Study on Seismic Dynamic Failure of Tunnel-Soil- Frame Structure System through Shaking Table Test and Numerical Simulation

Study on Seismic Dynamic Failure of Tunnel-Soil- Frame Structure System through Shaking Table Test and Numerical Simulation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Study on Seismic Dynamic Failure of Tunnel-Soil- Frame Structure System through Shaking Table Test and Numerical Simulation Xiaogang Wei, Zhifan Qin, Shiao Wang, Shuaixin Ma, Mengqing Shi, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6508067/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract To investigate the dynamic response of an underground structure-soil-aboveground structure interaction system under seismic action, a shaking table test was conducted with a section of Zhengzhou Metro as the engineering background. A three-dimensional numerical model covering the aboveground and underground multi-structure system was established using ABAQUS. Four working conditions were designed, and three representative seismic motions were selected as input seismic waves. The variation characteristics of key parameters, such as acceleration, shear force, bending moment, and inter-story displacement angle, during the seismic response process of the tunnel and frame structure were systematically analyzed. The research findings indicate that significant dynamic coupling exists between the aboveground and underground structures, with the overall structural system playing a significant role in modulating the propagation path and energy distribution of seismic waves in the site. The acceleration exhibits a trend of attenuation in the near-field response and enhancement in the far-field response. The aboveground frame structure absorbs and dissipates substantial seismic energy in the near-field, while the underground tunnel structure induces amplification of vibration response in the far-field region. In the scenario with aboveground structures, the tunnel's acceleration response exhibits stronger spatial non-uniformity, with distinct points of amplification, reflecting the dynamic disturbance effect of the upper structure. In contrast, in the condition without the upper structure, the tunnel response is relatively symmetric and stable. Regarding force analysis, the inclusion of the aboveground structure improves the force distribution path of the tunnel, reduces the risks associated with sharp fluctuations in bending moments and stress concentration, and also delays and attenuates seismic input via the "energy storage-energy release" mechanism in the time domain, thus enhancing the overall seismic resilience and stability of the system. Moreover, the inter-story displacement angle of the aboveground frame structure is significantly affected by the underground structure, manifested as a weakening of shear stiffness in the lower floors and an increase in the concentration of deformation. The response differences expand significantly under different seismic spectra, showing that the underground structure enhances the system's sensitivity to seismic spectral characteristics. In conclusion, the interaction between aboveground and underground structures has a significant impact on seismic response in complex urban environments. Seismic design should fully consider these structural synergies to enhance the overall seismic performance and safety of the building group. Physical sciences/Engineering Physical sciences/Engineering/Civil engineering Physical sciences/Mathematics and computing/Information technology Physical sciences/Mathematics and computing/Software Seismic response Tunnel–soil–structure interaction Shake-table tests Numerical simulation Dynamic coupling effect Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 1 Introduction As urbanization progresses, diverse underground infrastructure including metro lines, utility corridors, and subterranean commercial areas are becoming densely distributed in developed urban zones, forming a complex three-dimensional structure–soil–structure interaction (SSSI) system with above-ground buildings and infrastructure. Especially in seismically active regions, seismic waves propagate through foundation soils, inducing dynamic responses in above-ground structures and potentially exerting significant impacts on underground structures, which may lead to functional failure or catastrophic damage. Gaining insight into the interaction mechanisms between underground structures, soil, and above-ground structures under seismic influence has emerged as a key topic in contemporary earthquake-resistant engineering research. Conventional seismic analysis and design approaches often treat above-ground frames and underground structures as independent systems, modeling them separately while representing the soil medium with basic boundary conditions or spring elements. While such simplifications are practical for engineering applications, they fail to capture the global response patterns of structural systems under complex seismic wave paths and strong mutual dynamic interactions. For instance, during earthquakes, the above-ground structures can modify the dynamic characteristics of the underground components, while underground structures may disrupt the seismic wave field, subsequently affecting the stress and deformation of surface structures. Therefore, analyzing individual structures in isolation cannot accurately reflect the synergistic response mechanisms of complex structural systems under seismic excitation. In recent years, extensive research has been conducted by scholars both at home and abroad on the dynamic response characteristics of underground structures and their coupling effects with surface buildings [1–7]. Some studies have revealed certain interaction laws through simplified models and theoretical derivations[8–12](Luco and Contesse, 1973; Mylonakis and Gazetas, 2000; Tao et al., 2021;Ding et al., 2023༛ Ansari et al., 2025). However, the high degree of model idealization and the challenges in accurately describing soil nonlinearity limit the engineering applicability of the research findings, which still need further enhancement. Other studies have used shaking table tests to simulate the real response process under seismic effects through scaled models [13–17] (Hokmabadi et al., 2015; Goktepe et al., 2020; Tao et al., 2019, 2022; Fang, 2025), providing intuitive evidence for understanding the coupling effects of structural systems. However, due to the high cost of physical experiments and the limited testing conditions, it is often difficult to cover multiple working conditions and types of seismic motions, making a comprehensive and systematic response analysis challenging. Therefore, combining experiments with numerical simulations to conduct dynamic coupling research of multi-structure systems in typical sites holds significant scientific and practical value [18–21](Toki and Miura, 1983 ; Ding et al., 2019; Tao et al., 2022;Shi et al ,2024). Pitilakis et al. (2008) [22]investigated the seismic response of segmental lining tunnels through experimental and numerical studies, revealing that inner linings amplify the transverse peak acceleration and minimize joint extension, ultimately improving the tunnel's seismic performance. Wang et al. (2013) [23]numerically investigated the dynamic through-soil interaction between an underground station and nearby pile-supported structures under vertically incident S waves using the ANSYS software, highlighting the influence of structural arrangement, shaking direction, distances between structures, and soil properties on the horizontal acceleration magnification factor of ground structures. Their findings showed that the system response can either be amplified or attenuated depending on the distance between adjacent buildings, with neighboring low-slung buildings being particularly affected by the seismic wave. Chen et al.(2018) [24]conducted experimental and numerical studies on the seismic response of segmental lining tunnels, demonstrating that inner linings increase the transverse peak acceleration and reduce joint extension, thus enhancing the tunnel’s seismic performance. Wang et al. (2018)[25] conducted shaking table tests and numerical simulations to study the seismic response of an underground structure-soil-surface structure interaction system, demonstrating that the presence of the tunnel amplifies seismic response in the surrounding soil while reducing the seismic response of the surface structure, especially at lower and medium floors. Tao et al. (2020) [26]conducted large-scale shaking table tests comparing the seismic performance of a newly designed prefabricated subway station structure and a traditional cast-in-place structure, finding that while the prefabricated structure showed better energy absorption, it had lower deformation resistance and more severe damage, but maintained relative stability under extreme seismic conditions. Shi et al. (2023) [27] analyzed the seismic response of the giant-span flat cavern, finding that its deformation, stress, and damage remained within safe limits, with the interaction between linings enhancing stability, while extreme earthquakes led to a stable double-hinged arch structure. Based on a new classification framework, Ebrahimipour and Eslami (2024) [28]explored the applicability of vector-acting foundations in complex offshore conditions, focusing on pile–soil interaction in sensitive and layered soils. Utilizing CPTu data and the neutral plane concept, they quantified sensitivity effects on resistance and proposed design criteria, with ground improvement effectiveness validated through case studies. Chandrawanshi and Garg (2025) [29]investigated the effect of structure-soil-structure interaction (SSSI) on the footing settlement of a three-story RCC building, finding that SSSI significantly amplifies vertical settlement in footings near adjacent structures, leading to notable changes in differential settlement compared to traditional soil-structure interaction (SSI) analysis. In summary, significant progress has been made in recent years in understanding the dynamic response of structure–soil–structure interaction (SSSI) systems under seismic loading, with steady advancements in theoretical modeling, experimental techniques, and numerical simulation methods. Nevertheless, limited research has addressed the seismic behavior of multi-structural systems like raft foundation frame structures above embedded tunnels, especially under the compounded effects of structural complexity, significant stiffness variation, and overlapping seismic wave paths. By combining shaking table experiments with 3D finite element modeling, this research investigates the seismic behavior of a tunnel–soil–frame system, highlighting the influence of the superstructure on wave propagation, the energy transmission between soil layers and tunnel, and the upper structure’s feedback effect on localized tunnel response. Multiple critical response parameters, such as acceleration, shear force, bending moment, and story drift, are analyzed to demonstrate how underground structures interfere with the distribution of shear capacity and spectral response of the above-ground building. The findings contribute to the refinement of current SSSI theory, the enhancement of collaborative seismic design for multi-structure systems in urban underground development, and provide theoretical and practical insights for seismic damage assessment and risk mitigation in complex engineering scenarios. 2 Shaking table test 2.1 Shaking table and model box parameters The shaking table test is conducted using a biaxial electro-hydraulic servo seismic simulation shaking table configured by the School of Civil Engineering at Liaoning Technical University (see Fig. 1). The table has a surface size of 3m×3m, with a maximum driving acceleration of ± 1.5g, a load capacity of 10t, and a frequency range of 0.1 to 50Hz, capable of simulating seismic motions in the horizontal X and Y directions. The test uses a rigid model box welded from 3mm thick steel plates, with dimensions of 2m×2m×1.5m. To enhance overall stiffness and prevent lateral instability, diagonal supports are added to the external structure. The inner walls of the box are lined with 200mm thick polystyrene foam boards to absorb boundary reflection waves and reduce test errors. A gravel layer is placed at the bottom to enhance the contact friction with the soil and prevent sliding during vibration. The model soil is taken from the sand layer of a real engineering site. As liquefaction is not a concern, the sand was air-dried, oven-dried, and sieved before the experiment to obtain homogeneous fine sand. Based on experimental conditions, a layered filling method was employed, with each layer compacted to 200mm up to a total depth of 1.3m, simplifying the field to a uniform one to enhance compaction and experimental reproducibility. The primary physical parameters are shown in Table 1. Table 1 Basic Physical Properties of the Test Sand Density (g/cm 3 ) Relative Density (%) Poisson's Ratio Internal Friction Angle (ฒ) Elastic Modulus (MPa) 1.614 80 0.30 30 12.69 2.2 Design Based on Similarity Ratio The experimental model design must satisfy the similarity of geometric, physical, and boundary conditions to ensure the engineering representativeness of the dynamic response. The prototype tunnel structure has a cross-section of 8.4m × 5.3m, with a top burial depth of 15.9m, and is 6.6m away from the foundation of the aboveground structure. The aboveground structure consists of a 7-story raft foundation frame, with floor slabs 0.12m thick and column sections of 0.6m × 0.6m. The tunnel and the frame structure use different grades of concrete, as detailed in Table 2. Table 2 Component Parameters of Tunnel and Frame Structure — Structural Location Concrete Strength Grade Elastic Modulus (×10 4 MPa) Poisson's Ratio Density (kg/m 3 ) Tunnel Structure — C50 3.45 0.2 2500 Frame Structure Beam C30 3.00 0.2 2500 Plate C30 3.00 0.2 2500 Column C40 3.25 0.2 2500 Foundation C35 3.15 0.2 2500 According to the Buckingham-π theorem, and considering the shake table and related experimental conditions, the elastic modulus, geometric dimensions, density, and acceleration were chosen as the basic physical quantities, resulting in a similarity ratio of 1:30 between the model and the prototype. The similarity ratios for the elastic modulus were 0.1 (beam, plate), 0.095 (foundation), 0.092 (column), and 0.087 (tunnel), with the remaining similarity relationships derived from the π theorem, as detailed in Table 3. Table 3 Similarity Ratios of Model Structure Physical Parameter Similarity Relationship Tunnel Foundation Beam Plate Column Length \({\gamma _l}\) 1/30 Displacement \({\gamma _x}={\gamma _l}\) 1/30 Material Density \({\gamma _\rho }\) 0.472 Elastic Modulus \({\gamma _E}\) 0.087 0.095 0.1 0.1 0.092 Stress \({\gamma _\sigma }={\gamma _E}\) 0.087 0.095 0.1 0.1 0.092 Time \({\gamma _t}=\sqrt {{\gamma _l}}\) 0.183 Velocity \({\gamma _v}=\sqrt {{\gamma _l}}\) 0.183 Acceleration \({\gamma _a}={\gamma _g}=1\) 1 Frequency \({\gamma _\omega }=\frac{1}{{\sqrt {{\gamma _l}} }}\) 5.477 After calculation, the total mass of the model structure, additional artificial mass, and non-structural component mass did not exceed the maximum load capacity of the shake table, so an artificial mass model was used for this experiment. The similarity ratio for the artificial mass is calculated as follows: $$\:{m}_{a}={\lambda\:}_{E}{\lambda\:}_{l}^{2}{m}_{p}-{m}_{m}$$ 1 In the equation: \(\:{m}_{a}\) is the additional artificial mass; \(\:{\lambda\:}_{E}\) is the similarity ratio of the elastic modulus; \(\:{\lambda\:}_{l}\) is the geometric similarity ratio; \(\:{m}_{p}\) is the prototype mass; \(\:{m}_{m}\) is the model mass. The additional artificial mass at each location for the tunnel and frame structure is calculated using the above formula, as shown in Table 4. During the calculation process, the mass of the frame structure's columns and slabs is allocated to the floor slabs of the adjacent upper and lower layers. Table 4 Additional Artificial Mass Model Structure Tunnel Structure Frame Structure Foundation First Floor Slab Second Floor Slab Standard Floor Slab Top Floor Slab Additional Artificial Mass 32.63kg 19.526kg 7.255kg 4.865kg 4.714kg 4.119kg Actual Counterweight Mass 33.00kg 20.00kg 7.25kg 5.00kg 4.75kg 4.25kg 2.3 Design of Scaled Model During the experiment, structural deformation predominantly remains in the elastic phase, so acrylic is chosen for the model material due to its excellent uniformity, light weight, high strength, and relatively low elastic modulus. The elastic modulus is measured at 3 GPa, and the density is 1180 kg/m³. With the consideration of similarity ratio and vibration table capacity, the tunnel model has a cross-sectional size of 28 cm × 17.6 cm and a lining thickness of 1 cm; the column cross-section of the frame structure is 2 cm × 2 cm, while the beam cross-section is 1 cm × 2 cm, with the bottom beam being 2 cm × 2 cm. To mitigate boundary effects, the tunnel model is set at a length of 70 cm, as shown in Fig. 2. 