Shaking table test on a tunnel-group metro station in rock site under harmonic excitation

Abstract

A tunnel-group metro station built in rock site is composed of a group of tunnels. Different tunnels and their interconnections can show inconsistent responses during an earthquake. This study investigates the dynamic responses of such a metro station in a rock site, by shaking table tests. The lining structures of each tunnel and surrounding rock are modeled based on the similitude law; foam concrete and gypsum are used to model the ground-structure system, keeping relative stiffness consistent with that of the prototype. A series of harmonic waves are employed as excitations, input along the transverse and longitudinal direction of the shaking table. The discrepant responses caused by the structural irregularities are revealed by measurement of acceleration and strain of the model. Site characteristics are identified by the transfer function method in white noise cases. The test results show that the acceleration response and strain response of the structure are controlled by the ground. In particular, the acceleration amplification effect at the opening section of the station hall is more significant than that at the standard section under transverse excitation; the amplification effect of the structural opening is insignificant under longitudinal excitation.

Graphical abstract

Keywords

metro station / tunnel-group / shaking table test / harmonic excitation / dynamic response

1 Introduction

Although metro stations built in rock sites are common in cities such as Stockholm, Naples, and Stuttgart, there are concerns regarding their construction in seismic risk zones like Qingdao or Xiamen, and regarding the resilience of the relevant infrastructures. Underground structures can suffer damage or even destruction, not only in soft ground but in rock sites during strong earthquakes. In the 1999 Chi-Chi earthquake, 49 out of the total 57 mountain tunnels were found to be damaged [1]. During the Wenchuan earthquake in 2008, the mountain road tunnels suffered severe damage mainly at the entrances due to landslides. The interior sections of those tunnels were affected by faults and displacement, leading to damage [2–5]. In addition, a reinforced concrete structure in the underground powerhouse had a large area affected by cracking and spalling [6]. These damages show that the dynamic impact of earthquakes on underground caverns still needs further study.

Seismic performance of shallow underground cavities in rock sites needs special attention, as the acceleration amplification effect is more pronounced in shallow buried ground [7,8]. Factors such as structure layout, lining type, inverted arch setting, and lining reinforcement, affect the seismic responses of underground caverns [1]. Most analytical solutions were specifically developed for dynamic analyses of tunnel with circular or rectangular cross sections [9,10], and so numerical modeling has become the most commonly employed method for studying the seismic responses of complex underground cavities. Wang et al. [6,11] provided a reasonable assessment of the seismic damage of an underground powerhouse by means of a full three-dimensional (3D) dynamic finite element model. In another paper [12], the researchers established a nonlinear finite element model to capture the intricate physical characteristics of faults, and evaluated their impact on the seismic performance of underground caverns. As well as the finite element model, the discrete element model has been utilized to simulate joint properties, for evaluation of the effects of adverse geological discontinuities and associated earthquakes [13–15]. Chang and Seo [16] proposed a seismic vulnerability analysis method specifically for underground caverns of nuclear facilities. Such underground caverns are deeply buried. However, the dynamic response of shallow metro stations in rock sites constructed with tunnel-group has not yet been investigated.

To examine the seismic performance of shallow buried tunnels in rock sites, and the interaction between the rock mass and the structure, shaking table tests have been carried out, but the test objects are either single tunnel [17–19] or fault effect [20,21]. Some Researchers [22–27] studied the impact of earthquakes on the response and collapse of underground caverns in continuous and discontinuous media through various model tests on shaking tables. However, the underground cavern that the researchers focused on was relatively simple, and the geometric scale was relatively small. An underground metro station is a complex and large-scale structure of caverns, as shown in Fig.1, generally composed of service hall, platforms, horizontal passages connecting platforms, lift shafts and escalator shafts between the hall and the platform or ground, and ventilation shafts. All of those are excavated by tunneling processes. Furthermore, it is worth noting that tunnel-group metro stations are typically shallow-buried, and therefore their seismic performance becomes even more crucial. As far as we know, there have been no previous studies on the seismic response of tunnel-group metro stations using shaking table tests. Considering the specific characteristics of burial depth and geometric structure, this research topic presents an important area that requires further investigation.

