Shaking Table Testing of Liquefied Soil Layer Located in the Bottom Slab of a Subway Station

Abstract

In this study, a shaking table test was conducted to investigate the presence of a liquefied soil layer at a subway station bottom plate. The seismic responses to soil and station structure were investigated by inputting seismic waves of different intensities. The following test results were obtained. As the intensity of the seismic response increases, liquefaction occurs in the soils located at the base of the station. The remainder of the soil liquefies to a lesser degree but still results in soil subsidence and damage to the soils on both sides of the station. In seismic loading conditions, the pore water pressure undergoes a process of “rapid growth and slow dissipation”. As the seismic intensity increases, the main frequency of the soil near the structure develops from a high to a low frequency, and the main frequency of the soil far away from the structure does not change significantly, indicating that the presence of the structure has a significant effect on the working conditions of the soil. The peak acceleration, as well as the peak maximum dynamic strain in the center column of the station, occurs at the bottom of the center column at the platform level, and the maximum dynamic strain in the slab occurs at the bottom slab at the concourse level.

1. Introduction

One of the catastrophes brought on by earthquakes is the liquefaction of sand. The phenomenon of liquefaction in sandy soils has been documented in numerous seismic events. Gao Zhenhuan et al. [1] examined the seismic damage caused by the Tangshan earthquake in 1976. They discovered that both the Luanhe impact plain and the coastal plain displayed significant and severe liquefaction of sandy soils. Gao Zhenhuan [2] carried out a comparative investigation into the effects of the Tangshan earthquake on the Beijing area. The authors observed the occurrence of sand liquefaction phenomena simultaneously in the densely populated regions of the ancient river channels, particularly along the Chaobai River. Over 1000 locations experienced the discharge of water and sand, resulting in the subsidence and tilting of multiple granaries. Okamura M et al. [3] conducted an investigation into Nepal’s 2015 earthquake. They discovered that the liquefaction of sandy soil caused the Nepal Engineering College building to move. Longwei Chen et al. [4] examined the damage caused by the 2011 Christchurch earthquake in New Zealand. This earthquake is thought to have been the first in which liquefaction caused the majority of the damage. Wilkinson S et al. [5] conducted a field investigation of the seismic damage caused by the 2011 Christchurch earthquake in New Zealand. The earthquake caused significant damage to buildings, dams, and underground lifeline facilities, as supported by the available evidence. The 2010 Haiti earthquake, the 1995 Kobe earthquake, the 2011 Tohoku earthquake, and the 2008 Wenchuan earthquake all involved liquefaction and resulting structural damage to buildings. This means that the study of sand liquefaction must receive adequate attention.

Currently, researchers are conducting relevant studies and are making significant progress in investigating the seismic response of underground structures in the presence of liquefied soil. Wang Jianning et al. [6,7] conducted a significant study on the seismic response of a hetero-span subway station at a liquefied site using numerical modeling and shaking table experiments. In a study conducted by Chen Guoxing et al. [8,9,10,11], shaking table tests were performed to investigate the seismic damage characteristics and dynamic damage characteristics of a three-story, three-span standard station located at a liquefied site. Tang Bozan et al. [12,13] conducted pertinent investigations on subway stations with irregular sections in liquefied foundations via shaking table tests. Furthermore, Yao et al. [14] investigated the seismic response of rectangular tunnels in liquefied soils using shaking table tests. They found that liquefied soils have a seismic isolation effect and reduce the acceleration of the upper soil layer. Zhu Tong et al. [15] used an elastoplastic finite element dynamic analysis procedure to describe in detail the seismic response and seismic performance of shield tunnel joints under liquefied sites. Long Hui et al. [16] performed a numerical analysis of a two-layer, three-span island station on a liquefied foundation to derive the liquefaction distribution of soil around the structure and establish the deformation law of the structure. Shen et al. [17,18] investigated the seismic response of shield tunnels in liquefied interbedded soils using numerical simulations. They found that both the arch shoulders and the tunnel footings are potentially at risk of damage in liquefied soils. Yin Zhenyu, Wang Pen, et al. [19,20] investigated microscopic properties, such as the shape of soil particles and the contact characteristics of soil grains, via numerical simulation and triaxial testing. They also explained the influence of the microscopic action mechanisms of soil on its macroscopic performance.