2.4 Sensor Arrangement and Test Loading Conditions To capture the seismic response of the system at various locations, the experiment deployed 14 accelerometers (labeled as A) to measure the acceleration responses at different points: within the soil, on the surface of the soil, on the sides and bottom of the tunnel, near the ground surface of the tunnel, at the bottom of the foundation of the frame, and at each floor. Additionally, 8 strain gauges (labeled as S) were used to collect strain data from the tunnel's roof, floor, and sidewalls. The sensor layout is shown in Fig. 3. The test was performed under four loading conditions: free field (FF), soil-tunnel structure system (ST), soil-raft foundation frame structure system (SRF), and tunnel-soil-raft foundation frame structure system (STRF). The sensor layouts for FF with ST, and SRF with STRF conditions were identical. The tunnel structure is positioned in the center of the box, 0.66 m from the left and right boundaries, while the frame structure is positioned 0.4 m above the tunnel. Considering the natural vibration characteristics of the structural system, the Chi-Chi, El-Centro, and Kobe waves were chosen as seismic inputs. The seismic waves were adjusted for time and peak acceleration according to similarity laws, and then used to excite the model test. The Fourier transform was applied to the adjusted 0.1g acceleration time history to obtain the corresponding frequency spectrum curve (refer to Fig. 4). During the experiment, seismic waves were applied unidirectionally in the X direction, with four loading conditions applied stepwise at 0.1g, 0.2g, and 0.3g loading gradients. Before and after each loading stage, a 0.1g white noise unidirectional sweep was performed to measure the changes in the structure interaction system and the structure's natural frequencies. A total of 39 experimental sets were carried out, with the loading scheme illustrated in Fig. 5. 2.5 Analysis of boundary effect influence The boundary effect is also known as the model box effect. To ensure the validity of the experiment and the reliability of the data, the 2-norm deviation proposed by Chen [30] is used to evaluate the quality of the model box boundary effect. The 2-norm deviation value is used to measure the difference between two signals at any given moment, defined as the square root of the ratio of the squared difference to the squared sum of the reference signal. In this experiment, the vibration response at the center point of the same layer of soil is selected as the reference signal. The boundary effect is assessed by comparing it with the vibration response at boundary points. Generally, the closer the two signals are, the smaller the boundary effect. $$\mu =\frac{{\left\| {{x_i} - {x_j}} \right\|}}{{\left\| {{x_i}} \right\|}}=\sqrt {\frac{{\sum\nolimits_{{i=1}}^{n} {{{\left( {{x_i} - {x_j}} \right)}^2}} }}{{\sum\nolimits_{{i=1}}^{n} {{x_i}^{2}} }}}$$ 2 In this case, the reference signal is denoted as \({x_i}\) , and the comparison signal is denoted as \({x_j}\) . Taking the Chi-Chi wave under the FF condition as an example, experimental data from measuring points A10-A14 were used for validation analysis, with the final calculation results shown in Table 5. This demonstrates that the boundary effect issue in this experiment has been properly handled. Table 5 2-norm deviation of acceleration at each measurement point Measurement point \(\mu\) Measurement point \(\mu\) A10 0.143 A13 0.164 A11 0.179 A14 0.157 A12 0.188 — — 3 Establishment of the numerical model 3. 1 Establishment of the scaled model A numerical simulation model consistent with the scaled model used in the shaking table test is established using ABAQUS finite element analysis software. Material properties are detailed in Table 6, and the Rayleigh damping model is selected with a damping ratio of 0.05, applied in the calculation of the structural model. Table 6 Material Parameters of the Scaled Model Structure Materials Density (kg/m 3 ) Elastic modulus (Pa) Poisson's ratio Acrylic glass 1180 3.0×10 9 0.2 Polystyrene foam board 15 4.13×10 6 0.46 Rigid box 7850 2.06×10 11 0.3 Counterweight block 7645 1.2×10 11 0.25 According to the study by Kuhlemeyer and Lysmer [31], the finite element mesh size should meet the following conditions: $$\:{l}_{0}\le\:\frac{\lambda\:}{10}=\frac{{v}_{s}}{10\bullet\:{f}_{max}}$$ 3 In this case, λ represents the wavelength of the selected seismic wave, \(\:{v}_{s}\) is the shear wave velocity of the model soil in the shake table experiment, and \(\:{f}_{max}\) is the maximum frequency of the chosen seismic wave. The shear wave velocity \(\:{v}_{s}\) is calculated by dividing the time difference between the peak accelerations measured at monitoring point A01 at the bottom of the model box and monitoring point A14 at the center of the soil surface during the free-field (FF) condition by the model soil thickness. After calculation, an element size of 0.05 m was chosen. The simulation of the four conditions is carried out using three-dimensional eight-node linear solid elements (C3D8), as shown in Fig. 6. 3. 2 Model Verification A comparative analysis of the modal responses of the shaking table model and numerical simulation model for the four conditions (FF, ST, SRF, STRF) was conducted to obtain the first-order natural frequencies, with the first-order mode shapes shown in Fig. 7 and the comparison results presented in Table 7. The comparison results show that the relative error of the first natural frequency for the four structural systems between the shaking table test and numerical simulation is within 10%, indicating that the difference in natural frequencies between the experimental results and numerical simulation is small. Table 7 First Natural Frequencies of the Shaking Table Test and Numerical Simulation Models for Each Condition Structural system Shaking table test (Hz) Numerical simulation (Hz) Relative error FF 15.966 16.640 4.05% ST 14.375 15.523 7.40% SRF 13.569 14.430 5.97% STRF 13.633 14.462 5.73% In order to further validate the accuracy of the numerical simulation results, the Chi-Chi wave with a 0.1g amplitude was used as the input, comparing the shaking table test and numerical simulation results for both the ST and STRF conditions. The acceleration-time history and Fourier spectrum for measurement point A11 (soil surface) under the ST condition, and the acceleration-time history and Fourier spectrum for measurement point A14 (top slab of the raft foundation framework) under the STRF condition, are shown in Fig. 8. The comparison reveals that the acceleration-time history curves at the same measurement points exhibit good fitting between the shaking table test and numerical simulation, and the Fourier spectrum fitting results fall within the error range, suggesting that the numerical model developed in this study is highly reliable, with accurate calculation results. In this section, based on the completion of the shaking table test for the tunnel-soil-frame structure system, further scale ratio numerical simulation analysis is conducted. The simulation process adopts the same geometry, materials, and boundary conditions as the test model to ensure comparability between the two. By comparing the fundamental frequency, floor acceleration-time history curves, and Fourier spectrum response characteristics obtained from both the test and simulation, the results indicate that the numerical model can accurately reproduce the dynamic response behavior of the physical model, thereby validating the rationality and effectiveness of the adopted modeling approach under seismic excitation. Therefore, the same modeling method used for the scaled model will be applied in subsequent prototype-scale three-dimensional finite element modeling analysis to ensure the accuracy of the simulation results. 3. 3 Establishment of the full-scale model 3.3.1 Calculation scope The full-scale numerical model features a surface building structure consisting of a six-story aboveground and one-story underground bidirectional single-span frame structure. The design information and component dimensions of the frame structure are shown in Table 8, while the size design of the underground tunnel structure is provided in Section 2.2 . Table 8 Component Dimensions of the Full-Scale Numerical Model of the Frame Structure (Unit: mm) Component type Cross-section of the frame beam Cross-section of the foundation beam Cross-section of the column First-floor height Standard floor height Basement floor height Floor slab thickness Prototype dimensions 600×300 1200×600 600×600 3600 3450 4500 120 To prevent the seismic waves reflected at the boundaries of the full-scale numerical model from re-entering, it is essential to establish a sufficiently large computational domain for the soil, ensuring that the surrounding soil meets the free-field conditions. To optimize both computational efficiency and accuracy, the soil model's computational domain should be set according to the ratio L s /H s , which needs to be at least 5, as proposed by Miao et al. (2020) [32]. Here, H s refers to the soil height, and L s is the distance between the outermost structural boundary and the soil boundary. Figure 9 illustrates the computational domain of the full-scale numerical model under the STRF condition. 3.1.2 Selection of Seismic Motions To enhance the engineering applicability of this study, seismic motions were selected based on the design parameters and site characteristics of the Zhengzhou region, ensuring compatibility with the target response spectrum within the primary structural period range (with a deviation not exceeding 20%). Two natural earthquake records were selected from the PEER database, and one artificial ground motion was generated based on code specifications. All three seismic inputs were amplitude-scaled to 0.055g to simulate frequent earthquake scenarios. A comparison between the response spectra and the code spectrum is shown in Fig. 10, and the corresponding acceleration time histories and Fourier spectra are presented in Fig. 11. As shown in Fig. 11, the dominant energy of the selected seismic waves is concentrated within the 0–10 Hz frequency band. Considering the velocity similarity ratio of 0.183 in Table 3 and the shear wave velocity of the model soil, an element size of 1.8 m was adopted for the full-scale numerical model to balance computational precision and efficiency, as illustrated in Fig. 9. 4 Dynamic Response Analysis To further elucidate the dynamic response characteristics of the tunnel–soil–frame structure system under seismic loading, this study conducts a comparative investigation based on experimental and numerical simulations, focusing on acceleration response, internal force evolution, and frame displacement. Special emphasis is placed on analyzing the modulation effects of different working conditions on the system’s response patterns, thereby providing support for engineering evaluation of interaction effects. 4. 1 Mode Shape Analysis The modal response represents a crucial dynamic property of structural or soil–structure interaction systems, facilitating the prediction of seismic behavior. For the STRF condition, the fundamental frequency is 1.9275 Hz. As illustrated in Fig. 12, the first mode is characterized by shear deformation of the structure. The theoretical natural frequency of the model soil is given by: In the equation: \({f_n}\) is the n-th natural frequency, \({v_s}\) is the shear wave velocity of the soil, and is the thickness of the soil layer. The calculated first natural frequency is\({f_1}\) = 1.9365 Hz, which agrees well with the modal analysis result. 4. 2 Acceleration Response Analysis 4.2.1 Acceleration Response of Ground Soil Figure 13 illustrates the spatial distribution of peak ground surface acceleration under the SFRF condition. Here, L denotes the soil width along the longitudinal direction of the tunnel. As shown in the figure, the peak ground surface acceleration is significantly influenced by the interaction between the frame structure and the tunnel. The peak acceleration at the central location of the ground surface is noticeably lower than that in the far field. Moreover, it can be observed that the structural system significantly affects the site soil within an approximate range of 400 m, which is 33.3 times the total width of the structure (12 m). Figure 14 illustrates the peak ground surface acceleration distribution along the central cross-section of four distinct site-structure combinations under ASW input. It is evident that when the frame structure exists alone (SRF), the peak surface acceleration near the frame markedly decreases, especially at the soil-frame interface, where the reduction is most pronounced. Compared to the FF condition, the maximum peak acceleration drops by 0.4% (from 0.12047g to 0.12g). Moving away from the frame, the surface acceleration response of the soil increases at first, then decreases, and ultimately becomes steady. In the SRF case, at around 105 m from the site center, the soil surface acceleration gradually reduces to match that of the free field. This suggests that the frame structure influences the surface acceleration of surrounding soil only within a limited region, approximately 8.75 times the structure's width (12 m). Comparing the ST and STRF conditions, it is evident that the presence of the structure weakens the acceleration response of the soil near the structure within a certain range, while causing an amplification effect on the far-field acceleration response. The overall pattern is characterized by "initial increase—subsequent decrease—final increase." This suggests that the propagation of seismic waves in the soil is significantly influenced by the structural system, especially in the STRF condition, where the presence of the superstructure, with its large stiffness and mass, has a stronger ability to absorb and dissipate seismic energy, effectively suppressing the near-field acceleration response. Regarding the reduction in peak surface acceleration, the peak acceleration under STRF is 0.1167g, which is a 2.75% decrease compared to the free-field condition (FF) at 0.12g, while the ST condition only shows a reduction of 0.75%, further validating the enhanced seismic response control capacity of the superstructure. The trend in acceleration response illustrates the complex interaction between the structure and the soil, producing nonlinear effects such as reflection, scattering, and interference in the seismic wave propagation. In terms of amplifying the far-field acceleration response, compared to the free-field condition, STRF begins to amplify the surface acceleration response around 86 meters from the center of the site, while ST shows a similar trend around 92 meters. This indicates that the influence of the structural system on the acceleration response of the soil differs with distance: in the near-field region, STRF, due to the combined effect of the superstructure's mass and stiffness, more effectively suppresses the transmission of seismic energy, delaying the onset of far-field amplification, while ST, which includes only the tunnel structure, has limited energy absorption and dissipation capacity, resulting in a later onset of the far-field amplification effect. Furthermore, the structural system’s modulation of the seismic wave path and field characteristics amplifies the tunnel’s influence on the acceleration response over greater distances, emphasizing the complementary roles of aboveground and underground structures in seismic response control. The near-field response is predominantly influenced by the superstructure, while the far-field response is mainly shaped by the tunnel’s modulation of the seismic wave propagation and energy distribution. The tunnel’s presence significantly amplifies the far-field acceleration response, suggesting that underground structures lead to energy concentration or superposition in the seismic wave propagation process, thereby increasing far-field vibration levels. 4. 