Seismic Response of a Bridge Pile Foundation during a Shaking Table Test

Puqian Bridge is located in a quake-prone area in an 8-degree seismic fortification intensity zone, and the design of the peak groundmotion is the highest grade worldwide. Nevertheless, the seismic design of the pile foundation has not been evaluated with regard to earthquake damage and the seismic issues of the pile foundation are particularly noticeable. We conducted a large-scale shaking table test (STT) to determine the dynamic characteristic of the bridge pile foundation. An artificial mass model was used to determine the mechanism of the bridge pile-soil interaction, and the peak ground acceleration range of 0.15 g–0.60 g (g is gravity acceleration) was selected as the input seismic intensity..e results indicated that the peak acceleration decreased from the top to the bottom of the bridge pile and the acceleration amplification factor decreased with the increase in seismic intensity. When the seismic intensity is greater than 0.50 g, the acceleration amplification factor at the top of the pile stabilizes at 1.32. .e bedrock surface had a relatively small influence on the amplification of the seismic wave, whereas the overburden had a marked influence on the amplification of the seismic wave and filtering effect. Damage to the pile foundation was observed at 0.50 g seismic intensity. When the seismic intensity was greater than 0.50 g, the fundamental frequency of the pile foundation decreased slowly and tended to stabilize at 0.87Hz. .e bending moment was larger at the junction of the pile and cap, the soft-hard soil interface, and the bedrock surface, where cracks easily occurred..ese positions should be focused on during the design of pile foundations in meizoseismal areas.


Introduction
Earthquakes are natural disasters with great destructive power. Considerable damage to pile-supported bridges has been observed in many earthquakes worldwide, especially in China, where nearly 50% of the land is located in seismic fortification intensity zones that exceed 7 degrees; the earthquake intensity zoning map of China is shown in Figure 1. In recent decades, large-span bridges with high bearing capacity and excellent seismic performance have been designed for use in meizoseismal areas, but the damage has occurred to these bridges. Seismic damages include not only the failure of the upper structure, such as girder failure, support failure, and bridge pier slip but also the occurrence of concrete cracks and ring cracks of the pile and even complete failure after earthquakes, which are shown in Figure 2 [1]. Once the pile foundation is damaged, the entire bridge poses a safety risk. e mechanical behavior of pile foundations subjected to kinetic forces has been investigated experimentally and numerically by many researchers. Mylonakis et al. [2] proposed a substructuring method for the seismic analysis of bridge piers supported on vertical piles and pile groups in multilayered soil. Haeri et al. [3] studied the response of a group of piles subjected to liquefaction-induced lateral spreading caused by liquefaction by using large 1 g shaking table test and proposed a simple numerical method to predict the behavior of single piles under lateral spreading. Montejo et al. [4], Mostafa and Naggar [5], and Naggar and Gazetas [6] proposed a seismic deformation method (SDM) to assess the seismic performance of pile foundation of buildings based on the inertial interaction between the pile, the soil, and the structure. Boulanger et al. [7] evaluated the dynamic beam on a nonlinear Winkler foundation analysis method for analysing seismic soil-pile-structure interaction based on a series of dynamic centrifuge model test results. A seismic evaluation of pile foundations was conducted using three di erent methods based on a 3D elastic-plastic nite element analysis [8,9]. Di Laora and Rovithis [10] investigated the dynamic characteristics of the pile by simplifying the Winkler foundation beam model and putting forward the concept of the e ective length of the pile foundation and conducted a theoretical calculation of the liquefaction at the site. A shaking table test (STT) is commonly used to study the characteristics of piles embedded into di erent types of soil. Suzuki et al. [11] conducted a large-scale STT to investigate the factors in uencing the stress distributions of pile groups during earthquakes in dry sand. Dungca et al. [12], Yao et al. [13], and Motamed and Towhata [14] conducted an STT to study the dynamic behavior of pile foundations during liquefacation. Shirato et al. [15] and Ecemis [16] conducted a large-scale STT and numerical simulation on the nonlinear behavior of pile groups subjected to lateral loading during a very large earthquake. Most researchers have mainly focused on the dynamic response during soil liquefaction and soft soil foundation [17][18][19][20][21][22][23][24]. However, few studies have been conducted on the response characteristics of a bridge rock-socketed pile foundation for di erent seismic intensities. erefore, it is essential to research the seismic response characteristics of a large-diameter rock-socketed pile foundation.
In this study, an arti cial mass model was used to determine the dynamic response of rock-socketed pile foundations for a seismic intensity range of 0.15 g-0.60 g using a large-scale STT and the inertial soil-pile interaction mechanisms were investigated. e results of this research provide  guidance and technical support for engineers who work in practice.