The purpose of this study is to assess the seismic response of the tunnel-group metro station in a rock site through shaking table tests. The prototype is based on a metro station on Line 4 of the Qingdao Metro. The configuration of the investigated station is described in Section 2. To accurately replicate the key structural and site characteristics of the prototype, a synthetic model rock and model lining structure were designed using the similitude relations, as described in Section 3. In Section 4, the installation, into the model, of instrumentation of accelerometers and dynamic strain gauges is described. Vibration under sinusoidal excitation with 5 specific frequencies was applied in either transverse or longitudinal direction, with a consistent peak acceleration magnitude of 0.1g. Prior to and after the sinusoidal excitations, white noise with an amplitude of 0.05g was applied. Section 5 reports on the verification of the boundary effect of the rock model, the amplification effect along the height of the rock model, the time-history records of structural acceleration and dynamic strain. In Section 6, the transfer functions (TFs) between free field and structure model are compared, and the feasibility of multi-input excitations is assessed. The seismic response of the rock model is further evaluated using the power spectrum density. Additionally, changes in peak tensile strain at the structural connections are discussed, before making a summary.

2 Prototype of the tunnel-group metro station

2.1 Tunnel-group metro station

The excavation of tunnels in rock sites typically employs mining methods. The prototype metro station for this test is shown in Fig.1. This study focuses on a newly built metro station in Qingdao designed with a separate hall and platform structure. The station spans a tunnel length of 183 m for the hall and 169 m for the platform, with a burial depth of 15 m. The station hall and the platform are connected by multiple horizontal and vertical connecting passages, forming an unusual complex 3D spatial structure. Passengers pass between the hall and platforms through the vertical passages and transfer between the left and right lines through horizontal passages, while air ducts connect the hall and platforms for air exchange in the station. The geological survey report reveals that the stratum profile comprises artificial fill, strongly weathered rock, moderately weathered granite, and weakly weathered granite, with the main station structure located within the moderately weathered rock layer.

To accommodate the size and load capacity of the shaking table, and to concentrate on examining the impact of the conjunction between the connecting passages and the station, certain simplifications have been implemented in the study. These simplifications include: 1) the length of station segments was assumed to be only 90 m (Fig.2); and 2) neglecting non-structural elements such as staircases, working shafts, and the connection to metro track tunnels.

2.2 Cross passages

Fig.3 illustrates the precise dimensions of the horizontal and vertical connecting passages. The horizontal connecting passage is 24.5 m long and 11.5 m high, featuring a centrally located door is 8.9 m long and 6.9 m high. The vertical connecting passage measures 34.6 m at the bottom and 22.7 m at the top, with a height of 6.9 m.

Fig.4 illustrates the cross-sectional dimensions of the main structure. The span of the station hall is 20.6 m, the height is 16.46 m, and the thickness of the lining is 0.8 m. The span of the platform is 10.05 m, the height is 12.04 m, and the thickness of the lining is 0.7 m.

3 Preparation of model station

3.1 Similitude relations

Previous model tests [28–30] often used two sets of independent similitude ratios for the ground medium and underground structure, which can affect the interaction relationship between stratum-structure and the authenticity of model tests. Therefore, the similitude theory needs to be applied to keep the model tests representative. In this study, both the dimensional analysis [31]and the Buckingham-π theorem were employed to establish similitude relations. Yan et al.’s paper [32] showed the specific derivation process. The physical parameters for the model were determined based on the similitude ratio of geometry, elastic modulus, and density, which used ratios 1/30, 1/100, and 1/3.33, respectively. According to the dimensional analysis, the following similitude ratio relationship can be obtained:

(1)S_{\mathrm{a}}=\frac{S_{\mathrm{G}}}{S_{\mathrm{l}}{S}_{\text{ρ}}},

where S_{\mathrm{a}}, S_{\mathrm{G}}, S_{\mathrm{l}}, S_{\text{ρ}} were the similitude ratios of acceleration, dynamic shear modulus, geometry, and density, respectively. According to Eq. (1), the acceleration similitude ratio is equal to 1. Tab.1 contains the main similitude relations employed in this test.

