Seismic response characteristics of multi-story subway station through shaking table test

Abstract

A series of shaking table tests were carried out to investigate the seismic response characteristics of a multi-story subway station. Dynamic responses, including accelerations of the soils and the underground structure, layer drift, dynamic earth pressure, and lateral deformation of soils were recorded and analyzed. Several seismic characteristics of multi-story subway station structures are figured out. It is found that in addition to the racking deformation, the rotation vibration is observed for the multi-story subway station subjected to acceleration waves. From the viewpoint of frequency, the low-frequency component and high-frequency component of the acceleration response of the subway station represent the translation and rotation component of the multi-story subway structure, respectively. In addition, the rotation vibration of the deep-depth structure leads to the local squeezing and detachment from the surrounding soils alternately at both top and bottom ends of the sidewalls. This results in the hump-shaped distribution of dynamic earth pressure. The racking deformation of the multi-story subway station has a linear relationship with the dynamic earth pressure at a certain area along the sidewall, where the top of hump-shaped distribution of dynamic earth pressure is.

Keywords

dynamic earth pressure multi-story subway station shaking-table test seismic responses

Introduction

With the rapid development of the economy and technology in China, there has been a trend to develop deep and large-scale subway stations to solve the conflict between limited land resources and increasing demand for transportation capacity. It is generally believed that underground structures are safer than ground structures during earthquakes. However, researches show that severe damage and collapse of underground structures have occurred during earthquakes (Huo et al., 2005; Wang et al., 2001). The deep and large-scale underground structures, due to the increasing water and earth pressure along structural depth, is more vulnerable to earthquakes. A subway station with a four-story island platform structure and a height of 28.3 m in Shanghai is taken as a prototype structure in the present study. The station was designed originally to be a six-story subway station, and then the first to third story were merged into one story to function as a stereo garage. Increasing with the layer number and the earth and water pressure, the axial compression ratio of the central column increases as well. As a result, its bearing capacity degrades sharply under high axial compression and lateral seismic loading (Chen et al., 2016). Additionally, an increase in structural depth reduces the overall lateral structural stiffness, which results in greater lateral deformation during earthquakes. It is also unfavorable to the earthquake resistance of multi-story subway structure.

It is commonly believed that the underground structure has completely different seismic response characteristics, although it is mainly designed according to seismic design methods for ground structures. Being different from ground structures whose seismic responses are mainly controlled by its vibration characteristics, the underground structure is restricted by the surrounding soils, which makes its seismic responses to be controlled by the deformation of surrounding soils (Hashash et al., 2001; Wu and Penzien, 1994). Therefore, it is of great importance to study the seismic response characteristic of underground structure considering the interaction between soils and underground structures. That is, different from the analysis of the seismic response of ground structure where only the structure is considered, the seismic responses of underground structure should be investigated considering the underground structure and soils as a whole. Shaking table test based on similarity theory and using similar material has been widely used to study the seismic responses and failure mechanism of underground structure and soils. It is noteworthy that the shaking table tests may not able to reflect the actual seismic response of structures precisely, especially entering the nonlinear state. But it is still a common and effective way to study the seismic performance of underground structures. (Chen et al., 2015, 2019; Kheradi et al., 2018; Tao et al., 2019; Zhao et al., 2019; Zhuang et al., 2016). The seismic response characteristic of several underground structures has been well investigated in these researches using shaking table tests. However, these researches mainly focus on typical subway stations and small-scale underground structures such as two-story and two-span subway stations, two-story and three-span subway stations, underground reservoir structures, and tunnels, etc. The study on seismic response characteristics of multi-story subway station remains few and not systematic.