At present, significant progress has been made in studying the seismic analysis of underground structures situated in liquefiable areas, with investigations encompassing their seismic behavior and methods of damage. Nevertheless, the findings primarily focus on underground water levels situated at the top slab of the station, with minimal consideration given to cases when the underground water level is located at the bottom slab of the station.

Clause 4.4.5 of the explanation of the provisions of the Code for Seismic Design of Urban Rail Transit Structures (GB 50909-2014) [21] states that when the depth of the underground station structure and the bottom of the tunnel exceeds 20 m, it is necessary to carry out special studies on the liquefaction of the deep soil layer.

Clause 4.2.2 of the Standard for Seismic Design of Underground Structures (GB/T 51336-2018) [22] states that when a saturated sandy soil exists in the stratum within a depth of 10 m from the base of the structure, the liquefaction properties of the soil layer should still be judged in detail.

This study investigates the seismic response law of subway station structures in deep liquefied soil layers by using the station bottom plate at a buried depth of 20 m while also taking into account the presence of saturated sandy soil below the station bottom plate as the research direction in designing the shaking table test.

2. Preparation for Shaking Table Test

2.1. Test Equipment and Scale Relationship

The shaking table test was performed on a shaking table located in the Key Laboratory of Urban Security and Disaster Engineering of Education at Beijing University of Technology, as shown in Figure 1. It merely vibrates horizontally in one direction. The plane possesses dimensions of 3 m by 3 m. It can support up to 10 tons of weight. The frequency range spans from 0.5 Hz to 50 Hz. The device can accelerate up to 1.0 g when fully loaded.

The model box used for this experiment is shown in Figure 2. The dimensions of the model box are 2.5 m in length, 1.2 m in width, and 1.2 m in height. The model box consists of a stack of 14 square steel layers. Viscoelastic boundary conditions were simulated using springs and dampers between each layer of square steel.

In accordance with the principles outlined in the Buckingham π theory, the fundamental physical quantities employed to establish the scale relationship of the model structure were length, modulus of elasticity, and acceleration. Similarly, for the scale relationship of the modeled soil, the fundamental physical quantities considered were density, shear wave velocity, and acceleration. The scale relationships related to each physical quantity satisfied are displayed in

Table 1. Experimental scale relationships relationship of the model.

Style	Physical Quantity	Scale Relationship	Model Structure	Model Soil
Geometrical features	Length l	$S_l$	1/40	1/4
	Inertial moment I	$S_I=S_l^4$	1/2,560,000	/
Material characteristics	Density ρ	$S_{\rho }$	1	1
	Elastic modulus E	$S_E$	1/4	/
	Shear wave velocity of soil v	$S_v$	/	1/2
Dynamical properties	Force F	$S_F=S_{\rho }{S}_l^3{S}_a$	1/64,000	/
	Acceleration a	$S_a$	1	1
	Time t	$S_t=\sqrt{S_l/S_a}$	0.158	1/2
	Dynamic Response Stress σ	$S_{\sigma }=S_l{S}_a{S}_{\rho }$	0.025	1/4
	Pore water pressure u	$S_u=S_l{S}_a{S}_{\rho }$	/	1/4

.

Achieving a complete simulation of real-world engineering using model tests is essentially impossible. During the testing phase, it is imperative to ensure that specific model characteristics closely approximate those of the actual engineering situation. To ensure that the model test findings accurately reflect real-world conditions, the notion that “qualitative analysis is primary and quantitative analysis is secondary” is applied.

2.2. Model Structure Production

The experimental setup involved the utilization of particulate concrete to replicate the concrete components of the structure, while galvanized steel wire was employed to replicate the steel reinforcement. The coarse aggregate in concrete is substituted with coarse sand measuring 2.5—5.0 mm in size. The fine aggregate in concrete is substituted by fine sand particles ranging from 0.15 to 1.0 mm in size. In the proposed model, the primary reinforcement has a diameter of φ1.4 mm, the hoop reinforcement has a diameter of φ0.8 mm, and the distribution reinforcement has a diameter of φ0.8 mm with a spacing of 20 mm. The mixture ratios of particulate concrete are displayed in

Table 2. Mixing ratios for particulate concrete.

Material	Clinker	Coal Ash	Yellow Sand	Travertine	Water
Micronized concrete	1	0.4	5.8	0.6	1.33

, and the material characteristics of galvanized steel wires are displayed in

Table 3. Parameters of galvanized steel wire.

