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Article

Seismic Response and Mitigation Measures of Large Unequal-Span Subway Station Structures in Liquefiable Sites

by
Jing Yang
1,2,
Jianning Wang
3,*,
Zigang Xu
1,
Chen Wang
4,5 and
Ruimeng Xia
4
1
Jiangxi Provincial Key Laboratory of Traffic Infrastructure Safety, East China Jiaotong University, Nanchang 330013, China
2
College of Architectural Engineering, Yangzhou Polytechnic Institute, Yangzhou 225100, China
3
China National Machinery Industry Co., Ltd., Beijing 100080, China
4
Beijing Urban Construction Design and Development Group Co., Ltd., Beijing 100037, China
5
National Engineering Research Center of Green & Safe Construction Technology in Urban Rail Transit, Beijing 100037, China
*
Author to whom correspondence should be addressed.
Buildings 2026, 16(7), 1359; https://doi.org/10.3390/buildings16071359
Submission received: 3 March 2026 / Revised: 25 March 2026 / Accepted: 26 March 2026 / Published: 29 March 2026
(This article belongs to the Special Issue Building Response to Extreme Dynamic Loads)
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Abstract

The deformation of surrounding soil primarily governs the behavior of underground structures. Consequently, variations in their external geometry significantly affect their overall seismic response. Moreover, large soil deformations and structural uplift caused by liquefaction severely threaten their seismic safety. While most previous studies have focused on conventional rectangular subway stations, the seismic performance of novel varying-span structures remains largely unexplored. In this study, nonlinear dynamic time-history analyses are conducted to investigate the soil–structure interaction (SSI) of large unequal-span subway stations in liquefiable sites. Furthermore, the seismic responses of both the structure and the surrounding soil are systematically evaluated under various burial depths of the liquefiable layer. Finally, a U-shaped foundation reinforcement method is proposed to mitigate structural uplift. The results show that unequal-span structures suppress liquefaction in lateral soil, whereas significant liquefaction occurs beneath the base slab and cantilevered middle slabs. The burial depth of the liquefiable layer has a negligible effect on the liquefaction state directly under the center span. Regarding structural response, global uplift follows a spatial pattern that peaks at the center span and gradually attenuates laterally. Although the proposed U-shaped reinforcement effectively reduces both total and differential uplift, it does not fundamentally change the underlying liquefaction mechanism. Specifically, reinforcing the soil under cantilevered sections minimizes differential uplift while enhancing the overall economic efficiency of the seismic design. These findings provide a scientific basis for optimizing the seismic resilience of complex underground structures, contributing to the development of resource-efficient and disaster-resilient urban underground infrastructure in liquefaction-prone regions.

