Dynamic Response of Pile-Raft Systems with Various Forms of Connection under Cyclic Condition

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Introduction
Pile raft foundations (PRFs) have been extensively used in many engineering practices owing to a series of advantages including favorable seismic performance, slight settlement, and high bearing capacity [1][2][3][4].Piles in PRF are generally utilized as settlement reducers, not structural members for carrying load.In design, fewer piles may be installed to meet the settlement requirements, but result in higher axial stress in the piles.In addition, the rigid connection between the pile head and raft will produce large shear stresses and bending moments at the connection point, especially under seismic loads.Terefore, the shear and bending failure on the pile head may precede the soil failure [5].
To address the high stress problems of piles and rafts [6,7], Wong et al., Lawal, and Doi et al. [8][9][10] proposed disconnected pile-raft systems, which settled an interposed layer between the raft and piles.According to the materials used in the interposed layer, disconnected pile-raft systems can be divided into cushion layer pile-raft systems (CLPRS) and compressible block pile-raft systems (CBPRS).
Laboratory tests and numerical simulations revealed that the settlement and bending moments in the piles and rafts of CLPRS were efectively dropped under static load conditions [11,12].Tis was attributed to the cushion layer efectively regulating the bearing capacity of the foundation, playing an important role in improving the load transfer mechanism of the pile and reducing the overall settlement and stifness of the foundation [13][14][15].As for CBPRS, researches have dedicated that the appropriate stifness of compressible blocks can be selected to adjust the reaction force distribution at the pile head and obtain the specifed settlement [16,17].
Te mechanism of pile-raft systems under seismic conditions is relatively less studied compared with that under static load conditions, mainly focusing on the PRF and CLPRS.In general, the interaction and acceleration of the pile-raft systems are afected under seismic conditions.Kumar et al. [18] conducted a series of centrifuge model tests to evaluate the behavior of PRF under dynamic loading conditions and found that the maximum displacement and bending moment were observed at the pile head, which was attributable to the rigid fxity of the piles with the raft.Te crossover point in the bending moment profle was observed at shallow depths for all cases of loading.Fioravante and Giretti [19] used a series of centrifuge model tests to investigate the load transfer mechanisms of PRF and CLPRS and found that PRF acted as a settlement reducer while CLPRS played the role of soil reinforcement.Based on the shaking table tests, Azizkandi et al. [20,21] found that PRF and CLPRS efectively reduced the ground settlements.It was also concluded that CLPRS decreased the maximum bending moment of piles by 20%-60%, based on input motion amplitudes and cushion layer material.Han et al. [22] used numerical simulation on the diference in the seismic responses of PRF and CLPRS and found that the seismic absorption efect of a cushion was good, with an absorption ratio of approximately 0.85.
While it has been confrmed that CLPRS have some good seismic performance under seismic conditions, the dynamic behavior of CBPRS, such as bending moments in the piles and ground motion efect, has not been reported experimentally or numerically.
In this study, a series of model tests on the pile-raft systems with various connection modes was conducted to further examine the operating mechanism of the pile-raft systems under dynamic loading conditions.Additionally, fnite element software was used for numerical simulations and supplementary analysis of the model tests.Te pile-soil interaction, the bending moment of the pile, and the acceleration of the soil and raft of PRF, CLPRS, and CBPRS were analyzed to elaborate on the dynamic performance of the pile-raft systems.

Testing Apparatus.
All the experiments in the present study were carried out using the shaking table at Hainan University, as shown in Figure 1.Te shaking table had a maximum vibration acceleration of 3 g, maximum horizontal displacement along the shaking direction of ±7 mm, and a vibration frequency of 1-3000 Hz.Te rubber membrane was applied inside the model box, which could efectively weaken the refection and scattering efects of dynamic waves on the boundary.

Model Confguration.
High acceleration and a scaled model were adopted in the shaking table tests to simulate the same stress conditions in the prototype.Based on the characteristics of the model and the performances of the shaking table, Young's modulus (E), length (L), and density (ρ) were selected as basic physical quantities to acquire the similarity ratio.For example, a prototype pile-raft modulus of 3 × 10 4 MPa was modeled by 3 × 10 3 MPa in shaking table tests; a prototype pile length of 7.5 m was modeled by 0.25 m; and a prototype pile-raft density of 2.36 × 10 3 kg/cm 3 was modeled by 1.18 × 10 3 kg/cm 3 .Furthermore, the similarity ratios of other physical model parameters, such as time (t) and acceleration (a), were deduced from the Buckingham π theorem [23].Te similarity ratios of the model system are shown in Table 1.Te properties of elements used in the pileraft systems are shown in Table 2. Tree types of the pile-raft systems are shown in Figure 2.