Diameter (mm)	Area (mm2)	Yield Strength (MPa)	Ultimate Strength (MPa)
1.4	1.539	349	420
0.8	0.502	328	396

, both of which are based on considerable experimental experience [23,24].

The actual station structure has been slightly simplified to take into account the test’s actual circumstances, and a station model based on a geometric scale relationship has been created. The station model is constructed as a single unit without any joints connecting the primary partition to the subsidiary parts. The success or failure of the liquefaction test is directly contingent upon the waterproofing of the model structure. During the testing process, artificially created end-of-structure waterproofing measures were not completely effective. Therefore, the general rule for waterproofing the structure in the liquefaction test is that some seepage is allowed but never bubbling. The overall arrangement of the test model is shown in Figure 3.

The openings situated at both ends of the station model were effectively sealed by employing foam boards 10 mm in thickness. This can be attributed to the multiple benefits associated with foam boards: (1) Foam boards possess a lightweight composition and exhibit reduced rigidity, minimizing their impact on structural deformation. (2) Foam boards offer ease of cutting and demonstrate a high degree of adaptation to various shapes. (3) Foam boards exhibit resistance to deformation when exposed to water. To simulate the interaction of the soil and structure as closely as possible in the actual environment, the structure was not waterproofed throughout this test.

2.3. Filling of Foundation Soils and Arrangement of Points

The sandy soil employed in the shaking table test was sourced from a construction site. The following method was used to prepare model soil (shown in Figure 4):

(1)

Bags are used to dry and sieve the sandy soil, making the test site tidier and cleaner;

(2)

A flexible measuring scale is securely attached to the interior surface of the model box in order to accurately measure and load sand in a quantitative manner;

(3)

Based on the experimental protocol, the acceleration sensors employed in the soil model, as well as the pore water pressure sensors, were suspended at their designated positions using a fishing line. To ensure that the sensors remained in place during the soil loading procedure, one end of the fishing line was secured to the top shelf of the model box, while the other end was secured to the bottom of the model box;

(4)

After adding a specified amount of water into the model box, the sand is spread evenly with a bucket and then leveled with a shovel. It is noteworthy that the water injection and sand flattening procedures are conducted in a coordinated manner to ensure that the water level surface is maintained at a higher elevation than the sand surface, thus ensuring the saturation of the sand. During the loading procedure, samples are collected at suitable sites using the ring knife method, and geotechnical tests are conducted to determine the parameters of saturated sand;

(5)

Once the sand becomes saturated and reaches a pre-established elevation, the injection of water should stop. Subsequently, the structure should be raised into its designated location, and the model box should be further filled with unsaturated sand in incremental layers until the specified height is achieved. Unsaturated sand is compacted into layers with a tamper throughout the filling process to confirm the degree of compactness and soil samples are taken at suitable locations using the ring knife method to determine the parameters of the unsaturated sand through geotechnical tests;

(6)

Once the sand has been loaded, the surface of the simulated soil is leveled and protected with a layer of plastic sheeting in order to minimize the loss of moisture. This facilitates the natural consolidation of the simulated soil due to gravitational forces over a period of 24 h.

Figure 4. Foundation soil manufacturing process.

Figure 4. Foundation soil manufacturing process.

2.4. Loading Cases

The Ming Shan wave and the Beijing Hotel wave of the Tangshan earthquake are used as the test input seismic waves in this study. Among them, the Tangshan earthquake Beijing Hotel wave was recorded in the 1976 Tangshan earthquake, with an epicenter distance of 157 km, an original peak acceleration of 0.39 g, and a duration of 50 s. The Ming Shan wave was recorded in the 2008 Wenchuan earthquake, with an epicenter distance of 103 km, an original peak acceleration of 0.16 g, and a duration of 100 s. The acceleration time history and Fourier spectrum of the seismic wave are shown in Figure 5.

The seismic wave’s peak acceleration was modified to 0.1 g. Step-by-step loading was used for the test, with the load increased by 0.1 g each time until it reached 0.6 g. The model was scanned using 0.1 g of white noise during each stage of loading. When a seismic wave was loaded, it was necessary to wait for the sensor readings to smooth out before inputting the next seismic wave. Throughout the loading procedure, the pertinent staff members are provided with interphones to facilitate effective communication, hence ensuring the efficient advancement of the test. Case loading options are shown in

Table 4. Seismic wave loading cases.