2.2 Tunnel acceleration response Figure 15 presents the three-dimensional distribution of peak acceleration response along the longitudinal direction and at various cross-sectional positions (angles) of the tunnel structure under two different scenarios (STRF and ST). In this figure, STRF represents the condition where the tunnel structure and the framework structure interact together, while ST refers to the comparative condition considering only the tunnel. In the STRF condition, the peak acceleration of the tunnel structure exhibits significant spatial non-uniformity along both the longitudinal and angular directions. Specifically, within the angular range of about 30° to 150° and the length positions between − 10 m and + 10 m, the acceleration reaches a maximum value of approximately 0.106g. This localized response enhancement is primarily due to the dynamic interference from the upper framework structure under seismic excitation, which is transferred to the tunnel structure, causing a notable increase in the dynamic response at the junction between the tunnel's upper section and sidewalls. This dynamic coupling mechanism alters the stress concentration and seismic wave propagation paths within the structural system, thereby forming regions of amplified response at certain locations. In comparison, the peak acceleration distribution of the tunnel structure under ST conditions is generally more uniform, with smaller gradients in both the longitudinal and angular directions. This suggests that, in the absence of the upper structure’s interference, the seismic wave propagation within the tunnel structure is primarily influenced by the structure-soil interaction, leading to a symmetric and stable response distribution. Additionally, under STRF conditions, there are localized peak variations at multiple points, while the ST condition exhibits high symmetry and stability, indicating that the response distribution at different positions along the tunnel section shows greater asymmetry and variance when the upper structure is present. Figure 16 illustrates the distribution of acceleration responses at the central cross-section of the tunnel under different operational conditions. Comparison reveals that the acceleration response at the tunnel’s central cross-section under the STRF condition is slightly higher than under the ST condition, with a peak acceleration increase of approximately 5%. This result suggests that the upper framework structure has a certain strengthening effect on the dynamic acceleration response of the tunnel. The additional mass and stiffness of the superstructure modify the propagation and reflection characteristics of seismic waves within the structure-soil system, resulting in the amplification of seismic motion in localized tunnel areas, especially at the central cross-section. This phenomenon should be given attention in practical seismic design, requiring comprehensive consideration of the coupling effect of the upper structure on the dynamic behavior of the underground structure. 4. 3 Internal force response analysis Since this study considers only the horizontal X-direction as the direction of seismic excitation, the internal forces generated in the frame structure and tunnel under seismic action are primarily influenced by bending moments and shear forces along the excitation direction. Therefore, this study focuses on the bending moments, shear forces in the tunnel and frame structure along the excitation direction as the primary research subjects for internal force response analysis of the structural system. 4.3.1 Tunnel internal force response Figure 17 shows the spatiotemporal evolution of shear force and bending moment responses under seismic excitation for the ST condition (only considering the tunnel structure) and the STRF condition (with the frame structure superimposed above the tunnel structure). A clear comparison of the 3D response diagrams under the ST and STRF conditions reveals that under the ST condition, where the upper frame structure is not considered, the shear force and bending moment responses of the tunnel structure exhibit strong nonlinear characteristics, especially during the main seismic event phase (approximately 5s to 15s). The shear force and bending moment distributions along the tunnel length direction show multi-peaks with significant fluctuations. In the ST condition, the maximum shear force is approximately ± 4×10⁴ N, and the maximum bending moment response is approximately ± 1×10⁵ N·m. The response surface exhibits noticeable discontinuities and peak concentrations at both ends and the center of the tunnel, indicating significant force concentration and potential weak spots in the structure under this condition. The shear effect and rotational inertia induced by the earthquake are particularly pronounced in localized areas. In the STRF condition, where the upper framework structure is considered, significant differences in the structural response are observed. The maximum shear force response increases dramatically to ± 1.2×10⁶ N, indicating that the seismic excitation causes a larger reverse shear force along the tunnel structure due to the combined influence of both above-ground and underground structures. However, the overall response surface exhibits a more continuous and smoother distribution, lacking the abrupt changes seen frequently in the ST condition. This change suggests that the above-ground structure modulates and couples the seismic input, potentially amplifying the shear response locally, but overall maintaining the stability of the force transfer path and the smoothness of the time history. Regarding the bending moment response, the maximum bending moment under the STRF condition is almost the same as under the ST condition, remaining around ± 1×10⁵ N·m. However, the distribution along the length of the tunnel becomes more uniform, with fewer peaks, and the response surface tends toward a smoother elliptical shape. This feature indicates that the upper framework structure partially restrains the local rotation and twisting of the tunnel structure, shifting its bending moment response from sharp jumps to a continuous distribution, thus reducing stress concentration caused by inertial coupling within the structure. From the time dimension analysis, the peak values of shear and bending moment responses under the STRF condition occur slightly later than those under the ST condition, with the main response duration being shorter, exhibiting certain hysteresis and attenuation characteristics. This phenomenon further indicates that the above-ground structure, through its own mass and stiffness characteristics, plays a buffering role of "energy storage and release" in the structure-soil-structure coupled system, capable of partially absorbing and redistributing seismic energy, thus effectively delaying and weakening the dynamic response transmitted to the underground structure. It is evident that under the ST condition, the single tunnel structure, due to the lack of collaborative effects from the upper structure, experiences seismic loads that directly act on the tunnel body, resulting in significant local shear and bending moment concentrations. However, under the STRF condition, the above-ground frame structure, through its collaborative effects with the foundation and tunnel, not only acts as a "response regulator" but also facilitates the formation of a more rational force transfer path throughout the system, thereby enhancing the overall stability and seismic resilience of the tunnel structure under seismic excitation. In conclusion, the shear and bending moment three-dimensional spatiotemporal evolution characteristics presented in this section fully reveal the differences in the force responses of the tunnel structure under different boundary conditions under seismic loading and their underlying causes. The results suggest that the STRF condition, considering the soil-structure-structure coupling effect, not only reduces stress fluctuations and the intensity of the response over time but also optimizes the overall response shape of the underground structure, thereby improving its load-bearing capacity and safety redundancy under strong seismic environments. 4.3.2 Internal Force Response of the Frame Structure Figure 18 illustrates the spatial response characteristics of shear force and bending moment as a function of time and beam length for the top beam of the frame structure under seismic excitation, in two conditions: STRF (with tunnel structure) and SRF (without tunnel structure). This figure reflects the nonlinear response behavior of the structural system under complex dynamic loads and reveals the influence mechanism of the underground structure on the load-bearing performance of the upper frame structure. In order to gain a deeper understanding of the interaction between structures, the analysis is conducted from four aspects: shear force response, bending moment response, time evolution characteristics, and structural collaboration effects. From the Fig. 18, it can be observed that the shear response under both STRF and SRF conditions is mainly concentrated in the main seismic shaking phase from 5s to 15s, showing typical seismic excitation features. Along the length of the beam, the shear force shows a clear trend of gradually transitioning from negative to positive values, reflecting the formation of a complex bending-shear coupled internal force state in the beam section under the action of horizontal inertial forces and node restraints. Under STRF conditions, the maximum shear response is about ± 2×10⁴ N, and the spatial distribution of shear along the beam length exhibits a continuous slope change trend, with local shear peaks occurring at the beam ends and in the middle region. On the whole, the macroscopic shape of the shear spatial distribution under both STRF and SRF conditions is essentially the same, showing a linear variation trend from one end to the other. This suggests that the shear transfer in the frame structure is primarily influenced by its own stiffness distribution and the direction of seismic excitation, with the underground structure not causing any fundamental changes in the overall shear transfer path. The right side of the figure shows the bending moment response of the top beam with respect to time and length changes, where both exhibit a similar spatial distribution trend, with response peaks occurring at the beam ends and middle regions. Under STRF conditions, the maximum bending moment value reaches ± 6×10³ N·m, and the response surface shows a multi-peak dense distribution, with a steep response gradient forming especially in the beam end region, reflecting a typical bending moment concentration phenomenon. This suggests that the change in the dynamic stiffness of the soil layer due to the tunnel structure further affects the force distribution in the upper structure, increasing the rotational inertia response of the beam, thereby intensifying the bending moment distribution. In comparison, the bending moment response under SRF conditions shows a highly consistent spatial distribution with STRF conditions, both exhibiting a typical distribution characteristic of “the main peak regions at the middle and both ends of the beam,” reflecting that the structure is primarily controlled by mid-span bending moments under seismic loading, with a stable vibration mode. The maximum bending moment under SRF conditions is approximately ± 5×10³ N·m, slightly lower than under STRF conditions, indicating that in the absence of underground structure disturbance, the dynamic response of the frame structure is mainly dominated by its own structural form and stiffness distribution, showing a typical alternating feature of mid-span and end-span, which is consistent with the response characteristics of bending components commonly seen in engineering. The distribution of each response variable along the time axis reveals a distinct "initial gradual rise—sharp increase—fall" trend in structural response intensity as the earthquake unfolds. The peak response under STRF conditions lags slightly behind that under SRF conditions, suggesting that the underground structure induces a transient delay effect in the system's energy transfer. More significantly, the period of sustained high-intensity response under STRF conditions is noticeably longer than under SRF conditions, particularly in the shear response, which lasts for over 10 seconds. This indicates that the SSSI system creates a vibration extension effect during energy dissipation and transfer, requiring higher seismic performance from structural materials, component ductility, and construction joints. Based on the above analysis, it is evident that under STRF conditions, the shear and bending moment responses of the top-level beams are superior in terms of intensity, spatial distribution, and time continuity compared to SRF conditions. This reflects that the presence of the underground tunnel structure has a significant impact on the seismic wave propagation path, the participation of structural modes, and the internal force transfer path. This phenomenon reveals the typical "above-ground—underground" structural coupling response characteristics. The underground structure not only serves as the medium for wave propagation but also exerts a feedback effect on the upper structure through foundation deformation and stiffness changes. This response mechanism suggests that the construction of tunnel structures, such as subways and underground passages, in densely built urban areas significantly affects the surrounding above-ground buildings. In structural seismic design, this coupling mechanism should be fully taken into account, and a collaborative design strategy should be adopted to optimize the overall seismic performance of both the upper and lower structures, ensuring the overall safety and stability of the building complex under strong seismic forces. 4.3.3 Displacement response of the frame structure Figure 19 illustrates the variation distribution of interstory drift angles along the building height direction under the influence of three typical seismic motions (RSN9, RSN32, RG) for SRF (left) and STRF (right) conditions. This reflects the evolution of the structural interstory deformation capacity and demand with height. The interstory drift angle is a key metric in assessing a building's seismic deformation capacity and interstory damage potential, which directly correlates with the structure's ductility performance and failure mode under seismic loading. Under the SRF condition, the inter-story drift angle variation under different seismic motions shows some irregular patterns. For the RSN32 seismic excitation, the inter-story drift angles show a relatively large overall magnitude, with a peak value of about 0.021% at the second floor. This behavior demonstrates the dominant response of the lower floors, which is linked to the concentration of spectral energy in the lower-frequency modes of the seismic motion. The response curves for RSN9 and RG show clear “inflection points”, especially under RG seismic excitation, where the inter-story drift angle at the fourth floor peaks and then quickly drops, reflecting a resonance or interference effect between the seismic spectrum characteristics and the structural modes. Furthermore, RSN9 exhibits similar response amplitudes at both the lower and upper floors, showing a relatively smooth trend with minimal fluctuations. This indicates that the seismic energy does not demonstrate a clear concentration effect during its transmission through the structure, leading to a more balanced dynamic response. In comparison, under STRF conditions (right figure), the overall inter-story drift angle magnitude significantly increases, especially under the RSN32 condition, where the maximum drift angle rises to 0.030%. This indicates that the presence of the underground tunnel structure enhances the overall seismic response of the structure. This amplification effect results from the change in the coupled dynamic characteristics of the foundation-structure system, leading to more complex reflection and superposition of seismic energy within the structure, thereby inducing larger inter-story relative displacements. Additionally, compared to SRF conditions, under STRF, the curves exhibit a more pronounced "larger at the bottom, smaller at the top" trend, with inter-story drift angles at the lower floors greater than those at the upper floors, especially under RSN9 excitation. This suggests that the underground structure weakens the shear capacity at the bottom of the structure or enhances the soft soil effect, leading to more concentrated inter-story deformation in the lower floors. From the comparison of the response differences among the three seismic motions, RSN32 excitation causes the largest inter-story drift angle under both SRF and STRF conditions, which is related to its high energy density or proximity to the structure's natural frequency. It is noteworthy that under STRF conditions, the variation of inter-story deformation among different seismic motions becomes more pronounced, and the dispersion of the curve distribution increases. This reflects an enhanced sensitivity of the underground structure to the seismic motion spectrum characteristics, indirectly indicating an amplifying effect on the uncertainty of the structural response. The figure reveals the significant impact of the complex interaction between the foundation-structure dynamic system and seismic response in the presence of underground structures. Under STRF conditions, the structure not only experiences an overall increase in inter-story drift angles, but the distribution trend of inter-story deformation shifts from "upper-floor dominant" to "lower-floor dominant". This suggests that in practical engineering design, special attention should be given to the coupling relationship between the lower structure and underground facilities, and their impact on the concentration of inter-story deformation. 