On the other hand, current researches focus not only on seismic responses of underground structures and soils, but also on interaction between them. However, soil-structure interaction, taking the dynamic earth pressure as an example, is a very complicated problem. Previous experimental results obtained from shaking-table tests and centrifuge tests show that the form and magnitude of the distribution of dynamic earth pressure may be affected by the configuration of underground structures. Generally, it can be grouped into a convex distribution (Hushmand et al., 2016; Keykhosropour and Lemnitzer, 2019) or a hump distribution (Chen et al., 2019). Shaking-table tests conducted on a two-story, two-span subway station by Chen et al. (2019), for instance, showed a hump-shaped (or so-called trumpet-shaped) distribution of the dynamic earth pressure on the sidewall while the dynamic earth pressure distribution of a shaft obtained by Keykhosropour and Lemnitzer (2019) had a convex peak (or so-called belly shape). Distributions of dynamic earth pressure other than these forms have also been observed. For example, an irregular dynamic earth pressure was observed in shaking-table tests conducted by Zhuang et al. (2016), where the dynamic earth pressure acting on the sidewall of a two-story and three-span subway station was high at the bottom and was low at the top. The contact area between the multi-story subway structure and surrounding soils is large owing to the great depth. The interaction between the underground structure and the surrounding soils, therefore, must be different from that for typical subway structures, resulting in different seismic response characteristics. Thus, it is necessary to figure out the seismic characteristics of a multi-story subway structure.

In view of this, shaking table tests were conducted to investigate the characteristics of seismic responses of multi-story subway station. For the first time these tests reveal that the multi-story subway station rotationally vibrates during the shaking process by shaking table tests, as far as the authors know. The present study reveals the relationship between the dynamic earth pressure, the rotation vibration, and the lateral deformation of the multi-story subway station, which provided a reference for the seismic induced soil-underground structure interaction and characteristics of seismic responses of multi-story subway station.

Experimental design

Shaking table and model soil container

A series of shaking table tests were conducted at the State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, to study the seismic behavior of a multi-story subway structure. The size of the shaking table used in the test was a 4 m × 4 m square. This shaking-table test system can produce three-dimensional motion of a frequency ranging from 0.1 to 50 Hz and maximum accelerations of 1.2 and 0.8g in the two horizontal directions and 0.7g in the vertical direction.

The cylindrical shear container used in the test had a 5-mm-thick rubber membrane, a diameter of 3000 mm, and a height of 1800 mm, as shown in Figure 1. A more detailed description of the model soil container was provided and the rationality of the model soil box was also verified by Zhao et al. (2019).

Figure 1.

Soil container (unit: mm).

Material of the model and scale factor design

A four-story and three-span model of an underground structure was made from organic glass for the shaking-table tests, as shown in Figure 2. The scale factors of the model are listed in Table 1. Geometric, physical, and mechanical similarities first needed to be set first according to similarity theory. This model was based on a modern reinforced concrete subway station whose cross-section had a height of 28.30 m and width varying from 23.60 to 28.35 m. C45 concrete and HRB400 rebar were used for the central column and C35 concrete and HRB335 rebar for the remaining parts of the subway station. The height of the underground structure was greater than that of a typical subway station, and the geometric scale factor was set at 1:50 considering the size of the soil container and boundary effects. The elastic modulus of the organic glass was determined to be 3.33 GPa from the results of material tests, and the scale factor of the elastic modulus was thus 0.106. The acceleration scale factor was set at 3.00 to match the performance of the shaking table and to maintain the acceleration and frequency similarity ratios within reasonable ranges. According to the Buckingham π law, we have (Chen and Wei, 2013)

Figure 2.

(a) Model structure and (b) cross-section of the model structure (unit: mm).

Table 1.

Scale factors of the model structure.

Item	Scale factor	Item	Scale factor
Elastic modulus	$S_{E} = 0.106$	Mass	$S_{m} = S_{ρ} S_{l}^{3} = 1.410 \times 10^{- 5}$
Geometry	$S_{l} = 0.020$	Duration	$S_{t} = S_{l} S_{E}^{- \frac{1}{2}} S_{ρ}^{\frac{1}{2}} = 8.160 \times 10^{- 2}$
Equivalent density	$S_{ρ} = 1.765$	Frequency	$S_{ω} = S_{E}^{\frac{1}{2}} S_{l}^{- 1} S_{ρ}^{- \frac{1}{2}} = 12.253$
Strain	$S_{ε} = 1.000$	Velocity	$S_{v} = S_{E}^{\frac{1}{2}} S_{ρ}^{- \frac{1}{2}} = 0.245$
Stress	$S_{σ} = S_{E} = 0.106$	Acceleration	$S_{a} = S_{E} S_{l}^{- 1} S_{ρ}^{- 1} = 3.003$