3.2 Model materials

The selection of foam concrete as the material for simulating the surrounding rock was based on its mechanical properties and low density [18]. The foam concrete was made by mixing cement, foam and water. After extensive testing to evaluate the performance at different densities, a specimen with a density of 730 kg/m³ was selected. The mechanical properties of the foam concrete and the prototype rock are presented in Tab.2.

Concrete lining is simulated using plaster materials. Pure plaster cannot meet the physical and mechanical parameters required for this test. Therefore, diatomite was added to the plaster as a light aggregate to reduce the material density while improving its mechanical properties. When making the structural model, water, plaster and diatomite were made into several sets of standard specimens. Through material property tests, the elastic modulus, Poisson’s ratio, and other parameters were measured. The mechanical parameters of both the lining model and prototype structure are presented in Tab.3. The finalized mass ratio of plaster, diatomite, and water was chosen as 1:0.1:1.6.

3.3 Model preparation

The preparation of the model mainly includes three steps: pouring of gypsum lining, assembly of lining structure, and pouring of foam concrete. Fig.5 presents the construction process of the model. A photograph of the inner and outer formwork is shown in Fig.5(a), the inner mold is made of foam board, the outer mold is made of wooden boards, while wire mesh was included to simulate the distribution of rebar in the lining. The model was worked outdoors, and after removing the formwork it was moved indoors, where it was possible to control the humidity and speed up the drying of the plaster material. The lining structure used for assembly is shown in Fig.5(b), where the substructure and superstructure were assembled separately and precisely. Fig.5(c) shows the formwork for foam concrete, and the entire rock model is poured on a rigid reinforced concrete base plate.

4 Test setup

4.1 Installing the model on the shaking table

The model test was carried out at Tongji University using a six-degree-of-freedom shaking table system, which is 4 m long and 4 m wide with a load capacity of 25 t. The structural layout of the test was determined considering the similitude relation of the model and the load capacity of the shaking table. The outer contour of the whole model was 3.0 m long in the x-direction (transverse direction), 3.0 m wide in the y-direction (longitudinal direction), and 2.0 m high in the z-direction. Fig.6 illustrates the test system, and the complete test model. The bottom plate was constructed of reinforced concrete and secured to the shaking table using bolts.

4.2 Instrumentation

The instrumentation layout for the model test included 3D accelerometers and strain gauges. To study the amplification phenomenon of the rock model and the dynamic response of the lining structure, accelerometers monitored two separate components of acceleration: ground acceleration and structural acceleration. The layout of the accelerometers is presented in Fig.7(a) and 7(b). The rock model was arranged vertically from the bottom to the top with accelerometers numbered AS0, AS3 and AS2; AS1 was arranged at the top center of the rock model. Two observation sections for the hall, names O1-O1 for the opening section and O2-O2 for the normal section, were selected. Accelerometers with numbers A1 to A4 were placed at the sections. The accelerometers at the platform, numbered as A5, A6 for normal section and A7, A8 for open section, were also arranged in the same way.

Strain gauges were used to measure structural strain and investigate their spatial distribution, with a particular focus on the connection between the connecting passages and the tunnel. Fig.7(c) illustrates the arrangement of the strain gauges. The placement of these strain gauges was guided by numerical analyses [33]. Reference [33] was found that the stress concentration at the location where the station connects with the connecting passage was significant in producing damage. VL represents the lower section of the vertical connecting passage, and HR represents the right section that connects the horizontal connecting passage and the tunnel, and each section is arranged with bidirectional strain gauges on the vault, spandrel, arch footing and arch bottom.

