Accurate control of shield tunneling m requires a clear and profound understanding of their dynamic response characteristics. However, existing models predominantly rely on quasi-static frameworks, which fail to reveal the underlying dynamic behavior. This study develops an 18th-order state-space model of the shield-soil system to enable comprehensive dynamic response analysis of key state variables under diverse loading conditions and to assess system controllability. The proposed dynamic model is validated through analyses with both traditional quasi-static theories and field monitoring data. Results show that articulation center displacements and front/rear shield pitching angles are highly sensitive to vertical loads and segment buoyancy, exhibiting delayed responses and overshoot, which induce significant axis deviation and posture instability, especially in ultra-soft soils. Loads were categorized as controllable (jacking thrust) or uncontrollable (self-weight, segment buoyancy, soil–water pressures), with the front shield primarily governed by jacking. In contrast, the tail shield remains strongly affected by uncontrollable loads. Crucially, the proposed model reveals the inherent underactuation of the system, specifically highlighting the absolute uncontrollability of the rolling angles and roll rates, alongside the non-independent controllability of the pitch and yaw angles. To enhance system controllability, operational strategies are proposed, including optimizing shield configuration, employing fast-setting grout, and matching advance speed to regulate segment buoyancy, while structurally expanding the multi-dimensional controllability of the thrust system. These findings provide new theoretical insights into shield-soil dynamic interactions and practical guidance for real-time posture regulation and operational control in complex tunneling environments.

The construction of twin shield tunnels has become increasingly prevalent in densely populated urban areas. Accurately predicting the surface settlement induced by twin-shield tunnelling is of great significance for risk mitigation and refined settlement control. This study proposes a novel intelligent approach that integrates numerical modelling, empirical formula, and automated machine learning (AutoML) to predict surface settlement troughs induced by twin-shield tunnelling. Using a well-validated numerical model that considered 11 input parameters (including geological, geometric, and operational factors), 2000 settlement trough datasets were generated through numerical modelling. Subsequently, an improved superposition method was applied to extract six characteristic control parameters of the settlement troughs, thereby constructing a high-quality dataset. A multi-output AutoML model was then developed to predict the control parameters of the twin-tunnel-induced settlement troughs. Compared with six conventional machine learning models and two classical ensemble strategies, the AutoML model exhibited superior predictive accuracy and generalization capability, achieving average R2 values of 0.9977 and 0.9835 for the training and test sets, respectively. The Shapley Additive Explanations (SHAP) method was employed to analyze the interpretability of the AutoML model. The results highlight the significant influence of construction parameters (e.g., tunnelling contraction ratio) on the maximum settlement, as well as the regulatory effects of geometric parameters (tunnel diameter, burial depth, and twin-tunnel spacing) on the shape of the settlement trough, thereby providing valuable guidance for design optimization and precise construction control. Finally, the proposed AutoML model was validated using five real-world engineering cases, where the predicted settlement troughs closely matched the measured data, thereby confirming the robustness, reliability, and practical applicability of the model and demonstrating its promising potential for engineering practice.

To reveal the dynamic response characteristics and failure mechanism of such slopes, a large-scale shaking table test and numerical simulation study were conducted based on a bedding-plane rock slope at the entrance of a tunnel in China. A multi-domain coupling analysis method was adopted to investigate the influence of weak interlayers and tunnels on the seismic response and failure evolution process of the slope. The results show that the weak interlayer has a significant amplification effect on the peak ground acceleration amplification coefficient (MPGA). The MPGA of Model 2 shows a trend of "first decreasing and then increasing" along the elevation, and its amplification factor ε is approximately 1.5 to 2.48 times that of the homogeneous slope with a tunnel (Model 1). Weak interlayers amplify the energy in the 2.30−2.70 Hz frequency band in the middle to upper part of the slope, with an amplitude about twice that of the first-order frequency band f1 (1.56−1.99 Hz). In addition, the tunnel structure significantly changes the energy propagation path of seismic waves, causing the Hillbert spectrum in the middle part of the slope to change from a double-peak to a multi-peak and the marginal spectrum to undergo a sudden change, indicating local failure and energy transmission obstruction in this area. The Arias intensity increases overall along the elevation and suddenly increases at the middle part of the slope, which is highly consistent with the local failure area. Combining the energy transmission characteristics and failure evolution process, an earthquake failure mode of bedding rock slopes overlying tunnels is proposed: upper tensile cracking→middle part damage expansion→crack connection to form a sliding surface→upper rock mass shear sliding. This study can provide theoretical basis and technical support for the seismic design and disaster prevention and mitigation of bedding rock slopes overlying tunnels.

