Shaking table test and numerical simulation study on a tunnel-soil-bridge pile structure interaction system

In this study, the dynamic interaction (SSSI) of a double tunnel–sand–soil–bridge pile system under earthquakes is investigated by conducting a shaking table test in the context of an actual project in Dalian. The dynamic response laws of the structure and site are determined and compared with the results obtained using ABAQUS numerical simulation. In the numerical model introduces, the Kelvin intrinsic model subroutine is introduced, and the equivalent linear method is used to deal with the nonlinearity of the sandy soil in the calculation process. The experimental results are compared with the results obtained using the numerical model to verify the reliability of the numerical simulation. Based on this, eight work - ing conditions are designed, and the interaction law between the structures in the system is investigated through a comparative analysis. The results showed that the tunnel amplifies the dynamic responses of the bridge pile, adjacent tunnel, and far field, while the bridge pile attenuates the dynamic responses of the side tunnel and far field; the presence of both the tunnel and bridge pile increases the internal force of the adjacent structure, and the peak internal force often occurs near the intersection of the structure or at the pile–soil interface.


Introduction
In recent years, the world has entered a golden period of underground space development and utilization.With the development of construction technology, a significant breakthrough has been made in the construction of underground structures in terms of their size and scale.Given the limited urban underground space resources, there has been an increasing number of close crossing projects between underground and above-ground structures.
The existence of underground structures destroys the integrity of the soil, and the multiple reflections and refractions of seismic waves by underground structures affect the dynamic response characteristics of the soil in the site and thus the seismic response of the neighboring above-ground structures.In addition, the fluctuation field and additional stress field due to the inertia of the aboveground structures cause disturbances to the site soil and thus affect the seismic response of underground structures.For example, many underground projects and adjacent above-ground structures were damaged during the Hanshin earthquake in Japan (Samata et al.1997), the Jiji earthquake in Taiwan (Wang et al.2001) and the Wenchuan earthquake, the above-ground structure-soil-underground structure interaction has attracted research attention.Chen et al. (2016) and Wang et al. (2018) believed that the existence of underground structures cannot be ignored for the influence of surface structures.Lou et al. (2011) emphasized the importance of surface structure-soil-underground structure interaction.The surface structure-soil-subsurface structure interaction should be considered in the structural design.
Therefore, to ensure the overall seismic disaster prevention capability of cities, it is necessary to consider the seismic performance of both underground and adjacent above-ground structures, to study the seismic response law of the above-ground structure-soil-underground structure system as a whole, and to establish a simple, practical, reasonable, and feasible seismic analysis method.
With the development of computer technology, numerical methods for subsurface structures have emerged, including the substructure method, finite element method, and hybrid method (Wolf et al. 1994).
Since numerical simulation methods are more economical and can be verified using shaking table test results to investigate the seismic response law of underground structures, they have become a favored research method.Many domestic and foreign scholars have studied the effects of different factors on the seismic response of the complex system of above-ground structure-soil-underground structures.Abate et al. (2016) systematically studied the seismic response of a tunnel-soil-superstructure interaction system in the context of an actual Italian project.The results showed that the presence of the tunnel played a certain function of seismic isolation.Dashti et al. (2016) designed and implemented a series of centrifuge shaking table tests on an aboveground structure-soil-subsurface structure interaction system, and analyzed the rationality of the test scheme based on the test results.Pitilakis et al. (2014) investigated the effect of surface structures on the seismic response of adjacent tunnels using a 2D numerical approach.The presence of adjacent surface structures was found to increase the seismic response of shallow-buried tunnels.Chen et al. (2004) conducted a 2D finite element simulation analysis of a multistory basement-pile-twin-tower high-rise building and found that the effect of soil-structure interaction on the seismic response of the high-rise building is related to the site conditions and input ground shaking; the softer the site, the more significant the interaction effect.Chen et al. (2012) and He et al. (2009) studied the two-dimensional seismic response law of underground structure-soil-surface structure against the background of actual engineering.The study found that the existence of underground structure would increase the seismic response of a certain range of soil surface and surface structure.Lia et al. ( 2020) performed 3D nonlinear finite element simulation of a subway station considering the effects of vertical ground shaking and the depth of the structural cover.The results showed that the consideration of vertical seismic motion increases the seismic response of the structure; the degree of this effect depends largely on the characteristics of the vertical seismic excitation.Miao et al. (2020) studied the dynamic interaction of a system comprising multiple above-ground buildings, soils, and subway stations under the action of ground motions through an automatic modeling system.The numerical calculation results showed that several key factors, such as the number of buildings and the depth of burial, significantly amplify or attenuate the seismic response of underground structures.
With urbanization, an increasing number of taller and smaller urban buildings are urban building clusters.The shaking of building complexes during earthquakes will reflect a part of the ground shaking energy into the foundation soil, thus changing the dynamic response of the soil; this is the structure-soilstructure interaction (SSSI) that is currently receiving much attention.However, most current research has focused on 2D or frequency-domain analyses; studies on 3D models considering the nonlinearity of the soil are lacking.Three-dimensional models can more accurately reflect the characteristics of complex structural systems with a complex spatial distribution, and the soil nonlinearity has a non-negligible impact on the seismic resistance of such systems.Therefore, it is necessary to conduct further research on the SSSI system considering 3D model of the soil nonlinearity.
This study adopts shaking table experiments and numerical simulation research methods in the context of an actual project.The reliability of the numerical modeling is first verified through experiments, and the verified numerical models are then compared and analyzed to reveal the variation laws of the peak acceleration and internal force of the tunnel and bridge pile under different working conditions.
A preliminary and systematic study is conducted on the interaction law of the tunnel-soil-bridge pile structure system under the action of earthquakes.It provides a reference and guidance for studying the regularity of the seismic damage and can aid the structural design of bridge pile structures and underground tunnel structures.