General Project Information
e Puqian Bridge, which crosses Puqian Bay in the northeast of Hainan province in China, is a bridge linking Wenchang City with Haikou City. e bridge site is located at the epicenter of the Qiongshan earthquake that occurred in 1605 and had a Richter magnitude of 7.5. e area is seismically active with multiple faults and active faults and is the site of frequent earthquakes. e seismic forti cation intensity of the bridge site is 8 degrees, and the peak ground acceleration that has a 10% (2%) probability of being exceeded in 50 years is 0.35 g (0.59 g). e peak ground acceleration exceeds the upper limit of the acceleration response spectrum of the horizontal design for a bridge provided in Section 5.2.2 of the Speci cation of Seismic Design for Highway Engineering (JTG B02-2013) [25]. e potential damage to the pile foundation as a result of seismic events is relatively high.
Four piles of reinforced concrete (RC) with a cap numbered 38# were selected as prototype piles; the details were as follows: the piles were end-bearing piles, 2.4 m in diameter, 54 m in length, the pile spacing was 5.5 m, and the cap dimension was 9.2 m (length) × 9.2 m (width) × 3.0 m (height). e soil layers at the pile site from top to bottom were 14 m of mucky clay, 10 m of coarse sand, 22 m of gravelly soil, and 6 m of lightly weathered granite. Table Test is study was conducted using shake table facility of the earthquake engineering and engineering vibration laboratory at the Institute of Engineering Mechanics (IEM), China Earthquake Administration. IEM shaking table is a 5 m × 5 m, 3DOFS facility, capable of taking vertical loads up to 300 kN. e maximum horizontal acceleration of the shaking table was 1.0 g, the maximum vertical acceleration was 0.7 g, and the vibration frequency ranged from 0.1 Hz to 50 Hz.

Model Box.
Considering the operability of the STT, a laminate shear model box was used to investigate the dynamic response of the pile foundation. e dimension of the box was 3.7 m (length) × 2.8 m (width) × 2.0 m (height), as shown in Figure 3. e seismic response of the free eld was simulated by using a shaking table to reduce the error of peak acceleration of the soil layer, the waveform, and the Fourier amplitude spectrum. Boundary condition in this study is of low degree of importance. When the length of the laminate shear model box is no less than 2 m and the width is no less than 1.5 m, the frequency deviation in the STT is ±5% and the in uence of the height of the box can be ignored [26].

Scaling Factors.
e test materials were selected from the prototype materials used in the actual construction of the Puqian Bridge. e key parameter to characterize the reliability of the results of the STT is the dynamic similarity between the parameters of the model and the prototype. In this study, all required material properties of the physical model were scaled using similitude law suggested by Iai et al. [27]. Structures are usually scaled down to a smaller size [28,29]. Considering the dimensions of the laminate shear model box, a geometric scale of λ 30 was used. Based on the actual bearing capacity of the vibrating table and the similar conditions of the arti cial mass [30,31], the required payload capacity was 100 kg. Table 1 summarizes the scaling factors applied in this study. Figure 4 shows the schematic cross section of the physical model along with the general layout of transducers. As seen in this gure, the physical model consists of four piles with a cap. Before the soil stratum was constructed, the piles were connected to the base to achieve a xed base condition. e material of the model piles and cap was concrete C35 and the reinforcement ratio of the model pile was 2.4%; a steel bar (HPB235 type) with a diameter of 4 mm was used. e physical parameters of the pile are listed in Table 2, and the model pile is shown in Figure 5.

