Joint earthquake, wave and current action on the pile group cable-stayed bridge tower foundation: An experimental study

Applied Ocean Research 63 (2017) 157–169

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Applied Ocean Research journal homepage: www.elsevier.com/locate/apor

Joint earthquake, wave and current action on the pile group cable-stayed bridge tower foundation: An experimental study Chunguang Liu a,b , Shibo Zhang a,∗ , Ertong Hao a a b

Institute of Earthquake Engineering, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, Liaoning, 116024, China State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning, 116024, China

a r t i c l e

a b s t r a c t

i n f o

Article history: Received 16 May 2016 Received in revised form 9 September 2016 Accepted 4 January 2017 Keywords: Bridge pylon foundation Scale model design EWCJSS Hydrodynamic pressure Collapse mechanism

Sea-crossing cable-stayed bridges located in areas of active seismicity are generally subjected to earthquakes, waves, current and other dynamic loads of potential threat during their service period. The pile group foundation, which is composed of bored piles and elevated pile caps, has been applied widely for pylons to ensure the stability of cable-stayed bridge towers. Owing to its large dimensions, complexity and marked three-dimensional characteristics, it is difficult to model the precise dynamic response of the pile group pylon foundation under the joint action of various dynamic loads by means of existing theory. In this paper, an experimental study is presented for a 1/100 scale dynamic test model of a bridge tower with a grouped pile foundation. The model was designed according to elasticity-gravity similarity laws and tested using the Earthquake, Wave and Current Joint Simulation System. The structural response of the bridge tower in air and water conditions with and without incident sine waves and current was investigated. The test results may be used for engineering practice and further research. © 2017 Published by Elsevier Ltd.

1. Introduction With the advancement of society and the development of scientific technology, there is a demand for higher quality and more efficient transportation. In coastal areas, large-scale cross-sea bridges can provide direct connections between and within cities. They play a very important role, not only by improving the quality of transport but also by offering convenience for travel, thus the construction and maintenance of such bridges have drawn a great deal of attention. In general, two main effects, i.e., ocean wave and current loads, are considered when designing offshore bridge structures. This is reasonable only for a long-term analysis or when the offshore environment is not located in an area of active seismicity. If the offshore environment is seismically active, such as the eastern coast of China or the western coast of the USA, the earthquake load will dominate the design, even in the long-term analysis. In offshore areas of active seismicity, therefore, the combination of earthquake loads with sea wave and current loads threatens the safety of offshore bridge structures. History has recorded several cases of cross-sea bridge destruction, which caused huge economic losses and adverse social impacts. The main reason for the destruc-

∗ Corresponding author. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.apor.2017.01.008 0141-1187/© 2017 Published by Elsevier Ltd.

tion in these cases is the lack of knowledge about the complexity of the offshore deepwater environment [1]. To ensure the stability of a cable-stayed bridge tower, a pylon pile group foundation consisting of elevated piles and caps is commonly used. It is difficult to effectively calculate the dynamic response of such a bridge tower-foundation system under the joint action of various dynamic loads by means of existing theories because of the system’s large dimensions, complexity and marked three-dimensional characteristics. Therefore, this field has attracted researchers to focus on the dynamic response of offshore structures under the joint action of earthquake and wave in recent years. Yamada et al. [2] investigated the dynamic response of offshore structures subjected to random sea waves and strong earthquake motion using the mode superposition method and the frequency-domain random vibration approach. Sea waves were modelled using Bretschneider’s wave energy spectrum and ground motions were represented by Kanai’s power spectrum. Karadeniz [3] presented a general spectral analysis procedure for steel offshore structures, which were subjected to simultaneous random wave and earthquake loading processes. 3D modelling of the structure and the deepwater condition of the wave model were used. The random wave was represented by a surface elevation spectrum (Pierson-Moshowitz or Jonswap) and the random earthquake was represented by the ground acceleration spectrum, a modification of the well-known Kanai-Tajimi spectrum. Abbasi et al. [4]