Driven by the “dual carbon” strategy, the functionality of coal mine underground reservoirs is transitioning toward multimedia collaborative storage, such as CO2 geological sequestration and strategic energy reserves. The microscopic structures of the coal pillar dams, which are subjected to mining-induced damage and long-term infiltration erosion by highly mineralized mine water, continuously deteriorate over time, posing significant risks to the long-term safety and stability of the reservoirs. This study, based on the Lingxin Coal Mine Underground Reservoir Demonstration Project, employs a multi-technique characterization approach including X-ray diffraction (XRD), scanning electron microscope, nuclear magnetic resonance, and computed tomography to systematically reveal the multiscale collaborative erosion mechanisms of highly mineralized mine water on the mineral composition, crystal structure, and pore development of coal pillar dams. The results indicate: (1) significant concentration-dependent deterioration of mineral composition and crystal structure; kaolinite hydrolysis had a weakening effect on XRD peaks while quartz remained inert; (2) initiation of progressive microstructural damage at boundaries via dissolution/loosening; this damage advanced through layered mineral delamination and pore development (evidenced by NMR T2 broadening), resulting in irreversible void formation with chloride precipitation; (3) formation of pore-throat halite crystals, primarily due to chloride ions (Cl–); these crystals propagated microfractures through salt-expansion stress, establishing a cyclic dissolution–migration–crystallization–cracking process; (4) triggering of accelerated deterioration of the coal matrix owing to prolonged retention; this induced time- and concentration-dependent expansion and interconnection of pore-fracture networks, resulting in geomechanical deterioration.

This study investigates the fracture behavior of hard rock subjected to waterjet-assisted disc-cutter indentation, with particular emphasis on the effect of waterjet cutting angle. Laboratory experiments and finite-discrete element method (FDEM) simulations were conducted to analyze crack initiation, crack propagation, fragmentation behavior, and specific energy under cutting angles ranging from 30° to 90°. The results show that the cutting angle critically governs fracture evolution, failure mode, and energy dissipation during cutter-rock interaction. An optimal cutting angle of approximately 60° was identified, at which the specific energy reaches its minimum and rock fragmentation efficiency is maximized. At this angle, the pre-cut kerf generated by the waterjet aligns effectively with the indentation zone of the disc cutter, promoting the initiation and propagation of tensile-dominated cracks, which account for nearly 80% of the total fracture network. Numerical simulations further indicate that the kerf inclination controls local stress redistribution, crack-path guidance, and crack coalescence, with the most favorable coordination occurring near this angle. In contrast, smaller angles lead to dispersed energy dissipation, while larger angles intensify vertical impact and expand the crushing zone, resulting in a U-shaped variation of specific energy. These findings clarify the tensile-dominated fracture mechanism induced by the interaction between cutter indentation and the waterjet-generated weak plane, and provide a fracture-mechanics-based basis for selecting effective cutting angles in hard rock excavation.

Local deformation around cracks within rock masses critically influences rock mass deformation and instability. However, correlation between internal and surface deformation at cracks remains poorly studied. This study prepared rock-like models to analyze the feasibility of using local strain direction deflection as a precursor to surface cracking, and examined the modulating effect of compressive strength on this precursor phenomenon. It discusses the feasibility of using internal strain direction deflection as a precursor to model instability and the influence of strength on this effect. Before instability, strain values on both sides of the internal fracture increases significantly, accompanied by abrupt changes in the deflection angle. Relative slip progressed through three stages: minor deformation, stable deformation, and rapid deformation. During the stable deformation stage, the deflection angle within the compression quadrant was strongly correlated with the sliding velocity. Higher compressive strength resulted in greater internal deformation before instability, more pronounced growth, lower relative sliding velocity, as well as a larger time and stress range over which surface deformation occurred. Lower compressive strength corresponded to a smaller ratio of the recovery stress to the peak strength.