4.3 Excitation sequence

Sinusoidal waves have a simple mathematical description and clear frequency characteristics, which facilitate experimental analysis of the dynamic response of structures. In contrast, actual seismic records usually show complex waveforms with long input times and low repeatability. In the test, ramped sinusoidal accelerations with frequencies of 12, 17, 19, 21, and 23 Hz were used as input cases due to the model’s estimated dominant frequency of 20 Hz and in order to cover the dominant frequencies of the natural waves (such as the Chi-Chi wave and the Wenchuan wave).

Each acceleration case consisted of 3 ramp cycles at the beginning, 5 constant cycles in the middle, and 3 ramp cycles at the end. The purpose of the 3 ramp cycles at the beginning and end of each acceleration signal was to facilitate the operation of the hydraulic instrumentation. These ramped cycles allowed for a smooth transition in the applied acceleration. The constant cycles of each acceleration sequence were used to realize the stable state for the model. This allowed the structures to experience sustained dynamic loading, which is necessary for capturing the accurate dynamic response and behavior of the test model. The series of seismic excitations are illustrated in Fig.8, the X coordinate represents the time axis, whose length indicates the excitation time of the harmonics, and the Y axis represents the amplitude of the harmonics.

Prior to applying the harmonic cases, a white noise excitation was used to investigate the inherent dynamic properties of the rock model. The peak value of the white noise excitation was set to a small value of 0.05 g, aiming to conduct a “zero test” [34]. During this test, the rock model was subjected to a low level of deformation, allowing the initial elastic dynamic properties to be estimated from the TF. Following the sinusoidal excitations, the same white noise excitation was again employed, to examine the dynamic response of the model. Tab.4 presents the input excitation sequences used in the tests, where “x” and “y” represent the transverse and longitudinal directions, respectively.

5 Test results

5.1 Boundary effects

The acceleration measurement points AS1 and AS2 located on top of the model were selected to analyze the response of transverse and longitudinal displacement to the five input frequencies along the x and y directions. Fig.9 shows the accelerations over a specific period of time. By calculation, the errors in acceleration corresponding to AS1 and AS2 for transverse excitation are within 3%, while the error range for longitudinal excitation is within 9%. To further illustrate the influence of boundary effects, the one-dimensional (1D) TF analytical solution [35] was utilized to compare the surface response. The following is the theoretical analysis formula:

(2)TF=\frac{1}{\sqrt{{\mathrm{c}\mathrm{o}\mathrm{s}}^2(\omega H/v_{\mathrm{s}})+{\left[D\right(\omega H/v_{\mathrm{s}}\left)\right]}^2}},

where ω = 2πf is the angular frequency of excitations; v_{\mathrm{s}}=4H{f}_{\mathrm{s}} is the shear wave velocity of the ground; f is the excitation frequency; f_{\mathrm{s}} and D are the main frequency and damping ratio of the ground, respectively; and H is the height of the ground.

The maximum accelerations at measurement points AS1 and AS2 were chosen to compare with the peak acceleration measured at AS0, to obtain the surface amplification response for transverse and longitudinal excitation, respectively, as shown in Fig.10. In particular, each value of AS2-x/AS0-x and AS2-y/AS0-y is closer to the 1D TF curve than AS1-x/AS0-x and AS1-y/AS0-y, which further explains that the boundary effects of the rock model are negligible, AS2 can be considered to be in the “free field” range.

5.2 Acceleration in the rock model

To assess the acceleration amplification effect in the rock model, three measurement points were selected along the vertical direction, namely AS0, AS3, and AS2, and harmonics of five frequencies were input along the x and y directions, then comparing the peak acceleration of AS3 and AS2 to the peak acceleration of AS0, respectively, the acceleration amplification factor is obtained. As illustrated in Fig.11, the bottom-up acceleration of the model gradually increases during transverse excitations, with the acceleration amplification effect becoming more pronounced as the frequency increases. The amplification effect of the model reached its peak at 21 Hz, with the top amplification factor reaching 2.88 during longitudinal excitations. Overall, these results suggest that the rock model exhibits a noticeable amplification effect in response to input motions, and that this effect is frequency-dependent and direction-specific.