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analysed a 3D model of the Iran-Khazar Jack-up using ANSYS software. The wave and current characteristics were obtained based on field data. The time-history records of the earthquake used in this research were based on the Manjil earthquake in the same area. Bai et al. [5] presented a 2D finite element analysis using ABAQUS software to simulate the pier-piles-soil system under combined seismic and wave action. The wave characteristics were based on Morison’s hydrodynamic pressure formula. The time-history records of earthquakes used in this research were the Taft earthquake, the El Centro earthquake and the Nanjing artificial wave. Li et al. [6] established a hydrodynamic pressure formula for bridge piers using radiation wave theory, while the wave action was modelled using diffraction wave theory. The dynamic responses of bridges in deep water under the combined actions of earthquakes and waves were calculated in ABAQUS general FEA software by the time-history method. However, in the research so far, the dynamic response of offshore structures under the joint action of earthquakes and waves have only been studied by theoretical analysis and numerical simulation, and the conclusions are still in need of experimental validation. The shaking table test is the most effective method to study the dynamic response of structures under earthquake excitation because it can reproduce seismic excitations and realize the earthquake actions. There is no doubt that the underwater shaking table test provides the necessary environment to study the dynamic response of offshore structures. Tanaka et al. [7] conducted two model tests with a rigid squat circular cylinder (representative of a gravity-type submerged oil storage tank) and a flexible slender cylinder (representative of an intake tower or a large concrete column in an oil production and storage platform) in the earthquake simulator wave tank at Nippon University, Narashino, Japan. Maheri et al. [8] presented the results of a number of experimental investigations using hammer tests and forced-vibration tests which examined the natural frequencies and mode shapes of the added mass during flexible vibration of three cylindrical models in air, containing water, and surrounded by water. Taking the pier of the Ping Tan sea-crossing bridge approach as an engineering background, Lai et al. [9] designed a 1/30 organic glass model of a bridge pier with a pile foundation according to similar principles and studied the dynamic response of the bridge pier model during a simulated earthquake with the underwater shaking table at Dalian University of Technology, China. Taking the south pylon pier pile foundation of Nanjing No. 3 Yangtze River Bridge as an engineering background, Song et al. [10] designed a 1/50 model of a pylon pier pile foundation. In the model, the tower and platform were made of reinforced concrete, whereas the pile was made of steel. The model was tested on the shaking table with sine wave and Tianjin wave loads for two cases—in water and in air—at the University of Science and Technology Beijing, China. Li et al. [11] designed a 1/50 scale bridge pier model according to the similarity principle to study the side pier of an actual deep-water bridge. A homemade rubber was adopted as the model material, and the absorbing material was placed in a steel box lateral wall; a shaking table test of the scaled bridge pier model was performed underwater and out of the water at Tianjin University. Liu et al. [12] designed a 1/32 model of a pier pile made from steel wires and micro-concrete to study the pier foundation of the north channel of Hangzhou Bay Bridge. A series of underwater shaking table tests were conducted in air and water at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. In their tests, however, the initial flow field in the flume was static, thus, it was not strictly the joint action of an earthquake and incident waves. Due to the limitations of knowledge and laboratory conditions, fluid actions were simplified in the abovementioned experimental research and theoretical analyses. All of the above research ignored not only the nonlinear interaction between the fluid and the pile groups of offshore structures but also the effects of pile-to-

pile interaction and pile-cap interaction. Therefore, an underwater shaking table experimental study of the structural performance of a cable-stayed bridge tower foundation under the joint effects of earthquakes, waves and current was required, which had not been carried out to date. This research objective was fulfilled with the Earthquake, Wave and Current Joint Simulation System (EWCJSS) that was completed by Dalian University of Technology in December 2012. This paper first describes the design of a 1/100 scale dynamic test model of a pylon pile group foundation according to the geometric dimensions of the simplified model of the actual bridge pylon foundation that is limited by the test conditions, the laws of similarity for elasticity and gravity, and some processing techniques. Second, the process for the underwater shaking table test based on EWCJSS is introduced. Finally, the peak accelerations, corresponding dynamic amplification factors and the dynamic hydraulic pressure of the pylon, submerged piles and cap subjected to earthquakes, waves and current individually or jointly are studied through the test data. 2. Cable-stayed bridge pylon foundation scale model similitude design 2.1. Prototype A proposed concrete cable-stayed bridge with two pylons and double cable planes spanning 1400 m is shown in Fig. 1a. The main tower is a concrete structure with an ‘A’ form and two cross beams, an upper cross beam and a lower cross beam in the main girder. The tower is 357 m high and rises 287 m above the deck level. The anchorage zone is 8 m high. The bored pile-group is used for the foundation of the main pylon pier and is 2.8 m in diameter. There are 162 group piles of length 117 m and height 45.2 m above the scoured basal surface, and the caps are 105.6 m by 59 m. The pylon foundation is show in Fig. 1b. This paper is devoted to the study of the hydrodynamic pressure during loading due to earthquakes, waves and current individually or jointly, and the dynamic characteristics and collapse mechanism of the pylon foundation using the EWCJSS. To simplify the actual bridge pylon foundation, some processing techniques and equivalent transformations are made as follows: (1) The motion constraint on the bridge tower due to the stay cables and main girder is simplified as an additional mass assigned to the anchorage zone and the lower cross beam of the pylon. (2) The equivalent transformation of the group pile foundation is calculated using the following considerations:  1 the pile diameter and the interval between piles in the same direction are equal behind merged piles, and  2 the compressive strength, flexural stiffness and torsional stiffness of the merged group pile foundation before and after the transformation are equal. (3) The study assumes the bottom of the pylon foundation to be a fixed end and considers the actual pile to consist of the pile above the seabed and the effective pile beneath the seabed. The effective pile length beneath the seabed is an important problem which does not consider the soil behaviour or the composite foundation of flexible piles, and the effective piling length can be calculated according to code [13]. The simplified model (Fig. 2a) of the actual bridge pylon foundation was used as the prototype for the scale model test. 2.2. Scale model design The design of the scale model is one of the keys to ensure that the shaking table test really reflects the dynamic characteristics of