5 Conclusion This study preliminarily explores the dynamic coupling effect between above-ground frame structures and underground tunnels under seismic excitation. By establishing a finite element model based on ABAQUS and validating the structural response through shake table tests, the variation patterns of shear force, bending moment, and inter-story drift angle of the tunnel and frame structure under different conditions are revealed. In the comparative analysis section, three sets of typical seismic motions were input, and extensive numerical calculations were performed. The main conclusions are as follows: (1) The interaction between the above-ground frame structure and underground tunnel significantly affects the seismic response characteristics of the site, exhibiting a near-field attenuation and far-field amplification trend. The upper structure governs near-field energy dissipation, while the tunnel structure amplifies the far-field vibration response. The structural system plays a role in modulating the seismic wave propagation path and energy distribution, with an influence range up to 33.3 times the width of the structure. (2) In the dynamic response analysis of the tunnel structure, under STRF conditions, the peak acceleration of the tunnel exhibits significant spatial nonuniformity, especially with amplified responses at specific locations, mainly due to the dynamic interference from the upper frame structure. Under ST conditions, the acceleration distribution of the tunnel is relatively uniform, and the response tends to be symmetric and stable. Moreover, the acceleration at the tunnel's center section under STRF conditions is approximately 5% higher than that under ST conditions, indicating that the upper frame structure enhances the dynamic response of the tunnel. Overall, the influence of the upper structure on the tunnel's dynamic response cannot be ignored, and the coupling effect between the two should be considered in seismic design. (3) Under ST conditions, the shear and bending moment responses of the tunnel structure show significant nonlinear behavior, with intense fluctuations and stress concentrations in certain regions, indicating the presence of potential weak spots in the structure. Under STRF conditions, the upper frame structure, in cooperation with the underground structure, significantly improves the stability of the shear force response, and the bending moment response is more evenly distributed, minimizing sharp variations. The peak response under STRF conditions occurs slightly later, with a shorter duration, indicating that the above-ground structure plays a "energy storage-release" buffering role under seismic excitation, effectively delaying and weakening the dynamic response transmitted to the underground structure. Overall, STRF conditions not only optimize the load path of the tunnel structure but also increase its stability and seismic resilience in severe earthquake environments. (4) Under STRF conditions, the shear and bending moment responses are better than those under SRF conditions, indicating that the underground tunnel structure significantly affects the seismic wave propagation path and the forces within the structure. Particularly, the response under STRF conditions exhibits strong non-uniformity in intensity, spatial distribution, and temporal continuity, reflecting the influence of the soil-structure-structure coupling effect. In comparison, the response under SRF conditions is more stable, with a more gradual bending moment distribution and no localized response amplification due to the interference from the underground structure. The analysis results indicate that the impact of the underground tunnel on the above-ground structure should not be ignored, especially in urban dense areas, where the coupling effect between underground structures and above-ground buildings should be included in seismic design to ensure the overall seismic performance and safety of the building complex. (5) Under SRF conditions, the variation of inter-story drift angles is irregular, particularly for the RSN32 seismic motion, where the lower-story response is stronger, reflecting the dominant characteristics of low-order modes. Under STRF conditions, the inter-story drift angles increase significantly, especially under the RSN32 seismic motion, where the overall structural response is further amplified, and the inter-story drift angle in the lower floors is greater than in the upper floors, indicating that the underground tunnel structure weakens the shear capacity at the bottom, increasing deformation in the lower floors. Notably, the inter-story drift angle response under STRF conditions shows greater variability across different seismic motions, indicating that the underground structure is more sensitive to the seismic motion spectrum, thus amplifying the uncertainty in the structural response. The results suggest that the presence of the underground structure significantly influences the seismic response, particularly in terms of the concentration effect of inter-story deformation, and that the coupling effect between underground and above-ground structures should be fully considered in engineering design to improve seismic performance. In conclusion, the coupling interaction between the underground tunnel and the above-ground frame structure has a significant impact on the building's seismic response under seismic loading. Seismic design should thoroughly consider the interaction between above-ground and underground structures, especially in densely populated urban areas. The shear resistance of the lower floors should be optimized, the coupling effect between the two structures should be strengthened, and the design should account for the effects of various seismic motion spectra. Declarations Author Contribution All authors contributed to the conceptualization and design of the study. Data curation was performed by Shiao Wang and Shasha Lu. Funding acquisition was managed by Xiaogang Wei. Investigation was conducted by Shiao Wang and Mengqing Shi. Methodology was developed by Xiaogang Wei, Zhifan Qin, and Junheng Guo. Resources were provided by Shasha Lu. Software development was handled by Zhifan Qin and Shuaixin Ma. Supervision was led by Xiaogang Wei. Validation was carried out by Zhifan Qin and Runze Zhang. Visualization was done by Mengqing Shi. The original draft of the manuscript was written by Xiaogang Wei and Zhifan Qin. All authors reviewed and approved the final manuscript. 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Ocean Engineering, 292, 116514. https://doi.org/10.1016/j.oceaneng.2023.116514 Chandrawanshi S, Garg V. (2025). Structure-Soil-Structure Interaction Effect on Footing Settlement due to Varying Height of Adjacent Building. National Academy Science Letters, 1-5. https://doi.org/10.1007/s40009-025-01612-7 Chen J, Shi X, Li J. (2010).Shaking table test of utility tunnel under non-uniform earthquake wave excitation. Soil Dynamics and Earthquake Engineering, 30(11), 1400-1416. https://doi.org/10.1016/j.soildyn.2010.06.014 Kuhlemeyer R L, Lysmer J. (1973). Finite element method accuracy for wave propagation problems. Journal of the soil mechanics and foundations division, 99(5), 421-427. https://doi.org/10.1061/JSFEAQ.0001885 Miao Y, Zhong Y, Ruan B, et al. Seismic response of a subway station in soft soil considering the structure-soil-structure interaction[J]. Tunnelling and Underground Space Technology, 2020, 106: 103629. Additional Declarations No competing interests reported. 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structure\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/8f1049dd4ac5e69d94719f81.jpg"},{"id":82588522,"identity":"fbebe8e6-a343-4c09-9b2e-883c191d8d4d","added_by":"auto","created_at":"2025-05-13 07:33:16","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":64649,"visible":true,"origin":"","legend":"\u003cp\u003eSensor layout for ST and STRF conditions\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/092f9881d3c884a5a32dda32.jpg"},{"id":82587842,"identity":"01ffe23c-da43-4aa8-b008-49d3c9a927eb","added_by":"auto","created_at":"2025-05-13 07:25:16","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":201244,"visible":true,"origin":"","legend":"\u003cp\u003eAcceleration time history and Fourier spectrum of the input seismic waves\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/16abcbeb219a8e68142c1b35.jpg"},{"id":82587829,"identity":"4f8ce396-04a3-483c-b75e-1087050e1a22","added_by":"auto","created_at":"2025-05-13 07:25:16","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":70724,"visible":true,"origin":"","legend":"\u003cp\u003eLoading sequence of the experiment\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/e4c9797d597f6b188a553f9e.jpg"},{"id":82589521,"identity":"c9b355d3-1bf3-48c5-80e4-fabfaa9c51e5","added_by":"auto","created_at":"2025-05-13 07:41:16","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":89587,"visible":true,"origin":"","legend":"\u003cp\u003eSTRF Structural System Computational Modeling\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/9e117e2c1d5a220b585b6763.jpg"},{"id":82588532,"identity":"bcdc4c9a-78ba-48de-877f-aa4186dccdbe","added_by":"auto","created_at":"2025-05-13 07:33:16","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":50713,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-order vibration mode diagrams of each working condition model system\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/3f8943adba1568ad9328c76c.jpg"},{"id":82589865,"identity":"1c90a898-a89e-475e-998b-7c8525cc35d0","added_by":"auto","created_at":"2025-05-13 07:49:17","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":143556,"visible":true,"origin":"","legend":"\u003cp\u003eThe acceleration curves and Fourier spectrum curves of 0.1g Chi-Chi waves at measurement points A11 and A14 under ST and STRF conditions\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/3b4d0720d566cde1cbf592de.jpg"},{"id":82587856,"identity":"96d42821-62f5-4533-8535-e7e097dc8db7","added_by":"auto","created_at":"2025-05-13 07:25:17","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":48588,"visible":true,"origin":"","legend":"\u003cp\u003eMesh Division and Boundary Conditions\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/0914c2e678a8dab6bcb4e0cb.jpg"},{"id":82587824,"identity":"ad3f51d9-14d9-4bf4-b801-511432f3cadb","added_by":"auto","created_at":"2025-05-13 07:25:16","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":79203,"visible":true,"origin":"","legend":"\u003cp\u003eAcceleration response spectra with 5% damping ratio\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/31bdbc4169c784d30c5484f5.jpg"},{"id":82589540,"identity":"972deed0-3bf7-486f-afdd-283663442cfa","added_by":"auto","created_at":"2025-05-13 07:41:18","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":229292,"visible":true,"origin":"","legend":"\u003cp\u003eAcceleration time histories and Fourier spectra\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/2fcc0037a47352dfa1f0e93c.jpg"},{"id":82588525,"identity":"5cb375f7-a887-4dbd-93e0-adff727681ff","added_by":"auto","created_at":"2025-05-13 07:33:16","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":57388,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-Mode Shape of the STRF System\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/19e43b53cdfa47c49896f508.jpg"},{"id":82587831,"identity":"0f14e428-e454-4138-8874-e99bc34ed9bd","added_by":"auto","created_at":"2025-05-13 07:25:16","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":45860,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial Distribution of Peak Ground Surface Acceleration under the SFRF Condition\u003c/p\u003e","description":"","filename":"13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/47938c281781deaf38d4bd4f.jpg"},{"id":82588534,"identity":"311e3c99-5845-4ce4-baa6-46f90ca02dcb","added_by":"auto","created_at":"2025-05-13 07:33:17","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":35340,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of Peak Surface Acceleration at the Central Cross-Section of Four Site-Structure Systems under ASW Excitation\u003c/p\u003e","description":"","filename":"14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/6a3e22c8d68399de698dfea9.jpg"},{"id":82589525,"identity":"843cfc6f-0de4-47cb-9e29-e24a435a6825","added_by":"auto","created_at":"2025-05-13 07:41:16","extension":"jpg","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":95040,"visible":true,"origin":"","legend":"\u003cp\u003eThree-dimensional distribution of peak acceleration along the longitudinal direction and at different cross-sectional angles of the tunnel structure under STRF and ST conditions\u003c/p\u003e","description":"","filename":"15.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/da1ab70b57ff9bb6a5e43040.jpg"},{"id":82589522,"identity":"a3905e38-5ba2-4d3b-b7c2-3c4d2a97f5e0","added_by":"auto","created_at":"2025-05-13 07:41:16","extension":"jpg","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":64495,"visible":true,"origin":"","legend":"\u003cp\u003eThe acceleration response at the center section of the tunnel under different working conditions\u003c/p\u003e","description":"","filename":"16.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/44e8105172cfc34dd2b92a65.jpg"},{"id":82589866,"identity":"81d843d8-da8d-45c4-b74a-ce7bfc2a3847","added_by":"auto","created_at":"2025-05-13 07:49:17","extension":"jpg","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":104633,"visible":true,"origin":"","legend":"\u003cp\u003eSpatiotemporal evolution diagram of the shear force and bending moment responses of the tunnel structure under ST and STRF conditions\u003c/p\u003e","description":"","filename":"17.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/7b17783ddf02c228ca73d9c9.jpg"},{"id":82587898,"identity":"9ef21d61-4c14-4817-a29a-2204ba95254a","added_by":"auto","created_at":"2025-05-13 07:25:18","extension":"jpg","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":93785,"visible":true,"origin":"","legend":"\u003cp\u003eSpatiotemporal Distribution of Shear and Bending Moment Responses of the Top Beam of the Frame Structure under STRF and SRF Conditions\u003c/p\u003e","description":"","filename":"18.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/cb325bb3edc5e5b8b2df6a40.jpg"},{"id":82589546,"identity":"0602079f-5099-472e-86d8-ddffee74c7d2","added_by":"auto","created_at":"2025-05-13 07:41:19","extension":"jpg","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":95143,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of inter-story drift angles along the floor height direction under different seismic excitations for SRF and STRF conditions.\u003c/p\u003e","description":"","filename":"19.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/94e6f6295234e160f45b68dc.jpg"},{"id":89316013,"identity":"06373e8d-97ea-4fcd-9c69-18480daff27b","added_by":"auto","created_at":"2025-08-18 17:01:58","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2957843,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6508067/v1/690b69de-4664-42df-acb6-8453795f7cde.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Study on Seismic Dynamic Failure of Tunnel-Soil- Frame Structure System through Shaking Table Test and Numerical Simulation","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eAs urbanization progresses, diverse underground infrastructure including metro lines, utility corridors, and subterranean commercial areas are becoming densely distributed in developed urban zones, forming a complex three-dimensional structure\u0026ndash;soil\u0026ndash;structure interaction (SSSI) system with above-ground buildings and infrastructure. Especially in seismically active regions, seismic waves propagate through foundation soils, inducing dynamic responses in above-ground structures and potentially exerting significant impacts on underground structures, which may lead to functional failure or catastrophic damage. Gaining insight into the interaction mechanisms between underground structures, soil, and above-ground structures under seismic influence has emerged as a key topic in contemporary earthquake-resistant engineering research.\u003c/p\u003e \u003cp\u003eConventional seismic analysis and design approaches often treat above-ground frames and underground structures as independent systems, modeling them separately while representing the soil medium with basic boundary conditions or spring elements. While such simplifications are practical for engineering applications, they fail to capture the global response patterns of structural systems under complex seismic wave paths and strong mutual dynamic interactions. For instance, during earthquakes, the above-ground structures can modify the dynamic characteristics of the underground components, while underground structures may disrupt the seismic wave field, subsequently affecting the stress and deformation of surface structures. Therefore, analyzing individual structures in isolation cannot accurately reflect the synergistic response mechanisms of complex structural systems under seismic excitation.