1. Introduction

Urban underground space is increasingly moving toward three-dimensional and deep-seated utilization. Consequently, the construction of large-scale underground structures, including subway stations, tunnels, and utility tunnels, is expanding rapidly in seismically active regions. Historically, these structures were deemed seismically resilient due to the confinement of the surrounding soil. However, this assumption was overturned by the collapse of Daikai Station during the 1995 Kobe earthquake and subsequent damage in the Kocaeli and Chi-Chi events [1,2,3]. Further evidence from the 2010–2011 Christchurch and 2011 Tohoku earthquakes highlighted the catastrophic effects of liquefaction-induced settlement and lateral spreading [4,5]. These field observations demonstrate that liquefaction-triggered foundation failure induces structural uplift and complex soil–structure dynamic interaction, ultimately leading to severe damage to underground facilities and their appurtenances.
Extensive physical model tests and numerical simulations have been conducted to explore the seismic responses of underground structures in liquefiable sites [6,7,8]. Chian et al. [9] demonstrated that soil softening is the primary driver of structural uplift. This process is typically triggered by the accumulation of excess pore water pressure. Cheng et al. [10] and Chen et al. [11] performed shaking table tests to confirm the high nonlinearity of soil–structure dynamic coupling in liquefiable sites. Furthermore, Zhuang et al. [12] revealed the shear modulus degradation of saturated sand under large liquefaction-induced deformations through cyclic torsional shear tests. Bao et al. [13] and Zhuang et al. [14] demonstrated the significant impact of large underground structures on the stress state of surrounding soil. Consequently, they highlighted that constitutive models incorporating cyclic mobility and large-deformation characteristics are essential to capture the complex seismic behavior of such structures in liquefiable sites. Liu and Song [15] and Wang et al. [16] investigated the effects of vertical ground motion and concluded that it significantly increases the internal force of underground structures. Furthermore, they demonstrated that the coupling of vertical and horizontal seismic actions aggravates the plastic flow of liquefied soil. Hu and Pang [17] conducted sensitivity analyses on 74 cases, identifying relative density, ground motion intensity, burial depth, and liquefiable layer thickness as the primary factors governing the uplift response of underground structures. Guo et al. [18] introduced deep learning to liquefaction assessment and developed a soil liquefaction prediction model. Furthermore, they proposed a modified transfer learning scheme between different data sources. With the advancement of performance-based seismic design (PBSD), selecting optimal intensity measures (IMs) and conducting seismic fragility analyses have emerged as key research focuses. Shen et al. [19] and Zhang et al. [20] investigated shield tunnels in liquefiable sites and concluded that peak ground acceleration (PGA) is often a suboptimal IM. Their findings suggest that velocity-related or vector-valued IMs more effectively reduce the bias in seismic fragility predictions. Shen et al. [21] and Lu et al. [22] developed seismic fragility curves for shield tunnels and shallow-founded buildings in liquefiable sites using Incremental Dynamic Analysis (IDA). Their work quantifies structural damage risks across varying seismic intensities from a probabilistic perspective.
However, most existing studies focus on homogeneous sites and regular structural geometries, which deviate from practical engineering conditions. Focusing on stratified soil deposits, Shen et al. [23] demonstrated that liquefiable interlayers can function as either seismic isolators or motion amplifiers. This dual response is contingent upon the specific thickness and burial depth of the interlayers. Yao and Lin [24] and Yan et al. [25] recently confirmed that underground structures crossing liquefiable interlayers exhibit shear deformation patterns distinctly different from those in homogeneous soil layers. Furthermore, the rise of subway transfer stations has led to the widespread application of irregular cross-sections, such as unequal-span and variable-section structures. Wang et al. [26] investigated large subway station structures with unequal spans, identifying pronounced stress concentrations at geometric discontinuities of these irregular structures. Their study further revealed that the special cross-sectional geometry significantly alters the flow patterns of the surrounding liquefied soil. Moshirabadi et al. [27] and Yao et al. [28] demonstrated that a single liquefaction assessment criterion is insufficient to ensure the safety of such complex underground structures. They emphasized that the coupling between non-uniform structural loading and soil rheology must be explicitly considered. Given these risks, implementing effective foundation reinforcement measures is crucial. Huang and Wen [29] systematically categorized existing liquefaction mitigation techniques. Regarding the anti-uplift of underground structures, Liu and Song [15] elucidated the mechanism of cutoff walls, demonstrating that they suppress flotation by intercepting the flow of liquefied soil toward the structural base. Kang et al. [30] and Mahmoud et al. [31] further confirmed that reinforcing the structural base or installing high-stiffness cutoff walls can significantly enhance uplift resistance. Additionally, Valizadeh and Ecemis [32], along with Zhou et al. [33], respectively investigated the mechanisms of utilizing rubber-sand mixtures and stone columns to mitigate liquefaction-induced deformations.
While research on conventional underground structures is extensive, the seismic performance of large unequal-span subway stations in liquefiable sites remains poorly understood. Specifically, the influence of irregular structural geometry on localized soil flow and uplift mechanisms requires further investigation. To address this, this study employs nonlinear dynamic time-history analyses to systematically evaluate site liquefaction, structural deformation, and uplift responses. Furthermore, a U-shaped foundation reinforcement method is proposed, and its effectiveness in mitigating both total and differential uplift is assessed. These findings provide theoretical insights and practical guidance for enhancing the seismic resilience of irregular underground structures in complex geological environments.