Design of similarity ratio
For the choice of the model material, particulate concrete is generally used to simulate the elasticplastic seismic response of structures.However, Plexiglas was chosen in the test to consider the elastic seismic response law of the system.Plexiglass has the advantages of good homogeneity, high strength, and low modulus of elasticity (Chen et al.2016).The sandy soil was chosen as the model soil, with a density of 1614 kg/m3 and a shear wave velocity of 55 m/s 2 .The density of the Plexiglas is 1180 kg/m 3 , and the modulus of elasticity is 3 GPa.The corresponding similarity ratio of the density is 0.442, and the similarity ratios of the modulus of elasticity are 0.1 (bridge pile), 0.09 (mine tunnel), and 0.087 (shield tunnel).The similarity ratios between the physical quantities can be derived using Buckingham's law (Moncarz et al.1981).Table 1 presents the similarity ratios between the bridge piles and tunnels.

Model structure and instrumentation
Based on the actual engineering background and combined with the similarity ratio, a plexiglass model of the bridge pile and the tunnel was made and counterweighted.Considering the limited size of the model box and the boundary effect, the length of the tunnel was 0.7 m.The masses were added to the model surface structure and tunnel to meet the density similarity ratio, match the performance of the shaking table, and keep the acceleration and frequency similarity ratios within a reasonable range.After the calculation, masses of 120, 60, and 30 kg (Zhang 1997) were added to the bridge piles and the left and right tunnel structures, respectively.The acceleration was recorded using a Donghua power collector DH5922D, and the strain and earth pressure were recorded using a Donghua strain collector DH3817K.
Figure 3 shows the model, counterweight, and collector.