\u003c/p\u003e \u003cp\u003eIn recent years, extensive research has been conducted by scholars both at home and abroad on the dynamic response characteristics of underground structures and their coupling effects with surface buildings [1\u0026ndash;7]. Some studies have revealed certain interaction laws through simplified models and theoretical derivations[8\u0026ndash;12](Luco and Contesse, 1973; Mylonakis and Gazetas, 2000; Tao et al., 2021;Ding et al., 2023༛ Ansari et al., 2025). However, the high degree of model idealization and the challenges in accurately describing soil nonlinearity limit the engineering applicability of the research findings, which still need further enhancement. Other studies have used shaking table tests to simulate the real response process under seismic effects through scaled models [13\u0026ndash;17] (Hokmabadi et al., 2015; Goktepe et al., 2020; Tao et al., 2019, 2022; Fang, 2025), providing intuitive evidence for understanding the coupling effects of structural systems. However, due to the high cost of physical experiments and the limited testing conditions, it is often difficult to cover multiple working conditions and types of seismic motions, making a comprehensive and systematic response analysis challenging. Therefore, combining experiments with numerical simulations to conduct dynamic coupling research of multi-structure systems in typical sites holds significant scientific and practical value [18\u0026ndash;21](Toki and Miura, 1983 ; Ding et al., 2019; Tao et al., 2022;Shi et al ,2024). Pitilakis et al. (2008) [22]investigated the seismic response of segmental lining tunnels through experimental and numerical studies, revealing that inner linings amplify the transverse peak acceleration and minimize joint extension, ultimately improving the tunnel's seismic performance. Wang et al. (2013) [23]numerically investigated the dynamic through-soil interaction between an underground station and nearby pile-supported structures under vertically incident S waves using the ANSYS software, highlighting the influence of structural arrangement, shaking direction, distances between structures, and soil properties on the horizontal acceleration magnification factor of ground structures. Their findings showed that the system response can either be amplified or attenuated depending on the distance between adjacent buildings, with neighboring low-slung buildings being particularly affected by the seismic wave. Chen et al.(2018) [24]conducted experimental and numerical studies on the seismic response of segmental lining tunnels, demonstrating that inner linings increase the transverse peak acceleration and reduce joint extension, thus enhancing the tunnel\u0026rsquo;s seismic performance. Wang et al. (2018)[25] conducted shaking table tests and numerical simulations to study the seismic response of an underground structure-soil-surface structure interaction system, demonstrating that the presence of the tunnel amplifies seismic response in the surrounding soil while reducing the seismic response of the surface structure, especially at lower and medium floors. Tao et al. (2020) [26]conducted large-scale shaking table tests comparing the seismic performance of a newly designed prefabricated subway station structure and a traditional cast-in-place structure, finding that while the prefabricated structure showed better energy absorption, it had lower deformation resistance and more severe damage, but maintained relative stability under extreme seismic conditions. Shi et al. (2023) [27] analyzed the seismic response of the giant-span flat cavern, finding that its deformation, stress, and damage remained within safe limits, with the interaction between linings enhancing stability, while extreme earthquakes led to a stable double-hinged arch structure. Based on a new classification framework, Ebrahimipour and Eslami (2024) [28]explored the applicability of vector-acting foundations in complex offshore conditions, focusing on pile\u0026ndash;soil interaction in sensitive and layered soils. Utilizing CPTu data and the neutral plane concept, they quantified sensitivity effects on resistance and proposed design criteria, with ground improvement effectiveness validated through case studies. Chandrawanshi and Garg (2025) [29]investigated the effect of structure-soil-structure interaction (SSSI) on the footing settlement of a three-story RCC building, finding that SSSI significantly amplifies vertical settlement in footings near adjacent structures, leading to notable changes in differential settlement compared to traditional soil-structure interaction (SSI) analysis.\u003c/p\u003e \u003cp\u003eIn summary, significant progress has been made in recent years in understanding the dynamic response of structure\u0026ndash;soil\u0026ndash;structure interaction (SSSI) systems under seismic loading, with steady advancements in theoretical modeling, experimental techniques, and numerical simulation methods. Nevertheless, limited research has addressed the seismic behavior of multi-structural systems like raft foundation frame structures above embedded tunnels, especially under the compounded effects of structural complexity, significant stiffness variation, and overlapping seismic wave paths. By combining shaking table experiments with 3D finite element modeling, this research investigates the seismic behavior of a tunnel\u0026ndash;soil\u0026ndash;frame system, highlighting the influence of the superstructure on wave propagation, the energy transmission between soil layers and tunnel, and the upper structure\u0026rsquo;s feedback effect on localized tunnel response. Multiple critical response parameters, such as acceleration, shear force, bending moment, and story drift, are analyzed to demonstrate how underground structures interfere with the distribution of shear capacity and spectral response of the above-ground building. The findings contribute to the refinement of current SSSI theory, the enhancement of collaborative seismic design for multi-structure systems in urban underground development, and provide theoretical and practical insights for seismic damage assessment and risk mitigation in complex engineering scenarios.\u003c/p\u003e"},{"header":"2 Shaking table test","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Shaking table and model box parameters\u003c/h2\u003e \u003cp\u003eThe shaking table test is conducted using a biaxial electro-hydraulic servo seismic simulation shaking table configured by the School of Civil Engineering at Liaoning Technical University (see Fig.\u0026nbsp;1). The table has a surface size of 3m\u0026times;3m, with a maximum driving acceleration of \u0026plusmn;\u0026thinsp;1.5g, a load capacity of 10t, and a frequency range of 0.1 to 50Hz, capable of simulating seismic motions in the horizontal X and Y directions. The test uses a rigid model box welded from 3mm thick steel plates, with dimensions of 2m\u0026times;2m\u0026times;1.5m. To enhance overall stiffness and prevent lateral instability, diagonal supports are added to the external structure. The inner walls of the box are lined with 200mm thick polystyrene foam boards to absorb boundary reflection waves and reduce test errors. A gravel layer is placed at the bottom to enhance the contact friction with the soil and prevent sliding during vibration.\u003c/p\u003e \u003cp\u003eThe model soil is taken from the sand layer of a real engineering site. As liquefaction is not a concern, the sand was air-dried, oven-dried, and sieved before the experiment to obtain homogeneous fine sand. Based on experimental conditions, a layered filling method was employed, with each layer compacted to 200mm up to a total depth of 1.3m, simplifying the field to a uniform one to enhance compaction and experimental reproducibility. The primary physical parameters are shown in Table\u0026nbsp;1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBasic Physical Properties of the Test Sand\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity (g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRelative Density (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson's Ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInternal Friction Angle (ฒ)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eElastic Modulus (MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e12.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Design Based on Similarity Ratio\u003c/h2\u003e \u003cp\u003eThe experimental model design must satisfy the similarity of geometric, physical, and boundary conditions to ensure the engineering representativeness of the dynamic response. The prototype tunnel structure has a cross-section of 8.4m \u0026times; 5.3m, with a top burial depth of 15.9m, and is 6.6m away from the foundation of the aboveground structure. The aboveground structure consists of a 7-story raft foundation frame, with floor slabs 0.12m thick and column sections of 0.6m \u0026times; 0.6m. The tunnel and the frame structure use different grades of concrete, as detailed in Table\u0026nbsp;2.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComponent Parameters of Tunnel and Frame Structure\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStructural Location\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eConcrete Strength Grade\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eElastic Modulus (\u0026times;10\u003csup\u003e4\u003c/sup\u003eMPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePoisson's Ratio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eDensity (kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTunnel Structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eFrame Structure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBeam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePlate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eColumn\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFoundation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to the Buckingham-π theorem, and considering the shake table and related experimental conditions, the elastic modulus, geometric dimensions, density, and acceleration were chosen as the basic physical quantities, resulting in a similarity ratio of 1:30 between the model and the prototype. The similarity ratios for the elastic modulus were 0.1 (beam, plate), 0.095 (foundation), 0.092 (column), and 0.087 (tunnel), with the remaining similarity relationships derived from the π theorem, as detailed in Table\u0026nbsp;3.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSimilarity Ratios of Model Structure\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhysical Parameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSimilarity Relationship\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTunnel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFoundation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBeam\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePlate\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eColumn\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _l}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e1/30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDisplacement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _x}={\\gamma _l}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e1/30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial Density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _\\rho }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElastic Modulus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _E}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _\\sigma }={\\gamma _E}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _t}=\\sqrt {{\\gamma _l}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e0.183\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVelocity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _v}=\\sqrt {{\\gamma _l}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e0.183\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAcceleration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _a}={\\gamma _g}=1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFrequency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\gamma _\\omega }=\\frac{1}{{\\sqrt {{\\gamma _l}} }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003e5.477\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003eAfter calculation, the total mass of the model structure, additional artificial mass, and non-structural component mass did not exceed the maximum load capacity of the shake table, so an artificial mass model was used for this experiment. The similarity ratio for the artificial mass is calculated as follows:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{m}_{a}={\\lambda\\:}_{E}{\\lambda\\:}_{l}^{2}{m}_{p}-{m}_{m}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn the equation: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{a}\\)\u003c/span\u003e\u003c/span\u003e is the additional artificial mass; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{E}\\)\u003c/span\u003e\u003c/span\u003e is the similarity ratio of the elastic modulus; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{l}\\)\u003c/span\u003e\u003c/span\u003e is the geometric similarity ratio; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the prototype mass; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{m}\\)\u003c/span\u003e\u003c/span\u003e is the model mass.\u003c/p\u003e \u003cp\u003eThe additional artificial mass at each location for the tunnel and frame structure is calculated using the above formula, as shown in Table\u0026nbsp;4. During the calculation process, the mass of the frame structure's columns and slabs is allocated to the floor slabs of the adjacent upper and lower layers.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAdditional Artificial Mass\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eModel Structure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTunnel Structure\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c7\" namest=\"c3\"\u003e \u003cp\u003eFrame Structure\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFoundation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFirst Floor Slab\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSecond Floor Slab\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eStandard Floor Slab\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTop Floor Slab\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdditional Artificial Mass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e32.63kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19.526kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.255kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.865kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.714kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.119kg\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActual Counterweight Mass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.00kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20.00kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.25kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.00kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.75kg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.25kg\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Design of Scaled Model\u003c/h2\u003e \u003cp\u003eDuring the experiment, structural deformation predominantly remains in the elastic phase, so acrylic is chosen for the model material due to its excellent uniformity, light weight, high strength, and relatively low elastic modulus. The elastic modulus is measured at 3 GPa, and the density is 1180 kg/m\u0026sup3;. With the consideration of similarity ratio and vibration table capacity, the tunnel model has a cross-sectional size of 28 cm \u0026times; 17.6 cm and a lining thickness of 1 cm; the column cross-section of the frame structure is 2 cm \u0026times; 2 cm, while the beam cross-section is 1 cm \u0026times; 2 cm, with the bottom beam being 2 cm \u0026times; 2 cm. To mitigate boundary effects, the tunnel model is set at a length of 70 cm, as shown in Fig.\u0026nbsp;2.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Sensor Arrangement and Test Loading Conditions\u003c/h2\u003e \u003cp\u003eTo capture the seismic response of the system at various locations, the experiment deployed 14 accelerometers (labeled as A) to measure the acceleration responses at different points: within the soil, on the surface of the soil, on the sides and bottom of the tunnel, near the ground surface of the tunnel, at the bottom of the foundation of the frame, and at each floor. Additionally, 8 strain gauges (labeled as S) were used to collect strain data from the tunnel's roof, floor, and sidewalls. The sensor layout is shown in Fig.\u0026nbsp;3. The test was performed under four loading conditions: free field (FF), soil-tunnel structure system (ST), soil-raft foundation frame structure system (SRF), and tunnel-soil-raft foundation frame structure system (STRF). The sensor layouts for FF with ST, and SRF with STRF conditions were identical. The tunnel structure is positioned in the center of the box, 0.66 m from the left and right boundaries, while the frame structure is positioned 0.4 m above the tunnel.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eConsidering the natural vibration characteristics of the structural system, the Chi-Chi, El-Centro, and Kobe waves were chosen as seismic inputs. The seismic waves were adjusted for time and peak acceleration according to similarity laws, and then used to excite the model test. The Fourier transform was applied to the adjusted 0.1g acceleration time history to obtain the corresponding frequency spectrum curve (refer to Fig.