2. Numerical Model

The prototype for the unequal-span subway station is based on a typical shallow-buried reinforced concrete (RC) frame structure from Suzhou Metro Line 1. This complex underground structure consists of five spans on the upper story and three spans on the lower story. Specifically, the upper cantilevered sections are designed for commercial use, while the lower story accommodates a dual-track island platform. As illustrated in Figure 1, the structure has a burial depth of 3.0 m and a total height of 13.38 m. The maximum outer widths of the upper and lower stories are 31.5 m and 18.9 m, with clear heights of 5.15 m and 6.03 m, respectively. To enhance structural integrity, longitudinal beams and 0.3 m × 0.9 m corner haunches are provided at the joints. Additionally, a 1.0 m × 1.2 m RC ring beam is installed at the intersection of the cantilevered slab and the lower sidewall. The site profile is modeled after typical floodplain deposits in the lower Yangtze River region (e.g., Nanjing and Suzhou). The bedrock depth is set at 60 m, and the shear modulus of the sand layers ranges from 39.3 to 118.2 MPa with increasing depth. Detailed soil parameters are listed in Table 1.
To minimize artificial boundary effects, the lateral distance from the structure to the model boundaries was set to at least five times the structural width, resulting in a total model width of 231.5 m. The maximum element size along the direction of shear wave propagation should be limited to 1/10 to 1/8 of the ratio between the soil’s shear wave velocity and the cut-off frequency [34]. A cutoff frequency of 10 Hz was adopted, which dictates a maximum soil element height of 1~3 m. To balance computational accuracy and efficiency, a graded meshing strategy was employed. The soil elements within 16 m of the structure were refined to 1 m × 1 m, whereas the far-field elements were coarsened to 1 m × 2 m, 2 m × 1 m, and 2 m × 2 m. For the structural components, the mesh size for the main frame and columns was approximately 0.2 m × 0.2 m, and the reinforcement element length was set to 0.3 m. The established numerical model is illustrated in Figure 2. To investigate the influence of the liquefiable layer’s burial depth, five cases are considered: d = 3.0 m, 6.6 m, 9.6 m, 12.99 m, and 16.38 m. As shown in Figure 3, these depths correspond to the elevations of the roof slab, the mid-height of the upper sidewall, the middle slab, the mid-height of the lower sidewall, and the base slab, respectively. The case with d = 3.0 m serves as the baseline for comparative analysis.
The structure and soil are discretized using 4-node plane strain fully integrated elements (CPE4) and reduced integration elements (CPE4R), respectively. To address mesh distortion induced by large liquefaction deformations, the Arbitrary Lagrangian–Eulerian (ALE) adaptive meshing technique is applied to simulate soil flow. The out-of-plane continuity of the columns in the 2D nonlinear finite element model is approximated using the equivalent stiffness reduction method, as shown in Equation (1).
E e q I e q = E c I c D
where EeqIeq is the equivalent stiffness per unit width of the wall in the longitudinal direction; EcIc represents the stiffness of the column; and D denotes the longitudinal column spacing. Consequently, the equivalent stiffness of the column is 3.85 × 103 MPa. The reinforcement is modeled using beam elements (B21) and embedded into the concrete, neglecting bond-slip behavior. The dynamic contact between the soil and the structure is simulated using the contact pair method. The normal behavior is defined by a hard contact model, which allows for interface separation while preventing interpenetration. For tangential behavior, the Coulomb friction law is applied with a friction coefficient of 0.4. This formulation implies that relative sliding occurs once the interface shear stress exceeds the maximum frictional resistance [35]. The reinforcement obeys a bilinear elastoplastic constitutive model characterized by Es = 210 GPa, fy = 400 MPa, a post-yield hardening ratio of 0.01, and a Poisson’s ratio of 0.3. A memory-based viscoplastic dynamic constitutive model is employed to characterize the clay layers [36]. The liquefiable soil layers are represented by a dynamic constitutive model specifically developed for large liquefaction-induced deformations [37], which is based on the large-deformation liquefaction model proposed by Yang and Elgamal [38]. The theoretical details and experimental validation of this constitutive model are presented in [39,40,41,42]. Within an effective stress site response framework, the generation of excess pore water pressure is simulated using a mechanically coupled approach. Rather than solving fully coupled fluid flow equations, the model relates pore pressure changes directly to the volumetric deformation tendencies of the soil skeleton. Guided by a non-associative flow rule, the plastic flow direction is decomposed into deviatoric and volumetric components, enabling the explicit definition of contractive, dilative, and neutral phases relative to the phase transformation (PT) surface. Based on the volumetric compatibility condition of dynamic Biot theory, the excess pore water pressure increment under completely undrained conditions is calculated as shown in Equation (2).
Δ P = K Δ ε V
where Δ P is the excess pore water pressure increment, K is the bulk modulus and Δ ε V is the volumetric strain increment. This pore pressure modeling approach relies on two critical assumptions. First, according to Zhuang et al. [36,42], it assumes completely undrained conditions during the extremely short duration of strong seismic loading, neglecting any pore water dissipation or fluid migration across boundaries. This assumption maximizes the accumulation of excess pore water pressure and the loss of soil shear strength, thereby providing a conservative estimate for the resulting structural uplift and the extent of liquefaction zones. Second, the model employs a phenomenological dilatancy logic to capture the large accumulation of shear deformation at extremely low effective confinement. This assumption ensures that the cyclic mobility of the sand and the complex soil flow patterns. According to Zhuang et al. [42], during the extremely short duration of strong seismic loading, the soils exhibit an approximately undrained response. Therefore, undrained boundary conditions are adopted in this study.
The unequal-span subway station structure is constructed of C30 concrete. The Concrete Damaged Plasticity (CDP) model is employed to capture the dynamic nonlinear behavior of the concrete [43]. The corresponding material parameters are summarized in Table 2. The evolution of the compressive stress and damage variables with respect to plastic strain is listed in Table 3, while the tensile behavior relative to cracking displacement is provided in Table 4.
To accurately capture the seismic response of underground structures, geostatic stress equilibrium must be established within the SSI system prior to dynamic analysis. Accordingly, the boundary conditions are reconfigured during the transition from the static to the dynamic step. Initially, a static analysis is conducted with horizontal constraints applied to the lateral boundaries and full fixity at the base. The resulting stress state is then imported into ABAQUS as a predefined field to achieve the initial geostatic stress state. Prior to the application of seismic loading, the horizontal constraints at the base are released while vertical support is maintained, thereby allowing the input of horizontal ground motions at the bedrock. Simultaneously, the static horizontal constraints on the lateral boundaries are removed. A tied degrees-of-freedom (TDOF) boundary is implemented by constraining nodes at equivalent elevations on opposite lateral boundaries to ensure synchronized horizontal motion [44]. This boundary condition is computationally efficient and provides high fidelity for horizontally stratified sites [45]. The numerical modeling approach used in this study has been validated against shaking table tests, with more details provided in [41,46]. As shown in Figure 4, the results demonstrate that this method effectively captures the fundamental dynamic features of the test system, thereby satisfying practical application requirements.
Three ground motion records—Kobe, El-Centro, and Nanjing—are selected as bedrock inputs. The Kobe record, representing a typical near-field motion from the 1995 Kobe earthquake, was recorded about 1 km from the epicenter; it features an original PGA of 0.833 g, a strong motion duration of 10 s, and a dominant frequency range of 0.5–4 Hz. Under this ground motion, underground structures are highly susceptible to significant seismic shear deformations. The El-Centro record, a medium-to-far-field motion from the 1940 Imperial Valley earthquake, exhibits a PGA of 0.349 g, a duration of 26 s, and a frequency range of 0.2–10 Hz. This ground motion features rich frequency content and a long strong-motion duration, which are the primary drivers for pore water pressure accumulation and soil liquefaction. The Nanjing record, synthetically generated to reflect the specific geological conditions of Nanjing, has a PGA of 0.15 g, a duration of 22 s, and a frequency range of 0.7–8 Hz. To fully capture the post-earthquake uplift response of the underground structure, all ground motions are scaled to a uniform duration of 40 s and applied at the bedrock. The peak bedrock acceleration (PBA) is scaled to 0.1 g, 0.2 g, and 0.3 g. According to GB 18306-2015 [47], this intensity range covers the potential seismic intensities from frequent to extremely rare earthquakes in the middle and lower reaches of the Yangtze River. Figure 5 presents the acceleration time-histories and the corresponding response spectra for the three ground motions scaled to a PBA of 0.1 g.