5.3 Acceleration of the structure lining

The response of horizontal acceleration between station hall and platform under sinusoidal excitation with 5 specific frequencies is presented in Fig.12. The acceleration waveform recorded by each measurement point is consistent with the input waveform, and the phase of acceleration is the same for each observation section. The magnitude of acceleration is dependent on the location of the measurement point and, in general, it is observed that the acceleration at the vault (top portion) of the structure is greater than the acceleration at the invert (bottom portion) under harmonic excitation. When the frequency of the harmonic is low, the difference in acceleration between the vault and invert is small. As the frequency increases, the difference in acceleration changes significantly. Meanwhile, the change in acceleration amplitude on the platform is smaller than that at the station hall.

5.4 Dynamic strain

Fig.13 presents a comparison of the dynamic strain variations with time for the measurement points within the two observation sections under five frequencies of excitation. The dynamic strain is characterized by the change between the total strain observed during shaking and the initial static strain existing before the shaking event begins. The dynamic strain trends show that the maximum tensile strain at the VL observation section under transverse excitations appears at the shoulder of the arch, and at the HR observation section under longitudinal excitations at the foot of the arch.

6 Discussion

6.1 Frequency response of the model

6.1.1 Transfer function

In the study of seismic response of underground engineering, the TF can succinctly express the correspondence between the input excitations and the seismic response of the rock mass. The TF can be defined as the ratio of the Laplace transform of the output signals to the Laplace transform of the input signals. Mathematically, it can be expressed as:

(3)H(s)=\frac{Y(s)}{X(s)}=\frac{L\{y(t)\}}{L\{x(t)\}},

where X(s)=L\{x(t)\} and y(s)=L\{y(t)\} represent the Laplace transforms of the input and output signals, respectively. To assess the impact of the buried station on the spectral characteristics of the rock-model, the TFs of AS1, AS2, and A3 under white noise excitation (WN1) were compared. The surface amplification factors under sinusoidal excitation are theoretically the same as those at the corresponding frequency in the TF, the surface amplification factors of the AS1 and AS2 measurement points were compared at the same time. The TF of the test results and the distribution of the ground amplification factors under harmonic excitation are given in Fig.14. Fig.14 also shows that the transverse fundamental frequency for all three regions is 22.1 Hz, while the longitudinal fundamental frequency is 20.3 Hz. This indicates that the spectral properties of the structure are dominated by the dynamic characteristics of the site. It also can explain the observation in Fig.10(a) that the acceleration amplification factor of the model rock increases with frequency for transverse excitation, since the selected frequency of 23 Hz is close to the transverse fundamental frequency of 22.1 Hz, and the amplification effect is not significantly weakened. It can also be observed that the surface amplification factors fall within the range expected, from the TFs of the measurement points AS1 and AS2, except that the surface amplification factors show larger values near the dominant frequency. The different input strengths of white noise and harmonics result in different surface amplification effects. Notably, the existence of the station structure results in a reduction in the magnitude of the surface TF compared to that in the free field (AS2) condition. This can be attributed to the dissipation of more input energy by the station structure, resulting in a reduced response at the top of the model. Additionally, the discrepancy between the transverse and longitudinal test results arises from the geometric asymmetry of the station structure.

6.1.2 Evaluating the feasibility of multiple input motions

It is crucial to understanding the accumulative effect of multiple excitations on the spectral response of the rock model. In this study, the TFs of the ground between the first white noise excitation (WN1) and the last white noise excitation (WN2) were compared to assess the accumulative effect of harmonic excitation on the spectral response of the model. The comparison of TFs between WN1 and WN2 is demonstrated in Fig.15. The results indicate that despite the 10th harmonic excitations applied to the model, the TFs of the surface before and after the excitations are nearly the same. This shows that the model is still in an elastic state before and after the harmonic excitations, and the initial state of the model is the same for each input seismic wave condition, verifying the reliability of the test design, which agrees with the results of previous studies [36,37]. Therefore, the feasibility of repeated excitations of the model in this investigation is demonstrated.