Model Piles.
e model was instrumented with sensors on the pile such as strain gauges, accelerometers, and a displacement gauge. Among them, strain gauges were attached to the pile to measure the bending strain. In this test, 18 strain gauges are evenly arranged on the left and right sides of the pile, mainly at the interface between the middle of each soil layer and the soil interfacial. 5 accelerometers are located on the side of the pile, mainly at the interface between the middle of each soil layer and the soil interfacial. A displacement meter is arranged at the top of the pile. In total, 24 channels of data were recorded during this test.

Physical Properties of Soil Layer.
e ground in the model consisted of a 47 cm thick mucky clay layer, a 33 cm thick coarse sand layer, and a 73 cm thick pebble layer, overlying a 40 cm bedrock. Based on the geological survey data of the bridge, the shear wave velocities of the soil layers were determined to ensure the similarity between the actual   Table 3. e shear wave velocity of the model soil is controlled by the shear wave velocity method to make it consistent with the shear wave velocity of the prototype soil. e method is to place an accelerometer in the lower part of the closed container, and then ll the test soil into the closed container. By lifting the tamping hammer to a xed height of 30 cm, the accelerometer is placed on the top of the model soil after the xed number of compaction, as shown in Figure 6. Hit the bottom of the closed container with an iron rod; two accelerometers were used to collect the acceleration response at the same time, and the shear wave velocity of model soil was measured by the following equation where Δt is the time di erence between the peak acceleration of vibration wave propagating from the bottom of the soil layer to the top of the soil layer and Δh is the distance of        of exceedance in 50 years) was selected as the ground motion in the STT. e matching software SEISMO-SIGNAL was used to lter and calibrate the seismic wave. e seismic wave was scaled down to ensure that its peak value was in the range of 0.15 g to 0.60 g with an increment of 0.05 g in a constant waveform. Figure 10 shows the 0.35 g seismic wave.

Pile Acceleration Response.
e distribution of the maximum acceleration and ampli cation factor of pile along the length for di erent seismic intensities are shown in Figure 11. e acceleration ampli cation factor α (shown in equation (2)) is the ratio of the maximum acceleration of pile (a pile max ) and the input maximum acceleration (a input max ): As can be seen from Figure 11, the distribution of the maximum acceleration and ampli cation factor along the     length of the pile shows a similar variation law under different seismic intensities, and the acceleration and amplication factor increases from the bottom to the top of the pile for di erent seismic intensities. e distribution curves have turning point at the pile length 54 cm (ACC4) in the mucky clay layer, and the maximum acceleration and magni cation factor of this point are smaller than those of the adjacent upper and lower soil layers, which may be related to the characteristics of the soil. Although the strength of each soil layer decreases from bottom to top, mucky clay has larger void ratio and water content than other soil layers.
e maximum acceleration at the bottom of the pile is close to the values of the seismic intensity, and the amplication factors at the bottom of the pile are less than 1.1. e maximum acceleration at the top of pile is larger, and the ampli cation factor is more than 1.3. It shows that under di erent seismic intensities, ampli cation e ect of the gravel layer and coarse sand layer on the acceleration is evident, while the ampli cation e ect of mucky clay on the acceleration is weakened, indicating that the weak soil layer can absorb a certain amount of seismic wave energy and the bedrock has a signi cant embedded e ect on the pile. As the seismic intensity increased from 0.15 g to 0.60 g with an increment of 0.05 g, the maximum acceleration of the pile increased rapidly. From the bottom to top, the total increases of maximum acceleration of ACC1∼ACC5 were 257.3%, 173.6%, 124.9%, 141.1%, and 121.8%, respectively. On the contrary, the ampli cation factor decreases with the increase of seismic intensity and changes little when the seismic intensity is greater than 0.50 g. It is deduced that with the increase of seismic intensity, the shear strain of soil increases, the sti ness modulus decreases, the damping ratio increases, and the ampli cation factor decreases. In addition, the foundation soil tends to become denser under continuous seismic vibration, which also reduces the seismic ampli cation e ect to some extent.
Taking the pile top data as an example (Figure 12(e)), as the seismic intensity increases, the acceleration at the top of the pile increases linearly, whereas the ampli cation factor decreases. When the seismic intensity increases from 0.15 g to 0.60 g, the maximum acceleration increases by 20 When the seismic intensity is greater than 0.50 g, the acceleration ampli cation factor at the top of the pile stabilizes at 1.32.
is occurs because the ability of soil to transmit seismic waves decreases with increasing seismic intensity.
e ampli cation factor of the pile decreased gradually due to the combination of lateral thrust and inertial forces of the rock or soil.
Time histories of pile acceleration for 0.35 g seismic intensity are plotted in Figure 13. As it can be observed in this gure, the peak of the acceleration at di erent depth lags behind from the bottom of the pile to the top of the pile and the amplitude of acceleration records present di erent laws. e acceleration amplitude at the bedrock near the bottom of the pile is close to the amplitude of the input seismic intensity. e acceleration record at the gravel layer (ACC2) shows signi cant ampli cation relative to the base motion because of its high shear strength.
e amplitude of pile acceleration in the coarse sand layer is similar to that in the gravel layer. e shear strength of the upper mucky clay layer is low, but the water content is high and it is in a semi uid state, which has an obvious ltering e ect on seismic waves. erefore, the acceleration amplitude of the pile in this layer Shock and Vibration 7 is slightly reduced. In addition, each layer has a relatively small in uence on the frequency of the seismic waves. e acceleration amplitude of the pile top is larger than that at other points and the acceleration frequency is lower than that at other points, which is related to the absence of soil constraints around the top of the pile.   Figure 14 shows the maximum relative horizontal displacements at the top of the pile for di erent seismic intensities from 0.15 g to 0.60 g. As the seismic intensity increases, the maximum relative displacement at the top of the pile increases approximately linearly. e maximum relative displacement ranges from Shock and Vibration 9 1.97 mm to 6.73 mm as the input seismic intensity increases from 0.15 g to 0.60 g.