3. Results

3.1. Site Liquefaction

Since the unequal-span structure exhibited consistent seismic response patterns across all three ground motions, this study focuses on the results from the Kobe motion, which possesses distinct near-field spectral characteristics. Figure 5 shows the spatial distribution of liquefaction under the Kobe motion (PBA = 0.2 g) across varying burial depths of the liquefiable layer. The state variable SDV52 is used to characterize the excess pore water pressure ratio, as defined in Equation (3).
r u = Δ P σ v 0 ′
where Δ P is the increment of earthquake-induced excess pore water pressure, and σ v 0 ′ is the initial vertical effective overburden stress. When the value of γ u approaches 1.0, it indicates that the effective overburden stress is completely counterbalanced by the pore water pressure, causing the soil to entirely lose its shear strength and enter a fully liquefied state. As shown in Figure 6a, the liquefaction zones on both sides of the unequal-span structure are generally symmetrical. Due to the presence of the underground structure, the adjacent lateral soil exhibits enhanced liquefaction resistance, with no significant liquefaction observed. This indicates that the subway station effectively inhibits liquefaction in the surrounding lateral soil. In contrast, pronounced liquefaction occurs in the soil beneath the base slab and the cantilevered middle slabs. Notably, the liquefaction zone under the cantilevered slabs is confined to the height of the lower story. As shown in Figure 6b–e, the burial depth of the liquefiable layer has a negligible effect on the liquefaction state directly beneath the structure’s center, though minor variations occur in the lateral soil zones. In the far-field, liquefaction consistently initiates at the sand–clay interface. As the burial depth increases, the extent of liquefaction at the upper sand boundary gradually decreases. This reduction is attributed to the thicker clay overburden, which raises the initial effective overburden pressure and subsequently enhances the liquefaction resistance of the sand during seismic loading.