Number	Input Seismic Waves	Cases	Peak Acceleration/g	Duration/s
1	White noise	B-1	0.1	/
2	Ming Shan wave	MS-1	0.1	50
3	Beijing Hotel Wave	FD-1	0.1	25
4	White noise	B-2	0.1	/
5	Ming Shan wave	MS-2	0.2	50
6	Beijing Hotel Wave	FD-2	0.2	25
7	White noise	B-3	0.1	/
8	Ming Shan wave	MS-3	0.3	50
9	Beijing Hotel Wave	FD-3	0.3	25
10	White noise	B-4	0.1	/
11	Ming Shan wave	MS-4	0.4	50
12	Beijing Hotel Wave	FD-4	0.4	25
13	White noise	B-5	0.1	/
14	Ming Shan wave	MS-5	0.5	50
15	Beijing Hotel Wave	FD-5	0.5	25
16	White noise	B-6	0.1	/
17	Ming Shan wave	MS-6	0.6	50
18	Beijing Hotel Wave	FD-6	0.6	25
19	White noise	B-7	0.1	/

.

The input process of seismic waves is as follows: First, the seismic waves are saved in text format, with “.txt” as the unit of “g”. Then, the control system of the shaker, as well as the power system, are turned on. After the power system is stabilized, the seismic wave is input into the control system, which can edit the peak value and duration of the seismic wave to meet the needs of different working conditions. Finally, the seismic wave is output from the control system to the power system, thus completing the seismic wave loading process.

3. Analysis of Test Results of Foundation Soil

3.1. Macro-Phenomena of the Model

A comparison of the model soil’s macroscopic phenomena before and after the test is shown in Figure 6.

Following the application of a sequence of seismic waves, fractures oriented in a north–south manifested on the surface. These fractures were observed to be in close proximity to the area where the soil and the structure were in contact, as shown in Figure 6b. In this particular experiment, it was seen that the saturated sand layer did not extend directly to the surface. Instead, it terminated at the base of the structure, leaving the remaining portion filled with unsaturated sand. These pore pressure monitoring data make it obvious that when the seismic intensity rises, the soils below the base plate of the structure continue to liquefy. Despite the absence of sandblasting and water bubbling on the model’s surface, soil liquefaction remains a significant factor contributing to soil subsidence, resulting in damage to the soil around the structure. This is shown in Figure 6c, where the depth of damage is about 25 mm, and in Figure 6d, where the width of the crack is about 10 mm, which is also shown in Figure 6f. The extent of damage is about 140 mm, as shown in Figure 6g.

3.2. Model Box Boundary Effect Test

The input seismic waves propagate through the model and are reflected at the boundaries of the model box, thus affecting the test results. The shear model box is used in this test in order to reduce the reflection of seismic waves at the boundary, thus ensuring the correctness of the test results. Therefore, free-field vibration tests were used to test the boundary conditions of the model box. The boundary effects of the model box are evaluated by analyzing acceleration test data at different locations at the same depth. The accelerometer arrangement in the free-field test is shown in Figure 7.

To perform testing, we input 0.1 g of white noise, input 0.1 g and 0.5 g of the Ming Shan wave, and input 0.1 g and 0.5 g of the Beijing Hotel wave. The acceleration amplification factors of points A2, A4, and A11 at 60 mm below the surface of the model soil are shown in Figure 8a. The acceleration amplification factors for points A3, A5, and A12 at 337 mm below the modeled soil surface are shown in Figure 8b.

Points A2 and A3 are 0.24 m from the model box boundary; points A4 and A5 are 0.49 m from the model box boundary; and points A11 and A12 are 1.17 m from the model box boundary. When the peak acceleration of the input seismic wave is 0.1 g or 0.5 g, the acceleration amplification factors of A2, A4, and A11 do not differ considerably, as is the case with the acceleration amplification factors of A3, A5, and A12. This indicates that the boundaries of the shear model box have less influence on the acceleration response of the modeled soil, which in turn indicates that the model box boundaries have less influence on the test results.

Since the acceleration amplification factor is related to the peak acceleration at each measurement point, evaluating the boundary effect of the model box using only the acceleration amplification factor is not sufficiently comprehensive. Here, the boundary effect index is used to evaluate the boundary effect of the model box from the whole process of vibration [25]. The boundary effect indices of the model box under seismic wave action are shown in

Table 5. Boundary effect indices of the laminar shear container under seismic waves.

