Response Comparisons of Prefabricated and Cast-in-Place Subway Station Structures in Liquefiable Soil Foundation with the Ground Surface Slight Inclined

: In recent years, the prefabricated subway station structure (PSSS) has become a hot spot of underground structure research. In this paper, the numerical model of a soil–subway station structure in a slowly inclined liquefiable site at the surface is established by using FLAC3D finite difference software. And the applicability of the PSSS under the gently inclined liquefiable site is investigated through the foundation pore water pressure, lateral movement of liquefied soil, and dynamic response and uplift characteristics of the subway station structure. It is found that under the gently inclined liquefiable site conditions, the PSSS exhibits tilting and floating behaviors and has an anti-liquefaction effect within a certain range of surrounding soil layers. Compared with the same type of cast-in-place subway station structure (CIPSSS), it has better resistance to overturning and uplift, and the structure has less stress. Under the premise of ensuring static waterproofing, the PSSS can be applied to surface inclined liquefiable sites.


Introduction
At present, the traditional subway station construction method primarily involves castin-place subway station structures (CIPSSSs); this approach involves a long construction period, poor site conditions, difficulty in controlling project quality, high resource consumption, low production efficiency, and poor utilization of materials, leading to significant social and environmental problems and constraints on its sustainable development.The prefabricated subway station structure (PSSS) construction method is an important alternative to the traditional subway construction method, offering clear advantages in resource utilization, green environmental protection, construction industrialization, etc. [1,2].
In the 20th century, prefabricated assembly technology has been applied to subways in developed countries.In the 1980s, the former Soviet Union [3,4], in order to solve the problems associated with constructing subways in cold winter areas, employed prefabricated components in the cut-and-cover method for the construction of subway tunnels, stations and ancillary access points.The precast reinforced concrete tube sheet assembly arch technology was pioneered for the construction of subway stations in the 1990s in France [5] for the Regional Express Line of the Paris Metro.While the domestic research on prefabricated subway station technology started late, Yang Xiuren and Huang Meiqun [3] took the lead in developing single-arch, large-span prefabricated subway station construction technology in China, which was successfully applied in five stations of Changchun Metro Line 2.
With the fast speed development of China's urban rail transport, the PSSS have been built and put into use in large numbers.For example, the total-prefabricated subway station structure has been used in the construction of underground structures in urban areas such as Changchun, Shenzhen and Qingdao.Assembly construction technology has dramatically accelerated the construction speed of underground structures, improved the project's quality, and reduced environmental pollution during the construction process.At the same time, it solved the problem that the underground could not be constructed in cold winter areas.However, compared with the CIPSSS, the PSSS is prefabricated from multiple prefabricated components.Under seismic action, there is bound to be a difference in the seismic performance of the two.Therefore, it is necessary to study the seismic performance of the PSSS further.
In recent years, the PSSS has become a hotspot in the research of underground structures.Tao Lianjin et al. [6] investigated the effect of enclosure structure on the seismic performance of the PSSS based on shaking table tests.They found that the enclosure structure effectively improves the deformation-resistant strength and node stiffness of the PSSS.Liu Hongtao and Du Xiuli [7,8] carried out tests on the damage pattern and mechanical properties of PSSS components spliced nodes with different connection modes under seismic action and found that there is a noticeable stiffness domain effect in the region of the grouting sleeve.The cracks after damage of specimens are mainly distributed in a particular range at the upper and lower ends of the sleeve.Ding Peng and Tao Lianjin et al. [9,10] used Abaqus finite element software to analyze the seismic performance of a PSSS under different site class conditions and compared the seismic response of the structure under different seismic wave incidence angles.The study results show that PSSS has better seismic performance than CIPSSS under seismic action of the fortification.Jiang et al. [11] investigated the difference in the response of fully assembled and homogeneous CIPSSS under different seismic intensities in terms of deformation, internal force, and damage based on numerical simulation.Qin Yiwen et al. [12] investigated the seismic response of PSSS under different directions of ground shaking and found that the vertical seismic performance of PSSS is more robust.Currently, studies on the seismic performance of PSSSs are conducted mainly on general strata, and the effect of liquefiable strata still needs to be included.
The damaging effects of strong earthquakes on underground structures can be classified into two main groups: damage caused by soil shaking and damages due to soil failures.The second major group includes a broad spectrum of different failure modes, such as faulting and tectonic uplift, liquefaction, subsidence and slope instabilities [13].In the large-scale construction of urban rail transit in China, subway construction in many areas crosses liquefiable strata.According to the 1978 definition of the Geodynamics Committee of the Geotechnical Engineering Division of the American Society of Civil Engineers [14], liquefaction is the act or process of transforming any solid material into a liquid.In the case of liquefaction of saturated sandy soils, the transformation from a solid to a liquid state is the result of an increase in pore pressure and a decrease in effective stress.The liquefaction of saturated sandy soil under the action of natural earthquakes is one of the important topics of geotechnical earthquake engineering research, which has been highly valued by domestic and foreign scholars and engineering circles [15][16][17].In China, the 1976 Tangshan earthquake caused a large area of sand foundation liquefaction in the coastal area, and the 2008 Wenchuan earthquake also caused multiple saturated sand foundation liquefaction in the main earthquake area.As a result of the propagation of seismic waves generated by an earthquake, the soil will undergo vibrations that are manifested as soil shaking [18]; consequently, underground structures will suffer more or less deformations simultaneously with the soil deformations.It has been shown [19][20][21] that under seismic action, the main factor affecting the seismic response of underground structures is the displacement change in the soil around the structure rather than the inertial force of the earthquake on the underground structure.Therefore, the liquefaction phenomenon of saturated sandy soil under seismic action leads to foundation slip, which causes damage to the underground structure.
Scholars have also researched the seismic performance of CIPSSS in inclined liquefiable foundations.Chen Jihua et al. [22] studied the deformation characteristics of liquefied soil surfaces at different inclination sites based on shaking table tests.They found that a more significant surface inclination increases the seismic subsidence phenomenon on the surface of liquefied foundations.Wang R et al. [23] studied the seismic response of two-story, three-span subway station structures in liquefiable sites with different inclinations based on numerical analysis.Based on shaking table tests, Zhuang Haiyang et al. [24] investigated the seismic response of the subway station structure and tunnel connection in a liquefiable site with a surface inclination of 6 • .It was found that an apparent uneven uplift phenomenon occurred in both structures, which might aggravate the damage of the connection part under seismic action.Zhang Xiwen et al. [25] analyzed the seismic response law of a two-story, two-span subway station structure in a gently inclined liquefiable site based on FLAC3D finite difference software.Qiu Yu and Zhang Xiwen [26] used FLAC3D finite difference software to establish a numerical model of soil-subway station structure in a gently inclined liquefiable site to study the influence of the ground inclination angle on underground stations.It was found that in the gently inclined liquefiable area, the underground station exhibited inclined floating behavior with larger horizontal displacement.From their perspectives, the above research investigates the seismic response and damage mechanism of inclined liquefiable sites and underground structures.However, the research objects are CIPSSS, and the influence of PSSS in inclined liquefiable sites has not been considered.
The seismic damage and research results have shown that the large deformation of the soil body caused by seismic liquefaction is the most important external factor for the damage to underground structures [27].At present, the research on the seismic response characteristics and damage mechanism of PSSS in inclined liquefiable strata has yet to be published, which poses a significant challenge to its further popularization and application under different stratigraphic conditions.
In this paper, the first prefabricated subway station (Shuangfeng Station) of Changchun Subway Line 2 in China is taken as the engineering background, and the applicability of the PSSS in a slightly tilted liquefiable ground is investigated using numerical simulation by comparing it with the same type of CIPSSS in the hope that it can provide guidance and references for the design and construction of PSSS and fill in the blanks of the research on seismic performance of a new type of PSSS in a slightly tilted liquefiable ground.