\u0026nbsp;4).\u003c/p\u003e \u003cp\u003eDuring the experiment, seismic waves were applied unidirectionally in the X direction, with four loading conditions applied stepwise at 0.1g, 0.2g, and 0.3g loading gradients. Before and after each loading stage, a 0.1g white noise unidirectional sweep was performed to measure the changes in the structure interaction system and the structure's natural frequencies. A total of 39 experimental sets were carried out, with the loading scheme illustrated in Fig.\u0026nbsp;5.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Analysis of boundary effect influence\u003c/h2\u003e \u003cp\u003eThe boundary effect is also known as the model box effect. To ensure the validity of the experiment and the reliability of the data, the 2-norm deviation proposed by Chen [30] is used to evaluate the quality of the model box boundary effect. The 2-norm deviation value is used to measure the difference between two signals at any given moment, defined as the square root of the ratio of the squared difference to the squared sum of the reference signal. In this experiment, the vibration response at the center point of the same layer of soil is selected as the reference signal. The boundary effect is assessed by comparing it with the vibration response at boundary points. Generally, the closer the two signals are, the smaller the boundary effect.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\mu =\\frac{{\\left\\| {{x_i} - {x_j}} \\right\\|}}{{\\left\\| {{x_i}} \\right\\|}}=\\sqrt {\\frac{{\\sum\\nolimits_{{i=1}}^{n} {{{\\left( {{x_i} - {x_j}} \\right)}^2}} }}{{\\sum\\nolimits_{{i=1}}^{n} {{x_i}^{2}} }}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this case, the reference signal is denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_i}\\)\u003c/span\u003e\u003c/span\u003e, and the comparison signal is denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x_j}\\)\u003c/span\u003e\u003c/span\u003e. Taking the Chi-Chi wave under the FF condition as an example, experimental data from measuring points A10-A14 were used for validation analysis, with the final calculation results shown in Table\u0026nbsp;5. This demonstrates that the boundary effect issue in this experiment has been properly handled.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e2-norm deviation of acceleration at each measurement point\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMeasurement point\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMeasurement point\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\mu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.164\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.157\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eA12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.188\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 Establishment of the numerical model","content":"\n\u003ch3\u003e3. 1 Establishment of the scaled model\u003c/h3\u003e\n\u003cp\u003eA numerical simulation model consistent with the scaled model used in the shaking table test is established using ABAQUS finite element analysis software. Material properties are detailed in Table\u0026nbsp;6, and the Rayleigh damping model is selected with a damping ratio of 0.05, applied in the calculation of the structural model.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial Parameters of the Scaled Model Structure\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterials\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity (kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eElastic modulus (Pa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePoisson's ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAcrylic glass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.0\u0026times;10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePolystyrene foam board\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.13\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRigid box\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7850\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.06\u0026times;10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCounterweight block\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.2\u0026times;10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eAccording to the study by Kuhlemeyer and Lysmer [31], the finite element mesh size should meet the following conditions:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{l}_{0}\\le\\:\\frac{\\lambda\\:}{10}=\\frac{{v}_{s}}{10\\bullet\\:{f}_{max}}$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn this case, λ represents the wavelength of the selected seismic wave, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{v}_{s}\\)\u003c/span\u003e\u003c/span\u003e is the shear wave velocity of the model soil in the shake table experiment, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{f}_{max}\\)\u003c/span\u003e\u003c/span\u003e is the maximum frequency of the chosen seismic wave. The shear wave velocity \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{v}_{s}\\)\u003c/span\u003e\u003c/span\u003e is calculated by dividing the time difference between the peak accelerations measured at monitoring point A01 at the bottom of the model box and monitoring point A14 at the center of the soil surface during the free-field (FF) condition by the model soil thickness. After calculation, an element size of 0.05 m was chosen. The simulation of the four conditions is carried out using three-dimensional eight-node linear solid elements (C3D8), as shown in Fig.\u0026nbsp;6.\u003c/p\u003e \n\u003ch3\u003e3. 2 Model Verification\u003c/h3\u003e\n\u003cp\u003eA comparative analysis of the modal responses of the shaking table model and numerical simulation model for the four conditions (FF, ST, SRF, STRF) was conducted to obtain the first-order natural frequencies, with the first-order mode shapes shown in Fig.\u0026nbsp;7 and the comparison results presented in Table\u0026nbsp;7.\u003c/p\u003e \u003cp\u003eThe comparison results show that the relative error of the first natural frequency for the four structural systems between the shaking table test and numerical simulation is within 10%, indicating that the difference in natural frequencies between the experimental results and numerical simulation is small.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFirst Natural Frequencies of the Shaking Table Test and Numerical Simulation Models for Each Condition\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStructural system\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShaking table test (Hz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNumerical simulation (Hz)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRelative error\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15.966\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.640\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.05%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eST\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14.375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e15.523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.40%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.569\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.97%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSTRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13.633\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e14.462\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.73%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn order to further validate the accuracy of the numerical simulation results, the Chi-Chi wave with a 0.1g amplitude was used as the input, comparing the shaking table test and numerical simulation results for both the ST and STRF conditions. The acceleration-time history and Fourier spectrum for measurement point A11 (soil surface) under the ST condition, and the acceleration-time history and Fourier spectrum for measurement point A14 (top slab of the raft foundation framework) under the STRF condition, are shown in Fig.\u0026nbsp;8.\u003c/p\u003e \u003cp\u003eThe comparison reveals that the acceleration-time history curves at the same measurement points exhibit good fitting between the shaking table test and numerical simulation, and the Fourier spectrum fitting results fall within the error range, suggesting that the numerical model developed in this study is highly reliable, with accurate calculation results.\u003c/p\u003e \u003cp\u003eIn this section, based on the completion of the shaking table test for the tunnel-soil-frame structure system, further scale ratio numerical simulation analysis is conducted. The simulation process adopts the same geometry, materials, and boundary conditions as the test model to ensure comparability between the two. By comparing the fundamental frequency, floor acceleration-time history curves, and Fourier spectrum response characteristics obtained from both the test and simulation, the results indicate that the numerical model can accurately reproduce the dynamic response behavior of the physical model, thereby validating the rationality and effectiveness of the adopted modeling approach under seismic excitation. Therefore, the same modeling method used for the scaled model will be applied in subsequent prototype-scale three-dimensional finite element modeling analysis to ensure the accuracy of the simulation results.\u003c/p\u003e\n\u003ch3\u003e3. 3 Establishment of the full-scale model\u003c/h3\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.3.1 Calculation scope\u003c/h2\u003e \u003cp\u003eThe full-scale numerical model features a surface building structure consisting of a six-story aboveground and one-story underground bidirectional single-span frame structure. The design information and component dimensions of the frame structure are shown in Table\u0026nbsp;8, while the size design of the underground tunnel structure is provided in Section \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003e2.2\u003c/span\u003e.\u003c/p\u003e \n\u003cp\u003eTable 8 Component Dimensions of the Full-Scale Numerical Model of the Frame Structure (Unit: mm)\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"87%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003eComponent type\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003eCross-section of the frame beam\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 15.3061%;\"\u003e\n \u003cp\u003eCross-section of the foundation beam\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003eCross-section of the column\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10.2041%;\"\u003e\n \u003cp\u003eFirst-floor height\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2449%;\"\u003e\n \u003cp\u003eStandard floor height\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2449%;\"\u003e\n \u003cp\u003eBasement floor height\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10.2041%;\"\u003e\n \u003cp\u003eFloor slab thickness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003ePrototype dimensions\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003e600\u0026times;300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 15.3061%;\"\u003e\n \u003cp\u003e1200\u0026times;600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 13.2653%;\"\u003e\n \u003cp\u003e600\u0026times;600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10.2041%;\"\u003e\n \u003cp\u003e3600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2449%;\"\u003e\n \u003cp\u003e3450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 12.2449%;\"\u003e\n \u003cp\u003e4500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10.2041%;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTo prevent the seismic waves reflected at the boundaries of the full-scale numerical model from re-entering, it is essential to establish a sufficiently large computational domain for the soil, ensuring that the surrounding soil meets the free-field conditions. To optimize both computational efficiency and accuracy, the soil model\u0026apos;s computational domain should be set according to the ratio \u003cem\u003eL\u003csub\u003es\u003c/sub\u003e/H\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e, which needs to be at least 5, as proposed by Miao et al. (2020) [32]. Here, \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e refers to the soil height, and \u003cem\u003eL\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the distance between the outermost structural boundary and the soil boundary. Figure 9 illustrates the computational domain of the full-scale numerical model under the STRF condition.\u003c/p\u003e\n \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2 Selection of Seismic Motions\u003c/h2\u003e \u003cp\u003eTo enhance the engineering applicability of this study, seismic motions were selected based on the design parameters and site characteristics of the Zhengzhou region, ensuring compatibility with the target response spectrum within the primary structural period range (with a deviation not exceeding 20%). Two natural earthquake records were selected from the PEER database, and one artificial ground motion was generated based on code specifications. All three seismic inputs were amplitude-scaled to 0.055g to simulate frequent earthquake scenarios. A comparison between the response spectra and the code spectrum is shown in Fig.\u0026nbsp;10, and the corresponding acceleration time histories and Fourier spectra are presented in Fig.\u0026nbsp;11.\u003c/p\u003e\u003cp\u003eAs shown in Fig.\u0026nbsp;11, the dominant energy of the selected seismic waves is concentrated within the 0\u0026ndash;10 Hz frequency band. Considering the velocity similarity ratio of 0.183 in Table\u0026nbsp;3 and the shear wave velocity of the model soil, an element size of 1.8 m was adopted for the full-scale numerical model to balance computational precision and efficiency, as illustrated in Fig.\u0026nbsp;9.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4 Dynamic Response Analysis","content":"\u003cp\u003eTo further elucidate the dynamic response characteristics of the tunnel\u0026ndash;soil\u0026ndash;frame structure system under seismic loading, this study conducts a comparative investigation based on experimental and numerical simulations, focusing on acceleration response, internal force evolution, and frame displacement. Special emphasis is placed on analyzing the modulation effects of different working conditions on the system\u0026rsquo;s response patterns, thereby providing support for engineering evaluation of interaction effects.\u003c/p\u003e\n\u003ch3\u003e4. 1 Mode Shape Analysis\u003c/h3\u003e\n\u003cp\u003eThe modal response represents a crucial dynamic property of structural or soil\u0026ndash;structure interaction systems, facilitating the prediction of seismic behavior. For the STRF condition, the fundamental frequency is 1.9275 Hz. As illustrated in Fig. 12, the first mode is characterized by shear deformation of the structure. The theoretical natural frequency of the model soil is given by:\u003c/p\u003e\n\u003cdiv\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"560\" height=\"62\"\u003e\n \u003cp\u003eIn the equation: \\({f_n}\\) is the n-th natural frequency, \\({v_s}\\) is the shear wave velocity of the soil, and is the thickness of the soil layer. The calculated first natural frequency is\\({f_1}\\)\u0026thinsp;=\u0026thinsp;1.9365 Hz, which agrees well with the modal analysis result.\u003c/p\u003e\n \u003ch3\u003e4. 2 Acceleration Response Analysis\u003c/h3\u003e\n \u003ch2\u003e4.2.1 Acceleration Response of Ground Soil\u003c/h2\u003e\n \u003cp\u003eFigure 13 illustrates the spatial distribution of peak ground surface acceleration under the SFRF condition. Here, L denotes the soil width along the longitudinal direction of the tunnel. As shown in the figure, the peak ground surface acceleration is significantly influenced by the interaction between the frame structure and the tunnel. The peak acceleration at the central location of the ground surface is noticeably lower than that in the far field. Moreover, it can be observed that the structural system significantly affects the site soil within an approximate range of 400 m, which is 33.3 times the total width of the structure (12 m).\u003c/p\u003e\n \u003cp\u003eFigure 14 illustrates the peak ground surface acceleration distribution along the central cross-section of four distinct site-structure combinations under ASW input. It is evident that when the frame structure exists alone (SRF), the peak surface acceleration near the frame markedly decreases, especially at the soil-frame interface, where the reduction is most pronounced. Compared to the FF condition, the maximum peak acceleration drops by 0.4% (from 0.12047g to 0.12g). Moving away from the frame, the surface acceleration response of the soil increases at first, then decreases, and ultimately becomes steady. In the SRF case, at around 105 m from the site center, the soil surface acceleration gradually reduces to match that of the free field. This suggests that the frame structure influences the surface acceleration of surrounding soil only within a limited region, approximately 8.75 times the structure\u0026apos;s width (12 m).