6.1.3 Acceleration power spectral density (PSD) of the rock model

Acceleration PSD describes the energy distribution of earthquake motion at different frequencies. The PSD at the top of the model (AS1 & AS2) and the bottom of the model (AS0) in both directions of excitation are displayed in Fig.16, where the PSD amplitudes represent the distribution of the energy of the acceleration signal with frequency. AS2 is considered to be in the free field rock, away from the structure. The PSD is estimated using Welch’s method [38]. As the frequency of excitation increases, the PSD of AS0 exhibits a decreasing trend that is similar for both directions of excitation. However, the PSDs of AS1 & AS2 exhibit distinct patterns. Under transverse excitations, the maximum amplitude happens at 12 Hz, while under longitudinal excitation, the maximum amplitude happens at 19 Hz. This indicates that the surface amplification pattern of the same rock site depends on the direction of excitations. Furthermore, most acceleration power spectral densities of AS1 are smaller than those of AS2, which can be attributed to the influence of buried metro station.

To further examine the influence of station structure on the ground acceleration, the PSD ratios at the top and bottom of the rock model are shown in Fig.17. Under harmonic transverse excitations, the acceleration amplification effect increases with increasing frequency, whereas there is a peak at 21 Hz under longitudinal excitations. Furthermore, it can be observed that the ratios of the rock-structure field (AS1/AS0) are smaller than the ratio of the “free field” (AS2/AS0) in the test frequency range. As mentioned earlier, the magnitude of PSD represents the distribution of the energy of the acceleration signal with frequency. Therefore, a larger difference between the PSD ratios of the rock-structure field and the “free field” indicates that the metro station consumes more input energy and reduces the amplitudes at the ground surface, particularly when the input frequency approaches the eigenfrequency of the model.

6.2 Acceleration amplification factor of the lining structure

The ratio of the maximum acceleration recorded at the measurement point to the input seismic motion amplitude is the acceleration amplification factor [39]. The frequency response curves of the measurement points under transverse and longitudinal harmonic excitation are shown in Fig.18. The horizontal coordinates indicating the ratio of the input harmonic frequency to the model’s transverse or longitudinal fundamental frequency as

(4)\beta \left(x\right)=\frac{f_i}{f_x},

(5)\beta \left(y\right)=\frac{f_i}{f_y},

where f_i is the frequency of harmonic, f_x = 22.1 Hz, f_y = 20.3 Hz. The acceleration amplification factor is maximized when β is close to 1. That is, the maximum acceleration response of the model would be induced when β = 1. It is worth noting the fact that the fundamental frequency of a natural earthquake usually lies between 3–5 Hz, and using the frequency ratio of 5.48/1 as shown in Tab.1, the natural earthquake conversion frequency is 16.4–27.4 Hz, which would induce such a significant response.

Taking \beta \left(x\right) = 1.041, with harmonic transverse excitation, the acceleration at vault (point A1) produces an obvious amplification effect compared with that at the inverted arch (point A2), as listed in Tab.5 (A1/A2 = 1.38). Similarly, the difference of acceleration response at the opening section with respect to normal section of the station hall gives A1/A3 = 1.11 for the vault and A2/A4 = 1.18 for the invert arch, respectively.

On the other hand, taking β(y) = 1.034, during harmonic longitudinal excitation, the acceleration at the vault (point A1) produces an obvious amplification effect compared with that at the inverted arch (point A2), as listed in Tab.5, A1/A2 = 1.45. However, the amplification effect of the structural opening disappears when the difference of acceleration response at opening section, relative to the normal section of the station hall, gives A1/A3 = 0.98 for the vault and A2/A4 = 0.93 for the invert arch, respectively.