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Fig. 1. The cable-stayed bridge and the bridge pylon foundation.

Fig. 2. Elevation and placement views of bridge pylon foundation (Unit:mm).

the prototype. The scale model of the pylon foundation under the joint action of earthquakes, waves and current should be designed based on principles of similarity for the structural dynamics and hydrodynamics; in other words, the scale model needs to obey the similarity laws of gravity, elasticity, pressure and viscous force. The scale model design achieves vibrational similarity and flow similar-

ity only if the corresponding constants of Froude,  Cauchy, Euler and Reynolds all match. The velocity scale v = l (v is the velocity scale, l is the geometric scale) is derived from the similarity law of gravity. The velocity scale v =  /l ( is kinematic viscosity coefficient scale) can also be derived from the similarity law of viscous force. The dynamic viscosity coefficient is the same for both

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the model and prototype in water, so we have  = 1, and therefore we obtain v = 1/l . As a consequence, it is very difficult to simultaneously meet the similarity laws of gravity and viscous force. This paper presents a feasible simulation method which obeys the similarity laws for elasticity and gravity but ignores similarity in hydrodynamics, thus l = E −1 

(1)

where E is the elastic modulus scale and  is the density scale. It is very difficult to meet the requirements for similarity of both structural dynamics and hydrodynamics. The design for the dynamic test model used some processing techniques described in this paper:

Table 1 Scale relation of each physical quantity for the dynamic model. Physical parameter

Similitude coefficient

1/100 model

Density Elastic modulus Poisson ratio Stress Strain Height

 E  = 1  = E ε = 1 l

1 1/16 1 1/16 1 1/100

Length; Width; Diameter

b = h = d = l ·

Area Mass

s = 2d m =  · l · s

Time

t = 1/ω =



ω =

Frequency

1) In the shaking table test, the acceleration of gravity remains constant, so g = a = 1 (g is the gravitational acceleration scale and a is the acceleration scale); 2) The model reinforcement simulation is based on the basic principle of design for reinforced concrete structures [14], while the bearing capacity of a normal section is based on the principle of flexural capacity equivalence and the shear bearing capacity of an oblique section is based on the shear capacity equivalent principle; 3) We assume that the fluid is incompressible, such that the pile groups-pile cap and partial water surrounding the pile groupspile cap vibrate together. It is necessary to meet the similarity of hydrodynamic action when the pile groups-pile cap vibrates in water. Therefore, the ratios of liquid density and material density of the prototype and model must be equal [15] p /m = p /m

(2)

where p and m are the liquid density scales of the prototype and model, and p and m are the material density scales of the prototype and model. The liquids of the prototype and the model are the same, the density scale needs to satisfy  = 1. Once the model material is selected, the similarity ratio of the elastic modulus and density are also determined. The geometric scale is determined last, but it is very difficult to design and carry out the model test according to the traditional geometric similarity law. Thus, the following reasonable assumptions and simplifications can be made for this type of test model: 1) ‘bridge tower-pile cap-pile groups’ can be regarded as the series for a multiple degree of freedom system; 2) the constraint imposed by the bridge cable and main beam on the top of the bridge tower and the lower beam can be ignored; 3) the structure meets the plane section assumption; 4) to loosen the similarity requirements for the shape of the cross section, the similarity of stiffness of the cross section should be guaranteed. (To facilitate the design of the model, different similarity constants are given to the length, width and height of the model. This is called “distorted similarity”.) The distorted similarity law for elasticity and gravity is [16]: 3l = 2r E −1  .