3.2. Structural Deformation

The lateral displacement of unequal-span subway stations in non-liquefiable sites differs significantly from that of conventional rectangular structures [26]. Changes in the burial depth of the liquefiable layer modify the lateral soil confinement, which in turn affects the horizontal displacement of the unequal-span structure. Figure 7 shows the relative horizontal displacement curves of the sidewalls at the instant of maximum roof-to-base drift. Under the Kobe motion (PBA = 0.2 g), the displacement curves are similar during rightward rocking but vary significantly during leftward rocking. For leftward movement, the maximum displacement occurs when extensive liquefiable sand layers surround the structure (d = 6.6 m). The displacement for d = 3.0 m is slightly smaller and nearly identical to the case where the sand layer covers the full height of the lower story (d = 9.6 m). Notably, these displacements are much larger than those observed in cases with minimal (d = 12.99 m) or no liquefiable sand (d = 16.38 m).
Overall, the lateral resistance of the unequal-span subway station structure decreases when liquefiable sand layers flank the structure. Notably, the lateral deformation in the case with a shallow non-liquefiable layer (d = 6.6 m) is slightly greater than that of the fully embedded case (d = 3.0 m). This phenomenon is driven by the embedment effect of the overlying clay layer. Specifically, the roof and upper sidewalls form a mechanical interlock with the non-liquefiable clay. In addition to the horizontal shear stress on the roof, the complex normal and shear stresses at the clay–sidewall interface further amplify the global seismic deformation of the structure.

3.3. Structural Uplift

To characterize these uplift patterns, the time-history curves and peak amplitudes at various locations on the right half of the roof slab are presented in Figure 8 and Table 5. Overall, the structural uplift increases with the PBA. Under low-intensity ground motions (PBA = 0.1 g), the center span exhibits minor residual uplift, while the lateral cantilevered sections undergo slight settlement. As the PBA increases, the unequal-span structure predominantly experiences global uplift. Notably, a consistent differential uplift persists between the center span and the cantilevered sections. The uplift peaks at the center span and gradually diminishes toward the right roof corner. At PBAs of 0.1 g, 0.2 g, and 0.3 g, the ultimate differential uplifts between the center span and the roof corner are 2.51 cm, 2.23 cm, and 2.04 cm, respectively. These findings suggest that significant differential uplift occurs even under low-intensity motion, posing a threat to the seismic safety of the structure. Although the structure might paradoxically appear safer under stronger earthquakes if judged solely by differential uplift, the total uplift reaches a substantial 35.87 cm, leading to severe structural failure.
Around traditional regular rectangular underground structures, liquefied soil particles typically form a symmetric, circular flow path from the structure’s top toward both sides of the base slab [39]. However, this circular flow pattern is disrupted for large unequal-span station structures. This phenomenon stems from the early onset of liquefaction in the soil beneath the base slab. During the complex interaction between structural flotation and the progressive liquefaction of deeper soil strata, the three central spans experience significant uplift. In contrast, the soil beneath the cantilevered spans exhibits a lower degree of liquefaction. Consequently, soil particles in this region migrate toward the liquefied zone beneath the base slab, further suppressing the uplift of the cantilevered sections and ultimately exacerbating differential uplift. Due to this structural configuration, the central uplift of such large unequal-span station structures is significantly more pronounced than that at the lateral cantilevered sections. As a result, the cantilevered regions of the roof and middle slabs are subjected to substantial flexural deformations and endure additional internal forces. These areas constitute the primary seismically vulnerable zones for unequal-span structures in liquefiable sites.
Figure 9 presents the uplift time-history curves at the roof center of the unequal-span station structure for varying burial depths of the liquefiable layer. As shown in Figure 9a, the global uplift processes are generally consistent across all cases, although the final values differ slightly. Based on the peak values in Figure 9b, the overall structural uplift gradually diminishes as the burial depth increases. Consequently, the case with the minimal non-liquefiable clay overburden (d = 3.0 m) represents the most critical condition, yielding a maximum roof uplift of 11.68 cm. In contrast, the case with the maximum burial depth (d = 16.38 m) produces a minimum peak uplift of 6.06 cm, representing a 48.12% reduction relative to the critical case. Furthermore, Figure 9b indicates that the differential uplift between the central and cantilevered sections exhibits no discernible trend in response to variations in site conditions.