6.3 Peak tensile strain at structural connections

Fig.7(c) illustrates the arrangement of strain gauges of VL and HR at the connection between the connecting passages and the tunnel. The pattern of the peak strain variation in Fig.19 is consistent with the acceleration amplification factor variation in Fig.18, which again verifies that the dynamic response of the structure is controlled by the site. When the harmonic excites transversely, the tensile strain at VL section is much larger than that at HR section, and the maximum tensile strain at VL section appears at the spandrel with a value of 42 × 10⁻⁶ (micro strain), which generates a stress concentration in the spandrel and is prone to damage. On the other hand, the maximum tensile strain at HR section appears at the arch footing with a value of 20 × 10⁻⁶.

When the harmonic excites longitudinally, the situation is reversed, with the maximum tensile strain at HR section appearing at the arch footing with a value of 36 × 10⁻⁶, which is the part of stress concentration, and the maximum tensile strain at VL section appearing at the spandrel with a value of 19 × 10⁻⁶. This suggests that the spandrel and foot joints between the station and the connecting passage are the weak points of the tunnel-group metro station under seismic, and, at the same time, the influence of harmonic excitations on the dynamic tensile strain distribution is related to the direction of the excitation.

For further discussion, the stress concentration part SVL2 during transverse excitation and the stress concentration part SHR3 during longitudinal excitation are selected for curve fitting. The fitting Eqs. (6) and (7) can be obtained, as well as the fitting curves in Fig.20.

(6)S\left(x\right)=32.1{\left(\frac{f_i}{f_x}\right)}^3,

(7)S\left(y\right)=24.9{\left(\frac{f_i}{f_y}\right)}^3,

where S is the strain value. It can be seen from Fig.20 that the curve fitting is good enough to predict the actual lining strain value. From Eqs. (6) and (7), when β = 1, the maximum tensile strains in the transverse and longitudinal directions are 32.1 × 10⁻⁶ and 24.9 × 10⁻⁶, respectively, which are much smaller than the cracking strain of reinforced concrete of 320 × 10⁻⁶. Therefore, the test model is within the elastic range. The cracking strain needs to be further investigated in the subsequent analysis of strong seismic effects. Meanwhile, since there is only one harmonic excitation intensity in the test, the fitting equation cannot reflect the effect of seismic wave excitation intensity. Furthermore, vibrations due to natural earthquakes can be resolved into combinations of different waves with varying frequencies and amplitudes. When the fundamental frequency of natural earthquake is close to the fundamental frequency of the site, the site does not produce resonance phenomena; this is the biggest difference between a natural earthquake and harmonic excitation. Therefore, the current fitting formula cannot be applied to practical engineering, and subsequent analysis of the dynamic response of the test model under natural earthquake excitation is required.

7 Conclusions

In this study, the seismic response of the tunnel-group metro station is analyzed by shaking table tests. A scaled rock-station model was designed and constructed with a gypsum mixture used to simulate the lining and foamed concrete to represent the rock. The study considered the effect of harmonic frequency and excitation direction on the seismic response. The main conclusions can be summarized as follows.

1) The presence of the metro station had a significant impact on the spectral response of the surface, highlighted by the dissipation of the input energy and the geometric effects introduced by the presence of the metro station.

2) The amplification effect on the ground response was more pronounced when the excitation frequency was in proximity to the eigenfrequency of the site. Specifically, when the transverse main frequency is 23 Hz and the longitudinal main frequency is 21 Hz. In addition, a natural earthquake would induce such a significant response.

3) The direction of harmonic input had a notable effect on the acceleration amplification and tensile strain distribution within the rock-structure model. Under transverse excitation, the opening section of the station hall experienced significant acceleration amplification, while the lower section of the vertical connecting passage exhibited higher tensile strains, with maximum values occurring at the spandrel. Under longitudinal excitation, the amplification effect of the structural openings was not significant and the distribution of tensile strains was opposite to that under transverse excitation, with the maximum tensile strains occurring at the arch footing of the right section of horizontal connecting passage.

The dynamic response of the tunnel-group metro station model is investigated using white noise and harmonics, providing valuable insights into the effects of this particular station structure, harmonic frequency and excitation direction, while seismic mitigation measures also need to be considered for the joint of the connecting passage with the tunnel.

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