Underwater Shaking-Table Investigation of Complex Deep-Water Pile-Cap Foundation for Xihoumen Rail-cum-Road Bridge

. To study the mechanical characteristics of complex pile-cap foundations and the distribution law of hydrodynamic pressure acting on piles and cap in deep-water environments, the 60m deep-water pile-cap foundation of Xihoumen rail-cum-road bridge was considered for this investigation. Tis paper focused on introducing the design and implementation process of simulating an earthquake using an underwater shaking-table test for a 1: 60 complex pile-cap foundation model and systematically summarizing the test results. Te test results showed that water reduced the acceleration of complex pile-cap foundation; however, the strain, displacement, and hydrodynamic pressure increased in varying degrees with water depths, and the maximum strain of the piles increased by 13.8% for the X -direction earthquake excitation and 15.1% for the Y -direction earthquake excitation in 1.0m water-depth environment. Te strain of the corner pile was the largest under earthquake excitation, followed by that of the front-row pile, and the strain of the middle pile was the smallest. When the water depth was 1.0m, the maximum strain diference of each pile in the X - and Y -directions reached 26.4% and 27.5%, respectively. Te hydrodynamic pressure acting on the piles decreased gradually from bottom to top, the edge pile bore more hydrodynamic pressure than the middle pile, and the hydrodynamic pressure diference between the piles reached 20%. Owing to the infuence of the round-ended cap, the hydrodynamic pressure suddenly increased at the cap position, and the distribution law of the cap showed a gradually declining trend from front to side; however, the attenuation amplitude was afected by its shape.


Introduction
An increasing number of coastal and ofshore engineering structures, such as cross-sea bridges, ofshore oil platforms, wharfs, and wind-power towers, are being constructed in deep water. Te loads from deep-water environments are extremely complex; hence, when exploring the problem of structure-water coupling under earthquake excitation, most current research has focused on theoretical analysis and numerical calculation [1][2][3]. However, the hydrodynamic pressure and fuid-structure coupling of deep-water structures are arduous to simulate [4,5]. Based on diferent understandings of fuid-structure coupling between underwater structures and surrounding water bodies under earthquake excitation and the selection of calculation model parameters, the research results obtained by diferent researchers are often dissimilar [6][7][8]. Because of the sudden occurrence of earthquakes and the complexity of feld tests in deep-water environments, it is impossible to conduct feld research. Terefore, the underwater shaking-table test of scaled models is still considered a reliable and direct research approach that satisfes a similarity ratio relationship [9,10].
Many studies have used the shaking-table test to obtain the dynamic response of structures, particularly complex or underwater structures. Hazarika et al. [11] conducted a series of large-scale underwater shaking-table tests on waterfront structures, and the experimental results identifed that the seismic load against the caisson quay wall could be substantially reduced by a cushioning technique of using the tire chips cushion; in addition, the presence of the protective tire chip cushion could signifcantly reduce the earthquakeinduced residual displacement of the caisson quay wall. Haddad et al. [12] performed shaking-table model tests to evaluate liquefaction hazards to the behavior of ofshore wind turbines, and the results identifed the two controversial mechanisms controlling shear-induced caisson settlement; the liquefaction-induced bearing capacity failure as the skirt length of suction caisson increases, whereas the larger net excess pore-water pressures in suction caisson contribute more signifcantly to reducing seismic demand on wind turbine. At present, underwater shaking-table tests of bridges are less frequent, and the test objects are mostly single pier structures or simple pile-cap foundations [13,14]. Li et al. [15] conducted a series of shaking-table tests on four circular steel tubes with diferent diameters, and the main purpose was to determine the inertial coefcient in the Morison equation. Te test results showed that the hydrodynamic added mass increased with steel tube diameters and water depths, and a method to calculate the hydrodynamic added mass under the real earthquake was proposed. Huang and Li [16] studied the seismic response of a rectangular bridge pier in diferent water depths, and the research results indicated that the hydrodynamic pressure efect on the seismic response of bridge piers increased with the increase of the relative water depth; when the water depth was 80% of the pier height, the stress of the pier bottom increased by 21%, and the relative displacement of the pier top increased by 22.4% than that without water. Song et al. [17] performed a pile-cap foundation test on the south pier of the third Nanjing Yangtze River Bridge, the experimental results showed that the maximum acceleration in water increased 20% to 40% than that without water under diferent seismic waves, and the maximum displacement and strain increased 10% to 20% accordingly. Limited by the test conditions, the test model and water tanks were connected in the abovementioned test. Although some rules can be obtained, the study still has signifcant limitations. Liu and Sun [18] studied the natural frequency of concrete pile-cap foundation using the submerged shaking-table system, and the results showed that the natural frequency of pile-cap foundation model decreased by 9.1% in water than that without water. Lai et al. [19] conducted an underwater shaking-table test of a pile-cap foundation according to the approach bridge of the Pingtan Strait Bridge, the results of test shows that compared to that without water, the natural vibration frequency of the model in water was reduced by 2.6%, and the maximum strain at the bottom of the pile increased by 3.0% under Tianjin earthquake and 7.0% under Loma Prieta earthquake, respectively. Te layout of the piles was 2 × 2, and the simulated maximum water depth was 30 m. Te test results identifed that the water would change the dynamic characteristics and the responses of submerged bridge pier with pile foundation. Nevertheless, both the structural form and water depth were clearly diferent from those of the complex pile-cap foundation at a water depth of 60 m investigated in this study. Liu et al. [20] conducted an underwater shaking-table test of a 1 : 100 scale pile-cap foundation using eight piles instead of all piles, the experimental results indicated that the natural frequency of the tower of cable-stayed bridge in deep-water environment was reduced by 1.7% than that without water, hydrodynamic pressure efect increased the dynamic response of the model, and its magnitude was related to structural form. Although a smaller similarity ratio was adopted in the test and the form of the simplifed pile-cap foundation was relatively simple, it has certain reference signifcance for exploring the dynamic responses of deep-water pile-cap foundations under earthquake excitation. Previous studies mentioned above have shown that bridge pier foundation built in water responds diferently than that without water under seismic excitation.
At present, pile-cap foundations are widely used in deepwater bridges [21], but the diameter of the piles is generally within 4.5 m and there are no actual engineering cases for water depths exceeding 45 m; there are limited underwater shaking-table tests of the pile-cap foundation of deep-water bridges based on a particular engineering feld. Most structural models in existing tests are single and simple, and the simulated water depth is less than 45 m. Tere are almost no test reports that systemically investigate the efects of deep-water action on seismic responses and the distribution law of hydrodynamic pressure along the height of complex pile-cap foundation under earthquakes, particularly for complex pile-cap foundations with four or more rows of piles in deep-water environments. Moreover, almost no relevant experiments have been found to investigate the distribution law of hydrodynamic pressure on large-sized caps.
In practical projects, pile-cap foundations of deep-water bridges are mostly large in scale and typically have a relatively complex structure. As the largest span highwayrailway joint bridge under construction in the world, the total length of the Xihoumen rail-cum-road bridge of the Ningbo-Zhoushan Railway is 2664 m. Fifth pile-cap foundations on the main bridge were built in a 60 m deep-water environment, as shown in Figure 1. Te cap is round-ended with an overall dimension of 68 × 46.4 × 10 m, the diameter of eighteen piles is 6.3 m, and it is the largest bridge grouting pile in the world. Eighteen ultra-large-diameter piles are rock-socketed piles, and there is basically no soil covering layer on the seabed. Te length of eighteen piles from the seabed to the cap is 54 m. Te solid concrete used for the piles and cap was C45 marine concrete with a density of 2550 kg·m −3 and an elastic modulus of 3.35 × 10 4 MPa. Te seismic-peak ground acceleration of the site was 1.352 m·s −2 , corresponding to a 1 : 50 year event with a probability of exceedance of 10%, based on basic ground motion data.
For the abovementioned 60 m deep-water pile-cap foundation of Xihoumen rail-cum-road bridge, pile-cap foundation with 6.3 m super-large-diameter pile is frst applied to the practical engineering for water depths exceeding 60 m, and its scale and complexity are far more than previous pile-cap foundations of other sea-crossing bridges. Owing to its large dimensions, complexity, and signifcant three-dimensional characteristics, it is difcult to accurately simulate the dynamic response of complex deep-water pilecap foundation under the earthquake excitation by using existing theory. In view of the research defciency of complex pile-cap foundation in deep water, particularly for the Te dynamic scale-model test of fuid-structure coupling problems has more complex mechanical properties than ordinary dynamic tests. On the one hand, the model generates internal forces under shaking-table excitation; on the other hand, the surrounding fuid domain generates a restoring force on the model motion. Terefore, the characteristics of the structural model and fuid should be comprehensively considered when designing the structural model. According to previous studies [22,23], the dynamic scale-model test of fuid-structure coupling problems mainly followed the structure dynamic similarity and fuid similarity criteria, which typically include Euler similarity criterion and Froude similarity criterion. According to the similarity theory and reference [22], the main similitude criteria are described in equations (1)-(3).
(1) Structure dynamic similarity criterion: (2) Froude similarity criterion: (3) Euler similarity criterion: where M i is the similarity ratio of the physical quantities defned as S i � i mod /i pro . i mod and i pro represents the physical quantities of the test scale model and the prototype structure, respectively.  Figure 1: Layout of 60 m deep-water pile-cap foundation of Xihoumen rail-cum-road bridge.
Shock and Vibration 3 pressure, respectively. It is noted that the similarity ratio of the gravitational acceleration is 1.0, and the similarity ratio of the geometric dimensions is determined to be 1 : 60, which is limited by the maximum test water depth. Te values of these two parameters are frst determined and difcult to change.
To meet the structure dynamic similarity and fuid similarity criteria, it is assumed that there is an ideal material with an elastic modulus E � 558.3 MPa and a density ρ � 2550 kg/m 3 , that is, elastic modulus similarity ratio S E � 1 : 60 and density similarity ratio S ρ � 1.0. All the above similarity criteria can be well satisfed. At the same time, the material characteristics, geometric characteristics, and dynamic characteristics of the ideal material model can be determined accordingly.
In order to provide better feedback on the similarity relationship of the test model and prototype structure, Table 1 shows the similarity ratio parameters of the prototype structure and the test model using the above ideal materials.
In practice, it is difcult to obtain the abovementioned ideal materials, and it is necessary to replace piles and caps according to the available materials during the design and processing of complex pile-cap foundation models.