S_{E} / (S_{l} \cdot S_{ρ}) = S_{a},

(1)

where $S_{l}$ , $S_{E}$ , $S_{ρ}$ , and $S_{a}$ denote the scale factor of the geometry, elastic modulus, density, and inertial acceleration, respectively. To satisfy equation (1), artificial blocks with a mass of 236 kg were placed on each floor slab uniformly.

The scale factors of the model soil are given in Table 2. $S_{l}$ and $S_{a}$ were respectively set at 0.02 and 3.00, corresponding to the values for the underground structure. $S_{E}$ and $S_{ρ}$ of the model soil were required to satisfy equation (1) and match the bearing capacity of the shaking table simultaneously. Previous tests (Liu et al., 2020) showed that a mixture of sand and sawdust can be used as model soils. When the mass ratio of sawdust to sand was set at 1:2.5, the density and shear modulus of the mixture were respectively 700 kg/m³ and 1.81 MPa, meeting target values generally (i.e. the target modulus was 1.72 MPa, error: 5.2%). A $G_{d} / G_{d max} - γ_{d}$ curve and $λ - γ_{d}$ curve were obtained in a dynamic tri-axial test as presented in Figure 3, in which G_d and G_dmax represent the shear module and its maximum value; γ_d represents the shear strain of the soil; and λ is the damping ratio.

Table 2.

Scale factors of the model soil.

Item	Scale factor	Item	Scale factor
Geometry	$S_{l} = 0.020$	Shear modulus	$S_{G} = 0.020$
Density	$S_{ρ} = 0.333$	Acceleration	$S_{a} = 3.003$

Figure 3.

Dynamic properties of the model soil.

Layout of sensors

The observation plane was located in the middle of the model underground structure. A total of 20 strain gauges, 18 accelerometers, 10 displacement meters, 8 laser displacement meters, and 10 earth pressure gauges were used in the test. The layout of these sensors is shown in Figures 4 and 5. In figures, S, A, D, LD, and SP denote strain gauge, accelerometer, displacement meter, laser displacement meter, and earth pressure meter respectively. In Figure 4, VL1 and VL2 denote vertical reference lines where some of the accelerometers were placed.

Figure 4.

Layout of accelerometers and displacement meters (unit: mm).

Figure 5.

Layout of sensors in a model cross-section (unit: mm).

Strain gauges were used to calculate the dynamic internal forces of the central column and sidewall of the underground structure. Accelerometers in soils and the underground structure were used to record the propagation of seismic waves along the soil depth and height of the underground structure. Records from accelerometers A7 and A10 were compared with those from A9 and A12 to investigate the effect of the underground structure on the acceleration responses of the soils. Accelerometers A1–A4 were used to measure the horizontal acceleration of the soil surface and analyze the effects of the underground structure and the boundary of the soil container on the acceleration responses of the soils. Accelerometers A15–A18 were used to measure the acceleration responses of the underground structure. Displacement meters D1–D5 were used to measure the settlement of the soil surface, while D6–D10 were used to measure lateral displacement of the soil container. Laser displacement meters LD1–LD8 were fixed on the top of floors and matching organic glass tubes were bound on the bottom of floors. The displacement recorded by each laser displacement meter was the drift between both ends of a central column or a sidewall. Earth pressure gauges were used to obtain the maximum dynamic earth pressure envelopes.

Test scheme and verification of boundary effects

Input ground motions

The prototype model structure selected in this paper was a four-story subway station in Shanghai, where covers deep soft soils. This kind of stratum has the characteristics of long predominant period. According to the code (DGJ08-9-2013, 2013), most building sites in Shanghai belong to Class IV, which refers to muddy soils, loose fine and silty sands, or newly deposited cohesive soils. The predominant period of Class IV site is about 0.9 s.