(3)



I/A, I is where r is the inertia radius scale, the inertia radius r = the moment of inertia, and A is the cross-sectional area. To validate the elasticity-gravity distorted similitude law, the model structure is made from crumb rubber micro-concrete according to the simplified prototype. According to the test conditions, the height scale is 1/100. The similarity ratio of the elastic modulus is 1/16. The density ratio is 1. The damping ratio and Poisson’s ratio are same as the prototype structure. The design of the scale model (Fig. 2b) is based on prototype. The similarity relations used in the shaking table test are shown in Table 1.



v =

Velocity

E



  

·



·

E



l E

1/62500 1/6250000 1/10

l

d 2l

=

d = l

1

 

10 l

l

2 E d · =1  3 l x = l

a =

Acceleration Displacement

1/250

1/10

1 1/100

* is the Poisson ratio scale; is the Stress scale;ε is the Strain scale;b is the length scale;h is the width scale;d is the diameter scale;s is the area scale;m is the mass scale;t is the time scale;ω is the Frequency scale;x is the displacement scale.

Table 2 Verification of the frequency similitude relation between prototype and model. Mode

Prototype (Hz)

Model (Hz)

Error (%)

1 2 3

0.13448 0.38149 0.61503

1.3836 3.9716 6.5148

2.89 4.11 5.93

2.3. Validation of test model In this section, the basic frequency and the dynamic response time-history are verified by analysing the prototype and the scale model. 2.3.1. Verification of frequency similarity relation The modal analysis of the pylon foundation in the prototype and model was carried out using OPENSEES finite element computation software. The first three frequencies of the model are compared with those of the prototype. Because the hollow and variable crosssection structure of the prototype has been simplified as a uniform solid section in the model structure, the errors in natural frequency between the prototype and model are approximately 6%, as shown in Table 2. However, the error rate is acceptable. Therefore, the model similarity law and the equivalency principle are proposed in this paper to meet the needs of the dynamic model test of the underwater structure. 2.3.2. Analysis of the dynamic response time-history similarity relation To strictly follow the time scale, the input earthquake wave should be decreased by 9/10, which would mean that the actual duration of the input El Centro wave would be just five seconds. It was difficult to preserve the spectral characteristics of the El Centro wave, and the structural response of the scale model was not guaranteed. This problem had not been solved in current shaking table tests of scaled cable-stayed bridges [17–19]. Therefore, in this study, the input earthquake wave was scaled as follows: the acceleration response spectrum of the El Centro wave was firstly established, and then the artificial El Centro wave [Fig. 3] lasting for 260 s were produced using the acceleration response spectrum of the El Centro wave.

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Fig. 3. Acceleration time-history response curves and acceleration response spectrum of the Artificial El Centro wave.

With a seismic intensity of 8 ◦ and a peak horizontal ground acceleration of 0.2 g, the input artificial El Centro wave for the prototype as the earthquake wave with an adjusted amplitude. The input acceleration time history for the model is obtained by the similarity relation from the artificial El Centro wave. Dynamic time history analysis of the bridge tower pile group foundation is conducted for the original and model structures. The time, displacement, velocity and acceleration of the time history response curve of the model structure are scaled according to the similarity relation for comparison. The time-history responses of the bridge tower top of the model and prototype under seismic loading are shown in Fig. 4. The dynamic response curves of model agree well with those of the prototype, which proves the reliability of the design.