Design of Eighteen Piles.
Referring to the underwater shaking test performed in previous studies of [19], piles used in this study were made of polymethyl methacrylate. To accurately obtain the dynamic elastic modulus of polymethyl methacrylate, three beams of 4 × 4 × 40 cm were made of the same batch of materials. Te dynamic elastic modulus of polymethyl methacrylate material was obtained by measuring the fundamental frequency of three cantilever beams. Te fundamental frequency of the three cantilever beams is obtained by both sweeping resonance and hammering methods. Trough mutual calibration, the dynamic elastic modulus of polymethyl methacrylate is 4.01 GPa and the density is 1198.9 kg·m −3 .
For pile-cap foundation model with the ideal material, the outer diameter of piles is 105 mm, and the efective height of single pile is 0.9 m. Elastic modulus of ideal material is E i , area moment of inertia for single pile is I i , the efective height of the pile is L i and its value is 0.9 m, corresponding stifness of single pile is (E i .I i /L i ), and its value is 3699.4 N·m. On the premise of maintaining the overall layout of eighteen piles, the overall dimensions and stifness of each pile were unchanged, and polymethyl methacrylate was used to reasonably replace the above ideal materials of eighteen piles. It was determined that the eighteen piles can be made of hollow polymethyl methacrylate pipes; the outer diameter of the hollow pipe was 105 mm, the inner diameter was 101 mm, and the thickness was 2 mm. Elastic modulus of polymethyl methacrylate is E p , area moment of inertia for single pile is I p , the efective height of single pile is L p and its value is 0.9 m, corresponding stifness of single pile is (E p .I p /L p ) and its value is 3783.4 N·m, which is close to 3699.4 N·m, and the diference of stifness between ideal material pile and polymethyl methacrylate pile is 2.3%.
Te efective height of single pile is 0.9 m, and the mass of ideal material pile and polymethyl methacrylate pile is 19.9 kg and 0.7 kg, respectively. To compensate for the diference in mass density to satisfy the similarity relationship of material density, the counterweight should be uniformly increased from bottom to top in hollow polymethyl methacrylate pipes. To avoid afecting the stifness of the piles and reduce the infuence of the shaking impact on the test results, nine hollow cylindrical steel blocks were placed in the middle of each pipe. Te diameter of each block was 7 cm and the height was 10 cm, and the remaining gap was flled with prepared steel sand. Each hollow pipe was flled with 19.2 kg of counterweight, and the total weight of the eighteen pipes was 345.6 kg; through the design of counterweight, the ideal material piles and polymethyl methacrylate piles have the same mass.
Te elastic modulus of polymethyl methacrylate is about seven times that of ideal material. Trough the above design of equivalent stifness replacement by using hollow piles, the same position of ideal material pile and polymethyl methacrylate pile still has the same strain, acceleration, and displacement. Te new model still meets the structure dynamic similarity criteria and fuid similarity criteria of the dynamic scale-model test of fuid-structure coupling problems.

Design of Round-Ended Cap.
As the cap of the prototype structure is a large reinforced-concrete structure, it can be regarded as a rigid body whose deformation is far less than the displacement [24][25][26], the overall dimension of the model cap is 113.3 × 77.3 × 16.7 cm, and the cap mass of the test model is 320.0 kg. On the premise of ensuring the same mass and overall dimension of round-ended cap, whether using ideal material or other alternative materials can guarantee that the model design still meets the similarity relationship. Because the steel cap is easier to control its total mass and irregular shape, steel cap with same mass and size is used in the test instead of the ideal material cap, and it still can be regarded as a rigid body. Seven small grooves have been reserved in the designated position for installing hydrodynamic-pressure sensors.