Then, the ground motions to be input in this test should meet the above characteristics in soft soils. Figure 6 shows the acceleration time history and Fourier spectrum of the Shanghai artificial wave (AWX0.9-1) provided by the code (DGJ08-9-2013, 2013). The artificial wave is generated on the basis of recorded real earthquake wave (El-Centro wave), considering the geological characteristics of Shanghai. Figure 6(b) shows that the Shanghai artificial wave has rich low-frequency components (less than 1 Hz), matching the characteristics of ground motion in soft soil areas.

Figure 6.

(a) Acceleration time history and (b) Fourier spectrum of Shanghai artificial wave.

In addition, the seismic fortification intensity for Shanghai is taken as 7. That is, the peak values of 0.10 and 0.20g are specified as the designed acceleration to be input for the basic earthquake intensity level and the rare earthquake intensity level, respectively. Then the peak values of input ground motion are further scaled to 0.6g, and 1.0g to investigate seismic behavior of underground structures and soils subjected to extreme seismic excitation. In brief, a total of four cases, (i.e. the input ground motion was scaled to 0.1, 0.2, 0.6, and 1.0g, denoted as case 1, case 2, case 3, and case 4, respectively) are involved in the shaking table tests. The model soil will be compacted and its density may increase during shaking process if the model soil is not compacted during the filling process. White-noise cases were investigated after each Shanghai artificial wave case to make sure the density of the model soil is consistent during the shaking table test by checking the fundamental frequency of the soil.

Test verification of boundary effects

Figure 7 shows the acceleration time histories recorded at A8 and A9 in case 1. As can be seen from this figure the time histories and peak values of A8 and A9 are very close, which indicates that the boundary effects can be ignored. Besides, the maximum relative and absolute lateral displacements of the soil container are shown in Figure 8. Both the maximum absolute displacement and the maximum relative displacement of the soil container increase with peak acceleration and show shear-type deformation, which is consistent with the deformation of semi-infinite half space media under ground motions. Figure 8(b) shows that the relative lateral displacements of the left and right sides of the soils are not completely symmetrical. There may be two reasons for this asymmetry. First, the input ground motion is not completely symmetrical (Tao et al., 2019). Second, the displacements are obtained from discretely distributed displacement meters, and the actual displacements of the soils may deviate from the fitted polyline.

Figure 7.

Acceleration time histories recorded at A8 and A9 in case 1.

Figure 8.

Relative and absolute lateral displacements of soils in cases 1–4: (a) Absolute lateral displacement and (b) relative lateral displacement.

Seismic responses of soils

Amplification factors

Figure 9 shows acceleration amplification factors in cases 1–4, which is defined as the ratio of recorded peak acceleration along the soil surface to the peak acceleration of the input ground motion. In all cases, amplification factors are larger than 1.0, indicating that soils in Shanghai have significant amplification effects for input ground motions. With the increase in seismic intensity (from case 1 to case 4) less amplification effect is observed. This is mainly due to the fact that under ground motions with high intensity, the soils may have entered the plastic state, resulting in increased soil damping. This leads to lower vibration of the soils and the multi-story subway structure. It should be noted that the amplification factors at the soil surface decrease gradually when the measure point is close to the structural model and to the container as well. This phenomenon implies that existence of either an underground structure or the container boundary will restrict dynamic behavior of soils. Clearly, the intensity and range of the constraint determine the dynamic earth pressure, which will be discussed later.

Figure 9.

Peak acceleration amplification factors at the soil surface in cases 1–4.