Test items and measurement point arrangement
The test was divided into two stages: free field (FF) and dual tunnel-soil-bridge piles (DTSP).Each stage includes the same seismic wave input, as shown in Figure 4.The time interval was determined by the original time interval of 0.02 s and a time similarity ratio of 0.183.Moreover, considering the ability of the shaker control system, a time interval of 0.00125 s was selected in the experiment.
In the experiment, the acceleration responses of the tunnel, the bridge piles, and the surrounding soil, the strain of tunnel lining, and contact pressure between the model structure and the surrounding soil were measured.The sensors used in the shaking table test included accelerometers, strain gauges,  The measuring points are mainly distributed on the side of the tunnel close to the bridge pile, pile body, and soil surface according to the law.The main focus is on the measurement points A19, A02, A07, A12, A11, and A06 at the upper and lower ends of the tunnel and bridge piles for comparison with the subsequent numerical simulation results.In addition, after testing, the tunnel structure was excavated, and it was found that there was no damage to the tunnel structure.At the same time, it was found that the tunnel monitoring strain was excessively small.Therefore, only the acceleration response of the structure is given in the following.
The transfer function method was used to measure the intrinsic frequency of the system during the experiments.In the transfer function method, the frequency response function (FRF) is defined as the ratio of the recorded acceleration time course to the input time course.Figures 6(a) and (b) show the transfer functions of A14 in the free field and A19 in the double tunnel-soil-pile in WN0.1g, respectively.

Numerical simulation
3.1 Scaled-down numerical simulation A numerical model of the shaking table test was established using the finite element analysis software AB-AQUS, as shown in Figure 7.The first-order intrinsic frequencies under the two working conditions were calculated using the material parameters given by the shaking table test and compared with the experimental results, as presented in Table 2. El-Centro wave, Taft wave, and Chichi wave ground vibrations were inputted to the free-field and tunnel-soil-bridge pile systems with reference to the shaking table test.To verify the reliability of the numerical model, the acceleration peaks obtained from the numerical simulation were compared with those recorded from the shaker test, as presented in Table 3, and the differences were found to be within 30%.Figures 8(a 3.2 Numerical simulation of the prototype

Division of finite element model cells and mesh
The size of the soil element is related to the cut off frequency.The smaller the component, the higher the frequency that can be included in the simulation.However, the number of cells also significantly affects the computational time, particularly in nonlinear implicit dynamic analyses.Typically, in seismic analyses, the upper limit of the cell length is determined by the minimum expected wavelength.In this 1.The input wave is EI, the acceleration amplitudes are 1.3 m/s 2 ; 2. The data in parentheses is the difference ratio.analysis, the length of the earth element in the vertical direction   is controlled by the following factors: where   is the wave length of the transverse wave,   is the cutoff frequency, which is 25 Hz, and   is the transverse wave velocity.In the horizontal direction, regardless of the traveling wave, the length of the earth cell   is limited to 5 times in the depth direction.
The solid unit C3D8 was used to simulate the soil and concrete.Notably, the concrete native model is elastic, and the only source of nonlinearity in this system is the soil model.The soil and structural concrete are modeled and meshed separately, and then assembled using the pre-built cell technique.Thus,

Equivalent viscoelastic ontology and implementation in software
For a long time, the equivalent linear method has been used in the seismic analysis of structures to approximate the nonlinearity of the seismic process, and the experimental studies have been based on the equivalent linear method given that the principle of the method is concise, and the equivalent linear method has been written into the seismic design codes (GB50909-2014).The equivalent linear method approximates the nonlinear characteristics of the soil using the stepwise iterative method, and since each iterative process is linear, its computational volume is small, and its computational efficiency is high, which can be sufficient to meet the demand of engineering calculations.
To simplify the method, the Kelvin model is chosen in this study to simulate the hysteretic properties of the soil under loading, and the hysteretic properties and energy loss of the viscoelastic model are reflected in the stress-strain relationship of the model.The Kelvin model is in the form of a linear elastic spring and a viscous pot in parallel, and the stress-strain relationship is as follows: where G is the soil shear modulus, and   is the coefficient of viscosity, and τ is the shear stress, and γ is the shear strain.Based on the experience of previous studies (Zhuang et al.2006), the following empirical equation is used to express the maximum shear modulus, as expressed in the following equation.
=   (  ′ /  )   (3) where   ′ denotes the circumferential pressure of the soil.  denotes the standard atmospheric pressure; k and n are the experimentally determined material parameters.The shear modulus ratio of the soil body /  and damping ratio D are the key parameters in the equivalent linear analysis.For sandy soils, this study uses the /   relationship curves as well as the D  relationship curves (Wang et al.1995;Iida et al.1996;Bing et al.2002;Schnabel et al.1972) for the equivalent linear calculation.Figure 11 shows the curves for the sandy soils.
This study borrows the idea of the 1D site response analysis, given an initial shear modulus and damping ratio, to calculate the maximum shear strain obtained from each calculation.The interpolation method is then used to determine the equivalent shear modulus ratio and damping ratio D corresponding to the equivalent shear strain /  .Through iterative calculations, the iteration ends when the material properties no longer change significantly, i.e., the site response analysis can reflect the seismic effects of the site more realistically, as shown in Fig. 12.
Figure 13 shows the distribution of the maximum shear strain of the cell with depth during each iteration.Since the damping ratio was not included in the first iteration process, the obtained shear strain was instead greater, but after four calculation iterations, the results of the third and fourth iterations were found to be similar.Therefore, the dynamic shear modulus ratio and damping ratio obtained from the results of the fourth iteration could be used for the formal calculation.Fourier spectra are plotted in Fig. 14.Fig. 15 shows the recorded 5%-damped acceleration spectrum.