Rock strength plays a key role in controlling fracture propagation and the stability of rock masses. However, how rock mass strength influences its internal deformation and fracture process remains poorly understood. This study investigates the effect of compressive strength on the damage evolution and instability mechanisms of rock-like models containing fractures. By combining failure stages and stress percentage, acoustic emission (AE) technology, strain blocks, and digital image correlation (DIC) technology were employed to analyze the signal characteristics of acoustic emissions prior to model instability, as well as the internal and surface deformation characteristics of the models and their interrelationships. The experimental results indicate that the acoustic emission signals generally exhibit a high–low–high trend during loading. The models with lower compressive strength demonstrate a more uniform distribution of signals over time and release less acoustic emission energy. Before global instability occurs, the local deformation at the prefabricated fracture was faster than the global deformation before the model reached global instability. Additionally, significant growth in internal deformation is observed prior to model instability, and the deformation characteristics inside and outside the model generally exhibit a certain functional relationship.

Settlement prediction is crucial in the design and construction of mechanized tunnels, with numerical simulation serving as an effective tool for estimating settlement trough. This study proposes a simplified two-dimensional simulation method as an alternative to complex and time-consuming three-dimensional simulations for predicting settlement trough. By integrating the volume loss method and grouting pressure method, this study introduces a hybrid volume loss-grouting pressure (VL-GP) method, a two-dimensional simplified simulation approach for estimating settlement in single and twin mechanized tunnels. The proposed method was validated using six historical cases, demonstrating its advantages over other simplified simulation methods in accurately reflecting the construction process and improving prediction accuracy. A parameter study on the hybrid VL-GP method examined the influence of soil properties, tunnel geometry, and construction parameters on settlement troughs in mechanized tunnels. Results indicate that clay exhibits greater sensitivity than sand, emphasizing the need to consider multiple factors when using settlement control as a design and construction criterion. To facilitate the application of the hybrid VL-GP method, a graphical user interface (GUI) was developed using FLAC3D and Gmsh, integrating Python and Fish programming to provide a user-friendly tool for predicting and evaluating induced settlement in mechanized tunnels.

The freeze–thaw (F-T) cycle constitutes a critical factor in the instability of slopes under seismic loading. To investigate the dynamic response and failure mechanism of slopes subjected to the coupled effects of F-T cycles and earthquakes, this study reveals the damage evolution from a time–frequency domain perspective. Through the results of the temperature field, Arias intensity, and Fast Fourier Transform, it can be observed that the F-T cycle results in the formation of a F-T interface on the slope surface, which significantly contributes to the initiation of slope sliding failure. The propagation mechanism of seismic wave energy at the F-T interface was further analyzed through Hilbert-Huang Transform. The Hilbert spectrum and marginal spectrum indicate that the high frequency component (38–45 Hz) of the slope above the F-T interface is more obvious than the low frequency component (0–15 Hz). This is because the seismic wave energy will produce refraction, reflection and transmission after passing through the F-T interface, resulting in the amplification of the seismic wave energy of the high frequency component. To further characterize F-T interface effects on seismic wave propagation, the RPMSA coefficient is introduced. Under excitation of low amplitude, the F-T interface has a stronger influence on seismic wave energy transfer in the freeze coagulation (FC) slope than in the thermal melting (TM) slope. However, once the excitation amplitude exceeds 0.8 g, the effect of the interface on seismic waves weakens, and the FC slope undergoes more severe damage than the TM slope. Finally, MIE and RMIE show that TM slope will enter the plastic stage earlier. Therefore, the failure process of the FC slope can be divided into three stages: an elastic stage (0.1–0.4 g), a plastic stage (0.4–0.8 g), and a sliding failure stage (0.8–1.0 g). By contrast, in the TM slope, both the plastic stage (0.4–0.6 g) and the sliding failure stage (0.6–1.0 g) occur earlier.

Underground water-sealed caverns are critical infrastructures for China’s strategic oil reserves. Seepage control is highly stringent, and existing sealing techniques often fail to meet the requirements for managing water in water-rich fractured rock masses, thus failing to ensure the airtightness of the cavern. In this study, an underground water-sealed cavern project was used as a case study, with geological drilling, geological sketching, and advanced water exploration methods applied to assess the surrounding rock conditions and identify water-rich sections. Based on these assessments, a comprehensive grouting strategy based on the principle of “prioritizing pre-grouting, supplemented by post-excavation grouting, with multi-batch grouting” was proposed, and the grouting effect was evaluated using ground penetrating radar (GPR) and water pressure testing methods. Meanwhile, the theories of grouting in rock fractures were integrated with the practical techniques used in this project to analyze the mechanisms of slurry diffusion and blockage in the multi-batch grouting process. The research results indicated that advanced pre-grouting successfully filled most of the seepage channels within 20 m ahead of the excavation face, resulting in a significant decline in the permeability of the surrounding rock. The water inflow was reduced by 62.67 L per minute (L/min) after pre-grouting, which achieved a reduction rate of up to 94