3.3. Layout of the sensors The model was tested under the joint action of earthquakes, waves and current. Test data, including the acceleration and strain along the height of model, the hydrodynamic pressure, and the properties of the wave and current underwater, were expected to be obtained. Therefore, instruments such as accelerometers, a hydrodynamic pressure transducer, strain gauge, wave sensor and current metre, were employed in the experiment, and arranged according to the properties of vibration and deformation of the model under the input earthquake. The layout of the transducers and sensors is shown in Fig. 6. During the test, a digital camera was used to record the experiment in video and photos. 3.4. Input earthquake and incident wave

3. Experimental instrumentation and setup 3.1. Ewcjss At the end of 2015, EWCJSS at Dalian University of Technology is still unique in the world because it can simulate the joint action of waves, current and earthquakes simultaneously [20]. For the model test, the flume has dimensions of 21.6 m × 5.0 m × 1.0 m, and a maximum water depth of 0.8 m, respectively. The dimensions of the work area of the shaking table are 4 m × 3 m. The maximum dead load that the shaking table can carry is 10,000 kg. The system can be used to simulate an earthquake in three degrees of freedom: horizontal along the long axis, vertical, and pitch in the same plane. The maximum horizontal displacement, velocity, and acceleration are ±75 mm, ±50 cm/s, and 1.0 g, respectively. The frequency range of all motions varies from 0 to 50 Hz. The wave generation system is located at the end of the flume, which can make a wave with a maximum height, peak flow and velocity of 0.33 m, 1.0 m3 /s and 0.5 m/s, respectively. The wave period ranges from 0.5 s to 4 s. To simulate the boundary condition of the wave radiating infinitely far away, energy-absorbing nets are installed at the other side of the flume, which can eliminate the influence of reflected waves on the test results. 3.2. Test model In the current study, as shown in Fig. 5, the bottom of the model was fixed to the shaking table with a rigid connection, whereas the lateral displacement out of the plane was restricted by a cable connecting the top of the model to a fixed point. These methods prevented the shaking table from being destroyed by the collapse of the specimen.

According to the code [21] for seismic design, when choosing the time-history curve of the input earthquake, the spectral characteristics, effective peak and time duration should satisfy the demand. To ensure that the analysis results are convincing, it is important to choose reasonable earthquake waves considering the loading properties and the actual geological conditions of the model. As a result, one artificial wave and the El Centro wave [Fig. 3] were chosen for further analysis. The artificial wave [Fig. 7] lasting for 260 s were produced using the standard spectrum. The peak acceleration was adjusted during the test according to the loading demand. To satisfy the similarity requirement of the experiment, the duration of the input earthquake wave was decreased to 26 s. Moreover, the effects of earthquakes, waves and current were only considered in the transverse direction of the bridge, waves travel with the current. 3.5. Test condition In this test, the load was applied step by step to improve the comparability of the test results and to better understand the mechanism of the fluid-solid interaction of the model. As shown in Table 3, all test conditions were conducted in the water, except for conditions 1 and 2. With the purpose of identifying the dynamic characteristics, such as the natural frequency of the structure and to check whether the model had defects, the white noise and sine wave were used to sweep through the frequencies of the model in a non-water environment. For condition 6, on the other hand, the white noise was replaced by an artificially generated wave to sweep through the frequencies, which showed the effect of water on the structural behaviour by comparison of the natural frequency in the water and non-water environments.

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Fig. 4. Comparison of the time-history response curves of the head pylon between prototype and model.

To prevent the model from damage due to the cyclic earthquake loading, earthquake accelerations of 0.05g, 0.1 g and 0.15 g, wave heights of 0.03 m, 0.04 m and 0.05 m, and a current velocity of 0.25 m/s were selected as input loadings in the test. As shown in Table 3, the two types of earthquake wave were combined alternately with wave and current with increasing acceleration for conditions 6–30. At the end of the test, the acceleration of the input earthquake wave was increased until the model failed.

4. Experiment and results analysis 4.1. Experimental observation The dynamic model was tested to evaluate the individual and joint action of the earthquakes, waves and current. Because the test underwater, it was difficult to observe the damage to the model during the experiment. However, the test data, which were recorded by a 48-channel data collection instrument, could be used to analyse the failure process of the model and to control the loading

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Fig. 5. Photograph of pylon foundation in model test.

Fig. 6. The distribution of transducers (Unit:mm).

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Fig. 7. Acceleration time-history response curves and acceleration response spectrum of the Artificial wave.

Fig. 8. Picture of broken model.

pattern. When the test was finished, the water was pumped out of the pool and the model was checked for macroscopic damage. Failure occurred at (1) the joint of the lower beam and pylon (Fig. 8a),

and (2) the joint of the pylon and cap (Fig. 8b), where the damage eventually resulted in the collapse of the bridge tower (Fig. 8c). The

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Table 3 Experimental loading programme for model test. No.