Te Connection of Complex Model.
To achieve the arrangement of the signal wires from the sensors and realize the rigidity connection between the bottom of the cap and the top of eighteen piles, there are eighteen reserved holes evenly arranged at the cap according to the position of the eighteen piles. In order to realize the fxed boundary connection between piles and the cap, according to the mass requirements of the excavated cap, the upper diameter of 18 reserved holes is 8 cm and corresponding height is 10.67 cm, and the lower diameter is 11.3 cm and corresponding height is 6.0 cm, such that the top of eighteen piles can extend into the cap for 6 cm. Te gap between the outer side of the pile top and the cap is about 0.4 cm, the upper surface of the pile top is in contact with the cap, and the contact surface and the tiny gap are frmly connected with the structural adhesive, which is mainly composed of epoxy resin, etc. Eighteen piles and the cap are connected in the same way, and the piles and the cap can be considered as a fxed boundary condition.
Te connection of the piles and the adapter plate is similar to the fxed connection of eighteen piles and the cap. Te reserved hole diameter of adapter plate is 11.3 cm, which is larger than the outer diameter of the piles. Te gap between the outer surface of pile bottom and the adapter plate is about 0.4 cm, and the bottom of the eighteen piles can extend into the adapter plate for 3.6 cm. Te remaining 0.4 cm adapter plate is mainly used to bear the weight of counterweight and prevent the outfow of steel sands. Te bottom surface of the piles is in contact with the adapter plate. Both the contact surface and the tiny gap are frmly connected with structural adhesive, and the pile and the cap can be considered as a fxed boundary condition. In order to simulate the anchoring boundary between rock-socketed pile and rocks, the adapter plate is connected to the shaking table with 6 bolts, which can also be seen as a fxed boundary condition. Figures 2 and 3 present the connection diagram of the pile, cap, and adapter plate. After the completion of all tests, the connections between eighteen piles and the cap and the adapter plate are still frm without looseness.

Layout of Measuring Points.
Te pile-cap foundation is symmetrical along the X-and Y-directions, with the sensor layout shown in Figures4 and 5. Te DEWE2-M18 dynamic data-acquisition system of Dewetron GmbH, Austria, was used in this test. In Figure 4, measuring points L1 and L2 are laser-displacement sensors, which are used to measure the displacement of the model top in the X-and Y-directions. AX1-AX5 and AY1-AY3 are eight underwater acceleration sensors, AX1/AX2 is used to monitor the X-direction acceleration at the top of the shaking table and adapter plate, and AY1/AY2 is used to monitor the Y-direction acceleration at the top of the shaking table and adapter plate. In Figure 6, measuring points S1 to S33 are strain gauges, measuring points S1 to S27 are arranged at the bottom of piles, S1/S28/S29 is arranged on pile B1, S9/S30/S31 is arranged on pile B5, and S18/S32/S33 is arranged on pile B9, with heights of 2 cm, 45 cm, and 80 cm from the top of the adapter plate.
In Figure 5, P1-P20 are the integrated hydrodynamicpressure sensors. To avoid the infuence of the shaking table and adapter plate on the bottom water, the layout of the hydrodynamic-pressure sensors was started at a height of 16.7 cm. Te height of P1, P4, P8, and P11 from the top surface of the adapter plate was 16.7 cm, the height of P2, P5, P7, P9, and P12 was 45 cm, and the height of P3, P6, P10, and P13 was 83.3 cm. P14-P20 were arranged at the cap with a height of 4 cm from the bottom of the cap and were used to study the distribution law of hydrodynamic pressure on a round-ended cap under earthquake excitation.
To reduce the infuence of sensors and signal wires on the fow feld around the pile-cap foundation model, microsized sensors and thin signal wires were used in an underwater shaking table. Hydrodynamic-pressure gauges were placed in the designated positions of the piles and cap through a 1 cm reserved hole, and the tiny gap between the sensors and the piles was flled with sealant to achieve waterproofng. Te signal wire extends from the interior of the piles and the steel cap to the top of the model, all of which are led to the pool side along the wire rope suspended in the air and then connected to the acquisition instrument. Te signal wires of the strain gauges and acceleration sensors at the bottom of the model are fxed to the top of the shaking table, and only a few thin signal wires are arranged along the pile shafts. Tose signal wires are led to the pool boundary along the pool bottom, and there is basically no interference to the fow feld. A panoramic view of the test site is shown in Figure 7.

Loading Conditions.
Te duration time of actual seismic waves generally does not exceed 60 seconds, since the time step must be compressed according to the time scale λ T �1/ 7.75. Te duration time of input seismic waves in underwater shaking-table test is only a few seconds, which is closer to the pulse load rather than the seismic load. Moreover, seismic waves with too short duration do not meet research standards. Terefore, two artifcial waves are input along the X- Dynamic characteristics Shock and Vibration 5 and Y-directions in this test. Based on the geological conditions of the deep-water pile-cap foundation of the Ningbo-Zhoushan Railway, the specifcation spectrum is determined according to Specifcations for Seismic Design of Highway Bridges (JTGT2231-01-2020) [27]. Tereafter, two artifcially synthesized waves were generated according to the specifcation spectrum of basic ground motion data, and the seismic-peak acceleration was 1.352 m·s −2 . In order to avoid short loading times of seismic waves, the time of two artifcial waves without time compression was set to 93 s, while the loading-wave time was set to 12 s. Te acceleration-time curve of artifcial wave 1 without time compression is shown in Figure 8, and the acceleration response spectrum is shown in Figure 9.
Te efective water depth of underwater shaking table is 0.0 m (no water), 0.5 m, and 1.0 m. Te loading conditions are presented in Table 2.

B1
B2 B4 S1/S28/S29 S2 S3 S4 S5 S6 S7 S8 S9/S30/S31 S10 S11 S12 S13 S14 S15 S16 S17  Shock and Vibration height meter 1 is arranged in the X-direction of the model motion, and the distance is 1.5 m from the edge of the cap. Wave-height meters 2 and 3 are arranged at the pool boundary and the distance is 1.0 m from double-wave absorbers of the pool boundary, and wave-height meter 2 is perpendicular to the X-direction of the model motion, whereas wave-height meter 3 is parallel to the X-direction of the model motion. Tose wave-height meters are also used as a judging rule to determine whether the water surface is in static state. Te macroscopic phenomena of underwater shaking-table test are as follows.
(1) As the motion of the model, radial surface waves are generated from the center position where the model is located due to the dynamic interaction between pile-cap foundation model and the surrounding water. When the motion of the model stops, the surface waves disappear quickly. It indicates that the fuctuation of the water surface is caused by the motion of the model. When an earthquake occurs, the excitation of seismic wave can cause the motion of pile-cap foundation in water, which would disturb the water body and cause the fuctuation of the water surface. Earthquake load is a reciprocating load and the disturbed water body would act on the model structure in turn, which leads to the pier-water interaction. (2) When artifcial wave 1 and artifcial wave 2 are excited along the X-direction, water surface waves mainly occur within 5 m of the model, and there is no obvious disturbance on the water surface away from 5 m. According to the displacement similarity ratio 1/60 and time similarity ratio 1/7.75, the displacement of the model is millimeter level, the duration time of the input seismic waves is 12 s, the water surface fuctuation caused by structure-water interaction is also millimeter level, and the scope of disturbance to water body is relatively limited. When artifcial waves 1 and 2 are excited along the Xdirection, the maximum wave height of waveheight meter 1 is 2.14 mm and 2.47 mm, the maximum wave height of wave-height meters 2 and 3 is less than 0.09 mm, and the wave height near the pool boundary is basically unchanged, which indicates that the water body at the pool boundary is basically undisturbed, and the wave-height monitoring results   Shock and Vibration are consistent with the macroscopic phenomenon of water surface.
Te length, width, and height of the test pool were 30, 20, and 1.5 m, respectively, double-wave absorbers were set around the pool boundary, the distance between the pool boundary and the edge of the model is more than 9 m, sufcient water area of test pool is one major advantage of this test, the water pool can well simulate the infnite water area, and the water pool boundary efect has no interference efect on surface wave.  Table 3 shows the natural vibration period of the complex pile-cap foundation model in diferent water depths. Te natural vibration period of the test model was 0.1148 s under the waterless condition, 0.1172 s for a 0.5 m water depth, and 0.1212 s for a 1.0 m water depth, respectively. Compared with the waterless condition, the increase rates were 2.1% and 5.6%, respectively, the increase rate of natural vibration period in 1 m water depth is 2.7 times that of 0.5 m water depth, and the corresponding ratio is greater than water depth ratio of 2.0, which indicates that the existence of water can prolong the natural vibration period of complex pile-cap foundation, while the increase in natural vibration period is non-linear related to water depths. At present, the theory of hydrodynamic pressure was mainly about single pier structures, the relevant theoretical explanation of hydrodynamic pressure for complex pile-cap foundations under earthquake action has not yet been well understood [28,29], and the main reason was that the surrounding piles can infuence the hydrodynamic pressure of a certain pile and the infuence varies with diferent factors such as the arrangement and spacing distance. According to the contribution of Liaw and Chopra [30] and Li and Yang [31] for single cylindrical piers, the dynamic equilibrium equation of the submerged cylindrical pier under seismic excitations can be simplifed as follows:

Infuence of Water Depth on Dynamic
where M, C, and K represent structural mass, damping, and stifness matrices, respectively; € x, _ x, and x represent cylinder acceleration, velocity, and displacement, respectively; and € x g is acceleration of the ground.
Although there are some assumptions and simplifed processing methods that difer from the actual situation, equation (4) developed a method to transform the hydrodynamic forces during an earthquake into a hydrodynamic added mass, which is meaningful for theoretical exploration. Although difering from vibration of traditional single pile, the existence of adjacent piles changes the distribution of hydrodynamic pressure on each pile of pile-cap foundation, and water body has the same infuential mechanism on single pier or complex pile-cap foundation.
Te added mass theory of the hydrodynamic forces mentioned above can be used to explain the variation of the natural vibration period of pile-cap foundation model in diferent water depths. Te added mass is dependent on water depths, a higher water depth causes a larger added mass, resulting in an increase in the natural vibration period, and the tendency in theoretical analysis is consistent with the conclusion obtained from experimental investigation results of natural vibration period.

Analysis of Water Depth Infuence on Acceleration.
Artifcial wave 1 is excited along the X-direction under three diferent water depths of 0.0 m, 0.5 m, and 1.0 m. Te maximum acceleration of measuring points AX3, AX4, and AX5 is divided by the maximum acceleration of measuring point AX2, which is on the top surface of the adapter plate. Te normalized acceleration-amplifcation coefcient of the model is obtained, and the corresponding value is shown in Figure 10. Te distribution of the acceleration-amplifcation coefcient in the model did not show a consistent increasing trend from bottom to top. Compared with the values on the bottom and top of the model, the acceleration-amplifcation coefcient of measuring point AX3 in the middle of pile B7 is signifcantly larger, which is related to the complex structural form of the pile-cap foundation. Due to the large diameter and large number of piles, the volume and mass of the cap are huge, and the cap motion will produce great horizontal inertia force under earthquake excitation because their high-rise pile caps are top-heavy. Te piles between the adapter plate and the cap have no lateral restraint; meanwhile, the cap and 18 piles are rigidly connected, and the coupling efect of the piles and the cap will restrict the top Var R is defned as follows: Previous studies of reference [17] have shown that the presence of water signifcantly increases the acceleration of pier top because the water around the pier increases added inertial forces of the pier under earthquake. However, the results in this study obtained the opposite conclusion; when considering the water efect, the seismic acceleration of complex pile-cap foundation model decreased. Te main reason for this experimental phenomenon is that the acceleration response of complex pile-cap foundation model in water is not only increased by the hydrodynamic pressure resulting from water-pier interaction but also decreased by the damping forces of the water body, and the efect of the damping forces has a larger infuence on acceleration than that of hydrodynamic pressure, so the acceleration responses of complex pile-cap foundation model measured from the underwater shaking-table test decrease. Te infuence of water depths on acceleration response of complex pile-cap foundation model can also be explained based on the spectral characteristics of artifcial seismic waves. Trough underwater acceleration sensor AX2, the actual acceleration-time curve of input seismic wave can be obtained, the acceleration response spectrum of artifcial wave 1 is shown in Figure 11, and the local enlarged drawing highlights the change of the natural vibration period in three diferent water depths. It is evident that the amplitude of the acceleration response spectrum decreases with the increase of the period, which shows that the accelerationamplifcation coefcient will theoretically decrease in a higher water depth, and the test result is in accordance with the theoretical analysis of the acceleration response spectrum. From the experimental results and the above analysis, it can be concluded that the existence of water can prolong the natural vibration period of pile-cap foundation; meanwhile, the infuence of the water depths on the acceleration depends on the acceleration response spectrum of the input seismic wave.

Analysis of Water Depth Infuence on Pile Strain.
Artifcial wave 1 was excited along the X-direction when the water depth was 0.0 m, 0.5 m, and 1.0 m. Te maximum tensile strain of the pile-cap foundation model occurred at strain measuring point S9, which is at the bottom of pile B5. Figure 12 presents a comparison of the maximum tensile strain of pile B5 along the model height. Te maximum tensile strain of pile B5 decreases frst and then increases from bottom to top, the tensile strain value of the measuring point S9 is obviously larger than that of S30 and S31, and the strain distribution of pile B5 under three diferent water depths is similar, so the bottom of complex pile-cap foundation was most likely to be damaged frst under earthquake action, which demonstrates that the bottom of the pile is the key control section and the weak point of complex pile-cap foundation. With an increase in water depth, the maximum tensile strain at measuring points S9, S30, and S31 of pile B5 showed an increasing trend, which indicates that the hydrodynamic pressure on complex pilecap foundation increases the strains of the piles, and the maximum strain of the pile-cap foundation increased signifcantly with an increase in water depth.
When the water depth is 0.0 m and 1.0 m, the strain-time curve of measuring point S9 at the bottom of pile B5 is  shown in Figure 13. Te trend of strain-time curve in 1.0 m water depth is similar to that of the waterless condition; because of hydrodynamic pressure efect, the water body can afect the dynamic response of the model strain, the hydrodynamic force is signifcantly less than the structural force, and variation trends of the dynamic response in 1.0 m water depth are still similar to waterless condition, but the dynamic response peak is signifcantly diferent. Te maximum tensile strain of measuring point S9 was 126.7 με when the water depth was 0.0 m, and the strain value of S9 was 131.7 με and 144.2 με when the water depth was 0.5 m and 1.0 m, respectively. Compared with the waterless condition, the maximum tensile strain increment was 5.0 με for 0.5 m water depth and 17.5 με for 1.0 m water depth, and the increase rates were 3.9% and 13.8%, respectively. It is obvious that a higher water depth results in a considerably larger strain. Te strain at the bottom measuring point S9 of the pile B5 increases much faster with increasing water depth. Te reasons for the above phenomena are as follows: the seismic excitation will cause the motion of the pile-cap foundation model in water, the relative motion of the model and the surrounding water body will generate the hydrodynamic added mass induced to the hydrodynamic pressure, and the hydrodynamic added mass increases the additional inertial forces on the pile-cap foundation model, which has a large bending moment on the bottom of the piles resulting in a larger strain at the bottom in comparison with the upper positions of the piles.
Artifcial wave 1 is excited along the Y-direction when the water depth was 0.0 m and 1.0 m, and the maximum tensile strain was 128.8 με and 148.2 με, respectively, and occurred at measuring point S21, which is at the bottom of pile B1. Compared to the waterless condition, the maximum tensile strain increment was 19.4 με for 1.0 m water depth and the increase rate was 15.1%. In conclusion, when artifcial wave 1 was excited along the X-or Y-directions, the strain of deep-water pile-cap foundation was greater than that without water, which indicated that the infuence of hydrodynamic pressure should be considered in the seismic design of complex deep-water pile-cap foundation.
Artifcial wave 1 was excited along the X-and Ydirections when the water depth was 0.0 m, and the maximum tensile strain of pile-cap foundation model was 126.7 με and 128.8 με and the value of the latter was 101.7% of the former. Artifcial wave 1 was excited along the X-and Y-directions when the water depth was 1.0 m, and the maximum tensile strain of pile-cap foundation was 144.2 με and 148.2 με, the value of latter being 102.8% of the former. Whether subjected to 0.0 m or 1.0 m water depth, the maximum tensile strain of pile-cap foundation model under X-and Y-direction excitation was relatively close, and the overall diference was within 3%. For complex pile-cap foundation used in Xihoumen rail-cum-road bridge, the layout of eighteen ultra-large-diameter piles can provide a meaningful reference for seismic design of deep-water pilecap foundation of other cross-sea bridges.