4. Anti-Uplift Measure

4.1. Numerical Modeling of Foundation Reinforcement

This study proposes a U-shaped foundation reinforcement scheme and evaluates its effectiveness in mitigating liquefaction-induced uplift by varying the reinforcement geometry. Following the previous study [29], the grouting material is assigned a unit weight of 19.4 kN/m3, an elastic modulus of 100 MPa, and a Poisson’s ratio of 0.3. The finite element model incorporating the U-shaped reinforcement is illustrated in Figure 10. The reinforcement depth, H, is defined as the vertical extent of the grouted zone beneath the base slab, ranging from 0 to 20 m. Specifically, the maximum depth (H = 20 m) slightly exceeds the width of the lower story (b = 18.9 m), while the minimum depth (H = 0 m) indicates that reinforcement is restricted to the saturated sand situated above the base slab and beneath the cantilevered spans. Intermediate cases consider H values of 4, 8, 12, and 16 m. The maximum reinforcement width, B, corresponds to the width of the upper story, as detailed in Figure 10b.

4.2. Site Liquefaction After Reinforcement

Figure 11 presents the spatial distribution of soil liquefaction under the Kobe motion (PBA = 0.2 g) for various reinforcement cases. Overall, the depth of far-field liquefaction increases slightly across the cases, though the variation remains minor. The reinforced zone beneath the unequal-span structure effectively resists liquefaction. However, at a shallow reinforcement depth (H = 4 m), the saturated sand underlying the reinforced zone still liquefies. As the reinforcement depth increases, this liquefaction is progressively suppressed, although high excess pore pressure ratios persist at soil layer interfaces. This occurs because the U-shaped reinforcement modifies the mechanical properties of the sand, effectively eliminating the conditions necessary for liquefaction. Nevertheless, the deeper unreinforced soil remains susceptible to liquefaction. This is because the increase in effective overburden pressure does not fully offset the unloading effect caused by the excavation of the unequal-span structure. Furthermore, while the U-shaped reinforcement significantly improves the soil state directly beneath the structure, it does not disrupt the hydraulic connectivity with the surrounding soil. Since the flow paths for deep soil particles remain intact post-liquefaction, the fundamental uplift mechanism of the structure remains essentially unaltered.

4.3. Structural Uplift After Reinforcement

Figure 12 shows the structural uplift responses at the roof of the unequal-span station structure across various reinforcement cases. As shown in Figure 12a, while the dynamic uplift processes remain broadly consistent across different reinforcement depths, the final uplift magnitudes differ significantly. In general, the global uplift observed in the reinforced cases is lower than that in the unreinforced scenario, demonstrating that the proposed U-shaped foundation reinforcement method effectively mitigates the overall uplift of large unequal-span structures. According to the peak uplift values presented in Figure 12b, as the reinforcement depth increases, the uplift initially decreases and subsequently increases. Case 2 (H = 4 m) achieves the most substantial mitigation, whereas Case 1 (H = 0 m) exhibits the next-best improvement. Compared to the unreinforced baseline, the peak uplift in Case 2 and Case 1 is reduced by 79.68% and 51.32%, respectively. Notably, the effectiveness in mitigating peak structural uplift diminishes once the reinforcement depth exceeds 4 m. As H increases from 4 m to 20 m, the uplift increases by 134.17%, and the overall reduction in uplift relative to the unreinforced case drops to 52.42%. Furthermore, although the differential uplift between the center span and the cantilevered sections is highly sensitive to the reinforcement depth, no monotonic trend is observed. The most significant improvements in differential uplift occur when transitioning from the unreinforced state to the initial reinforcement stages (H = 0 m and H = 4 m), yielding reductions of 83.32% and 89.54%, respectively. These findings indicate that anti-uplift strategies relying solely on increasing the reinforcement depth become less cost-effective beyond a critical threshold. For large unequal-span station structures characterized by non-uniform uplift, targeted reinforcement of the saturated sand within a specific depth beneath the cantilevered sections can effectively mitigate the adverse effects of differential uplift. In engineering practice, U-shaped reinforcement can be achieved using low-vibration high-pressure jet grouting (HPJG). Specialized equipment drills inclined holes beneath the cantilever slabs to forcibly mix the in situ soil with grouting material. However, this technique faces potential challenges, including environmental issues caused by waste slurry disposal and its inability to alter the liquefaction mechanism of deep foundation soils.