Input motion

PGA (g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

White noise Sine wave

0.05 0.05

Wave (m)

Current (m/s)

0.03 0.04 0.05 Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial wave Artificial El Centro wave Artificial El Centro wave

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.05 0.1 0.05 0.1 0.05 0.1 0.05 0.15 0.15 0.15 0.05 0.15 0.05 0.15 0.05 0.15 0.05 0.2 0.05 0.2 0.05 0.3 0.05 0.3 0.05 0.4 0.05 0.4 0.05 Loading until failure

0.25 0.25

0.25 0.25 Fig. 9. Comparison of acceleration input between shaking table top and control room. 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

natural frequencies of the model in water are lower than those without water, and the differences are below 2%. 4.3. Deformation response The schematic layout of the base is shown in Fig. 10a. Figs. 10b–d show the strain versus time for the piles and tower, respectively, when a sine wave with a frequency of 4.07 Hz was input in the test. Fig. 10b and c indicate that the strain in p1 was larger than that in p2, which made p1 easier to be destroyed. Fig. 10d shows that the strain in the tower decreases as the height increases, thus the joint between the tower and the platform is most likely to fail.

*The corresponding wave period is 0.7 s.

Table 4 Natural frequency of model. Mode

1 2 3

Natural frequency (Hz) In air

In water

Error (%)

4.07 10.08 13.99

3.99 9.92 13.79

1.72 1.59 1.43

local failures emerged were in accordance with the results of other researches [22,23]. The collapse of the bridge tower is a process of quantitative change of cumulative damage. As the input peak earthquake wave increased, the middle and lower parts of the pylon presented the crack, then the width and the number of the crack got larger, meanwhile, the concrete cover spalled. The shear bearing capacity decreased because of the cumulative damage of the concrete in the area of plasticity hinge of the lower part of the bridge tower. When the input earthquake acceleration increased to 1.6 g, the model had been seriously damaged. The collapse of the model happened caused by brittle shear failure at the application of the next load increment. 4.2. Input and output of the earthquake wave As shown in Fig. 9, the input acceleration was compared with that recorded at the top of the shaking table. The peak values of the input and recorded accelerations were not the same, which may have been induced by errors in the test system. To overcome the effect of these errors, the recorded acceleration is used in the following analysis of the filtered test results. In the model test, the scanning of the white noise, as well as the resonance of the sine wave were conducted to identify deficiencies in the model. The first three orders of the natural frequency of the physical model are listed in Table 4 with and without water. The

4.4. Hydrodynamic pressure under the individual and joint action of earthquakes, waves and current When the earthquake acts alone, radial waves are generated from the centre of where the model is located due to the dynamic interaction between the model and the surrounding water. As shown in Fig. 11, the height of the generated radial wave increases with the peak value of the input acceleration. When only the wave was applied, as shown in Fig. 12a, the hydrodynamic pressure is dependent on the wave intensity, and increases with the height of the model. As a result, the maximum hydrodynamic pressure was reached at the piles close to the platform. This result can be explained by the dimension of the platform, which is large enough for the wave to pass over, and then the piles near the platform are simultaneously subjected to the coupling effect of the incident wave and the diffracted wave, which results in the peak value of hydrodynamic pressure on these piles. When the earthquake was imposed separately, as shown in Fig. 12b, the hydrodynamic pressure decreased with increasing pile height until the platform was reached, and then the pressure increased. Under the joint action of the earthquake, wave and current, as shown in Fig. 12c and d, the hydrodynamic pressure on the pile near the platform varied significantly when a small earthquake acceleration (i.e., 0.05 g) was imposed. It was because, with the increase due to the earthquake acceleration, the hydrodynamic pressure contributed by the earthquake was strong enough that the influence of the wave on the hydrodynamic pressure could be neglected. The hydrodynamic pressure under the action of the earthquakes, waves and current individually or jointly are shown in Fig. 12e. The hydrodynamic pressure induced by the joint action of the earthquake and wave increased by 21.58%, 13.21% and 9.23%, the

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Fig. 10. Time-history curves of strain along the height of the model.

hydrodynamic pressure induced by the joint action of the earthquake, wave and current increased by 13.34%, 6.86% and 4.81% than the hydrodynamic pressure induced by the joint action of the earthquake and wave, respectively, compared with the earthquake acting alone. It was concluded that the earthquake, wave and current contributed first, second and third, respectively, to the hydrodynamic pressure.