Subsequently, the changes in the acceleration amplification factor along the vertical direction will be further investigated to show how the soils amplify the acceleration of ground motion and how the underground structure decreases the seismic responses at the soil surface. Figure 10 plots acceleration amplification factors along the depth of the model underground structure (point along VL1 in Figure 4) and model soils (point along VL2 in Figure 4) for comparison. In each graph, the grey box represents the soil layers where the model of the underground structure is located (see Figure 11(c)). The dotted horizontal lines represent where the top and bottom plates and inner floors of the underground structure are located. For the weak seismic intensity cases (case 1 and case 2), the dashed curve (the amplification factor in the soils) increases from bottom to top, showing how the acceleration is amplified through soils. For cases having stronger ground motion (case 3 and case 4), the amplification factor decreases and are even less than 1.0 at A6, A9, and A12 because of the increasing damping ratio as mentioned before.

Figure 10.

Peak acceleration amplification factor of the model soil and model structure in case 1–4: (a) case 1, (b) case 2, (c) case 3, and (d) case 4.

Figure 11.

(a) Fourier amplitude spectra and (b) time histories of acceleration recorded by A1, A15, A16, A17, and A18 in case 2.

A comparison of solid and dashed curves in Figure 10 shows that the amplification factor in soils below the underground structure (0 m < height < 1.0 m) is consistent with that in soils, indicating that the underground structure does not notably affect the amplification factor in soils below the underground structure. However, the distribution of the acceleration amplification factor in the underground structure (1.0 m < height < 1.52 m) is different from that in soils. Different from the monotonous increase of amplification factor showing by the dashed curve, the amplification factor in underground structure decreases first and then increases (see the solid curve in Figure 10), showing a concave shape. This indicates that the motion states of the underground structure and soils are not synchronized, and local squeezing and detachment may thus occur.

Rotation vibration of multi-story subway station

To further understand the reason for the concave-shape distributed amplification factor along multi-story subway structure and the interaction between the structure and the soils, it is better to analyze the frequency component and time history of acceleration of each structural story as shown in Figure 11. It can be seen that the amplitude of low-frequency component of acceleration of each structural story are the same, while that of high-frequency component are quite different. The amplitude of high-frequency component decreases first and then increases from the bottom story to the top story and the high-frequency component of acceleration recorded by A16 is almost disappeared. The high and low-frequency component of acceleration can be easily recognized from Figure 11(b). This figure shows that the phases of low-frequency component are the same while that of high-frequency component are different. The phase of high-frequency component at A1 and A15 have a difference of about 180° with that at A17 and A18. The difference in the phase and amplitude of high-frequency component at each structural story is mainly caused by the rotation vibration of the underground structure during earthquake (Liang and Chen, 2019). Figure 12 shows the change in the acceleration of each story from $t$ = 0.6625 s to $t$ = 0.6825 s ( $Δ t$ = 0.02, which is half of the period of the high-frequency component) in case 2 to illustrate the rotation of underground structure. The amplitude and phase of high and low-frequency components at each structural story show that the low-frequency component represents the translation component and the high-frequency component represents the rotation component.

Figure 12.

Change in the acceleration of each story of the model subway station from t = 0.6625 to 0.6825 s in case 2.

Dynamic earth pressure

Figure 13 shows the distribution of the peak dynamic earth pressure acting on the sidewall obtained by the earth pressure gauges SP1–SP8 (see Figure 5). The record of SP6 is removed since this gauge is invalid during the test. When the peak acceleration of seismic wave is small (i.e. case 1 and case 2), the peak dynamic earth pressure is approximately linearly distributed and not sensitive to the peak acceleration. When the peak acceleration is large (i.e. case 3 and case 4), the peak dynamic earth pressure has an approximate hump shape. That is, the distribution of dynamic earth pressure along the depth of the multi-story subway structure is in such a mode that it is low in the middle areas while it is great in both bottom and top areas.

Figure 13.

Envelope of maximum dynamic earth pressure.