Project Overview
The Changchun prefabricated subway station structure (PSSS) in China is a two-story underground structure.The station structure is 20.5 m wide and 17.45 m high, and the station structure is prefabricated vertically one ring by one ring; each ring is 2 m wide, and a center column is set in every three rings.Each ring is connected by seven prefabricated components prefabricated on site.The joints between the members adopt a tongue-andgroove connection, and the joint gaps are sealed by injecting epoxy resin.All parts except the profile are cast afterward, and the detailed dimensions of the structure are shown in references [28,29].Figure 1 shows a schematic section of the station structure.significant surface inclination increases the seismic subsidence phenomenon on the surface of liquefied foundations.Wang R et al. [23] studied the seismic response of two-story, three-span subway station structures in liquefiable sites with different inclinations based on numerical analysis.Based on shaking table tests, Zhuang Haiyang et al. [24] investigated the seismic response of the subway station structure and tunnel connection in a liquefiable site with a surface inclination of 6°.It was found that an apparent uneven uplift phenomenon occurred in both structures, which might aggravate the damage of the connection part under seismic action.Zhang Xiwen et al. [25] analyzed the seismic response law of a two-story, two-span subway station structure in a gently inclined liquefiable site based on FLAC3D finite difference software.Qiu Yu and Zhang Xiwen [26] used FLAC3D finite difference software to establish a numerical model of soil-subway station structure in a gently inclined liquefiable site to study the influence of the ground inclination angle on underground stations.It was found that in the gently inclined liquefiable area, the underground station exhibited inclined floating behavior with larger horizontal displacement.From their perspectives, the above research investigates the seismic response and damage mechanism of inclined liquefiable sites and underground structures.However, the research objects are CIPSSS, and the influence of PSSS in inclined liquefiable sites has not been considered.The seismic damage and research results have shown that the large deformation of the soil body caused by seismic liquefaction is the most important external factor for the damage to underground structures [27].At present, the research on the seismic response characteristics and damage mechanism of PSSS in inclined liquefiable strata has yet to be published, which poses a significant challenge to its further popularization and application under different stratigraphic conditions.
In this paper, the first prefabricated subway station (Shuangfeng Station) of Changchun Subway Line 2 in China is taken as the engineering background, and the applicability of the PSSS in a slightly tilted liquefiable ground is investigated using numerical simulation by comparing it with the same type of CIPSSS in the hope that it can provide guidance and references for the design and construction of PSSS and fill in the blanks of the research on seismic performance of a new type of PSSS in a slightly tilted liquefiable ground.

Project Overview
The Changchun prefabricated subway station structure (PSSS) in China is a two-story underground structure.The station structure is 20.5 m wide and 17.45 m high, and the station structure is prefabricated vertically one ring by one ring; each ring is 2 m wide, and a center column is set in every three rings.Each ring is connected by seven prefabricated components prefabricated on site.The joints between the members adopt a tongueand-groove connection, and the joint gaps are sealed by injecting epoxy resin.All parts except the profile are cast afterward, and the detailed dimensions of the structure are shown in references [28,29].Figure 1 shows a schematic section of the station structure.

Numerical Models
Based on the structure of Changchun Metro Shuangfeng Station, numerical simulation analysis is carried out, and FLAC3D finite difference software is used to establish a numerical analysis model of soil-metro station structure interaction.The model size is 160 m long, 20 m wide, and 52.5 m high, the burial depth of the middle part of the subway station structure is 3 m, and the soil layer where the structure is located in the model is liquefiable.In the dynamic calculation, free-field boundary conditions are used around the model, and fixed constraints are used at the bottom of the model.The maximum grid size of the soil part of the model is 1 m, and the grid of the subway station structure model is encrypted, with a minimum grid size of 0.2 m, to ensure the accuracy of the calculation results.The numerical calculation model is shown in Figure 2.