Analysis of Water Depth Infuence on Model Top
Displacement. Artifcial wave 1 was excited along the Xdirection under 0.0 m and 1.0 m water depths, and the displacement-time curve of the model top is shown in Figure 14. Te maximum displacement was 2.074 mm when the water depth was 0.0 m, and its values were 2.101 mm and 2.155 mm when the water depth was 0.5 m and 1.0 m, respectively. Compared with the waterless condition, the maximum displacement increment was 0.027 mm for 0.5 m water depth and 0.081 mm for 1.0 m water depth; the increase rates were 1.3% and 3.9%, respectively.
At present, it was very difcult to measure the bottom displacement of model piles in water, the shaking table was a huge rigid body, and its motion characteristics were  basically consistent with the dynamic response of the pile bottom, so the displacement of the shaking table can be regarded as the bottom displacement of pile-cap foundation model and its value was equal to the rigid body displacement of the model caused by the seismic wave. When artifcial wave 1 was excited along the X-direction, the maximum rigid body displacement of pile-cap foundation model was 1.917 mm according to the feedback data of shaking-table sensor. When the water depth was 0 m, 0.5 m, and 1.0 m, the maximum rigid body displacement was 92.4%, 91.2%, and 89.0% of the maximum top displacement, respectively, which indicates that the value of the measured displacement of cap top was primarily that of a rigid-body displacement, the motion of the pile-cap foundation model under earthquake excitation is similar to that of rigid bodies, and this phenomenon is mainly caused by the high stifness of the pile-cap foundation.
Te maximum displacement increment caused by 0.5 m water depth was 0.027 mm, and the corresponding values were 1.4% of rigid-body displacement and 1.3% of the total displacement. Te maximum displacement increment caused by 1.0 m water depth was 0.081 mm, and the corresponding values were 4.2% of rigid-body displacement and 3.9% of the total displacement. Te displacement increment subjected to 1.0 m water depth infuence was basically 3.0 times that of 0.5 m water depth, and the ratio was far greater than water depth ratio 2.0, which indicates that the increase of model displacement was non-linear related to the water depth. Although the displacement increment caused by the water infuence accounts for a small proportion of the total displacement, the displacement increment change trend can still refect the water-depth change infuence trend of the top displacement of the pile-cap foundation, and the displacement of complex pile-cap foundation model measured from the underwater shaking-table test increased with increasing water depths. When considering the water infuence, the top displacement of complex pile-cap foundation model is decreased by the damping forces resulting from the water but also increased by the added mass induced to the hydrodynamic pressure, and the fnal trend of displacement response is the comprehensive result of two effects. Te infuence of hydrodynamic pressure on the top displacement is greater than that of the damping forces, so the top displacement of complex pile-cap foundation measured from the test increases with the increase of water depths. Te test results of diferent water depths show that the hydrodynamic pressure at the pile bottom increases with the increment of water depth. According to the acceleration test results in Section 3.2.2, when the water depth was 0.5 m and 1.0 m, the diference of model acceleration was basically within the range of 2.5%, which indicated that the dynamic response of the model was not the main reason for the signifcant diference of hydrodynamic pressure in diferent water depths. Te infuencing mechanisms for the above phenomena are as follows: the actual water body is compressible; meanwhile, the motion of the model under earthquake excitation will cause water surface waves. Tere is a boundary condition that the hydrodynamic pressure value is 0 Pa on the water surface, and those factors would afect the hydrodynamic pressure attenuation, and the attenuation infuence of hydrodynamic pressure increases with the decrease of the distance from the water surface. It is evident that a lower water depth results in a closer distance from the measuring point to the water surface, so the hydrodynamic pressure of the same location at 0.5 m water depth is signifcantly smaller than that of 1.0 m water depth. Te measuring points P12 of pile B1, P2 of pile B5, P5 of pile B6, and P9 of pile B9 were arranged at 45.0 cm from the top surface of the adapter plate. When the water depth was 0.5 m, four measuring points were all below the water surface and the distance from the water surface is 5.0 cm, while the distance of four measuring points from the water surface is 55.0 cm when the water depth was 1.0 m. To further investigate the impact of water depth on hydrodynamic pressure, for 0.5 m and 1.0 m water depth, the comparison of the maximum hydrodynamic pressure for abovementioned measuring point is shown in Figure 16. Compared with the 0.5 m water depth, the hydrodynamic pressure at the same location at 1.0 m water depth was signifcantly greater. Te maximum hydrodynamic pressures at measuring points P12, P2, P5, and P9 under a 0.5 m water depth are 51.6%, 57.6%, 50.9%, and 56.0% of the value under 1.0 m water depth, respectively, and the corresponding ratio is between 50.9% and 57.6%; there is a more signifcant diference in hydrodynamic pressure at this height. For these measuring points of hydrodynamic pressure, the water depth and distance from the water surface are the main diferences, which indicate that the hydrodynamic pressure is closely related to the water depth, and the attenuation efect signifcantly increases with the decrease of the distance from the water surface. Tese observations are in accordance with the results of theoretic analysis.