In fact, what are the factors that determine the distribution of dynamic earth pressure? Even the distributions of dynamic earth pressure are inconsistent in previous studies. Figure 14 plots several typical seismic dynamic earth pressure which are obtained from Hushmand et al. (2016), Chen et al. (2013, 2019), Zhuang et al. (2016), and Tao et al. (2019). For the underground reservoir structures with compacted silty sand as the backfill soil in Figure 14(d) (Hushmand et al., 2016), the peak dynamic earth pressure is high in the middle areas and low in the bottom and top areas, which is completely different from other underground structures. For the two-story and three-span subway station in liquefiable fine sand (Zhuang et al., 2016) and the prefabricated subway station in fine sand (Tao et al., 2019) as shown in Figure 14(c) and (e), the peak dynamic earth pressures have the shape of trumpet with the maximum value at the bottom of underground structure. However, for the two-story and two-span subway station (Chen et al., 2019) as shown in Figure 14(c) the trumpet-shaped dynamic earth pressure has the maximum value at the top of underground structure. The three-story and three-span subway station in liquefiable ground (Chen et al., 2013), shown in Figure 14(a), has the hump-shaped distribution of peak dynamic earth pressure, which is similar to that of the four-story three-span subway station tested in this paper.

Figure 14.

Distribution shapes of seismic dynamic earth pressure for different underground structure: (a) a three-story and three-span subway station, (b) a two-story and two-span subway station; (c) a two-story and three-span subway station, (d) an underground reservoir structure, and (e) a prefabricated subway station (where P is the earth pressure sensor and TP is tactile pressure sensor).

Although only a few earth pressure sensors were arranged and a few seismic earth pressure were recorded during the tests, the trend of earth pressure distribution may be concluded through polynomial fitting. Obviously, seismic dynamic earth pressure is very complicated and its distribution varies with the underground structure configuration and surrounding soils.

Attempt is then made to explain the hump-shaped distribution of dynamic earth pressure on multi-story subway structure in the present shaking table test. In addition to the racking deformation of rectangular underground structure, the rotation of an underground structure is observed as illustrated in Figure 15. Compared to a typical two-story-and-three-span subway structure, the multi-story subway structure has relatively low stiffness due to its large depth. Rotation responses aggravate local squeezing and detachment alternately at both top and bottom of the sidewalls during the earthquake. Therefore, the soil deformations at both ends of sidewall are larger than that in the middle, which causes a large earth pressure at the top end and bottom end and small earth pressure in the middle, showing the hump-shaped distribution of dynamic earth pressure.

Figure 15.

Rotation of underground structure during earthquake.

Seismic responses of multi-story subway structure

Deformation of central columns and sidewalls

Figure 16 shows the lateral relative displacements of center columns and sidewalls. The lateral displacements of the central column and the sidewall increase with the seismic intensity. The inverted-triangle-shaped deformation indicates that the underground structure has a racking deformation mode. The lateral displacement of the center column and the sidewall are almost the same under weak ground motions (i.e. case 1 and case 2) while the lateral displacement of the center column is larger than that of the sidewall, especially at the top story, under stronger ground motions (i.e. case 3 and case 4). In case 4, for instance, the maximum relative displacement of the sidewall at the top story is about (−0.4 and 0.3 mm) while that of the central column is about (−0.8 and 0.8 mm). The main reason is that under strong ground motion, there is large rotation at the top of the central column and the connecting floor slab owing to their low stiffness. The organic glass tube bound to the bottom of the floor rotates with the floor slab synchronously, and the measured relative displacement of the central column thus includes the displacement generated by the rotation of the organic glass tube. However, there is no appreciable rotation at the sidewall because of its high stiffness. The displacement of the central column obtained by laser displacement meters is thus larger than that of the sidewall. Besides, a comparison of the relative displacements of the sidewalls of different stories reveals that the layer drift on the top story is greater than that on other stories. It is mainly because the floor height is large and thus the layer stiffness is weak. When the peak acceleration of the seismic wave is 1.0g, the layer drifts from the top story to bottom story reach 1/254, 1/386, 1/574, and 1/325, respectively. The top and bottom stories are thus vulnerable in the presented study. However, it is important to note that the layer drifts measured are smaller than those in real situations because the model of the underground structure is elastic.

Figure 16.

Lateral relative displacements of the sidewall and central column in case 1–4: (a) case 1, (b) case 2, (c) case 3, and (d) case 4.