Numerical results
In this section, the effects of different working conditions on the seismic response of this structural system are discussed.The interactions are analyzed mainly from two perspectives: acceleration and internal forces.The acceleration is used as the evaluation index of the dynamic response, while for the internal force distribution, the cross-sectional bending moment M, shear force FV, and axial force FN of the tunnel and bridge pile are selected as the evaluation.The analysis is compared by selecting the representative surface and cross-section of the soil or structure.

Modal analysis
The modal response is an important dynamic characteristic of a structure or soil-structure interaction system; it helps predict the seismic performance of the structure during an earthquake.The fundamental frequency of the tunnel-soil-bridge pile system is 1.8724Hz.Figure 16 shows the firstorder mode, where the structure experiences shear deformation.On the other hand, the theoretical value of the intrinsic frequency of the model soil can be determined as: Here,   is the nth-order intrinsic frequency,   is the shear wave velocity of the soil, and H is the thickness of the soil body.The first-order frequency is calculated using Eq. ( 4) to be  1 =1.878Hz, which is consistent with the modal analysis results.From the figure, it can be found that the peak acceleration near the bridge pile and tunnel is lower than that at the distant site, whereas the peak acceleration of the central soil is significantly increased under the influence of the bridge pile.Moreover, the main influence range of the structure on the site soil (100 m) is approximately 4-5 times the width of the structure (23.6 m).
Figure 18 shows the distribution of the peak acceleration along the excitation direction for the central section of the structural system under the eight operating conditions.The dashed line in the middle represents the position of the outer edge of the two tunnels.The comparative analysis reveals that.
When the tunnel or the bridge pile acts alone, (1) the presence of the tunnel reduces the dynamic response of the soil surface directly above, and the minimum point is located near the edge of the corresponding tunnel.However, as it moves away from the tunnel, the ground dynamic response is amplified and tends to decay gradually.
(2) The presence of the bridge pile significantly increases the dynamic response of the nearby soil and peaks at the junction between the soil surface and the bridge pile surface.As it moves away from the bridge pile, it shows a similar trend as the tunnel: first decreasing, then increasing, and finally decaying.
When considering the tunnel-soil-bridge pile interaction, compared with the free field, the analysis of the increase and decrease in the peak acceleration shows that (1) the DTS is greater than the MTS and the STS for both the increase and decrease, which indicates that the effect of the double tunnel on the site is more significant than that of the single tunnel and is closely related to the tunnel size and location.
(2) In terms of the amplitude of increase, the DTS is greater than the DTSP, the MTS is greater than the MTSP, and the STS is greater than the STSP, while the opposite is true for the amplitude of the decrease.This indicates that the tunnel plays an amplifying role on the dynamic response of the soil surface in the tunnel-bridge pile-soil structure system.(3) For the decreasing amplitude, the MTSP is greater than the MTS, and the STSP is greater than the STS, while the opposite is true for the increasing amplitude, the opposite is true.This indicates that the bridge pile has a decreasing effect on the dynamic response of the soil surface in the tunnel-soil-bridge pile structure system.From the figure, it is found that the peak of the combined moment (bending moment dominant) is at the central section, while the corresponding combined force (shear dominant) is zero, which is in accordance with the differential relationship between the bending moment and the shear force.Both the combined force and the combined moment are along the direction of seismic excitation; therefore, the tunnel will bend along the excitation direction and produce a shear deformation.ends of the tunnel.When bridge piles are present, the peak bending moment remains at the center tunnel section, while the peak shear force is located near the outer edge of the bridge piles from the ends toward the center.

