lining displacement response characteristics and internal/external structural damage features with actual seismic damage.

Figure 12(a) shows post-shaking cable displacement meter monitoring results for the lining under Test Case 2. The 1# cable displacement meter at monitoring section 2# within the hanging wall range recorded a permanent offset of 41.37 mm, the 2# meter at section 3# at the hanging wall-fracture zone interface recorded 27.81 mm, the 3# meter at section 5# at the fracture zone-footwall interface recorded 12.67 mm, and the 4# meter at section 6# within the footwall range recorded 23.25 mm. This indicates a relative offset of 40.48 mm occurred within the fracture zone.

Figure 12(b) presents a horizontal relative displacement contour map from three-dimensional laser point cloud scanning of the lining interior under Test Case 2. Using the portal section as a reference, a relative horizontal dislocation of 64.10 mm was observed across the rupture surface, demonstrating that model box displacement response was transmitted to the lining structure. Overall, the deformation pattern of the lining structure within the fracture zone closely resembles the damage pattern of the severely damaged section of the Daliang Tunnel, effectively reproducing the dislocation deformation mode of fault-crossing tunnels under "shaking–dislocation" coupling effects.

Figure 13 [FIGURE:13] shows external damage characteristics of the lining structure under Test Case 2. The left sidewall of the lining at the hanging wall-fracture zone interface was sheared off, while the right sidewall at the fracture zone-footwall interface near the footwall side was significantly sheared, indicating that the severely damaged range of the lining structure extends beyond the fracture zone boundaries. A wide longitudinal crack developed at the arch crown within the fracture zone, with severe damage and spalling with rebar exposure at both the arch crown and invert. Multiple shear cracks at an angle to the longitudinal direction were observed on the external lining surface within the fracture zone, with shear failure being the dominant damage mode. These external lining damage patterns show high consistency with the damage observed in the Menyuan earthquake Daliang Tunnel.

Figure 14 [FIGURE:14] compares internal damage characteristics within the fracture zone captured by industrial endoscopy with actual damage features of the Menyuan earthquake Daliang Tunnel. Severe damage occurred within the fracture zone, including large-area spalling, exposed and bent rebar, development of diagonal or circumferential through-cracks, multiple parallel cracks, and intersecting crack networks. The arch bottom uplift, large-area concrete spalling with rebar exposure at sidewalls and arch shoulders, and circumferential and diagonal cracking at the arch crown all effectively reproduce the seismic damage phenomena observed in the Menyuan earthquake Daliang Tunnel.

Comprehensive analysis of the lining structure damage patterns confirms that the research approach and test methodology can effectively simulate the seismic damage characteristics of the Menyuan earthquake Daliang Tunnel under "strong shaking–fault movement" coupling effects, validating the rationality and effectiveness of the proposed fault-crossing tunnel "shaking–dislocation" coupling effect shaking table model test method.

Conclusions

Based on the independently developed physical simulation system for active fault-crossing tunnels under "strong shaking–fault movement" coupling effects and the proposed artificial ground motion synthesis method considering synchronous non-uniform "seismic motion–permanent displacement," this study establishes a hybrid input framework for "strong shaking–fault movement" coupling and realizes physical simulation of the mutual interaction between seismic wave fields and deformation-displacement fields on both sides of the fault zone. Combined with seismic damage characteristics, physical simulation test results were comparatively analyzed, yielding the following preliminary findings:

(1) A "seismic motion–permanent displacement" non-uniform loading model box was developed based on rigid model boxes and flexible displacement frames, combined with a twin shaking table array and co-moving sliding support module to complete the physical simulation system for active fault-crossing tunnels under "strong shaking–fault movement" coupling effects.

(2) An artificial ground motion synthesis method considering synchronous non-uniform "seismic motion–permanent displacement" was proposed. Using this method, two non-uniform seismic motion time histories with permanent displacements of 3.6 m and 2.2 m were synthesized, creating a special loading environment that simultaneously reflects high-frequency seismic energy components and low-frequency large deformation components.

(3) Verification through shaking table surface and model test box dynamic responses demonstrates that the current test method can faithfully reproduce input seismic data, successfully realizing physical simulation of the mutual interaction between seismic wave fields and deformation-displacement fields on both sides of the fault zone, providing assurance for reproducing seismic damage to surrounding rock and lining structures of fault-crossing tunnels under "strong shaking–fault movement" effects.

(4) Comparison of surface rupture and lining structure damage patterns with actual seismic damage shows good reproduction of the Menyuan earthquake Daliang Tunnel damage characteristics, including the large deformation dislocation mode within the fault fracture zone.

(5) The test system and method described herein provide a reference for physical simulation research means for subsequent in-depth studies on the "strong shaking–fault movement" coupling effect mechanism in fault-crossing tunnels. Due to space limitations, detailed analysis results of the coupling effects will be presented in subsequent papers in this series.

The accurate loading of synchronous non-uniform "seismic motion–permanent displacement" excitation by the twin shaking tables was key to the successful first implementation of the active fault-crossing tunnel "strong shaking–fault movement" coupling physical simulation test. The research team sincerely acknowledges the exquisite calibration work performed by Professor Ji Jinbao of Beijing University of Technology on the twin shaking tables.

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(Corresponding author: CUI Zhen, E-mail: zcui@whrsm.ac.cn)

*Author Contribution Statement:

MEI Xiancheng: Test scheme design, test implementation, data analysis, manuscript drafting;
CUI Zhen: Research proposition and design, test implementation, manuscript drafting;
SHENG Qian: Research concept proposal;
CHEN Jian: Research concept proposal;
FEI Yang: Test scheme design;
TANG Langzhou: Test scheme design;
ZHAO Xu: Test scheme design, test implementation;
LI Ruohan: Test scheme design, test implementation;
HUANG Jingqi: Test scheme design.

*Author contributions can be categorized as: 1) Research proposition and design, including specific ideas or methods; 2) Research implementation, such as conducting experiments or investigations; 3) Data acquisition, provision, and analysis; 4) Manuscript drafting or final revision. Each research paper can further detail author contributions according to its research activities. Some research activities may involve other contributions that can be specifically described. For papers with multiple authors, each author's specific contributions in the above four aspects must be indicated at the end of the paper.