Relationship between dynamic earth pressure and racking deformation

An earthquake-induced interaction between soils and the underground structure is achieved through the dynamic earth pressure. The interaction between subway station and the soils can therefore be investigated by studying the relationship between the dynamic earth pressure and representative seismic responses of underground structure. The lateral deformation of the multi-story subway station which represents the racking deformation was selected in this paper because it is the main factor that influences the internal force of underground structural members (it will be discussed later in Section 5.4). Analysis of the relationship between the dynamic earth pressure at SP1–SP8 and the maximum relative deformation of the structural top plate (which is the maximum absolute value of the displacement of the top plate minus that of the bottom plate) reveals that there is no obvious relationship between the two under weak seismic waves (i.e. case 1 and case 2). When the peak acceleration is large (i.e. case 3 and case 4), the dynamic earth pressure at SP2 has a linear relationship with the maximum relative deformation. Owing to space limitations, only results of the dynamic earth pressure versus the maximum relative deformation at SP2 in case 3 and case 4 are presented, as shown in Figure 17. The fitting of a straight line is also shown. It is concluded that for the multi-story subway station considered in this paper, the structural response is closely related to the dynamic earth pressure at SP2, which is the position of the top of hump in the distribution of the dynamic earth pressure.

Figure 17.

Time history points of the dynamic earth pressure versus the maximum relative deformation at SP2.

Internal dynamic forces in sidewalls and central columns

According to Lu and Hwang (2019), Li and Chen (2018), and Chen et al. (2014), the central column can be the most vulnerable member of a subway structure. Chen et al. (2016) showed that large axial compression on the central column results in concentrated damage to the column, which may further lead to the failure of the total subway structure. The central columns at the bottom story are subjected to the largest axial compression, which appreciably reduces the ductility of the central columns (Chen et al., 2016). The bottom story may be more vulnerable than top story although the top story has the maximum layer drift and thus the internal dynamic forces of central columns at the bottom story are analyzed as follows. The internal force is converted from model to prototype, and the dynamic axial forces and moments of the central column at the bottom story in each case are shown in Figure 18. The maximum and minimum dynamic internal forces are indicated in the figure. Except at peak acceleration of 0.2g, the envelope of the dynamic axial force enlarges with an increase in the peak acceleration. The positive and negative maximum dynamic axial forces are asymmetric, and the increment of the axial force is larger than the decrement. For the peak acceleration of 1.0g, the maximum axial force of the center column increases by 14.2%. The horizontal ground motion increases the vertical dynamic axial force of the central column and thus the axial compression ratio, which may result in concentrated damage to the central column. Figure 18(b) shows that the envelope of the dynamic moment of the central column enlarges with an increase in peak accelerations of seismic waves.

Figure 18.

Envelopes of the axial force and bending moment of the bottom-story central column: (a) Axial force and (b) Moment.

Axial force–moment time histories and axial force–moment bearing capacity curves of the central column at the bottom story are presented in Figure 19. All these internal forces are converted to those for the prototype. The underground structure is therefore safe in terms of the internal force.

Figure 19.

Capacity curves and axial force–moment time histories of the bottom-story central column: (a) case 1, (b) case 2, (c) case 3, and case 4.

Relationship between lateral deformation and internal force

The factors responsible for the internal forces of a member such as a beam include the bearing displacement of the beam and the distributed load acting on the beam. In the case of the subway station considered in this paper, the factors responsible for the dynamic internal forces of structural members can be similarly divided into interlayer displacements of the underground structure and the dynamic earth pressure and inertial force acting on the structural members. The effects of inertial force on the seismic responses of underground structure can be ignored due to the constraint of surrounding soils. Generally, only the lateral deformation is used to evaluate the damage state of a subway station (Chen and Liu, 2019; Huh et al., 2017; Liu et al., 2017) while the dynamic earth pressure is not considered. Considering the complicated interaction between soils and multi-story subway station, it is necessary to quantitatively analyze the most important factors responsible for the dynamic internal force of a multi-story subway station. The dynamic moment of the sidewall at the bottom story of the subway station generated by each factor is analyzed using static analysis method in the following steps.