Bending Moment of the Pile.
In order to evaluate the bending resistance of the pile, the exural capacity of the pile foundation was calculated according to the Speci cation of Design for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. (JTGD62-2018) [32], and the value was 168.54 kN·m (shown in Figure 15). e bending moment of the pile is shown in Figure 16. As the seismic intensity increases, the maximum bending moments of the pile increase gradually. e maximum bending moment occurs at the boundary between the mucky clay layer and the coarse sand layer.
ere is also an increase in bending moment between the bedrock and the gravel. It shows that the bedrock has a strong embedded e ect on the pile. At seismic intensities of 0.15 g-0.45 g, the surplus exural capacity of the pile foundation is 7.8%∼63.0%, while at seismic intensities greater than 0.50 g, the maximum bending moments of the pile exceeded the exural capacity by 13.5%∼ 81.2%. e results indicate that the seismic design of the pile foundation in the Puqian Bridge is appropriate for the seismic forti cation intensity of 8 degrees (0.35 g): where M ud is the design value of exural capacity of normal section (kN·m), A is the circular section area (m), A s is the cross-section area of all longitudinal ordinary steel bars (m), f cd is the design value of axial compressive strength of concrete (kN/m 2 ), f sd is the design value of tensile strength of ordinary steel bar (kN/m 2 ), r is the radius of a circular section (m), r s is the radius of the circumference, where the center of gravity of the longitudinal ordinary steel bar is located (m), α is the ratio of rad to 2pi corresponding to the area of concrete section in the compression zone, and α i is the ratio of the section area of the longitudinal tension common steel bar to that of all longitudinal ordinary steel bars. When α i is greater than 0.625, α i is 0.