Points	Distance to Model Box Boundary/m	Boundary Effect Indices (%)
		B-1	MS-1	MS-5	FD-1	FD-5
A2	0.24	1.22	1.74	2.92	1.03	1.02
A4	0.49	1.23	1.39	3.70	1.11	1.43
A3	0.24	4.65	4.60	6.37	3.72	4.44
A5	0.49	1.76	2.02	5.34	1.77	2.62

. It can be seen that the boundary effect indices of the model box under seismic waves are small, indicating that the shear model box used in this test can effectively reduce the influence of boundary effects on the test results.

3.3. Acceleration Response of Sandy Soil

The acceleration sensor is denoted by the symbol “A1~A11” in soil. The shape of the arrangement of the acceleration sensors in soil is shown in Figure 9.

The variation in acceleration with soil depth was subjected to different levels of seismic intensity, as shown in Figure 10.

When the peak acceleration of the input seismic wave is 0.1 g, the peak acceleration of the soil exhibits an even variation throughout the depth. The peak acceleration of the soil under the action of the Ming Shan wave is distributed in an “S” form from the bottom to the top of the model as the seismic intensity increases. This form of distribution is consistent with that displayed in the literature [23].

3.4. Analysis of Spectral Properties of Soil

The spectral pattern of the soil under the action of the Beijing Hotel wave is analyzed, and the primary frequency of points A4, A5, A6, A7, and A8 are shown in

Table 6. Primary frequency of each measurement point under different working conditions.

Points	Main Frequency (Hz)
	FD-2	FD-3	FD-4	FD-5
A4	6.968	7.216	7.220	5.126
A5	6.968	7.216	7.220	1.467
A6	6.968	7.216	1.468	1.477
A7	1.464	1.476	1.468	1.477
A8	1.464	1.476	1.468	1.477

.

The points A4 and A5 are located in the soil near the top and bottom slabs of the accessory structure, respectively. When the peak acceleration of the input seismic wave is below 0.5 g, there is minimal alteration in the primary frequencies of A4 and A5, suggesting that the soil at that location remains in the elastic phase. When the input seismic wave reaches a peak acceleration of 0.5 g, the main frequencies of A4 and A5 abruptly fall to 5.126 Hz and 1.467 Hz, respectively. At this point, the stiffness of the modeled soil decreases, and its nonlinearity increases, indicating that the soil enters the plastic phase at this location.

Point A6 is situated within the soil on the right-hand side of the base plate of the main structure. Additionally, this point is positioned at the division between the saturated and unsaturated sand. When the peak acceleration of the input seismic wave is below 0.4 g, there is minimal alteration in the primary frequency of A6, suggesting that the soil at the current location remains within the elastic phase. When the input peak acceleration is greater than or equal to 0.4 g, the primary frequency of point A6 suddenly decreases, indicating that the stiffness of the soil is weakened, and the soil at this location enters the plastic working stage.

Points A7 and A8 are located in saturated sand 700 mm and 900 mm below the model surface. Their principal frequencies do not change with the peak acceleration of the input seismic wave.

Generally, as the seismic intensity gradually increases, the primary frequency of points in close proximity to the structure and situated within the unsaturated soil demonstrates a transition from high frequency to low frequency. This may be due to the influence of the structure on the primary frequency of the soil. The points in the saturated sandy soil did not show a significant change in their primary frequency, which may be due to the effect of the saturated sandy soil on them.

3.5. Analysis of Pore Water Pressure

The pore water pressure sensor in the soil is denoted by the symbol “P1~P8”. The pore water pressure sensor in the soil is shown in Figure 11.

The pore pressure ratio time history curve is shown in Figure 12. Due to the failure of point P2, there is no pore pressure ratio time history curve for this point. The pore pressure ratio at each position exhibits a positive correlation with the rise in seismic intensity. Each point in the study observed a quick increase in pore pressure with the arrival of the peak of the seismic wave, followed by dissipation once the peak of the seismic wave has passed.

Point P1 is located at the interface between the saturated and unsaturated sand. During an earthquake, the pore water pressure accumulates within the saturated sandy soil and gradually dissipates into the unsaturated sandy soil. This dissipation occurs together with the self-weight of the unsaturated sandy soil. Consequently, the pore pressure ratio at point P1 is significantly reduced.

Point P3 is located at the interface between saturated and unsaturated sand, and point P4 is located in the saturated sand 200 mm below point P3. During seismic loading, the increase in pore water pressure at point P3 dissipates into the unsaturated sand. However, at point P4, there is no way for dissipation, resulting in a higher pore pressure ratio compared with point P3.