Bridge pile peak internal force distribution and comparative analysis
Figure 26 shows the spatial distribution of the internal forces at the moments corresponding to the peak seismic waves for different sections of the bridge pile under case 3. The direction of the combined force in the figure is downward, indicating that the axial force plays a dominant role and that it is significantly greater than the shear force.The bending moment direction makes the bridge pile to bend along the excitation direction, which is consistent with the tunnel.The peak joint moment of the bridge pile appears at approximately 1/4 of the lower end of the pile, and the peak axial force is located at the pile-soil interface.
Figure 27 shows the peak internal force curves of the bridge pile under different working conditions.
As the upper part of the bridge pile exerts a high concentrated load, resulting in a high axial force of the bridge pile, an axial force analysis was conducted in addition to the shear force and bending moment analyses.
The following results are obtained from the analysis:(1) Both the mine and shield tunnels increase the shear force and bending moment values of the bridge piles, with little effect on the axial force, and the magnitude of the increase in the internal force of the tunnel acting on the bridge piles is related to the distance between the tunnel and the bridge piles.The peak axial force appears at the pile-soil interface, while the shear force and bending moment appear at the lower end of the bridge pile.
(2) The internal force at the interface between the bridge pile and the soil has extreme values, and the presence of the tunnel shifts the extreme point upward.

Conclusions
In this study, the dynamic and internal force interaction mechanisms between the components of multistructure system were investigated.A finite element model of the multistructure system was established using the ABAQUS software and verified by conducting a shaking table test.The variation In the comparative analysis, a numerical calculation work was conducted by inputting three ground shocks.The main conclusions are as follows: (1) Tunnels and bridge piles have opposite acceleration effects on other structures in the system.
The tunnel amplifies the acceleration responses of the adjacent bridge piles, tunnel, and far while the bridge piles attenuate the acceleration response of the lateral tunnel penetration.
(2) The effects of the tunnel and bridge piles on the acceleration of the site are different: the tunnel amplifies the acceleration response in the far field and slightly reduces the dynamic response in the near field, while the presence of bridge piles significantly increases the acceleration response in the near field, but plays a weakening role on the acceleration in the far field.The analysis conducted in terms of the degree of influence showed that when the tunnel-soil-tunnel interaction is considered as a whole, it will cause a significant variation in the acceleration response in the site, with an influence range 4-5 times the width of the entire structure.
(3) The tunnel and bridge piles have similar effects on the internal forces of the other structures in the system.They increase each other's shear force, bending moment, and axial force to some extent, with the peak force often appearing in the local area where the tunnel and bridge pile meet.Notably, the internal force of the bridge piles at the pile-soil junction has extreme values, and the presence of the tunnel shifts the extreme points upward.
Based on the study results, there are complex and non-negligible dynamic interactions between the tunnel, soil, and bridge piles.Therefore, it is necessary to model and calculate this complex system in 3D refinement before proceeding with the structural design.The above analysis can provide a reference for the seismic design of underground structures and for determining the most unfavorable distribution of the dynamic and internal forces in this system.
To further discuss the SSSI issues, the following aspects are worth considering: Elastic-plastic or damage models of the structural materials to explore their damage during earthquakes; considering the influence of the soil layer distribution, the soil layers can be horizontally and vertically refined to explore the impact of different soil layers.This paper only reported on the unidirectional consistent ground motion input; future research can consider the two-way ground motion input, three-way input, and nonuniform input.
Taking the standard diameter shield section of the interval between Dalian Railway Station Station-Soyuwan South Station in China at a mileage of YK9+642.835 as the background, the planar relationship between the tunnel and the express rail line 3 and the cross-sectional relationship between the tunnel and the express rail line 3 are shown in Figs.1(a) and (b).A series of shaking table tests were designed on this basis.