Numerical Models
Based on the structure of Changchun Metro Shuangfeng Station, numerical simulation analysis is carried out, and FLAC3D finite difference software is used to establish a numerical analysis model of soil-metro station structure interaction.The model size is 160 m long, 20 m wide, and 52.5 m high, the burial depth of the middle part of the subway station structure is 3 m, and the soil layer where the structure is located in the model is liquefiable.In the dynamic calculation, free-field boundary conditions are used around the model, and fixed constraints are used at the bottom of the model.The maximum grid size of the soil part of the model is 1 m, and the grid of the subway station structure model is encrypted, with a minimum grid size of 0.2 m, to ensure the accuracy of the calculation results.The numerical calculation model is shown in Figure 2. The outer profile of the PSSS consists of seven (five types) prefabricated members, which are numbered A, B(1,2), C(1,2), D, and E. The members are connected by mortise and tenon joints.After assembling the outer contour of the structure, the center plate and center column were cast in place using concrete.The thickness of the center slab is 400 mm, and the cross-section size of the center column is 500 mm × 500 mm, as shown in Figure 3a. Figure 3b shows the structural model of the same cast-in-place subway station structure (CIPSSS) type.Figure 4a shows the sketch of the model, Figure 4b shows the layout of the monitoring points in the soil layer and Figure 4c shows the layout of the monitoring points in the structure, which are set up for four working conditions of 0°, 2°, 4° and 6° of the surface inclination angles, respectively.The letters P and A in Figure 4b are the monitoring points The outer profile of the PSSS consists of seven (five types) prefabricated members, which are numbered A, B(1,2), C(1,2), D, and E. The members are connected by mortise and tenon joints.After assembling the outer contour of the structure, the center plate and center column were cast in place using concrete.The thickness of the center slab is 400 mm, and the cross-section size of the center column is 500 mm × 500 mm, as shown in Figure 3a. Figure 3b shows the structural model of the same cast-in-place subway station structure (CIPSSS) type.

Numerical Models
Based on the structure of Changchun Metro Shuangfeng Station, numerical simulation analysis is carried out, and FLAC3D finite difference software is used to establish a numerical analysis model of soil-metro station structure interaction.The model size is 160 m long, 20 m wide, and 52.5 m high, the burial depth of the middle part of the subway station structure is 3 m, and the soil layer where the structure is located in the model is liquefiable.In the dynamic calculation, free-field boundary conditions are used around the model, and fixed constraints are used at the bottom of the model.The maximum grid size of the soil part of the model is 1 m, and the grid of the subway station structure model is encrypted, with a minimum grid size of 0.2 m, to ensure the accuracy of the calculation results.The numerical calculation model is shown in Figure 2. The outer profile of the PSSS consists of seven (five types) prefabricated members, which are numbered A, B(1,2), C(1,2), D, and E. The members are connected by mortise and tenon joints.After assembling the outer contour of the structure, the center plate and center column were cast in place using concrete.The thickness of the center slab is 400 mm, and the cross-section size of the center column is 500 mm × 500 mm, as shown in Figure 3a. Figure 3b shows the structural model of the same cast-in-place subway station structure (CIPSSS) type.Figure 4a shows the sketch of the model, Figure 4b shows the layout of the monitoring points in the soil layer and Figure 4c shows the layout of the monitoring points in the structure, which are set up for four working conditions of 0°, 2°, 4° and 6° of the surface inclination angles, respectively.The letters P and A in Figure 4b are the monitoring points

Site Conditions and Parameter Selection
The Mohr-Coulomb intrinsic model is selected for the general soil part of the computational model.The soil layer where the underground structure is located is saturated, and the fine sandy soil layer and the PL-Finn model in FLAC3D are used.The PL-Finn model was developed on the basis of the original FLAC3D liquefaction calculation model (Finn model) [30], and the post-liquefaction calculation module was added on the basis of the Finn model to consider the flow model in the zero-effective stress state and the nonzero-effective stress state after the initial liquefaction occurs.Since the procedure considers the morphology of sandy soil after liquefaction, the resulting model is named the PL-

Site Conditions and Parameter Selection
The Mohr-Coulomb intrinsic model is selected for the general soil part of the computational model.The soil layer where the underground structure is located is saturated, and the fine sandy soil layer and the PL-Finn model in FLAC3D are used.The PL-Finn model was developed on the basis of the original FLAC3D liquefaction calculation model (Finn model) [30], and the post-liquefaction calculation module was added on the basis of the Finn model to consider the flow model in the zero-effective stress state and the non-zero-effective stress state after the initial liquefaction occurs.Since the procedure considers the morphology of sandy soil after liquefaction, the resulting model is named the PL-Finn (post-liquefaction Finn) model.The distribution of the soil layer and its physical and mechanical parameters are shown in Table 1, and the isotropic elastic model is used for the subway station structure with local damping.The physical and mechanical parameters of the structure are shown in Table 2.

Contact Surface Setting
Contact surfaces are established between the assembled members at the joints to simulate the PSSS assembly nodes.The contact surfaces at the node locations of the PSSS are shown in Figure 5.The contact surface unit parameters are shown in Table 3, with stiffness values taken from joint performance tests [31,32] and construction experience.
Buildings 2024, 14, x FOR PEER REVIEW 6 of 19 Finn (post-liquefaction Finn) model.The distribution of the soil layer and its physical and mechanical parameters are shown in Table 1, and the isotropic elastic model is used for the subway station structure with local damping.The physical and mechanical parameters of the structure are shown in Table 2.

Contact Surface Setting
Contact surfaces are established between the assembled members at the joints to simulate the PSSS assembly nodes.The contact surfaces at the node locations of the PSSS are shown in Figure 5.The contact surface unit parameters are shown in Table 3, with stiffness values taken from joint performance tests [31,32] and construction experience.

Input Ground Shaking
The seismic waves are selected as Changchun artificial, Kobe, and EL-Centro waves.Three seismic waves with different spectral characteristics were excited from the bottom of the model for numerical analysis.These seismic waves were originally recorded at different durations, but in order to make them comparable, the parts of the original seismic waves that could adequately represent their properties were artificially selected, and these seismic waves were uniformly held for 30 s.The acceleration time curve and Fourier spectrum are shown in Figures 6 and 7.The power calculation results show that the seismic response of the structure and the surrounding soil body under the action of three kinds of ground shaking is consistent with the law [33], and the seismic response under the action of the Changchun artificial wave is the largest.Therefore, this paper explicitly analyzes the calculation results under the action of a 0.15 g and 0.25 g Changchun artificial wave.