Hydrodynamic-Pressure Analysis of Diferent Piles.
For 1.0 m water depth, the distribution of the maximum hydrodynamic pressure on edge piles B5 and B9 and the round-ended cap along the model height is shown in Figure 17. Te hydrodynamic pressure acting on each pile gradually decreased from bottom to top, while there was a sudden increasing trend at measuring points P14 and P20 of the round-ended cap. Te hydrodynamic pressure under earthquake is caused by the motion of the structure, and the Morison equation shows that the earthquake-induced hydrodynamic pressure depends on water depth, diameter and acceleration of the structure, and inertial coefcient. Due to the existence of large-sized cap, the model shape at the cap position increased suddenly, part of the large-sized cap was in contact with water and changed the distribution laws of hydrodynamic pressure, which indicates that the hydrodynamic pressure was related not only to the water depth but also to the actual engineering structure. From Figure 17, it can be seen that the distribution laws of hydrodynamic pressure on both sides of the pile-cap foundation model along the model height were consistent, and the values of measurement points at the same height were also relatively close, and this is mainly because seismic load is a reciprocating load, so the hydrodynamic pressure on positive side and negative surface is highly similar, and the distribution characteristics of hydrodynamic pressure on deep-water bridge piers are signifcantly diferent from hydraulic structures such as dams. According to the results of strain analysis in Section 3.2.3, the maximum tensile strain increment was 5.0 με for 0.5 m water depth and 17.5 με for 1.0 m depth water, the strain increment subjected to 1.0 m water depth infuence is basically 3.5 times that of 0.5 m water depth, and the ratio is far greater than the water depth ratio 2.0, which indicates that the strain increment of the pile-cap foundation model is non-linear to the water depths. Hydrodynamic pressure efect is the main reason for the increase of pile strain, and the variation in hydrodynamic pressure in Figures 15 and 16 indicates that the hydrodynamic pressure was related to the water depth; when the water depth is 1.0 m, the hydrodynamic pressure at the same position of the piles is greater than that of 0.5 m water depth, which is one reason for larger strain increment. Te variation of Figure 17 indicates that hydrodynamic pressure has a sudden increasing trend at the cap, the size of round-ended cap is much larger than that of the piles, it has larger contact area with the surrounding water, and special geometric characteristic easily leads to better blocking efect. Te interaction between the largesized cap and water is more direct and it will make the model bear greater hydrodynamic force, which is another important reason for the signifcant increase of pile strain in 1.0 m water depth.
Measuring point P11 was on edge pile B1 of the side-row piles, and measuring point P1 was on edge pile B5 of the middle-row piles. When the water depth was 0.5 m and 1.0 m, the hydrodynamic pressure at measuring point P11 was 88.7% and 84.9% of that of measuring point P1, respectively. Te hydrodynamic pressure on pile B5 was signifcantly larger under X-direction excitation, mainly because pile B5 was the front-row pile, and its position was closer to the seismic excitation center. Te small spacing of adjacent piles B1, B10, and B5 perpendicular to the excitation direction can easily lead to an interference efect, and the motion state of the fuid particle changed when the surrounding water passed through pile B5, which increased the hydrodynamic pressure acting on pile B5. Figure 18 shows the maximum hydrodynamic pressure of piles B5 and B6 along the model height. Viewed from the X-direction, pile B5 is an edge pile, whereas pile B6 is a secondary edge pile. Te hydrodynamic pressure on the secondary edge pile B6 was evidently less than that on pile B5, and the hydrodynamic pressure at the three measuring points on pile B6 was 85.4-88.9% of the corresponding measuring point of pile B5.
Measuring point P2 was on edge pile B5, measuring point P5 was on secondary edge pile B6, measuring point P7 was on middle pile B7, and the height of three measuring points was 45 cm from the top surface of the adapter plate. Figure 19 shows the maximum hydrodynamic pressures at the three measuring points under the excitation of artifcial waves 1 and 2. Te hydrodynamic pressure on the edge pile B5 was the largest, followed by secondary edge pile B6, and the hydrodynamic pressure acting on the middle pile B7 was the smallest. Under artifcial wave 1 excitation, the hydrodynamic pressures on piles B6 and B7 were 88.7% and 83.0% of those of edge pile B5, respectively. Te ratios under artifcial wave 2 excitation were 86.7% and 80.4%, which indicate that the hydrodynamic pressure acting on diferent piles under seismic excitation is diferent, and the magnitude of hydrodynamic pressure is related to the layout of the piles. Te diference of hydrodynamic pressure for diferent piles is mainly due to the complex structure form and the interference between front-and back-row piles of the pile-cap foundation. Due to the resistance characteristics of pile-cap foundation in deep water, the front piles play a role in blocking the fow and will weaken the interaction between the water and back piles. Due to the cumulative shielding efect of front pile B5 and the second front pile B6, the hydrodynamic pressure of middle pile B7 is the minimum. Under artifcial wave 1 excitation along the X-direction, the hydrodynamic pressures on piles B6 and B7 were 88.7% and 83.0% of those of edge pile B5, respectively. Te ratios under artifcial wave 2 excitation were 86.7% and 80.4%, and cumulative shielding efect does not increase linearly, which indicates that the interaction between pile-cap foundation and the water is extremely complex.
Diferent from vibration of traditional single pile, the existence of adjacent piles changes the distribution of hydrodynamic pressure on each pile of pile-cap foundation, making the structure-water dynamic interaction more complicated. For the complex pile-cap foundation model of Xihoumen rail-cum-road bridge, the center distance between front pile and back pile is 0.21 m, the diameter of piles is 0.105 m, and the ratio is 2.0. According to the abovementioned fndings, the hydrodynamic pressure on the edge pile was the largest, followed by secondary edge pile, the hydrodynamic pressure on the middle pile was the smallest, and the maximum hydrodynamic pressure diference acting on the piles can reach approximately 20%. Te experimental investigation results indicate that the infuence diference of hydrodynamic pressure acting at diferent group piles needs to be considered in seismic analysis of complex deep-water pile-cap foundation.