(1) The peak dynamic moment ( $M_{max}$ ) of the sidewall at the bottom story and the time ( $t_{max}$ ) at which the peak value is reached in each case are obtained.

(2) The structural deformation (i.e. the layer displacement ( $δ$ )) and the corresponding lateral earth pressure ( $P$ ) at $t_{max}$ are obtained.

(3) Two analysis models were established to calculate the moment generated by the layer displacement and soil pressure. In the case of the first model, the layer displacement $δ$ is applied to each floor and no earth pressure is applied on the sidewall as shown in Figure 20(a). The moment of the sidewall ( $M_{δ}$ ) at the bottom story is obtained.

(4) In the case of the second model, the displacement of each floor is fixed and earth pressure $P$ is applied on the sidewall to obtain the corresponding moment of the sidewall ( $M_{P}$ ) at the bottom story as shown in Figure 20(b).

Figure 20.

(a) Model subjected to interlayer deformation and (b) model subjected to earth pressure.

Results are given in Table 3, where $M_{max}$ , $M_{δ}$ , and $M_{P}$ are respectively the total moment of the sidewall of the prototype underground structure, moment generated by the layer drift, and moment generated by dynamic earth pressure while $t_{max}$ denotes the time at which $M_{max}$ is reached. The moment of the sidewall at the bottom story reaches a peak value at the same time in each case. A comparison of $M_{max}$ , $M_{δ}$ , and $M_{P}$ in Table 3 reveals that $M_{δ}$ increases with $M_{max}$ , but there is no obvious change law of $M_{P}$ . Besides, $M_{max}$ and $M_{δ}$ are similar while $M_{P}$ is small compared with $M_{max}$ . The lateral deformation is the main factor generating the dynamic moment of the sidewall, while the dynamic earth pressure has no obvious effect on the dynamic moment. It is concluded from the above analysis that for the multi-story subway station, the main factor corresponding to the dynamic internal forces is lateral deformation.

Table 3.

Contributions of layer drift and dynamical earth pressure to the bending moment of the sidewall.

Case	Peak acceleration (g)	$t_{max}$ (s)	$M_{max}$ (kN m)	$M_{δ}$ (kN m)	$M_{P}$ (kN m)
Case 1	0.1	0.680	37.292	61.726	9.092
Case 2	0.2	0.681	74.829	82.076	2.376
Case 3	0.6	0.684	229.225	204.850	34.882
Case 4	1.0	0.691	248.724	234.696	27.727

Conclusions

A series of shaking-table model tests were conducted to investigate the seismic response characteristics of multi-story subway stations subjected to Shanghai artificial waves. The following conclusions were obtained:

(1) The strong ground motion will decrease the amplification of acceleration due to the increasing soil damping. The multi-story subway station does not notably affect the amplification factor in soils below the underground structure but decreases the seismic responses of soil surface. The motion states of the underground structure and soils are not synchronized, and local squeezing and detachment may thus occur.

(2) The low-frequency component represents the translation component of subway station and the high-frequency component represents the rotation component of subway station. The local squeezing and detachment may occur alternately at both top and bottom ends of the sidewalls due to the rotating vibration of the underground structure, which leads to the hump-shaped distribution of dynamic earth pressure.

(3) The racking deformation of the multi-story subway station has a linear relationship with the dynamic earth pressure at a certain area along the sidewall, where the top of hump-shaped distribution of dynamic earth pressure is. The most important factor responsible for the dynamic internal force of a multi-story subway station is the layer drift, which is a commonly used index to evaluate the damage state of a subway station.

Footnotes

Acknowledgements

The authors gratefully acknowledge support from the National Natural Science Foundation of China (Grant No. 51778464) and State Key Laboratory of Disaster Reduction in Civil Engineering (SLDRCE19-B-38).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the National Natural Science Foundation of China (Grant No. 51778464), State Key Laboratory of Disaster Reduction in Civil Engineering (SLDRCE19-B-38).

ORCID iD

Zhiyi Chen

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