Input Ground Shaking
The seismic waves are selected as Changchun artificial, Kobe, and EL-Centro waves.Three seismic waves with different spectral characteristics were excited from the bottom of the model for numerical analysis.These seismic waves were originally recorded at different durations, but in order to make them comparable, the parts of the original seismic waves that could adequately represent their properties were artificially selected, and these seismic waves were uniformly held for 30 s.The acceleration time curve and Fourier spectrum are shown in Figures 6 and 7.The power calculation results show that the seismic response of the structure and the surrounding soil body under the action of three kinds of ground shaking is consistent with the law [33], and the seismic response under the action of the Changchun artificial wave is the largest.Therefore, this paper explicitly analyzes the calculation results under the action of a 0.15 g and 0.25 g Changchun artificial wave.

Pore Water Pressure Analysis
The time course curves of an excess pore pressure ratio (EPPR) at different locations on both sides of the structural floor slab of the PSSS and CIPSSS at different surface inclinations at an input peak ground vibration acceleration of 0.25 g are given in Figures 8 and

Input Ground Shaking
The seismic waves are selected as Changchun artificial, Kobe, and EL-Centro waves.Three seismic waves with different spectral characteristics were excited from the bottom of the model for numerical analysis.These seismic waves were originally recorded at different durations, but in order to make them comparable, the parts of the original seismic waves that could adequately represent their properties were artificially selected, and these seismic waves were uniformly held for 30 s.The acceleration time curve and Fourier spectrum are shown in Figures 6 and 7.The power calculation results show that the seismic response of the structure and the surrounding soil body under the action of three kinds of ground shaking is consistent with the law [33], and the seismic response under the action of the Changchun artificial wave is the largest.Therefore, this paper explicitly analyzes the calculation results under the action of a 0.15 g and 0.25 g Changchun artificial wave.

Pore Water Pressure Analysis
The time course curves of an excess pore pressure ratio (EPPR) at different locations on both sides of the structural floor slab of the PSSS and CIPSSS at different surface inclinations at an input peak ground vibration acceleration of 0.25 g are given in Figures 8 and

Pore Water Pressure Analysis
The time course curves of an excess pore pressure ratio (EPPR) at different locations on both sides of the structural floor slab of the PSSS and CIPSSS at different surface inclinations at an input peak ground vibration acceleration of 0.25 g are given in Figures 8 and 9.In the figure, P1 and P2 are the soil monitoring points at 5 m and 25 m on the left side of the structural footing, and P3 and P4 are the soil monitoring points at 5 m and 25 on the right side of the structural footing, respectively.The trend of EPPR changes at each monitoring point of the soil for both conditions is the same.The soil body close to the two sides of the structure showed an apparent negative pore pressure (NPP) phenomenon; the NPP on the uphill side of the structure was more significant than that on the downhill side of it, and the larger the surface inclination was, the more pronounced the NPP phenomenon was.This may be due to the uplift of the structure under seismic action, resulting in drainage channels around the structure, and under the action of dynamic soil pressure, resulting in the structure on both sides of the NPP phenomenon.The greater the slope of the ground surface, the greater the dynamic soil pressure on the uphill side of the structure, and the greater the NPP on both sides of the structure.The EPPR at locations 5 m from the subway station structure (points P1 and P3) are less than 1.0 throughout the 30 s of seismic wave excitation, while the EPPR at locations 25 m from the subway station structure (points P2 and P4) are already greater than 1.0 at the 13th moment of the seismic wave excitation.The further the distance from the station, the more likely it is to be liquefied.This indicates that the existence of an underground structure in the inclined liquefiable site still inhibits the liquefaction of the surrounding soil.At 25 m from both sides of the station structure, the larger the surface inclination, the smaller the soil EPPR.When the surface inclination angle is 2 • and 4 • , the liquefaction phenomenon occurs in both uphill and downhill directions, and the liquefaction phenomenon is more evident in the downhill direction.When the inclination angle of the ground surface is 6 • , liquefaction does not occur on the uphill side, and liquefaction occurs on the downhill side.This may be due to the different thicknesses of the overlying soil.Overall, the soil EPPR around the PSSS and CIPSSS changed in the same trend under other surface inclination conditions.The PSSS can be applied to inclined liquefiable site conditions to ensure static waterproofing.
of the structural footing, and P3 and P4 are the soil monitoring points at 5 m and 25 on the right side of the structural footing, respectively.The trend of EPPR changes at each monitoring point of the soil for both conditions is the same.The soil body close to the two sides of the structure showed an apparent negative pore pressure (NPP) phenomenon; the NPP on the uphill side of the structure was more significant than that on the downhill side of it, and the larger the surface inclination was, the more pronounced the NPP phenomenon was.This may be due to the uplift of the structure under seismic action, resulting in drainage channels around the structure, and under the action of dynamic soil pressure, resulting in the structure on both sides of the NPP phenomenon.The greater the slope of the ground surface, the greater the dynamic soil pressure on the uphill side of the structure, and the greater the NPP on both sides of the structure.The EPPR at locations 5 m from the subway station structure (points P1 and P3) are less than 1.0 throughout the 30 s of seismic wave excitation, while the EPPR at locations 25 m from the subway station structure (points P2 and P4) are already greater than 1.0 at the 13th moment of the seismic wave excitation.The further the distance from the station, the more likely it is to be liquefied.This indicates that the existence of an underground structure in the inclined liquefiable site still inhibits the liquefaction of the surrounding soil.At 25 m from both sides of the station structure, the larger the surface inclination, the smaller the soil EPPR.When the surface inclination angle is 2° and 4°, the liquefaction phenomenon occurs in both uphill and downhill directions, and the liquefaction phenomenon is more evident in the downhill direction.When the inclination angle of the ground surface is 6°, liquefaction does not occur on the uphill side, and liquefaction occurs on the downhill side.This may be due to the different thicknesses of the overlying soil.Overall, the soil EPPR around the PSSS and CIPSSS changed in the same trend under other surface inclination conditions.The PSSS can be applied to inclined liquefiable site conditions to ensure static waterproofing.