Analysis of Pile Damage.
e Fourier spectrum of the pile is shown in Figure 17. e pile foundation was not damaged at a seismic intensity of 0.35 g. erefore, the damage of the pile foundation was analyzed only when the seismic intensity exceeded 0.35 g. e fundamental frequency of the pile foundation decreases as the seismic intensity increases; at a seismic intensity of 0.50 g, the decrease in the fundamental frequency is 49.7% ( Figure 18). Figure 18 shows that when the seismic intensity is greater than 0.50 g, the pile foundation is being damaged, and the fundamental frequency of the pile foundation decreases slowly and tends to stabilize at 0.87 Hz.
At the end of the test, the model pile was taken out and observed, and it was found that the cracks appeared near the junction of the top of the pile and cap and at the interface of the soft and hard soil and the bedrock, as shown in Figure 19.

Back-Calculaction of p-y Curves.
A p-y curve de nes the relationship between the lateral soil pressure and the pile displacement, which is widely used in the analysis of soil-pile interaction problems. In order to further study the interaction between the pile and the laterally spreading soil in this study, p-y curves were back-calculated according to the recorded bending moment data. e relationship between the lateral soil pressure, the pile displacement, and the bending moment of the pile can be expressed by the following equations: In the above equations, M(z) is the bending moment of pile, y(z) is the horizontal displacement of pile, and p(z) is the lateral soil pressure on the pile due to lateral spreading, all at depth z. e lateral pressures should be determined by double di erentiation of bending moment data; however, double di erentiation procedure is associated with potential numerical errors. Di erent methods have been proposed to reduce or eliminate this error in order to obtain soil pressure  from discrete moment data points [33]. In this study, according to the principle of the weighted residual method proposed by Wilson et al. [34], the strain gauge attached to the pile body is taken as the separation node to divide the pile body into several elements. Let f(z) be the bending moment function along the depth distribution, and the value of f(z) at the node can be obtained from the strain gauges' recording data. Let g(z) f ′ (z), so that g(z) is a shear function along the depth distribution. According to the principle of the weighted residual method, the following equation is obtained: At the depth of 153 cm, it can be seen that the displacement of the pile decreases obviously, indicating that the soil has a strong restraint e ect on the pile and provides a greater resistance to the pile. For irregular seismic waves, the analysis of pile-soil interaction by p-y curve seems to be inconvenient.
For the model test in this research, the law of similitude was applied. Due to the limitation to scale down the modulus and shear wave velocity of the sand specimen, the law of similitude was only partially ful lled in this study. However, the strain ratio of the model and prototype was not a ected and the use of the strain to characterize the pile behavior appeared to be reasonable. e responses and ampli cation of the model test appeared to re ect the behavior of the prototype pile under seismic loading conditions reasonably well.

Conclusions
Based on the arti cial mass model and the pile-soil inertia interaction in the STT, the dynamic response of the pile foundation was analyzed for seismic intensity ranging from 0.15 g to 0.60 g. e following conclusions were drawn.
(1) e peak acceleration of the pile increased along the length of the pile. e overburden layer ampli ed the seismic wave, and the acceleration ampli cation factor at the top of the pile gradually decreased with increasing seismic intensity. When the seismic intensity is greater than 0.50 g, the acceleration ampli cation factor at the top of the pile stabilizes at 1.32. (2) e bending moment of the pile increased with the seismic intensity and exhibited a "3" shape along the pile length, reaching the maximum near the softhard soil interface and bedrock surface. In the seismic intensity range of 0.15 g to 0.45 g, the maximum bending moment did not exceed the exural capacity. e seismic design of the Puqian Bridge pile foundation is appropriate for the seismic forti cation intensity of 8 degrees (0.35 g). (3) e fundamental frequency decreased with increasing seismic intensity. When the seismic intensity was greater than 0.50 g, the fundamental frequency of the pile decreased significantly and the pile began to develop crack damage at the junction of the top of the pile and the cap, the soft-hard soil interface, and the bedrock surface. (4) In the seismic design of bridge pile foundations, the pile should be embedded in stable bedrock at a certain depth and greater focus should be placed on the seismic design of the joint at the top of the pile and the cap, the soft-hard soil interface, and near the bedrock surface. (5) With the increase of seismic intensity, the horizontal displacement of pile increases obviously, but the lateral soil pressure is irregular. e influence of seismic intensity on the horizontal displacement of the pile is greater than that on the lateral soil pressure.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.