5. Conclusions

This study develops a nonlinear numerical model accounting for soil–structure interaction (SSI) to evaluate large unequal-span subway station structures in liquefiable sites. By considering varying burial depths of liquefiable layers, the seismic response and failure mechanisms of large unequal-span structures are systematically investigated. Furthermore, a U-shaped foundation reinforcement method is proposed to mitigate the differential uplift. The primary conclusions are as follows:
(1)
The unequal-span subway station structure inhibits liquefaction in the lateral foundation zones, while significant liquefaction occurs beneath the base and cantilevered slabs. Specifically, the liquefaction zone under the cantilevered slabs is restricted to the height of the lower story. In contrast, the liquefaction depth beneath the base slab is extensive and increases progressively with seismic intensity. Furthermore, the burial depth of the liquefiable layer has a negligible impact on the liquefaction state directly beneath the center span.
(2)
The global uplift of the unequal-span structure increases with ground motion intensity and consistently shows non-uniform spatial patterns. Specifically, the uplift peaks at the center span and diminishes laterally as the distance from the center increases. This resulting differential uplift between the cantilevered and center spans is detrimental to the overall seismic performance of structures.
(3)
The proposed U-shaped reinforcement method significantly mitigates both global and differential uplift of the unequal-span structure, thereby improving its seismic resilience. However, this method does not fundamentally alter the underlying uplift mechanism. This is because flow paths and hydraulic connectivity persist within the deeper liquefied soil layers. Furthermore, increasing the reinforcement depth eventually yields diminishing returns. For large unequal-span structures, targeted treatment of the sand beneath cantilevered spans—rather than indiscriminately increasing the overall reinforcement depth—offers a more efficient and cost-effective approach to controlling differential uplift.
This study provides valuable insights into the seismic response of large unequal-span subway stations in liquefiable sites, offering a theoretical basis for anti-uplift engineering practices. Nevertheless, limitations exist within the current framework. Specifically, the model neglects longitudinal spatial effects and excludes the coupled influence of vertical seismic inputs and soil spatial variability on liquefaction evolution and structural differential uplift. Hence, extrapolating these findings to different geological or seismic conditions requires caution. Future research should be extended to large-scale 3D fluid–solid coupled finite element analysis to elucidate the 3D influence mechanisms of the aforementioned factors on the liquefaction flow field. Ultimately, this will contribute to a robust seismic evaluation and design system for underground structures with complex cross-sections in liquefiable areas.

Author Contributions

Writing—original draft, Methodology, Software, Conceptualization, Formal analysis, Visualization, Funding acquisition, J.Y.; Formal analysis, Supervision, Validation, Writing—review & editing, Funding acquisition, J.W.; Software, Data curation, Funding acquisition, Z.X. Software, Data curation, C.W.; Supervision, Validation, R.X. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Foundation of Yangzhou (YZ2025157), the National Natural Science Foundation of China (Grant Nos. 52508556, 52308496, and 52478519), the General Program for Basic Research (Natural Science) of Jiangsu Provincial Department of Education (25KJB560027), and the Young Elite Scientists Sponsorship Program (YESS2024065).