The hydrodynamic pressure induced by the joint or linear additive action of the earthquakes and waves are not equal, as shown in Fig. 12f. The hydrodynamic pressure is mainly influenced by the coupling effect of the earthquake, incident wave and current. 4.5. Acceleration at the top of the pylon When the artificial EI Centro waves with the same amplitude were applied, two similar but not identical peak accelerations were obtained. The dynamic response of the top of pylon was affected by the type of the input earthquake wave. As the acceleration of the input earthquake wave increased from 0.05 g to 0.15 g with an increment of 0.05 g, the acceleration of the top of the pylon induced by the joint action of the earthquake and wave [Fig. 13a–f] increased by 13.2%, 5.2% and 1.1%, respectively, compared with the earthquake acting alone. Therefore, the earthquake had more significant influence on the tower top acceleration than the wave. 4.6. Amplification coefficient of the acceleration

Fig. 11. Radial wave height under earthquake action.

The acceleration of an earthquake may increase or decrease as it proceeds, therefore, the amplification coefficient of the acceleration was defined to describe the distribution of the normalized earthquake acceleration along the height of the model as shown in Fig. 14. As the input peak earthquake wave increased, the amplification coefficient of the acceleration decreased. The reason was that the increasing input earthquake acceleration aggravated the

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Fig. 12. Hydrodynamic pressure under joint earthquake, wave and current action.

damage and decreased the stiffness of the model, which resulted in the deterioration of the natural frequency. The model remains the basic integrity when the input earthquake acceleration from 0.05 g to 0.1 g. When the input earthquake acceleration increased to 0.5 g, the middle and lower parts of the model presented the crack. The width and the number of the crack got larger, meanwhile, the concrete cover spalled when the input earthquake acceleration from 0.7 g to 1.2 g. When the input earthquake acceleration increased to 1.6 g, the amplification coefficient

of the acceleration decreased significantly, which indicated that the model had been seriously damaged. The collapse of the model happened at the application of the next load increment.

5. Concluding remarks This research work is focused on the hydrodynamic pressure distribution during a test to destruction under the joint action of earthquakes, waves and current. Extensive model tests with a scale

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Fig. 13. Comparison of the acceleration time-history response curves of the head pylon for earthquake action and joint earthquake and wave action.

ratio of 1/100 have been carried out in the unique EWCJSS facility. These include white noise tests, resonance frequency tests, and various earthquake excitations in low and high water levels, with and without regular waves and current, and a destructive test. Due to the limited length of this paper, not all measurements have been presented.

(1) Similarity laws for elasticity and gravity, and some processing techniques were used to design a cable-stayed bridge

tower foundation model with a scale ratio of 1/100 which was subjected to bending in a series of multi-degree of freedom systems. Comparison of the basic frequency and the time-history response of the head pylon agrees well between the prototype and the model. (2) Failure occurred at the joint between the lower beam and the pylon, and at the joint between the pylon and the cap, where the damage ultimately resulted in the collapse of the pylon. These observations were in accordance with the results of theoretical

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References

Fig. 14. Magnification factors of seismic response along scaled model.

analysis, confirming that the joint between the pylon and the cap is the key part of the design. (3) When only the wave was applied, the hydrodynamic pressure increased with the height of the model. As a result, the maximum hydrodynamic pressure was reached at the pile close to the platform. When the earthquake was imposed separately, the hydrodynamic pressure decreased as the pile height increased until the platform was reached, when the pressure increased. Under the joint action of the earthquake, wave and current, the hydrodynamic pressure on the pile near the platform varied significantly when a small earthquake acceleration was imposed. As the earthquake acceleration increased, the hydrodynamic pressure due to the earthquake was strong enough that the influence of the wave on the hydrodynamic pressure could be neglected. It was concluded that the earthquake, wave and current contributed first, second and third, respectively, to the hydrodynamic pressure. Moreover, the hydrodynamic pressure was mainly influenced by the coupling effect of the earthquake, incident wave and current. (4) The dynamic response of the top of pylon was affected by the type of the input earthquake wave. The earthquake had more significant influence on the acceleration of the bridge tower top than the wave when the earthquake and wave acted jointly.