Points P5 and P7 are located at the interface between the saturated sand and the bottom plate of the station and points P6 and P8 are located in the saturated sand 200 mm below the bottom plate of the station. Regardless of the intensity of the seismic wave, the pore pressure ratio at points P5 and P7 consistently exceeds that at points P6 and P8. The observed phenomena can be attributed to two primary factors. The first of these is the absence of suitable conditions for the dissipation of pore water pressure at the bottom plate of the station. Second, the gravitational force exerted by the subway station is comparatively lower than that exerted by an equivalent volume of sandy soil. Consequently, the subway station fails to generate sufficient counterforce to balance the increasing pore water pressure. When the peak acceleration of the seismic wave input reaches 0.5 g, the pore pressure ratio between points P5 and P7 is 0.5. However, when the peak acceleration of the seismic wave input increases to 0.6 g, the pore pressure ratio at point P5 approaches 1, while the pore pressure ratio at point P7 exceeds 1. This observation suggests that the soil at the bottom plate of the station undergoes complete liquefaction.

Points P1, P3, P5, and P7 are located at the same height as the bottom plate of the station and are all located at the interface between unsaturated and saturated sand. The distribution of the peak pore pressure ratio at the interface is shown in Figure 13. When the peak acceleration of the input seismic wave is below 0.5 g, there is minimal variation in the peak pore pressure ratio at any one location. The pore pressure ratio abruptly increases at points P5 and P7 when the seismic wave’s peak acceleration reaches 0.5 g, which indicates that the soil below the station’s bottom plate has clearly manifested liquefaction. When the peak acceleration of the seismic wave exceeds 0.5 g, the pore pressure ratio at point P5 approximates 1, and the pore pressure ratio at point P7 surpasses 1, suggesting that the soil at the bottom of the plate of the station has undergone total liquefaction. Nevertheless, as the peak acceleration of the seismic wave rises, there is a slight increase in the peak pore pressure ratios at both point P1 and point P3. The existence of unsaturated sand layers above points P1 and P3 facilitates the dissipation of pore water pressure, hence preventing the development of soil liquefaction.

4. Analysis of Station Structure Test Results

4.1. Middle Column Acceleration Analysis

The acceleration sensor is denoted by the symbol “A12~A25” in the structure. The acceleration sensor arrangement in the station structure is shown in Figure 14.

The peak acceleration at the top and bottom of the middle column of the station structure under the action of the Ming Shan wave is shown in Figure 15. The peak acceleration at the top and bottom of the middle column of the station structure under the Beijing Hotel wave is shown in Figure 16.

The acceleration response of the center column at points A23 and A24, regardless of its position at the top or bottom of the column, exhibits the highest magnitude. In contrast, the acceleration response of the center column at the station hall level and equipment level is comparatively lower. The alteration in the horizontal stiffness of the main structure is a consequence of the installation of ancillary structures at both the station hall level and the equipment level.

In the action of the Beijing Hotel wave, the disparity in peak acceleration between point A14 and point A19 is minimal, which is the same as the situation for point A15 and point A20. When the input seismic wave’s peak acceleration is between 0.1 and 0.2 g under the action of the Ming Shan wave, the difference in peak acceleration between points A14 and A19, as well as between points A15 and A20, is minimal. When the peak acceleration of the input seismic wave ranges from 0.3 g to 0.6 g, it is observed that the peak acceleration at point A14 is much greater than the peak acceleration at point A19. Similarly, the peak acceleration at point A15 is significantly larger than the peak acceleration at point A20.

When the peak acceleration of the input seismic wave is 0.1 g or 0.2 g, there is minimal variation in the peak acceleration at positions A23 and A24, regardless of whether it is the Ming Shan wave or the Beijing Hotel wave in play. When the peak acceleration of the input seismic wave is between 0.3 and 0.6 g, the peak acceleration at positions A23 and A24 under the action of the Beijing Hotel wave is much higher than that under the action of the Ming Shan wave. The spectrum characteristics of seismic waves may be relevant in this situation. The wave observed in the Beijing Hotel is predominantly characterized by low-frequency components, and the structural response of the station is more susceptible to these low-frequency elements. When working with this type of subway station structure, researchers should, therefore, concentrate their seismic analysis on the seismic response of the middle columns at the platform level.

4.2. Dynamic Strain Analysis of Structures

The strain gauges are denoted by the symbol “S1-A16” in the structure. The strain gauge arrangement in the station structure is shown in Figure 17.