Peak Acceleration Analysis of the Ground Surface
Figure 10 shows the peak acceleration curves at different locations of the ground surface when the input peak acceleration of ground vibration is 0.3 g.The horizontal coordinates 0-20 m in the figure show the area where the subway station structure is located.One monitoring point is taken every 5 m.The figure shows that the peak acceleration of the surface directly above the structure is smaller than that of the side of the structure under different surface inclination conditions.This indicates that the presence of subsurface structures has a dampening effect on the propagation of seismic waves in the original site soils.The peak acceleration curve is almost symmetrical when the surface inclination is 0°.When the ground surface is inclined, the larger the surface inclination, the larger the peak acceleration, and the peak acceleration on the downslope side is significantly larger than that on the upslope side.The downslope slip of the foundation may cause this due to the tilted surface.At a surface inclination of 2°, the range of influence of the PSSS on the peak ground acceleration is more extensive than that of the CIPSSS condition.The influence range for the PSSS condition is about 2.5 times the width of the subway station structure.The influence range of the CIPSSS condition is about 1.5 times the width of the station structure.With the increase in the surface inclination, the influence range of both structures on the surface's peak acceleration is about 1.5 times the width of the structure.This indicates that the range of seismic isolation influence of the PSSS on the surface acceleration response is better when there is a smaller inclination angle at the ground surface.

Peak Acceleration Analysis of the Ground Surface
Figure 10 shows the peak acceleration curves at different locations of the ground surface when the input peak acceleration of ground vibration is 0.3 g.The horizontal coordinates 0-20 m in the figure show the area where the subway station structure is located.One monitoring point is taken every 5 m.The figure shows that the peak acceleration of the surface directly above the structure is smaller than that of the side of the structure under different surface inclination conditions.This indicates that the presence of subsurface structures has a dampening effect on the propagation of seismic waves in the original site soils.The peak acceleration curve is almost symmetrical when the surface inclination is 0 • .When the ground surface is inclined, the larger the surface inclination, the larger the peak acceleration, and the peak acceleration on the downslope side is significantly larger than that on the upslope side.The downslope slip of the foundation may cause this due to the tilted surface.At a surface inclination of 2 • , the range of influence of the PSSS on the peak ground acceleration is more extensive than that of the CIPSSS condition.The influence range for the PSSS condition is about 2.5 times the width of the subway station structure.The influence range of the CIPSSS condition is about 1.5 times the width of the station structure.With the increase in the surface inclination, the influence range of both structures on the surface's peak acceleration is about 1.5 times the width of the structure.This indicates that the range of seismic isolation influence of the PSSS on the surface acceleration response is better when there is a smaller inclination angle at the ground surface.

Analysis of Lateral Deformation of Liquefiable Soil Body
The maximum lateral relative displacement curves of the liquefiable soil body of the foundation around the free-field, CIPSSS, and PSSS at an input ground vibration of 0.25 g are given in Figure 11.From the figure, it can be seen that the larger the ground inclination angle, the larger the lateral displacement of the soil body in each condition.In the freefield condition, the maximum lateral displacements of the soil body under different surface inclinations occurred at the top of the liquefied soil layer.In the non-free-field condition, the maximum lateral displacements at several locations occur at different burial depths of the liquefied soil layer when the ground surface inclination angle is slight (2°).As the surface inclination increased, the maximum values of lateral displacements of the soil almost always appeared at the top of the liquefied soil layer.
Compared with the free-field condition, both the PSSS and CIPSSS conditions inhibit the lateral displacement of the liquefied soil body of the foundation.The influence of the structure on the lateral displacement of the soil body is mainly in the area above the depth of the structural footing, and the closer to the station structure, the more pronounced the inhibition effect.Comparing the relative soil lateral displacements between the PSSS and CIPSSS conditions, it can be found that the suppression effect of the PSSS on the lateral displacement of the surrounding soil is significantly more significant than that of the CIPSSS.Especially on the uphill side, the suppression effect of the PSSS condition is more pronounced.
The lateral displacement of liquefied soil at different locations shows an increasing trend with the decrease in burial depth, and a sudden increase in the lateral displacement of soil is caused by soil flow and slip.However, the lateral displacement of the soil body at the depth of burial above the subway station structural floor shows a stable growth trend, and the sudden increase in lateral displacement mainly manifests in the area below the depth of burial of the subway station structural floor.

Analysis of Lateral Deformation of Liquefiable Soil Body
The maximum lateral relative displacement curves of the liquefiable soil body of the foundation around the free-field, CIPSSS, and PSSS at an input ground vibration of 0.25 g are given in Figure 11.From the figure, it can be seen that the larger the ground inclination angle, the larger the lateral displacement of the soil body in each condition.In the free-field condition, the maximum lateral displacements of the soil body under different surface inclinations occurred at the top of the liquefied soil layer.In the non-free-field condition, the maximum lateral displacements at several locations occur at different burial depths of the liquefied soil layer when the ground surface inclination angle is slight (2 • ).As the surface inclination increased, the maximum values of lateral displacements of the soil almost always appeared at the top of the liquefied soil layer.
Compared with the free-field condition, both the PSSS and CIPSSS conditions inhibit the lateral displacement of the liquefied soil body of the foundation.The influence of the structure on the lateral displacement of the soil body is mainly in the area above the depth of the structural footing, and the closer to the station structure, the more pronounced the inhibition effect.Comparing the relative soil lateral displacements between the PSSS and CIPSSS conditions, it can be found that the suppression effect of the PSSS on the lateral displacement of the surrounding soil is significantly more significant than that of the CIPSSS.Especially on the uphill side, the suppression effect of the PSSS condition is more pronounced.
The lateral displacement of liquefied soil at different locations shows an increasing trend with the decrease in burial depth, and a sudden increase in the lateral displacement of soil is caused by soil flow and slip.However, the lateral displacement of the soil body at the depth of burial above the subway station structural floor shows a stable growth trend, and the sudden increase in lateral displacement mainly manifests in the area below the depth of burial of the subway station structural floor.