Hydrodynamic-Pressure Analysis of Round-Ended Cap.
To obtain the distribution law of the hydrodynamic pressure acting on the round-ended cap under X-and Y-direction excitations, a system study was conducted to analyze the maximum hydrodynamic pressure at seven measuring points arranged on the cap surface.
Under X-direction excitation of artifcial waves 1 and 2, Figure 20 presents the maximum hydrodynamic-pressure distribution on the cap in 1.0 m water depth. For the seven measuring points, hydrodynamic pressure at measuring point P14 was evidently the maximum and its value was 96.7 Pa and 94.2 Pa, respectively, under X-direction excitation of artifcial waves 1 and 2, and hydrodynamic pressure at measuring point P20 was close to measuring point P14 and the corresponding value was 94.1 Pa and 92.4 Pa, respectively. Hydrodynamic pressure at measuring point P17 was always the minimum. Tis is because measuring points P14 and P20 are at the front and measuring point P17 is at the side under X-direction excitation, and the hydrodynamic pressure presents a gradual declining trend from front to side. Te maximum hydrodynamic pressure at measuring points P14 and P20 was 2.7 times the value of measuring point P17 under artifcial wave 1 excitation. Under artifcial wave 2 excitation, the ratios were 2.5 times and 2.6 times, respectively. Te hydrodynamic-pressure ratio at the front and side measuring points refects the infuence of the cap section form on the velocity of the surrounding fuid particles.
Under the X-direction excitation of artifcial waves 1 and 2, the hydrodynamic pressure at measuring point P15 was 87.2% and 84.8% of that at measuring point P14, and the hydrodynamic pressure at measuring point P16 was 47.4% and 46.5% of that at measuring point P14, which indicates that hydrodynamic pressure decreased relatively slowly between measuring points P14 and P15, while it decreased rapidly between measuring points P15 and P16. Hydrodynamic pressure at measuring points P16, P17, and P18 was between 35.5 Pa and 45.8 Pa under X-direction excitation of artifcial wave 1, whereas hydrodynamic pressure at measuring points P16, P17, and P18 was between 37.3 Pa and 45.3 Pa under X-direction of artifcial wave 2. Tis indicates that the hydrodynamic pressure at measuring points P16-P18 was similar, and the amplitude change in the three measuring points at the side of the cap was relatively small.
Under Y-direction excitation of artifcial wave 1 and 2, Figure 21 presents maximum hydrodynamic-pressure distribution on the cap in 1.0 m water depth. Measuring points P15-P19 are at the front and measuring points P14 and P20 are at the side. To compare with the hydrodynamic pressure under X-direction excitation, the same coordinate axis was used in Figures 20 and 21. Te hydrodynamic pressure at measuring points P14 to P20 frst increased and subsequently decreased gradually, and the variation trend of the hydrodynamic pressure acting along the round-ended cap was consistent under the Y-direction excitation of the two artifcial waves. For the seven measuring points, the hydrodynamic pressure at measuring point P17 was the largest and its value was 107.7 Pa and 105.1 Pa under Y-direction excitation of artifcial waves 1 and 2, respectively. Te hydrodynamic pressure at measuring point P14 was the smallest, and that at measuring point P20 was similar to measuring point P14. Te hydrodynamic pressure at measuring point P18 was 92.8% and 92.6% of that at measuring point P17, whereas the hydrodynamic pressure at measuring point P19 was 68.0% and 66.7% of that at measuring point P17. Te hydrodynamic pressure at measuring point P20 was 53.9% and 51.9% of that at measuring point P17. Te hydrodynamic-pressure distribution on the round-ended cap shows that hydrodynamic pressure decreased slowly between measuring points P17 and P18 but decreased rapidly between measuring points P18-P19 and P19-P20.
For seismic wave excitation in X-and Y-directions, the hydrodynamic pressure at the center of the seismic input direction was the largest, and the hydrodynamic pressure away from the seismic wave input direction gradually decreased. Although there are some diferences between the hydrodynamic-pressure values on the cap under the excitation of the two artifcial waves, the overall variation law was similar, and this is because the amplitudes of two artifcial waves at the values of natural frequency of the test model are close. Under Y-direction excitation of artifcial wave 1, the maximum hydrodynamic pressure at measuring point P17 was 1.8 times and 1.9 times that of measuring points P14 and P20, respectively. Te ratio was 2.0 and 1.9 times, respectively, under the Y-direction excitation of the artifcial wave 2. Compared with the Y-direction excitation, the maximum hydrodynamic pressure was signifcantly smaller, and the hydrodynamic-pressure ratio at the front and side was larger under X-direction excitation. Te hydrodynamic pressure on the round-ended cap decreased faster from front to side. Viewed from the X-direction, the upstream surface of round-ended cap is composed of curved surface, which is relatively smooth. Te fuid resistance efect of the cap under X-direction excitation was weaker, and the diversion role of curved surface was more conducive to the fow of fuid, which is advantageous for reducing the hydrodynamic pressure on the cap. Viewed from the Ydirection, the upstream surface of round-ended cap is composed of plane and curved surface, the contact area between the upstream surface and water is signifcantly larger and the normal direction of the plane coincides with the input direction of the artifcial wave, and these factors will lead to greater hydrodynamic pressure on the upstream surface of the cap under the Y-direction excitation. It was observed that the hydrodynamic pressure on the cap was signifcantly afected by its shape. To reduce the hydrodynamic pressure on the cap and minimize the impact of the hydrodynamic pressure efect on the internal force of the pile-cap foundation, the shape of the large cap should be fully optimized in the seismic design of a deep-water pile-cap foundation.

Strain Analysis of Complex Pile-Cap Foundation Model.
To study the mechanical characteristics of diferent piles of complex pile-cap foundations under earthquake excitation, the maximum tensile strain of piles under X-and Ydirection excitation was analyzed and discussed.

Strain Analysis of Diferent Piles under X-Direction
Excitation. Artifcial wave 1 was excited along the Xdirection when the water depth was 0.0 m and 1.0 m, and the maximum tensile strain of side-row piles B1-B4 is shown in Figure 22. Whether subjected to 0.0 m or 1.0 m water depth, the maximum tensile strain of edge piles B1 and B4 is signifcantly larger than that of middle piles B2 and B3. Te maximum tensile strain of edge pile B1 is 120.1 με under 0.0 m water depth, the maximum tensile strain of middle pile B3 is 104.1 με, and the strain value of the latter is 86.7% of the former. Te maximum tensile strain of edge pile B1 is 136.4 με under 1.0 m water depth conditions, whereas the maximum tensile strain of middle pile B3 is 113.7 με and the strain value of the latter is 83.4% of the former.
Artifcial wave 1 was excited along the X-direction when the water depth was 0.0 m and 1.0 m, and the maximum tensile strain of middle-row piles B5-B9 is shown in Figure 23. Whether subjected to 0.0 m or 1.0 m water depth, the maximum tensile strain of edge pile B5 was always the largest, and that of middle pile B7 was always the smallest. Te maximum tensile strain of middle pile B7 is 74.9% and 73.5% of that of edge pile B5 subjected to 0.0 m and 1.0 m water depths. Te strain results of piles B1-B9 under Xdirection excitation show that the maximum strain of different piles is clearly diferent. Te strain value is related to the layout of piles, and the maximum strain diference of piles reached 26.4% at 1.0 m water depth. Te main reasons for the above phenomena are as follows: complex pile-cap foundation is top-heavy because of the existence of largesized cap, and the strain of each pile is the comprehensive result of eccentric vertical force and bending moment caused by the upper structure under earthquakes. Te signifcant diference of the distance between each pile and the structure center and diferent eccentric efects of compression bending or stretch bending result in signifcant strain diferences for each pile. Besides, the test results in Section 3.3.2 show that the hydrodynamic pressure acting on diferent piles varies under seismic excitation, the hydrodynamic pressure on the edge pile is the largest, followed by secondary edge pile, and the hydrodynamic pressure acting on the middle pile is the smallest, which is another important reason resulting in the strain diference of the piles in water.
Whether subjected to 0.0 m or 1.0 m water depth, the maximum tensile strain of side-row piles occurred in edge pile B1 and the corresponding value was 120.1 με and 136.4 με, respectively. Te maximum tensile strain of middle-row piles occurred in edge pile B5 and the corresponding value was 126.7 με and 144.2 με, respectively. Te pile-cap foundation is completely symmetrical about the Xand Y-axis. Te edge piles B5 and B1 are located on the same side of the model, which conforms to the mechanical characteristics of the symmetric structure. Te maximum tensile strain of edge pile B5 was 105.5% and 105.7% of edge pile B1 under 0.0 m and 1.0 m water depth; in both cases, the maximum tensile strain of edge pile B5 was greater. Viewed from the X-direction, edge piles B5 and B1 were more outward than other piles in the layout of eighteen piles. In particular, pile B5 was not only the front-row pile but also the edge pile, that is, pile B5 is a corner pile, which indicates that the corner pile of the pile-cap foundation distributes the largest load under seismic excitation, followed by the frontrow pile, and the middle pile is the smallest.
In order to determine the scale for structural force and hydrodynamic force, a numerical analysis of prototype structure was conducted by using fuid-structure coupling model. When artifcial wave 1 was excited along the Xdirection, the horizontal force of the prototype structure without water was 152.4 MN, and the corresponding bending moment at the bottom of the pile-cap foundation was 7632.4 MN·m. Te horizontal force of the prototype structure was 183.3 MN in 60 m deep-water environment, and the corresponding bending moment at the bottom of the pile-cap foundation was 8697.2 MN·m. Structural force was the main factor in the waterless condition; meanwhile, structural force and hydrodynamic force were the main factors in 60 m deep-water environment, and the infuence diferences in the waterless condition and 60 m deep-water environment were mainly caused by hydrodynamic force. Compared with the waterless condition, the horizontal force increased by 30.9 MN and the bending moment at the bottom of the pile-cap foundation increased by 1064.8 MN·m in 60 m deep-water environment, and the increase rates were 20.3% and 14.0%, respectively. According to the structure similarity criteria and fuid similarity criteria followed by the test design, the ratio of structural force and hydrodynamic force in the test model was consistent with the prototype structure.
It can also be seen from Figures 22 and 23 that the strain increment of nine piles caused by 1.0 m water depth was signifcantly diferent, and Table 4 presents the strain increment values and corresponding increase rate of the measuring points at the bottom of piles B1 to B9. Te strain increase rates of nine piles are basically within 17% and the strain test results can also indirectly refect structural force and hydrodynamic force, and the overall trend of the test results was consistent with abovementioned numerical calculation result. Piles B1, B4, B5, and B9 were the edge piles, and the corresponding strain increment was larger than that of the secondary edge pile and middle pile. According to the abovementioned fndings of hydrodynamic pressure acting on diferent piles in Section 3.3.2, the hydrodynamic pressure acting on the edge pile was the largest, followed by the secondary edge pile, and the hydrodynamic pressure on the middle pile was the smallest. Te hydrodynamic pressure diference was an important reason for the phenomenon that the strain increment of the edge piles was greater than that of the middle piles.