The coupled effects of geological topography, weathering interfaces, and tunnel structures significantly influence the seismic stability of slopes. In this study, a stepped, highly weathered sandstone slope in southwestern China was investigated using three FLAC3D models: a homogeneous stepped slope, a stepped highly weathered sandstone slope, and a stepped highly weathered sandstone slope with a tunnel. A combined multi-domain framework integrating time-domain, frequency-domain, and time – frequency (HHT) analyses was adopted to evaluate the dynamic response of the slope system. The results show that stepped topography and highly weathered layers jointly amplify the seismic response and promote energy concentration in the platform region, where the maximum MPGA occurs. Compared with the homogeneous stepped slope, the MPGA of the stepped highly weathered slope increases by approximately 1.7–2.5 times. Frequency-domain and time – frequency analyses further reveal a coupled relationship between frequency-dependent dynamic response and seismic energy evolution: components below 2 Hz mainly govern the overall dynamic response of the upper slope, whereas higher-frequency components are associated with localized response concentration near the platform and crest. The tunnel does not substantially shift the four primary characteristic frequency bands, but increases the MPGA by approximately 12–13

Steep bedding slopes are widely distributed in Southwestern China's mountainous regions and have complex seismic responses and instability risks, causing casualties and property losses. Considering the high-seismic-intensity environment, the dynamic failure evolution and instability mechanism of high-steep bedding slopes are simulated via the discrete element method and shaking table test. The dynamic response characteristics and cumulative failure effects of slopes subjected to continuous ground motion are investigated. The results show that the dynamic response characteristics of slopes under continuous earthquakes are influenced by geological and topographic conditions. Elevation has a distinct impact on both the slope interior and surface, with amplification effects more pronounced on the surface. The weak interlayers have different influences on the dynamic amplification effect of slopes. Weak interlayers have dynamic magnification effects on the slope surface at relative elevations of 0-0.33 and 0.82-1.0 but have weakening effects between 0.33 and 0.82. Moreover, the weak interlayers also have controlling effects on the dynamic instability mode of slopes. The characteristics of intergranular contact failure, fracture propagation, and displacement distribution are analyzed to reveal the dynamic failure evolution and instability mechanism through the discrete-element model. The dynamic instability process of slopes includes three stages: fracture initiation (0-0.2g), fracture expansion (0.2g-0.3g), and sliding instability (0.3g-0.6g). This work can provide a valuable reference for the seismic stability and reinforcement of complex slopes.

The disturbance superposition effect induced by twin-tunnelling poses a significant challenge to the stability of the front tunnel. This study proposes a framework for assessing the reliability of front tunnel stability in twin-tunnelling using an automatic machine learning (AutoML) surrogate model that accounts for soil spatial variability. In this framework, a parameterized automatic numerical modelling process was developed to generate a high-fidelity dataset, and a multi-objective prediction model was constructed using AutoML method to predict the ultimate limit state and serviceability limit state of the front tunnel. This model exhibits strong fitting capability and generalization performance, achieving superior results compared to traditional machine learning methods, with aCC values of 0.9866 and 0.9762 on the training and test sets, respectively. In the reliability assessment, random field theory is used to characterize soil spatial variability, while Monte Carlo simulation is used to evaluate the failure probability of the leading tunnel. By replacing numerical modellings with an AutoML-based surrogate model, computational efficiency is significantly improved, reducing computation time by 47.42%-97.90% compared with direct Monte Carlo simulation. The reliability analysis results indicate that soil strength, tunnel interaction, construction control, and support stiffness are key factors influencing the probability of tunnel failure, underscoring the critical importance of considering soil spatial variability in the stability assessment of the front tunnel. Finally, a practical program was developed integrating surrogate model construction and reliability assessment functions, enabling rapid stability assessment of the front tunnel in twin-tunnelling and providing a reference for design optimization and construction decision-making in twin tunnels.