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

Author Jianning Wang was employed by the company China National Machinery Industry Co., Ltd. Author Chen Wang and Ruimeng Xia were employed by the company Beijing Urban Construction Design and Development Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Figure 1. Cross-sectional dimensions of the large unequal-span underground subway station structure.
Figure 1. Cross-sectional dimensions of the large unequal-span underground subway station structure.
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Figure 2. The finite element model.
Figure 2. The finite element model.
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Figure 3. The numerical models of the liquefiable layer with different burial depths: (a) d = 3.0 m; (b) d = 6.6 m; (c) d = 9.6 m; (d) d = 12.99 m; (e) d = 16.38 m.
Figure 3. The numerical models of the liquefiable layer with different burial depths: (a) d = 3.0 m; (b) d = 6.6 m; (c) d = 9.6 m; (d) d = 12.99 m; (e) d = 16.38 m.
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Figure 4. Comparison of numerical simulation results with shaking table test results [41,46].
Figure 4. Comparison of numerical simulation results with shaking table test results [41,46].
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Figure 5. The acceleration time-histories and response spectra of ground motions: (a) Kobe motion; (b) El-Centro motion; (c) Nanjing motion; (d) response spectra (5% damping ratio).
Figure 5. The acceleration time-histories and response spectra of ground motions: (a) Kobe motion; (b) El-Centro motion; (c) Nanjing motion; (d) response spectra (5% damping ratio).
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Figure 6. The distribution of liquefaction across varying burial depths of the liquefiable layer: (a) d = 3.0 m; (b) d = 6.6 m; (c) d = 9.6 m; (d) d = 12.99 m; (e) d = 16.38 m.
Figure 6. The distribution of liquefaction across varying burial depths of the liquefiable layer: (a) d = 3.0 m; (b) d = 6.6 m; (c) d = 9.6 m; (d) d = 12.99 m; (e) d = 16.38 m.
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Figure 7. Horizontal relative displacements of the unequal-span structure with its height: (a) leftward rocking and (b) rightward rocking.
Figure 7. Horizontal relative displacements of the unequal-span structure with its height: (a) leftward rocking and (b) rightward rocking.
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Figure 8. The uplift time-history curves of the structural roof.
Figure 8. The uplift time-history curves of the structural roof.
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Figure 9. The uplift response of the structural roof for various liquefiable layer burial depths: (a) the uplift time-history curves and (b) peak uplift and differential uplift values.
Figure 9. The uplift response of the structural roof for various liquefiable layer burial depths: (a) the uplift time-history curves and (b) peak uplift and differential uplift values.
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Figure 10. Numerical models of U-shaped foundation reinforcement beneath subway station: (a) Numerical Modeling of Foundation Reinforcement and (b) design cases for foundation reinforcement.
Figure 10. Numerical models of U-shaped foundation reinforcement beneath subway station: (a) Numerical Modeling of Foundation Reinforcement and (b) design cases for foundation reinforcement.
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Figure 11. The distributions of site liquefaction with U-shaped foundation reinforcement: (a) H = 0 m; (b) H = 4 m; (c) H = 8 m; (d) H = 12 m; (e) H = 16 m; (f) H = 20 m.
Figure 11. The distributions of site liquefaction with U-shaped foundation reinforcement: (a) H = 0 m; (b) H = 4 m; (c) H = 8 m; (d) H = 12 m; (e) H = 16 m; (f) H = 20 m.
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Figure 12. The uplift after reinforcement of structural roof: (a) the uplift time-history curves and (b) peak uplift and differential uplift values.
Figure 12. The uplift after reinforcement of structural roof: (a) the uplift time-history curves and (b) peak uplift and differential uplift values.
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Table 1. The parameters of the soils.
Table 1. The parameters of the soils.
Soil LayerClassificationThickness
(m)		Density
(kg/m3)		Shear Modulus
(MPa)		Elastic Modulus (MPa)Friction Angle (°)Poisson RatioVoid Ratio
1Plain fill3.0193025.27.0160.30-
2Fine sand (medium dense)47.0193060.07.0300.300.474
3Old clay (stiff)10.01930120.27.0180.35-
Table 2. The dynamic model parameters of C30 concrete.
Table 2. The dynamic model parameters of C30 concrete.
ParametersValuesParametersValues
Elastic modulus (MPa)3.0 × 104Limited compressive yield stress (MPa)20.1
Poisson’s ratio0.18Initial tensile yield stress (MPa)2.4
Density (kg/m3)2500Compression stiffness recovery parameter0.7
Dilation angle (°)36.31Tensile stiffness recovery parameter0.0
Initial compressive yield stress (MPa)14.64Damage factorsdc, dt
Table 3. The relations of compression stress and damage factor versus plastic strain.
Table 3. The relations of compression stress and damage factor versus plastic strain.
Plastic strain (%)0.000.040.080.120.160.200.240.360.500.751.00
Compression stress (MPa)14.617.319.420.120.218.717.312.98.666.253.98
dc0.000.110.250.340.430.500.570.710.820.920.97
Table 4. The relations of tension stress and damage factor versus plastic strain.
Table 4. The relations of tension stress and damage factor versus plastic strain.
Crack displacement (mm)0.0000.0660.1230.1730.2200.3080.3510.3940.4380.482
Tension stress (MPa)2.4001.6171.0840.7260.4870.2190.1470.0980.0660.042
dt0.0000.3810.6170.7630.8530.9440.9650.9780.9870.992
Table 5. The peak uplift values of the structural roof (cm).
Table 5. The peak uplift values of the structural roof (cm).
Ground
Motions		PBAPositionDifferential Uplift
ABC
Kobe motion0.1 g1.07−0.53−1.442.51
0.2 g11.6710.469.442.23
0.3 g35.8734.8933.832.04
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Yang, J.; Wang, J.; Xu, Z.; Wang, C.; Xia, R. Seismic Response and Mitigation Measures of Large Unequal-Span Subway Station Structures in Liquefiable Sites. Buildings 2026, 16, 1359. https://doi.org/10.3390/buildings16071359

AMA Style

Yang J, Wang J, Xu Z, Wang C, Xia R. Seismic Response and Mitigation Measures of Large Unequal-Span Subway Station Structures in Liquefiable Sites. Buildings. 2026; 16(7):1359. https://doi.org/10.3390/buildings16071359

Chicago/Turabian Style

Yang, Jing, Jianning Wang, Zigang Xu, Chen Wang, and Ruimeng Xia. 2026. "Seismic Response and Mitigation Measures of Large Unequal-Span Subway Station Structures in Liquefiable Sites" Buildings 16, no. 7: 1359. https://doi.org/10.3390/buildings16071359

APA Style

Yang, J., Wang, J., Xu, Z., Wang, C., & Xia, R. (2026). Seismic Response and Mitigation Measures of Large Unequal-Span Subway Station Structures in Liquefiable Sites. Buildings, 16(7), 1359. https://doi.org/10.3390/buildings16071359

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