Fig. 1
Fig. 1(a) Plane relationship between tunnel and fast rail line 3 Fig.1(b) Cross-sectional relationship between tunnel and fast rail line 3

Fig. 5
Fig. 5(a) Schematic of sensor arrangement for FF shakingtable model test
) and (b) show the acceleration-time course and Fourier spectra of the A02 and A19 sensors under DTSP, respectively.The Fourier amplitude spectrum results shown in Fig. 8 are normalized to a value equal to the data divided by its maximum value, as shown in Figs.9(a) and (b).The numerical calculation results are in good agreement with the experimental results.
the material properties of the soil and concrete are modeled separately, and the cell sizes are controlled separately.The numerical simulations of the proto type model are performed in a total of eight stages, as listed in Table 4.The case 5, case 7, and case 3 finite element discretizations are shown in Fig. 10(a) with 148,872,196,720, and 217,704 finite elements, respectively, where the details of case 3 are shown in Fig. 10 (b).

Fig
Fig. 10(b) Details of the DTSP

Fig. 16 .
Fig. 16.First vibration mode of the system

Figure 20 Fig. 19 .Fig. 20 .
Figure20shows the peak acceleration curves in the polar coordinates for the central section of the shield and mine tunnels under different working conditions.Since the difference in the peak acceleration variation at the different tunnel locations and conditions is less relative to the tunnel diameter, the scale near the origin is reduced in the figure for a clearer comparative analysis.The analysis reveals the following:(1) The peak acceleration curve values of the MTSP and STSP are lower than that of the shield and mine tunnels alone, which indicates that the bridge pile decreases the dynamic response of the nearby tunnels.(2) The peak acceleration curve values of the DTS are all greater than those of the shield and mine tunnels alone, which indicates that the tunnel increases the dynamic response of other nearby tunnels.(3)The peak acceleration curves of the DTSP are closer to the curves of the shield and mine tunnels alone than the above two cases, and whether they increase or decrease is related to the position relationship and distance between each component.

Figure 22
Figure22shows the local distribution curve of the peak acceleration along one side of the bridge pile under the different working conditions.Because the tunnel mainly affects the lower end of the bridge pile, and the peak acceleration velocity gradually tends to be the same as that away from the tunnel under different working conditions; therefore, only the local area of the lower end of the pile is taken in the figure for a clearer comparative analysis.From the figure, it can be found that: (1) the peak acceleration of the MTSP, STSP, and DTSP are all greater than the SP, which indicates that the tunnel amplifies the dynamic response of the bridge pile.(2) The DTSP is greater than the MTSP, which is greater than the STSP.This indicates that the amplification of the peak acceleration of the bridge pile due to the tunnel is closely related to the distance between the tunnel and bridge pile and the size of the tunnel.

Figures 24 andFig. 24 .Fig. 25 .
Figures 24 and Figure25show the peak internal force curves of the mine and shield tunnels under different working conditions, respectively.Since the shear force and bending moment play a dominant role for the tunnel, and only the influence along the direction of seismic excitation is considered.No analysis of the tunnel axial force, torque, and other directions of the shear force and bending moment is performed.The comparative analysis reveals that: (1) The presence of other tunnels near the tunnel will slightly reduce the value of its own shear force and bending moment.(2) Bridge piles significantly amplify the shear and bending moment values of nearby tunnels.(3) When there is no bridge pile, the peak bending moment occurs at the center section of the tunnel, and the peak shear force occurs at the

Fig. 26 .
Fig. 26.Spatial distribution of the internal force at the bridge pile section (Case 3)

Table 1
Similarity ratios of the model structure and tunnel.

Table 2 Comparison
between numerical and experimental results of the natural frequency.

Table 3
Comparison of numerical and test results in the peak response accelerations (unit: m/s 2 )