The damage process of geotechnical materials under hydro-dynamic coupling is nonlinear and time-varying, making it difficult to describe using hydraulic or dynamic analysis alone. A novel hydro-dynamic coupled similar material is urgently needed to study the disaster mechanisms of the slope and tunnel. Based on the seepage-vibration equation and dimensional analysis, similarity criteria under hydro-dynamic coupling were derived. A new similar material was developed using quartz sand, iron powder, barite powder, gypsum, sodium silicate, and glycerol. The influence of material composition on physical and mechanical parameters was explored through a series of laboratory tests, including dynamic triaxial tests, SEM, sensitivity analysis, and PCA. Meanwhile, the material was successfully applied in rock slope and tunnel model tests. The results show that the physical and mechanical parameters of the materials have a wide adjustable range. The dynamic elastic modulus and permeability depend on the model’s geometric dimensions, with permeability primarily controlled by gypsum and the elastic modulus by the binder. Additionally, a MIMO-PSO-BP neural network was proposed to predict physical parameters. Both the PCA and the MIMO-PSO-BP model effectively capture nonlinear relationships between composition and parameters. In summary, the novel similar material meets the requirements (parameter variation, hydraulic stability, and dynamic response) for slope shaking table model tests and tunnel excavation model tests under hydro-dynamic coupling effects. This work provides the theoretical support and experimental basis for understanding the disaster evolution mechanism of slopes or tunnels under complex geological conditions.

Natural gas hydrate reservoirs are susceptible to shear-induced destabilization in complex deep-water environments, posing significant geohazards. Existing acoustic-based stability assessment methods remain limited in ability to characterize the coupled mechanical-acoustic response, especially in sediments exhibiting layered hydrate heterogeneity. To address this gap, this study develops a coupled Finite-Discrete Element Method (FDEM) framework with active ultrasonic pulse velocity measurements to investigate multiscale failure mechanisms and associated acoustic responses during shear. Results reveal a layer-dependent transition in dominant failure modes: the low-saturation is governed by tensile-shear failure, whereas the higher-saturation sublayer is dominated by compressive-shear failure. A saturation contrast threshold of approximately 20% between layers critically controls the spatial decoupling of shear bands and fracture zones. At the micromechanical scale, strain hardening is associated with the formation of a robust force-chain network in the low-saturation layer, which provides a stable supporting skeleton. Spectral analysis further identifies features linked to these failure mechanisms: distributed narrow tensile cracks generate persistent lateral high frequency bands, localized wide shear bands produce truncated vertical bands, and their coupling in layered systems leads to distinctive L-shaped spectral interfaces. By correlating acoustic characteristics with mechanical behavior, this study provides mechanistic insights into the geomechanics of stratified hydrate reservoirs and offers a preliminary basis for interpreting active ultrasonic monitoring data, subject to further laboratory and field validation.

Accurate prediction of roof surface temperature is essential for assessing thermal stress, optimizing material performance, and improving energy management in large-span metal structures. This study develops a data-driven modelling framework for cold-formed stainless steel roof panels via field measurements collected from 15 spatially distributed sensors at Zhuhai Airport over one year, with data recorded every 5 min. The experimental setup covers multiple spatial configurations, including different roof orientations (north-south and east-west), inclination angles (0 degrees, 15 degrees, and 45 degrees), and solar exposure conditions (sun-facing and shaded surfaces), enabling a comprehensive analysis of the environmental and spatial effects on the thermal response. Optuna-based hyperparameter optimization was applied to five ensemble learning algorithms-XGBoost, LightGBM, CatBoost, random forest, and AdaBoost-and their performances were systematically compared. Among them, XGBoost achieved the best balance of accuracy, stability, and generalization, reducing the MAE, MSE, and RMSE by 41.3 %, 54.3 %, and 32.4 %, respectively, compared with linear regression. To further enhance the prediction performance, a two-stage sequential modelling approach, termed spatially enhanced XGBoost (SE-XGBoost), was proposed by incorporating spatial configuration features such as roof type, orientation, and slope into the second stage. This approach effectively corrects spatial residuals and improves generalization across different roof layouts, achieving a 21.7 % reduction in the MAE and a 45.3 % reduction in the MSE, with strong consistency between the training and testing results (R-2 > 0.98). Unlike previous temperature prediction studies that focused on single-surface or daily scale modelling, this work introduces a high-frequency, multipoint, and spatially enhanced ensemble framework capable of capturing hourly thermal dynamics. Furthermore, SHAP interpretation identifies atmospheric temperature, UV intensity, and light intensity as dominant predictors, validating the physical relevance and interpretability of the proposed model.