[1] C.G. Liu, Seismic Response and Seismic Performance Analysis of Bridges, 1st ed., Building Industry Press, Beijing: China, 2009. [2] Y. Yamada, K. Kawano, H. Iemura, K. Venkataramana, Wave and earthquake response of offshore structures with soil-structure interaction, Proc. Jpn. Soc. Civil Eng. 5 (2) (1988) 157–166 (399/I—10). [3] H. Karadeniz, Spectral analysis of offshore structures under combined wave and earthquake loadings, 9th International Conference on Offshore and Polar Eng, Brest: ISOPE (1999) 504–511. [4] M. Abbasi, A.R.M. Gharabaghi, Study the Effect of Wave Directionality on Dynamic Nonlinear Behavior of Jack-up Subjected to Wave and Earthquake Loading, 26th International Conference Shore Mechanics and Arctic Engineering, American Society of Mechanical Engineers, San Diego, 2007, pp. 377–384. [5] D.G. Bai, G.X. Chen, Z.H. Wang, Dynamic analysis of a single-column pier under ground motion and wave action, World Earthquake Eng. 24 (4) (2008) 82–88. [6] Z.X. Li, X. Huang, Dynamic responses of bridges in deep water under combined earthquake and wave actions, China Civil Eng J. 45 (11) (2012) 134–140. [7] Y. Tanaka, R.T. Hudspeth, Restoring forces on vertical circular cylinders forced by earthquake, Earthquake Eng. Struct. Dynamics 16 (1988) 99–119. [8] M.R. Maheri, R.T. Severn, Experimental added-mass in modal vibration of cylindrical structures, Eng. Struct. 14 (3) (1992) 163–175. [9] W. Lai, J.J. Wang, X. Wei, S.D. Hu, The shaking table test for submerged bridge pier, Earthquake Eng. Eng. Vibr. 26 (6) (2006) 164–171. [10] B. Song, G.M. Zhang, Y. Li, Shaking table test of pier-water interaction, J. Univ. Sci. Technol. Beijing 32 (3) (2010) 403–408. [11] Z.X. Li, Y.L. Li, X. Huang, N. Li, Dynamic interaction between water and bridge pier under earthquake excitation, 12th International Symposium on Structural Engineering I (2012) 106–120. [12] C.G. Liu, G.S. Sun, Calculation and experiment for dynamic response of bridge in deep water under seismic excitation, China Ocean Eng. 28 (4) (2014) 445–456. [13] Ministry of Transport of the People’s Republic of China Code for Pile Foundation of Harbor Engineering, China Communication Press, Beijing, 2012. [14] Y. ZHOU, X.L. Lv, Method and Technology for Shaking Table Model Test of Building Structures, 2nd ed., Science Press, Beijing, 2013. [15] G. Lin, Study on model similitude laws for vibration of arch dam, J. Hydraul. Eng. Soc. China 1 (1958) 79–104. [16] G. Lin, T. Zhu, B. Lin, Similarity technique for dynamic structural model test, J. Dalian Univ. Technol. 40 (1) (2000) 1–8. [17] Z.Z. Fang, C. Zhang, Y.J. Chen, Z.Q. Zheng, L. Xu, Research on the shaking table test of three towers cable-stayed bridge based on three shaking table system, China Civil Eng. J. 45 (2012) 25–29. [18] Z.H. Zong, R. Zhou, X.Y. Huang, Z.H. Xia, Seismic response study on a multi-span cable-stayed bridge scale model under multi-support excitations. Part I: shaking table tests, J. Zhejiang Univ. Sci. A 15 (5) (2014) 351–363. [19] C.Y. Yang, PhD Thesis]. Seismic Analysis of Long Span Bridges Including the Effects of Spatial Variation of Seismic Waves on Bridges, Hongkong University of Science and Technology, 2007. [20] X.Y. Zheng, H.B. Li, W.D. Rong, W. Li, Joint earthquake and wave action on the monopile wind turbine foundation: an experimental study, Mar. Struct. 44 (2015) 125–141. [21] Ministry of Transport of the People’s Republic of China Guidelines for Seismic Design of Highway Bridges, China Communication Press, Beijing, 2008. [22] D.B. Ji, X.Z. Duan, Y. Xu, J.Z. Li, Shake table test of cable-stayed bridge pylon subjected to longitudinal ground motions, J. Shijiazhuang Tiedao Univ. 26 (2) (2013) 1–7. [23] R.L. Wang, Y. Xu, J.Z. Li, Shake table test of a concrete cable-stayed bridge subjected to uniform seismic excitation, J. Tongji Univ. (Nat. Sci.). 43 (3) (2015) 357–363.