Stress Analysis of Structural Sidewalls (Member C1) in Subway Stations
The amplitude of the principal stress response of the left-and right-side walls (members C1 and C2) of the PSSS and CIPSSS at an input peak ground vibration acceleration of 0.25 g are given in Tables 4 and 5, respectively.In the table, LQ1-LQ5 are the monitoring points on the left side wall, and RQ1-RQ5 are the monitoring points on the right-side wall.Overall, the amplitude of the principal stress response of the side walls showed an increasing trend with the increase in the inclination angle of the ground surface, both for the PSSS structure and the CIPSSS.The stress response amplitude of the left side wall of the structure is significantly larger than that of the corresponding location of the rightside wall.The stress response at the location of monitoring point LQ5 at the bottom of the

Stress Analysis of Structural Sidewalls (Member C1) in Subway Stations
The amplitude of the principal stress response of the left-and right-side walls (members C1 and C2) of the PSSS and CIPSSS at an input peak ground vibration acceleration of 0.25 g are given in Tables 4 and 5, respectively.In the table, LQ1-LQ5 are the monitoring points on the left side wall, and RQ1-RQ5 are the monitoring points on the right-side wall.Overall, the amplitude of the principal stress response of the side walls showed an increasing trend with the increase in the inclination angle of the ground surface, both for the PSSS structure and the CIPSSS.The stress response amplitude of the left side wall of the structure is significantly larger than that of the corresponding location of the right-side wall.The stress response at the location of monitoring point LQ5 at the bottom of the left side wall is the largest.Therefore, the stress difference between the left-and right-side walls of the two structures is analyzed as an example.When the inclination angle of the ground surface is 2 • , 4 • and 6 • , the maximum stress ratios at the bottom of the left-and right-side walls of the PSSS (LQ5 and RQ5) are 1.08, 1.24, and 1.48, respectively.The maximum stress ratios at the bottom of the left-and right-side walls of the CIPSSS (LQ5 and RQ5) are 1.12, 1.25, and 1.50, respectively.The larger the inclination angle of the ground surface is, the larger the ratio of the maximum stresses is.This is because when there is an inclination angle of the ground surface, the soil body around the subway station structure will slip downhill, and the dynamic soil pressure on both sides of the structure will be different.The greater the surface inclination, the greater the dynamic soil pressure on the uphill the left side of the structure side of the structure.Compare the amplitude of the principal stress response of PSSS and CIPSSS.The maximum principal stress response amplitude of the side walls of the CIPSSS and the maximum stress ratio of the left-and right-side walls were significantly larger than those of the PSSS.This indicates that the PSSS with flexible connections has less stress in the surface-inclined liquefiable site, better structural stability, and a safer structure.

Stress Analysis at Node Locations of PSSS
Table 6 gives the amplitude of the principal stress response at the node locations of PSSS and CIPSSS.From Table 6, it can be seen that the magnitude of the principal stress response at the nodes of the PSSS and the corresponding locations of the CIPSSS show an increasing trend with the increase in the ground inclination.The node location on the left side of the structural floor (J4) is always in tension, while all other node locations are always in compression.Moreover, the node principal stresses in the underground second floor of the structure are significantly larger than those in the underground first floor.In the nodes of the underground first floor of the structure, the amplitude of the principal stress response of the two structures at position J1 is the same, and the principal stress response of the PSSS condition at positions J2 and J7 is more significant than that of the CIPSSS.In contrast, the principal stress response at the nodes of the underground second floor of the structure was more significant for the CIPSSS than for the PSSS.This may be due to the higher stresses in the underground first floor of the PSSS due to the tilted dynamic soil pressure at the surface.Therefore, the seismic design of PSSS in inclined liquefiable strata should focus on the underground first floor of the structure.

Analysis of Lateral Deformation of the Subway Station Structure
The maximum lateral relative displacement curves of PSSS and CIPSSS in liquefiable sites with different inclination angles for an input peak ground shaking acceleration of 0.25 g are given in Figure 12.Table 7 presents the inter-story displacement angles of the subway station structures for the input peak ground shaking acceleration of 0.15 g and 0.25 g for each condition.As seen in Figure 12, the maximum relative lateral displacements of the PSSS and CIPSSS gradually increase with the increase in ground surface inclination angle.When the ground surface inclination angle is 2 • , the lateral displacement of the PSSS is significantly larger than that of the CIPSSS.When the inclination angle of the ground surface increases to 4 • , the transverse displacement of the PSSS is slightly larger than that of the CIPSSS, and the difference between the two structures is minimal.When the ground surface inclination angle is 6 • , the maximum transverse displacement of the structure changes, and then the transverse displacement of the CIPSSS is more significant than that of the PSSS.As far as Table 7 is concerned, the interstory displacement angle of the PSSS is more significant than that of the CIPSSS when the ground surface inclination angle is 2 • and 4 • , respectively.maximum interstory displacement angle of the CIPSSS under the action of 0.25 g ground vibration reaches 1/41, which is more than 1/50, and at this time, the structure is in a state of destruction.This shows that the PSSS has better adaptability to ground deformation for the site with a larger inclination angle.

Analysis of the Uplift of the Subway Station Structure
The vertical displacement curves at different locations of the structural floor slabs of the PSSS and CIPSSS for an input peak ground vibration acceleration of 0.25 g are given in Figure 13.Meanwhile, Table 8 shows the uplift amount difference between the two sides of the structural base plate (B1-B9).It can be seen that both structures are in the uplift state under the action of ground vibration.The uplift of the PSSS is significantly smaller than that of the CIPSSS.The larger the inclination angle of the ground surface is, the more significant the difference between the uplift amount of the two structures is.It shows that the PS is less affected by the uplift caused by seismic liquefaction of the inclined liquefiable site.When the inclination angle of the ground surface is 0°, a slight counterclockwise deflection occurs during the uplift of the station structure, and the maximum uplifts of the PSSS and CIPSSS are 0.22 m and 0.23 m.When the inclination angle of the ground surface is changed to 2°, the PSSS first starts to undergo a clockwise deflection, and the maximum uplifts are 0.27 m and 0.29 m, respectively.When the inclination angle of the ground surface is 4°, the two structures start to undergo a more significant clockwise deflection.When the inclination angle of the ground surface is 4°, the two structures begin to have a more significant clockwise overturning phenomenon, and the maximum uplifts are 0.28 m and 0.29 m, respectively.When the inclination angle of the ground surface is 6°, the overturning phenomenon of the two structures is more pronounced, and the uplift of the CIPSSS at this time is obviously more significant than that of the PSSS, and the maximum  Furthermore, only in the case of a ground surface inclination angle of 2 • is the maximum inter-story displacement angle of the structure less than 1/550, which is in an elastic working condition.When the inclination angle of the ground surface is 6 • , the maximum interstory displacement angle of the PSSS is smaller than that of the CIPSSS.The maximum interstory displacement angle of the CIPSSS under the action of 0.25 g ground vibration reaches 1/41, which is more than 1/50, and at this time, the structure is in a state of destruction.This shows that the PSSS has better adaptability to ground deformation for the site with a larger inclination angle.