Strain Analysis of Diferent Piles under Y-Direction
Excitation. Artifcial waves 1 and 2 were excited along the Ydirection when the water depth was 1.0 m, and the maximum tensile strain at measuring points is shown in Table 5. For side-row piles under excitation of artifcial waves 1 and 2, the maximum tensile strain of edge pile B1 was slightly greater than that of middle pile B2, and the corresponding strain values of middle pile B2 were 95.7% and 96.6%, respectively, of edge pile B1. For the middle-row piles under excitation of artifcial waves 1 and 2, the maximum tensile  strain of edge pile B5 was the largest, secondary edge pile B6 was the second largest, and middle pile B7 was the smallest. Te strain value of secondary edge pile B6 was 95.8% and 94.7% for edge pile B5, respectively, and the strain value of middle pile B7 was 89.9% and 91.4% of edge pile B5, respectively. Under the excitation of artifcial waves 1 and 2, the maximum tensile strain of edge pile B5 was 80.7% and 79.8% for edge pile B1, respectively. Te strain results of side-row piles B1-B2 and middle-row piles B5-B7 under Y-direction excitation indicate that the maximum strain of diferent piles was clearly diferent. Te maximum strain was related to the layout of piles; the maximum strain of the middle pile B7 of the middle row was 72.5% and 73.0% of the edge pile B1 of the side row under the excitation of artifcial waves 1 and 2, respectively. Te maximum strain diference of the piles reached 27.5% at 1.0 m water depth.
Viewed from the Y-direction, pile B1 was not only a front-row pile but also an edge pile, that is, pile B1 is a corner pile in the layout of eighteen piles, which indicates that the corner pile of the pile-cap foundation distributed the largest load under seismic excitation, followed by the frontrow pile, and the middle pile was the smallest. Tis law is consistent with the strain characteristics of piles under the X-direction excitation. Terefore, strengthening the reinforcement of corner piles and front-row piles is recommended in the seismic design of a pile-cap foundation.

. Conclusion
To study the mechanical characteristics of complex pile-cap foundations under earthquakes and the distribution law of hydrodynamic pressure acting on piles and caps in deepwater environments, a series of underwater shaking-table tests on complex pile-cap foundation were conducted. Te main fndings are summarized as follows.
(1) Considering the structure-water interaction, the existence of water can prolong the natural vibration period of complex pile-cap foundation, and the natural vibration period of complex pile-cap foundation increases by 2.1% for 0.5 m water depth and 5.6% for 1.0 m water depth. Difering from the previous studies, the acceleration of pile-cap foundation decreases by 2.6% for 0.5 m water depth and 4.2% for 1.0 m water depth, and the impact of water bodies on the acceleration depends on the acceleration response spectrum of the input seismic wave. (2) Te strain, displacement, and hydrodynamic pressure increased in varying degrees with water depths. Te maximum strain occurred at the bottom of the piles, and the maximum at this location increased much faster with increasing water depths than the upper positions of the piles. Compared to the waterless condition, the maximum strain of the piles increased by 13.8% for the X-direction earthquake excitation and 15.1% for the Y-direction earthquake excitation in 1.0 m water-depth environment, and the infuence of hydrodynamic pressure should be considered in the seismic design of complex deepwater pile-cap foundation. (3) Te strain of each pile under earthquake excitation is related to the layout of the piles. Te maximum strain of the corner pile was the largest, followed by that of the front-row pile, and that of the middle pile was the smallest. Te maximum strain diference of the diferent piles under the X-and Y-direction excitations reached 26.4% and 27.5%, respectively. It was recommended to strengthen the reinforcement of corner piles and front-row piles in the seismic design of a complex deep-water pile-cap foundation. (4) Te hydrodynamic pressure is closely related to the water depth. As the distance from the water surface decreases, the attenuation efect signifcantly increases. Te hydrodynamic pressure acting on the piles gradually decreased from bottom to top. Te surrounding piles can infuence the hydrodynamic pressure of a certain pile, the hydrodynamic pressure acting on the edge pile was the largest, followed by the secondary edge pile, and the hydrodynamic pressure on the middle pile was the smallest. Te maximum diference of the hydrodynamic pressure between the piles was 20%. (5) Owing to the infuence of the round-ended cap, the hydrodynamic pressure acting on the pile-cap foundation model suddenly increased at the cap. Te hydrodynamic pressure anting on the cap gradually decreased from front to side, and the amplitude attenuation of the cap was signifcantly afected by its shape.
Based on complex deep-water pile-cap foundation for Xihoumen rail-cum-road bridge, the detailed data of dynamic response can be obtained from the test results, which provide the direct reference for the seismic design of actual bridge engineering. Experimental investigations discussed in this study clarify the weak point of complex pile-cap foundation under the earthquake and the infuencing extent of the water depths on dynamic response. Besides, the  research results are helpful for revealing the mechanical characteristics of complex group-piles and the distribution rules of hydrodynamic pressure on diferent piles and cap in deep water. Nevertheless, due to the complexity of structurewater coupling problem for four or more rows of group piles and round-ended cap under earthquake action, some indepth mechanisms can be further studied in future research.

Data Availability
Te data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that they have no conficts of interest.