The dynamic strain amplitude of the middle column and the slab of the station structure under the action of the Ming Shan wave and Beijing Hotel wave are shown in Figure 18 and Figure 19.

Overall, the variation trend in the peak tensile strain and peak compressive strain of the middle column is symmetrically distributed. The higher horizontal stiffness of the station hall level and equipment level compared to the platform level is a result of the existence of accessory structures on both sides of the former. Hence, the highest magnitudes of tensile and compressive strains within the middle column are observed at the platform level. The middle column’s bottom has the highest tensile and compressive strain values.

The dynamic strain trends of the middle column and plate are similar for both the Beijing Hotel wave and Ming Shan wave actions. However, the dynamic strain response amplitude is greater under the action of the Beijing Hotel wave compared to the action of the Ming Shan wave. This suggests that the station structure’s dynamic strain response is more susceptible to the low-frequency Beijing Hotel wave.

The phenomenon of soil liquefaction results in a reduction in the energy of seismic waves, causing a decrease in the tensile strain at point S12. This effect is observed when the peak acceleration of the seismic wave is specified as 0.6 g for the Ming Shan wave and 0.5 g for the Beijing Hotel wave. The base plate of the main structure experiences the influence of pore water pressure, resulting in an elevation of the axial force exerted on the middle column of the structure. This increase is evident through the amplification of compressive strain at points S7 and S12.

The magnitude of the dynamic strain experienced by the plate exhibits a positive correlation with the level of seismic intensity. For instance, the most significant alteration in strain is observed at point S14. During the action of the Beijing Hotel wave, it is observed that when the peak acceleration of the input seismic wave ranges from 0.1 g to 0.5 g, the compressive strain experienced by point S14 surpasses its tensile strain. Conversely, when the peak acceleration of the input seismic wave reaches 0.6 g, the compressive strain of point S14 is found to be smaller than its tensile strain. In conjunction with the findings from the pore pressure ratio analysis, it is evident that the soil located on the base plate of the main structure of the station undergoes total liquefaction when subjected to a peak acceleration of 0.6 g from the Beijing Hotel seismic wave. The base plate of the main structure experiences the influence of pore water pressure, whereas the accessory structure situated in the non-liquefied soil can be seen as an embedded end. Consequently, this leads to an increase in tensile strain exerted on the main structural plate.

5. Conclusions

In this study, the seismic response of subway station structures with liquefied soil layers in the bottom plate was investigated via shaker tests. The results of the tests on foundation soils and station structures were analyzed, and the following conclusions were obtained:

(1)

As the seismic intensity increases, the saturated sandy soils at the base of the structure liquefy to a higher degree, while the saturated sandy soils at other locations liquefy to a lower degree. This is due to the fact that the structure itself is less loaded and impermeable, meaning the saturated sandy soil below the structure is easy to liquefy. Conversely, the unsaturated sandy soil itself is more loaded and permeable, and so the saturated sandy soil at other locations is not easy to liquefy.

(2)

There is no water spraying or sand bubbling on the surface of the modeled soil, but there is still soil subsidence, and the modeled soil on both sides of the structure within a certain range is significantly damaged.

(3)

When the intensity of the seismic wave is small, the main frequency of each point does not obviously change. With an increase in the seismic intensity, the main frequencies of the points closer to the structure are altered from high frequency to low frequency, while the main frequency of the points farther away from the structure still does not obviously change. This indicates that the working condition of the soil is more obviously influenced by the structure than seismic wave size.

(4)

The acceleration response of the columns at the platform level is maximized. The acceleration response at the bottom of the column is greater than that at the top of the column for the same seismic wave. In the case of the same seismic intensity level, when the seismic intensity is small (0.1 g, 0.2 g), the acceleration response at the top of the column for the Ming Shan wave is larger than that of the Beijing Hotel wave. Conversely, when the seismic intensity is large (0.3 g to 0.6 g), the acceleration response at the top of the column for the Ming Shan wave is smaller than that of the Beijing Hotel wave. However, the acceleration response at the bottom of the column for the Beijing Hotel wave is always larger than that of the Ming Shan wave.

(5)

The maximum dynamic strain peak of the center column of the station occurs at the bottom of the center column of the platform level, the trend of tensile strain and compressive strain is symmetrically distributed, and the maximum dynamic strain of the slab occurs at the bottom slab of the station hall level.