\u003c/p\u003e\n \u003cp\u003eComparing the ST and STRF conditions, it is evident that the presence of the structure weakens the acceleration response of the soil near the structure within a certain range, while causing an amplification effect on the far-field acceleration response. The overall pattern is characterized by \u0026quot;initial increase\u0026mdash;subsequent decrease\u0026mdash;final increase.\u0026quot; This suggests that the propagation of seismic waves in the soil is significantly influenced by the structural system, especially in the STRF condition, where the presence of the superstructure, with its large stiffness and mass, has a stronger ability to absorb and dissipate seismic energy, effectively suppressing the near-field acceleration response. Regarding the reduction in peak surface acceleration, the peak acceleration under STRF is 0.1167g, which is a 2.75% decrease compared to the free-field condition (FF) at 0.12g, while the ST condition only shows a reduction of 0.75%, further validating the enhanced seismic response control capacity of the superstructure. The trend in acceleration response illustrates the complex interaction between the structure and the soil, producing nonlinear effects such as reflection, scattering, and interference in the seismic wave propagation. In terms of amplifying the far-field acceleration response, compared to the free-field condition, STRF begins to amplify the surface acceleration response around 86 meters from the center of the site, while ST shows a similar trend around 92 meters. This indicates that the influence of the structural system on the acceleration response of the soil differs with distance: in the near-field region, STRF, due to the combined effect of the superstructure\u0026apos;s mass and stiffness, more effectively suppresses the transmission of seismic energy, delaying the onset of far-field amplification, while ST, which includes only the tunnel structure, has limited energy absorption and dissipation capacity, resulting in a later onset of the far-field amplification effect. Furthermore, the structural system\u0026rsquo;s modulation of the seismic wave path and field characteristics amplifies the tunnel\u0026rsquo;s influence on the acceleration response over greater distances, emphasizing the complementary roles of aboveground and underground structures in seismic response control. The near-field response is predominantly influenced by the superstructure, while the far-field response is mainly shaped by the tunnel\u0026rsquo;s modulation of the seismic wave propagation and energy distribution. The tunnel\u0026rsquo;s presence significantly amplifies the far-field acceleration response, suggesting that underground structures lead to energy concentration or superposition in the seismic wave propagation process, thereby increasing far-field vibration levels.\u003c/p\u003e\n \u003ch3\u003e4. 2.2 Tunnel acceleration response\u003c/h3\u003e\n \u003cp\u003eFigure 15 presents the three-dimensional distribution of peak acceleration response along the longitudinal direction and at various cross-sectional positions (angles) of the tunnel structure under two different scenarios (STRF and ST). In this figure, STRF represents the condition where the tunnel structure and the framework structure interact together, while ST refers to the comparative condition considering only the tunnel.\u003c/p\u003e\n \u003cp\u003eIn the STRF condition, the peak acceleration of the tunnel structure exhibits significant spatial non-uniformity along both the longitudinal and angular directions. Specifically, within the angular range of about 30\u0026deg; to 150\u0026deg; and the length positions between \u0026minus;\u0026thinsp;10 m and +\u0026thinsp;10 m, the acceleration reaches a maximum value of approximately 0.106g. This localized response enhancement is primarily due to the dynamic interference from the upper framework structure under seismic excitation, which is transferred to the tunnel structure, causing a notable increase in the dynamic response at the junction between the tunnel\u0026apos;s upper section and sidewalls. This dynamic coupling mechanism alters the stress concentration and seismic wave propagation paths within the structural system, thereby forming regions of amplified response at certain locations.\u003c/p\u003e\n \u003cp\u003eIn comparison, the peak acceleration distribution of the tunnel structure under ST conditions is generally more uniform, with smaller gradients in both the longitudinal and angular directions. This suggests that, in the absence of the upper structure\u0026rsquo;s interference, the seismic wave propagation within the tunnel structure is primarily influenced by the structure-soil interaction, leading to a symmetric and stable response distribution. Additionally, under STRF conditions, there are localized peak variations at multiple points, while the ST condition exhibits high symmetry and stability, indicating that the response distribution at different positions along the tunnel section shows greater asymmetry and variance when the upper structure is present.\u003c/p\u003e\n \u003cp\u003eFigure 16 illustrates the distribution of acceleration responses at the central cross-section of the tunnel under different operational conditions. Comparison reveals that the acceleration response at the tunnel\u0026rsquo;s central cross-section under the STRF condition is slightly higher than under the ST condition, with a peak acceleration increase of approximately 5%. This result suggests that the upper framework structure has a certain strengthening effect on the dynamic acceleration response of the tunnel. The additional mass and stiffness of the superstructure modify the propagation and reflection characteristics of seismic waves within the structure-soil system, resulting in the amplification of seismic motion in localized tunnel areas, especially at the central cross-section. This phenomenon should be given attention in practical seismic design, requiring comprehensive consideration of the coupling effect of the upper structure on the dynamic behavior of the underground structure.\u003c/p\u003e\n \u003ch3\u003e4. 3 Internal force response analysis\u003c/h3\u003e\n \u003cp\u003eSince this study considers only the horizontal X-direction as the direction of seismic excitation, the internal forces generated in the frame structure and tunnel under seismic action are primarily influenced by bending moments and shear forces along the excitation direction. Therefore, this study focuses on the bending moments, shear forces in the tunnel and frame structure along the excitation direction as the primary research subjects for internal force response analysis of the structural system.\u003c/p\u003e\n \u003ch2\u003e4.3.1 Tunnel internal force response\u003c/h2\u003e\n \u003cp\u003eFigure 17 shows the spatiotemporal evolution of shear force and bending moment responses under seismic excitation for the ST condition (only considering the tunnel structure) and the STRF condition (with the frame structure superimposed above the tunnel structure).\u003c/p\u003e\n \u003cp\u003eA clear comparison of the 3D response diagrams under the ST and STRF conditions reveals that under the ST condition, where the upper frame structure is not considered, the shear force and bending moment responses of the tunnel structure exhibit strong nonlinear characteristics, especially during the main seismic event phase (approximately 5s to 15s). The shear force and bending moment distributions along the tunnel length direction show multi-peaks with significant fluctuations. In the ST condition, the maximum shear force is approximately\u0026thinsp;\u0026plusmn;\u0026thinsp;4\u0026times;10⁴ N, and the maximum bending moment response is approximately\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026times;10⁵ N\u0026middot;m. The response surface exhibits noticeable discontinuities and peak concentrations at both ends and the center of the tunnel, indicating significant force concentration and potential weak spots in the structure under this condition. The shear effect and rotational inertia induced by the earthquake are particularly pronounced in localized areas.\u003c/p\u003e\n \u003cp\u003eIn the STRF condition, where the upper framework structure is considered, significant differences in the structural response are observed. The maximum shear force response increases dramatically to \u0026plusmn;\u0026thinsp;1.2\u0026times;10⁶ N, indicating that the seismic excitation causes a larger reverse shear force along the tunnel structure due to the combined influence of both above-ground and underground structures. However, the overall response surface exhibits a more continuous and smoother distribution, lacking the abrupt changes seen frequently in the ST condition. This change suggests that the above-ground structure modulates and couples the seismic input, potentially amplifying the shear response locally, but overall maintaining the stability of the force transfer path and the smoothness of the time history.\u003c/p\u003e\n \u003cp\u003eRegarding the bending moment response, the maximum bending moment under the STRF condition is almost the same as under the ST condition, remaining around \u0026plusmn;\u0026thinsp;1\u0026times;10⁵ N\u0026middot;m. However, the distribution along the length of the tunnel becomes more uniform, with fewer peaks, and the response surface tends toward a smoother elliptical shape. This feature indicates that the upper framework structure partially restrains the local rotation and twisting of the tunnel structure, shifting its bending moment response from sharp jumps to a continuous distribution, thus reducing stress concentration caused by inertial coupling within the structure.\u003c/p\u003e\n \u003cp\u003eFrom the time dimension analysis, the peak values of shear and bending moment responses under the STRF condition occur slightly later than those under the ST condition, with the main response duration being shorter, exhibiting certain hysteresis and attenuation characteristics. This phenomenon further indicates that the above-ground structure, through its own mass and stiffness characteristics, plays a buffering role of \u0026quot;energy storage and release\u0026quot; in the structure-soil-structure coupled system, capable of partially absorbing and redistributing seismic energy, thus effectively delaying and weakening the dynamic response transmitted to the underground structure.\u003c/p\u003e\n \u003cp\u003eIt is evident that under the ST condition, the single tunnel structure, due to the lack of collaborative effects from the upper structure, experiences seismic loads that directly act on the tunnel body, resulting in significant local shear and bending moment concentrations. However, under the STRF condition, the above-ground frame structure, through its collaborative effects with the foundation and tunnel, not only acts as a \u0026quot;response regulator\u0026quot; but also facilitates the formation of a more rational force transfer path throughout the system, thereby enhancing the overall stability and seismic resilience of the tunnel structure under seismic excitation. In conclusion, the shear and bending moment three-dimensional spatiotemporal evolution characteristics presented in this section fully reveal the differences in the force responses of the tunnel structure under different boundary conditions under seismic loading and their underlying causes. The results suggest that the STRF condition, considering the soil-structure-structure coupling effect, not only reduces stress fluctuations and the intensity of the response over time but also optimizes the overall response shape of the underground structure, thereby improving its load-bearing capacity and safety redundancy under strong seismic environments.\u003c/p\u003e\n \u003ch2\u003e4.3.2 Internal Force Response of the Frame Structure\u003c/h2\u003e\n \u003cp\u003eFigure 18 illustrates the spatial response characteristics of shear force and bending moment as a function of time and beam length for the top beam of the frame structure under seismic excitation, in two conditions: STRF (with tunnel structure) and SRF (without tunnel structure). This figure reflects the nonlinear response behavior of the structural system under complex dynamic loads and reveals the influence mechanism of the underground structure on the load-bearing performance of the upper frame structure. In order to gain a deeper understanding of the interaction between structures, the analysis is conducted from four aspects: shear force response, bending moment response, time evolution characteristics, and structural collaboration effects.\u003c/p\u003e\n \u003cp\u003eFrom the Fig. 18, it can be observed that the shear response under both STRF and SRF conditions is mainly concentrated in the main seismic shaking phase from 5s to 15s, showing typical seismic excitation features. Along the length of the beam, the shear force shows a clear trend of gradually transitioning from negative to positive values, reflecting the formation of a complex bending-shear coupled internal force state in the beam section under the action of horizontal inertial forces and node restraints. Under STRF conditions, the maximum shear response is about\u0026thinsp;\u0026plusmn;\u0026thinsp;2\u0026times;10⁴ N, and the spatial distribution of shear along the beam length exhibits a continuous slope change trend, with local shear peaks occurring at the beam ends and in the middle region. On the whole, the macroscopic shape of the shear spatial distribution under both STRF and SRF conditions is essentially the same, showing a linear variation trend from one end to the other. This suggests that the shear transfer in the frame structure is primarily influenced by its own stiffness distribution and the direction of seismic excitation, with the underground structure not causing any fundamental changes in the overall shear transfer path.\u003c/p\u003e\n \u003cp\u003eThe right side of the figure shows the bending moment response of the top beam with respect to time and length changes, where both exhibit a similar spatial distribution trend, with response peaks occurring at the beam ends and middle regions. Under STRF conditions, the maximum bending moment value reaches\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u0026times;10\u0026sup3; N\u0026middot;m, and the response surface shows a multi-peak dense distribution, with a steep response gradient forming especially in the beam end region, reflecting a typical bending moment concentration phenomenon. This suggests that the change in the dynamic stiffness of the soil layer due to the tunnel structure further affects the force distribution in the upper structure, increasing the rotational inertia response of the beam, thereby intensifying the bending moment distribution. In comparison, the bending moment response under SRF conditions shows a highly consistent spatial distribution with STRF conditions, both exhibiting a typical distribution characteristic of \u0026ldquo;the main peak regions at the middle and both ends of the beam,\u0026rdquo; reflecting that the structure is primarily controlled by mid-span bending moments under seismic loading, with a stable vibration mode. The maximum bending moment under SRF conditions is approximately\u0026thinsp;\u0026plusmn;\u0026thinsp;5\u0026times;10\u0026sup3; N\u0026middot;m, slightly lower than under STRF conditions, indicating that in the absence of underground structure disturbance, the dynamic response of the frame structure is mainly dominated by its own structural form and stiffness distribution, showing a typical alternating feature of mid-span and end-span, which is consistent with the response characteristics of bending components commonly seen in engineering.\u003c/p\u003e\n \u003cp\u003eThe distribution of each response variable along the time axis reveals a distinct \u0026quot;initial gradual rise\u0026mdash;sharp increase\u0026mdash;fall\u0026quot; trend in structural response intensity as the earthquake unfolds. The peak response under STRF conditions lags slightly behind that under SRF conditions, suggesting that the underground structure induces a transient delay effect in the system\u0026apos;s energy transfer. More significantly, the period of sustained high-intensity response under STRF conditions is noticeably longer than under SRF conditions, particularly in the shear response, which lasts for over 10 seconds. This indicates that the SSSI system creates a vibration extension effect during energy dissipation and transfer, requiring higher seismic performance from structural materials, component ductility, and construction joints.