The excavation of underground engineering structures induces damage in the surrounding rock, resulting in the formation of an excavation damaged zone (EDZ) around the excavation profile. The evolving EDZ will alter the permeability of the surrounding rock mass and thus lead to a changing seepage field. In this article, underground water-sealed petroleum storage caverns are taken as study objects. Based on the measured fractures in the field, a random fracture network simulation technique is used to study the initial permeability characteristics. In addition, the occurrence of the EDZ and its evolution are studied. Combining the initial permeability with the EDZ-induced permeability alteration, and the rainfall process considered, the changing 3D seepage field is analyzed numerically. Water inflow into the cavern working face is predicted, and the influence of excavation on the groundwater table is examined. The results show that the simulation values of the groundwater table agreed well with the monitored ones, considering the effect of cavern excavation. As groundwater conditions are critical to the effectiveness and safety of petroleum storage, investigating the evolution of the groundwater regime during excavation is essential for optimizing construction sequencing and designing reliable water-sealing conditions during operation.

The tunnel portal represents a critical vulnerability in mountain tunnels under seismic loading, where strong earthquakes often trigger chain disasters such as slope instability and lining damage. The 2008 Wenchuan Earthquake revealed typical seismic damage at the Longdongzi Tunnel portal, including slope collapse, lining cracking, and portal burial, highlighting deficiencies in current seismic design methods in addressing the coupled effects of high-steep slope and weak interlayer. To address this, shaking table tests were conducted to systematically reproduce the seismic failure process of high-steep slopes at tunnel portal. Using multi-stage loading combined with acceleration response and lining strain monitoring, the tests quantitatively elucidated the seismic failure mechanism of high-steep slopes and the damage evolution mode of lining structures under strong seismic action. The results indicate significant differences in the seismic failure modes between the homogeneous slope and the slope containing a weak interlayer. The homogeneous slope exhibits a progressive failure process from top to bottom due to acceleration amplification effects. In contrast, the slope with the weak interlayer shows damage concentrated from the outset within the weak interlayer, characterized by a sudden “interlayer activation-rapid sliding” failure mode. The tunnel lining is particularly vulnerable at the crown and invert, where noticeable longitudinal and diagonal cracks develop. Numerical simulation further verifies the slope failure mechanism, indicating that the plastic zone initially forms at the weak interlayer at the foot of the slope and propagates upward, ultimately leading to overall slope instability. And theoretical analysis based on Green’s function confirms numerical results. Furthermore, this study reveals a progressive failure mechanism described as “slope sliding-lining cracking-tunnel portal buried” and clarifies the seismic disaster evolution process in high-steep slope-tunnel areas. The integrated “experimental-numerical-theoretical” research framework established in this study significantly enhances the reliability of the conclusions, provides a new paradigm for studying seismic failure mechanisms in similar engineering projects, and offers an important theoretical basis for seismic design and disaster prevention in similar structures.

Cross-fault tunnels are particularly vulnerable to damage during earthquakes, and aseismic joints are generally considered effective seismic mitigation measures. Two sets of shaking table model tests were designed to investigate the seismic mitigation and damage mechanisms of aseismic joints. The tests aimed to simulate the strike-slip phenomenon during earthquakes, for which a fault-crossing tunnel model capable of replicating this phenomenon was established. The dynamic response characteristics and seismic damage evolution process of the tunnel were analyzed. In addition, energy-based damage identification methods via the Hilbert-Huang transform were employed to examine the dynamic response and damage process and of the lining. The experimental results revealed that inverts and arch springs are the most vulnerable areas in tunnels crossing fault zones, highlighting the need to focus seismic mitigation design on these regions. Although aseismic joints do not significantly improve the stress state at the invert and arch springs, they do reduce the local acceleration response of the lining and help prevent the development of tunnel cracks. Furthermore, both aseismic joints and damping layers are effective seismic mitigation measures. However, when used together, the lining structure requires reinforcement to ensure its seismic resistance. Finally, theoretical derivations were conducted to obtain the longitudinal distribution formulae for the bending moment and shear force of the flexible lining with aseismic joints under seismic loads. These derivations show that aseismic joints enable the lining to adapt to rock movement, increase the displacement capacity during fault slip, and reduce the bending moments and shear forces. (c) 2026 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).