Analysis of the Uplift of the Subway Station Structure
The vertical displacement curves at different locations of the structural floor slabs of the PSSS and CIPSSS for an input peak ground vibration acceleration of 0.25 g are given in Figure 13.Meanwhile, Table 8 shows the uplift amount difference between the two sides of the structural base plate (B1-B9).It can be seen that both structures are in the uplift state under the action of ground vibration.The uplift of the PSSS is significantly smaller than that of the CIPSSS.The larger the inclination angle of the ground surface is, the more significant the difference between the uplift amount of the two structures is.It shows that the PS is less affected by the uplift caused by seismic liquefaction of the inclined liquefiable site.When the inclination angle of the ground surface is 0 • , a slight counterclockwise deflection occurs during the uplift of the station structure, and the maximum uplifts of the PSSS and CIPSSS are 0.22 m and 0.23 m.When the inclination angle of the ground surface is changed to 2 • , the PSSS first starts to undergo a clockwise deflection, and the maximum uplifts are 0.27 m and 0.29 m, respectively.When the inclination angle of the ground surface is 4 • , the two structures start to undergo a more significant clockwise deflection.When the inclination angle of the ground surface is 4 • , the two structures begin to have a more significant clockwise overturning phenomenon, and the maximum uplifts are 0.28 m and 0.29 m, respectively.When the inclination angle of the ground surface is 6 • , the overturning phenomenon of the two structures is more pronounced, and the uplift of the CIPSSS at this time is obviously more significant than that of the PSSS, and the maximum uplifts are 0.34 m and 0.38 m respectively.Table 8 shows that the difference in the vertical displacements of the bottom plate on both sides of the PSSS is smaller than that of the CIPSSS.This indicates that the overturning resistance of the PSSS in inclined liquefaction is better than that of the CIPSSS.

Discussion
Based on the engineering background of Changchun Metro Line 2 Shuangfeng Station, a numerical analysis model of the interaction between inclined liquefiable strata and PSSS was established.The seismic response results of the prefabricated subway station structure (PSSS) and cast-in-place subway station structure (CIPSSS) are compared, and the seismic response laws such as foundation pore water pressure at different surface inclination angles, foundation liquefaction soil lateral displacement, dynamic response, and uplift characteristics of underground structures are studied.
Consistent with the results of Qiu Yu and Zhang Xiwen [26], in the gently inclined liquefiable region, the underground station exhibits inclined floating behavior with large horizontal displacement.In this paper, both the PSSS and the CIPSSS eventually experience large clockwise overturning as the surface inclination gradually increases.Unlike the CIPSSS, the PSSS already starts to deflect clockwise at a surface inclination of 2°.Both structures were uplifted under ground shaking.The uplift of the PSSS is significantly smaller than that of the CIPSSS.The larger the inclination angle of the ground surface, the larger the difference between the uplift of the two structures.
The seismic response of the PSSS is consistent with that of the CIPSSS in that the ratio of the maximum stresses at the bottom of the left-and right-side walls of the structure increases as the inclination of the ground surface increases.This is due to the fact that when there is an inclination of the ground surface, the uphill soil around the subway

Discussion
Based on the engineering background of Changchun Metro Line 2 Shuangfeng Station, a numerical analysis model of the interaction between inclined liquefiable strata and PSSS was established.The seismic response results of the prefabricated subway station structure (PSSS) and cast-in-place subway station structure (CIPSSS) are compared, and the seismic response laws such as foundation pore water pressure at different surface inclination angles, foundation liquefaction soil lateral displacement, dynamic response, and uplift characteristics of underground structures are studied.
Consistent with the results of Qiu Yu and Zhang Xiwen [26], in the gently inclined liquefiable region, the underground station exhibits inclined floating behavior with large horizontal displacement.In this paper, both the PSSS and the CIPSSS eventually experience large clockwise overturning as the surface inclination gradually increases.Unlike the CIPSSS, the PSSS already starts to deflect clockwise at a surface inclination of 2 • .Both structures were uplifted under ground shaking.The uplift of the PSSS is significantly smaller than that of the CIPSSS.The larger the inclination angle of the ground surface, the larger the difference between the uplift of the two structures.
The seismic response of the PSSS is consistent with that of the CIPSSS in that the ratio of the maximum stresses at the bottom of the left-and right-side walls of the structure increases as the inclination of the ground surface increases.This is due to the fact that when there is an inclination of the ground surface, the uphill soil around the subway station structure will slip towards the downslope direction, resulting in the dynamic soil pressure on the uphill side of the structure being larger than that on the downhill side.This confirms the conclusion of scholars that the main factor affecting the seismic response of underground structures is the displacement change in the soil around the structure [27].
It is found that the PSSS is better than the CIPSSS in terms of resistance to overturning, uplift, and liquefaction.Therefore, the PSSS can be applied to surface inclined liquefiable sites under the premise of ensuring static waterproofing.This is consistent with the findings of Tao Lianjin [9,10].
The deficiencies in the thesis are listed below.The non-liquefied soil layer used in this paper adopts the Mohr-Coulomb constitutive model, and the elastic constitutive model for the structure, which does not take into account the nonlinear properties of the material.
Only three seismic waves were chosen, namely the Changchun artificial wave, the Kobe wave and the EL-Centro wave.
The research background of this paper is the new PSSS of Changchun Metro Line 2, which adopts the cut-and-cover method and is surrounded by a lot of supporting structures, and it is shown through the article of Tao Lianjin [34] that the steel support is an inseparable part of the structure as a whole.However, this paper focuses on the applicability of the structure itself under the slightly inclined liquefiable site at the surface, so the influence of this part of the supporting structure is ignored.
Future scholars can enrich this study by looking at the following points: The seismic response laws of the PSSS in liquefiable sites obtained in the paper are mainly analyzed by numerical simulations and need to be further verified by experiments.
There may also be cases where liquefiable soil layers are in different locations in an inclined site.In this paper, only the case where the structure is exactly in the liquefiable soil layer is investigated, and the seismic performance of the PSSS in other cases is still to be further investigated.