\u003c/p\u003e\n \u003cp\u003eBased on the above analysis, it is evident that under STRF conditions, the shear and bending moment responses of the top-level beams are superior in terms of intensity, spatial distribution, and time continuity compared to SRF conditions. This reflects that the presence of the underground tunnel structure has a significant impact on the seismic wave propagation path, the participation of structural modes, and the internal force transfer path. This phenomenon reveals the typical \u0026quot;above-ground\u0026mdash;underground\u0026quot; structural coupling response characteristics. The underground structure not only serves as the medium for wave propagation but also exerts a feedback effect on the upper structure through foundation deformation and stiffness changes.\u003c/p\u003e\n \u003cp\u003eThis response mechanism suggests that the construction of tunnel structures, such as subways and underground passages, in densely built urban areas significantly affects the surrounding above-ground buildings. In structural seismic design, this coupling mechanism should be fully taken into account, and a collaborative design strategy should be adopted to optimize the overall seismic performance of both the upper and lower structures, ensuring the overall safety and stability of the building complex under strong seismic forces.\u003c/p\u003e\n \u003ch2\u003e4.3.3 Displacement response of the frame structure\u003c/h2\u003e\n \u003cp\u003eFigure 19 illustrates the variation distribution of interstory drift angles along the building height direction under the influence of three typical seismic motions (RSN9, RSN32, RG) for SRF (left) and STRF (right) conditions. This reflects the evolution of the structural interstory deformation capacity and demand with height. The interstory drift angle is a key metric in assessing a building\u0026apos;s seismic deformation capacity and interstory damage potential, which directly correlates with the structure\u0026apos;s ductility performance and failure mode under seismic loading.\u003c/p\u003e\n \u003cp\u003eUnder the SRF condition, the inter-story drift angle variation under different seismic motions shows some irregular patterns. For the RSN32 seismic excitation, the inter-story drift angles show a relatively large overall magnitude, with a peak value of about 0.021% at the second floor. This behavior demonstrates the dominant response of the lower floors, which is linked to the concentration of spectral energy in the lower-frequency modes of the seismic motion. The response curves for RSN9 and RG show clear \u0026ldquo;inflection points\u0026rdquo;, especially under RG seismic excitation, where the inter-story drift angle at the fourth floor peaks and then quickly drops, reflecting a resonance or interference effect between the seismic spectrum characteristics and the structural modes. Furthermore, RSN9 exhibits similar response amplitudes at both the lower and upper floors, showing a relatively smooth trend with minimal fluctuations. This indicates that the seismic energy does not demonstrate a clear concentration effect during its transmission through the structure, leading to a more balanced dynamic response.\u003c/p\u003e\n \u003cp\u003eIn comparison, under STRF conditions (right figure), the overall inter-story drift angle magnitude significantly increases, especially under the RSN32 condition, where the maximum drift angle rises to 0.030%. This indicates that the presence of the underground tunnel structure enhances the overall seismic response of the structure. This amplification effect results from the change in the coupled dynamic characteristics of the foundation-structure system, leading to more complex reflection and superposition of seismic energy within the structure, thereby inducing larger inter-story relative displacements. Additionally, compared to SRF conditions, under STRF, the curves exhibit a more pronounced \u0026quot;larger at the bottom, smaller at the top\u0026quot; trend, with inter-story drift angles at the lower floors greater than those at the upper floors, especially under RSN9 excitation. This suggests that the underground structure weakens the shear capacity at the bottom of the structure or enhances the soft soil effect, leading to more concentrated inter-story deformation in the lower floors.\u003c/p\u003e\n \u003cp\u003eFrom the comparison of the response differences among the three seismic motions, RSN32 excitation causes the largest inter-story drift angle under both SRF and STRF conditions, which is related to its high energy density or proximity to the structure\u0026apos;s natural frequency. It is noteworthy that under STRF conditions, the variation of inter-story deformation among different seismic motions becomes more pronounced, and the dispersion of the curve distribution increases. This reflects an enhanced sensitivity of the underground structure to the seismic motion spectrum characteristics, indirectly indicating an amplifying effect on the uncertainty of the structural response.\u003c/p\u003e\n \u003cp\u003eThe figure reveals the significant impact of the complex interaction between the foundation-structure dynamic system and seismic response in the presence of underground structures. Under STRF conditions, the structure not only experiences an overall increase in inter-story drift angles, but the distribution trend of inter-story deformation shifts from \u0026quot;upper-floor dominant\u0026quot; to \u0026quot;lower-floor dominant\u0026quot;. This suggests that in practical engineering design, special attention should be given to the coupling relationship between the lower structure and underground facilities, and their impact on the concentration of inter-story deformation.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"5 Conclusion","content":"\u003cp\u003eThis study preliminarily explores the dynamic coupling effect between above-ground frame structures and underground tunnels under seismic excitation. By establishing a finite element model based on ABAQUS and validating the structural response through shake table tests, the variation patterns of shear force, bending moment, and inter-story drift angle of the tunnel and frame structure under different conditions are revealed. In the comparative analysis section, three sets of typical seismic motions were input, and extensive numerical calculations were performed. The main conclusions are as follows:\u003c/p\u003e \u003cp\u003e(1) The interaction between the above-ground frame structure and underground tunnel significantly affects the seismic response characteristics of the site, exhibiting a near-field attenuation and far-field amplification trend. The upper structure governs near-field energy dissipation, while the tunnel structure amplifies the far-field vibration response. The structural system plays a role in modulating the seismic wave propagation path and energy distribution, with an influence range up to 33.3 times the width of the structure.\u003c/p\u003e \u003cp\u003e(2) In the dynamic response analysis of the tunnel structure, under STRF conditions, the peak acceleration of the tunnel exhibits significant spatial nonuniformity, especially with amplified responses at specific locations, mainly due to the dynamic interference from the upper frame structure. Under ST conditions, the acceleration distribution of the tunnel is relatively uniform, and the response tends to be symmetric and stable. Moreover, the acceleration at the tunnel's center section under STRF conditions is approximately 5% higher than that under ST conditions, indicating that the upper frame structure enhances the dynamic response of the tunnel. Overall, the influence of the upper structure on the tunnel's dynamic response cannot be ignored, and the coupling effect between the two should be considered in seismic design.\u003c/p\u003e \u003cp\u003e(3) Under ST conditions, the shear and bending moment responses of the tunnel structure show significant nonlinear behavior, with intense fluctuations and stress concentrations in certain regions, indicating the presence of potential weak spots in the structure. Under STRF conditions, the upper frame structure, in cooperation with the underground structure, significantly improves the stability of the shear force response, and the bending moment response is more evenly distributed, minimizing sharp variations. The peak response under STRF conditions occurs slightly later, with a shorter duration, indicating that the above-ground structure plays a \"energy storage-release\" buffering role under seismic excitation, effectively delaying and weakening the dynamic response transmitted to the underground structure. Overall, STRF conditions not only optimize the load path of the tunnel structure but also increase its stability and seismic resilience in severe earthquake environments.\u003c/p\u003e \u003cp\u003e(4) Under STRF conditions, the shear and bending moment responses are better than those under SRF conditions, indicating that the underground tunnel structure significantly affects the seismic wave propagation path and the forces within the structure. Particularly, the response under STRF conditions exhibits strong non-uniformity in intensity, spatial distribution, and temporal continuity, reflecting the influence of the soil-structure-structure coupling effect. In comparison, the response under SRF conditions is more stable, with a more gradual bending moment distribution and no localized response amplification due to the interference from the underground structure. The analysis results indicate that the impact of the underground tunnel on the above-ground structure should not be ignored, especially in urban dense areas, where the coupling effect between underground structures and above-ground buildings should be included in seismic design to ensure the overall seismic performance and safety of the building complex.\u003c/p\u003e \u003cp\u003e(5) Under SRF conditions, the variation of inter-story drift angles is irregular, particularly for the RSN32 seismic motion, where the lower-story response is stronger, reflecting the dominant characteristics of low-order modes. Under STRF conditions, the inter-story drift angles increase significantly, especially under the RSN32 seismic motion, where the overall structural response is further amplified, and the inter-story drift angle in the lower floors is greater than in the upper floors, indicating that the underground tunnel structure weakens the shear capacity at the bottom, increasing deformation in the lower floors. Notably, the inter-story drift angle response under STRF conditions shows greater variability across different seismic motions, indicating that the underground structure is more sensitive to the seismic motion spectrum, thus amplifying the uncertainty in the structural response. The results suggest that the presence of the underground structure significantly influences the seismic response, particularly in terms of the concentration effect of inter-story deformation, and that the coupling effect between underground and above-ground structures should be fully considered in engineering design to improve seismic performance.\u003c/p\u003e \u003cp\u003eIn conclusion, the coupling interaction between the underground tunnel and the above-ground frame structure has a significant impact on the building's seismic response under seismic loading. Seismic design should thoroughly consider the interaction between above-ground and underground structures, especially in densely populated urban areas. The shear resistance of the lower floors should be optimized, the coupling effect between the two structures should be strengthened, and the design should account for the effects of various seismic motion spectra.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors contributed to the conceptualization and design of the study. Data curation was performed by Shiao Wang and Shasha Lu. Funding acquisition was managed by Xiaogang Wei. Investigation was conducted by Shiao Wang and Mengqing Shi. Methodology was developed by Xiaogang Wei, Zhifan Qin, and Junheng Guo. Resources were provided by Shasha Lu. Software development was handled by Zhifan Qin and Shuaixin Ma. Supervision was led by Xiaogang Wei. Validation was carried out by Zhifan Qin and Runze Zhang. Visualization was done by Mengqing Shi. The original draft of the manuscript was written by Xiaogang Wei and Zhifan Qin. All authors reviewed and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJiang, L., Chen, J., \u0026amp; Li, J. (2010). Seismic response of underground utility tunnels: shaking table testing and FEM analysis. \u003cem\u003eEarthquake engineering and engineering vibration\u003c/em\u003e, \u003cem\u003e9\u003c/em\u003e(4), 555-567.\u003cbr\u003eCheng, X., Zhou, X., Liu, H., Zhou, Y., \u0026amp; Shi, W. (2021). Numerical analysis and shaking table test of seismic response of tunnel in a loess soil considering rainfall and traffic load. \u003cem\u003eRock Mechanics and Rock Engineering\u003c/em\u003e, \u003cem\u003e54\u003c/em\u003e, 1005-1025. \u003c/li\u003e\n\u003cli\u003eLiu, C., Peng, L. M., Lei, M. F., \u0026amp; Li, Y. F. (2019). 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Tunnelling and Underground Space Technology, 2020, 106: 103629.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Seismic response, Tunnel–soil–structure interaction, Shake-table tests, Numerical simulation, Dynamic coupling effect","lastPublishedDoi":"10.21203/rs.3.rs-6508067/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6508067/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo investigate the dynamic response of an underground structure-soil-aboveground structure interaction system under seismic action, a shaking table test was conducted with a section of Zhengzhou Metro as the engineering background. A three-dimensional numerical model covering the aboveground and underground multi-structure system was established using ABAQUS. Four working conditions were designed, and three representative seismic motions were selected as input seismic waves. The variation characteristics of key parameters, such as acceleration, shear force, bending moment, and inter-story displacement angle, during the seismic response process of the tunnel and frame structure were systematically analyzed. The research findings indicate that significant dynamic coupling exists between the aboveground and underground structures, with the overall structural system playing a significant role in modulating the propagation path and energy distribution of seismic waves in the site. The acceleration exhibits a trend of attenuation in the near-field response and enhancement in the far-field response. The aboveground frame structure absorbs and dissipates substantial seismic energy in the near-field, while the underground tunnel structure induces amplification of vibration response in the far-field region. In the scenario with aboveground structures, the tunnel's acceleration response exhibits stronger spatial non-uniformity, with distinct points of amplification, reflecting the dynamic disturbance effect of the upper structure. In contrast, in the condition without the upper structure, the tunnel response is relatively symmetric and stable. Regarding force analysis, the inclusion of the aboveground structure improves the force distribution path of the tunnel, reduces the risks associated with sharp fluctuations in bending moments and stress concentration, and also delays and attenuates seismic input via the \"energy storage-energy release\" mechanism in the time domain, thus enhancing the overall seismic resilience and stability of the system. Moreover, the inter-story displacement angle of the aboveground frame structure is significantly affected by the underground structure, manifested as a weakening of shear stiffness in the lower floors and an increase in the concentration of deformation. The response differences expand significantly under different seismic spectra, showing that the underground structure enhances the system's sensitivity to seismic spectral characteristics. In conclusion, the interaction between aboveground and underground structures has a significant impact on seismic response in complex urban environments. Seismic design should fully consider these structural synergies to enhance the overall seismic performance and safety of the building group.\u003c/p\u003e","manuscriptTitle":"Study on Seismic Dynamic Failure of Tunnel-Soil- Frame Structure System through Shaking Table Test and Numerical Simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-13 07:25:10","doi":"10.21203/rs.3.rs-6508067/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d8c7a261-f9dd-4778-8a44-2a77e98c992d","owner":[],"postedDate":"May 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":48254442,"name":"Physical sciences/Engineering"},{"id":48254443,"name":"Physical sciences/Engineering/Civil engineering"},{"id":48254444,"name":"Physical sciences/Mathematics and computing/Information technology"},{"id":48254445,"name":"Physical sciences/Mathematics and computing/Software"}],"tags":[],"updatedAt":"2025-08-18T16:53:29+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-13 07:25:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6508067","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6508067","identity":"rs-6508067","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}