Conclusions
The main conclusions from the numerical analysis study of various working conditions are as follows: (1) The presence of underground structures has a dampening effect on the propagation of seismic waves in the original site soils.When the inclination angle of the ground surface is 2 • , the influences of PSSS and CIPSSS on the peak acceleration of the ground surface are 2.5 times and 1.5 times that the structural width of the subway station, respectively.With the increase in the surface inclination angle, the influence range of both structures on the peak acceleration of the surface is basically approximately 1.5 times that of the structure width, and the peak acceleration of the downslope side is significantly larger than that of the upslope side.(2) The PSSS with flexible connections exhibits less stress on a surface tilt liquefiable site.The maximum stress ratios (the ratio of the maximum stress at the bottom of the left-side wall to the maximum stress at the right-side wall) were 1.08, 1.24, and 1.48 for the left-and right-side walls of the PSSS when the inclination angle of the ground surface was 2 • , 4 • , and 6 • , respectively, and for the cast-in-place structure condition, they were 1.12, 1.25, and 1.50, respectively.The maximum amplitude of the principal stress response and the maximum stress ratio for the side walls of the CIPSSS were both significantly greater than those of the PSSS.
(3) When there is a slope in the ground surface, the soil around the subway station structure will occur due to the slip phenomenon.Whether it is an PSSS or a CIPSSS, the amplitude of the principal stress response of the sidewalls shows an increasing trend with the increase in the inclination angle of the ground surface, and the amplitude of the stress response of the sidewalls on the uphill side of the structure is significantly larger than that of the corresponding position of the sidewalls on the downhill side of the structure, due to the difference in the dynamic soil pressure on both sides of the structure.(4) The PSSS has better adaptability to ground deformation for sites with large inclination angles.When the inclination angle of the ground surface is 2 • , the transverse displacement of the PSSS is obviously larger than that of the CIPSSS, and at this time, the maximum interstory displacement angle of the structure is less than 1/550, which is in the elastic working state.When the inclination angle of the ground surface is increased to 4 • , the transverse displacement of the PSSS is slightly larger than that of the CIPSSS, and the difference between the two is very small.When the inclination angle of the ground surface is 6 • , the maximum inter-story displacement angle of the PSSS is smaller than that of the CIPSSS.Under 0.3 g ground shaking, the maximum interstory displacement angle of the CIPSSS reaches 1/41, which exceeds 1/50, and the structure is in a state of complete damage.(5) The PSSS has better overturning resistance than the CIPSSS on inclined liquefiable sites.Both structures were uplifted under ground shaking.As the surface inclination angle increases from 0 • to 6 • , the maximum uplift of the PSSS is 0.22 m, 0.27 m, 0.28 m, and 0.34 m, while that of the CIPSSS is 0.23 m, 0.29 m, 0.29 m, and 0.38 m.The PSSS first undergoes deflection in the clockwise direction when the surface inclination angle is 2 • , and the cast-in-place station structure undergoes deflection in the 4 • direction.During this process, the angle of deflection of the two structures was increasing, and the difference in uplift of the two structures was also increasing.(6) Under the premise of ensuring static waterproofing, the PSSS structure can be applied to the surface tilt liquefiable site.

Figure 2 .
Figure 2. The structural dynamic interaction model of a soil-subway station.

Figure 2 .
Figure 2. The structural dynamic interaction model of a soil-subway station.

Figure 2 .
Figure 2. The structural dynamic interaction model of a soil-subway station.

FigureFigure 4 .
Figure4ashows the sketch of the model, Figure4bshows the layout of the monitoring points in the soil layer and Figure4cshows the layout of the monitoring points in the structure, which are set up for four working conditions of 0 • , 2 • , 4 • and 6 • of the surface inclination angles, respectively.The letters P and A in Figure4bare the monitoring points

Figure 4 .
Figure 4. Modeling diagram and monitoring point layout.(a) Sketch of the model; (b) layout of the monitoring points in the soil layer; (c) layout of the monitoring points in the structure.

Figure 5 .
Figure 5. Schematic diagram of contact surface.Figure 5. Schematic diagram of contact surface.

Figure 5 .
Figure 5. Schematic diagram of contact surface.Figure 5. Schematic diagram of contact surface.Table 3. Contact surface unit parameters.

Figure 12 .
Figure 12.Maximum lateral relative displacement curve of the structure.

Figure 12 .
Figure 12.Maximum lateral relative displacement curve of the structure.

Figure 13 .
Figure 13.Vertical displacement of station structure base plate.

Table 1 .
Physical-mechanical parameters of soil layers at the site.

Table 1 .
Physical-mechanical parameters of soil layers at the site.

Table 4 .
Amplitude of principal stress response of structural side walls of PSSS (members C1 and C2).

Table 5 .
Amplitude of principal stress response of structural side walls of CIPSSS (members C1 and C2).

Table 6 .
Amplitude of principal stress response at node locations of PSSS and CIPSSS.

Table 8 .
Buildings 2024, 14, x FOR PEER REVIEW 15 of 19 uplifts are 0.34 m and 0.38 m respectively.Table8shows that the difference in the vertical displacements of the bottom plate on both sides of the PSSS is smaller than that of the CIPSSS.This indicates that the overturning resistance of the PSSS in inclined liquefaction is better than that of the CIPSSS.Difference in vertical displacements on both sides of the metro station structure (B1-B9).
B1 Figure 13.Vertical displacement of station structure base plate.

Table 8 .
Difference in vertical displacements on both sides of the metro station structure (B1-B9).