Soil Sample.
Te model ground used in the test was natural organic matter-disseminated sand (OMDS) on Hainan Island.Hainan Island is located at the edge of the Circum-Pacifc Seismic Belt, with a great earthquake intensity in the northern region [24].In addition, the partial regions are characterized by the extensive distribution of a large amount of OMDS [25].Its basic engineering properties acquired using geotechnical tests and consolidated drained triaxial tests, which are concluded in the Chinese Standard for geotechnical testing method [26], are shown in Table 3. Te soil was packed layer by layer to ensure the uniformity of the soil in the model box.Te soil was divided into six layers; each layer was 60 mm, and the total height was 300 mm.Te surface of each layer was scraped to ensure good contact between the layers flled separately.
2.4.Instrumentation.Figure 3 displays the placement of instruments.Six electrical resistance-type strain gauges, three pore water pressure sensors, and three soil pressure sensors were arranged 5 cm, 12.5 cm, and 20 cm away from the top of the pile.Te strain gauges were symmetrically distributed on both sides of the pile along the shaking direction.A soil pressure sensor was also set at the corresponding height with each pair of strain gauges.Te accelerometers were set on the shaking table, the top of the raft, and the surface of the soil.
Te pore water pressure sensor [27] used is the DSP-I-3BS high-precision miniature split-type pore pressure sensor produced by the Institute of Engineering Mechanics, China Earthquake Administration, to measure the time characteristics of the excess pore pressure under vibration.
Te strain gauge used is the BFH120-10AA-D150 strain gauge produced by Guangce Electronics Co., Ltd. in Heshan District, Yiyang City.It has a rated resistance of 120 Ω and a sensitivity factor of 2.0 ± 1%.It is symmetrically attached to both sides of the pile body along the vibration direction to measure the strain of the pile body.
Te accelerometer selected is the piezoelectric accelerometer produced by Beijing Spectrum Century Technology Development Co., Ltd.It is placed on the vibration table, top of the soil, and top of the raft to obtain the acceleration time history curves of the vibration table input, soil surface, and raft top.
Te dynamic acquisition system adopts the IMC dynamic data acquisition instrument from Germany, as shown in Figure 1.It has 16 channels and is connected to the soil pressure box and pore pressure sensor through the bridge box to obtain the corresponding signals, which are ultimately converted into

Test Program.
A sine wave with an acceleration of 1.8 g was adopted to scale the peak ground acceleration of 0.3 g so as to examine the efect of the earthquake intensity of the northern region on Hainan Island.In combination with the test conditions, the test samples were divided into

Numerical Simulation
Based on the aforementioned experimental results, the fnite element software ABAQUS was used to provide more insight into the dynamic load-bearing mechanism of the pileraft systems.4 Shock and Vibration failure criterion was adopted in this study with a nonassociated fow rule.Te calculation models for all scenarios in this section were implemented using the C3D8R element, an eight-node linear reduced integration solid element, available in the ABAQUS general-purpose fnite element software.Tis element was capable of efectively simulating the 3D pile-soil model.Te material properties of the soil, pile, raft, compressible block, and cushion layer are presented in Tables 2 and 3.Meanwhile, Rayleigh damping was used to describe the damping of all materials.Finally, each element of the model was meshed in the Mesh module.Te elements on the contact surface had diferent material properties; hence, the soil closer to the pile was more densely divided to ensure the convergence of the calculation.

Numerical Modeling
Procedure.Te numerical modeling analysis had three steps: geostress equilibrium, vertical static load, and dynamic load.Te vertical static load, a total of 450 kN, was applied to the center of the raft in fve stages.Te cyclic loading in the sinusoidal waveform was used on the bottom of the sand, which lasted 20 s.Te dynamic boundary condition adopted staticdynamic coupling boundary processing technology [28].Specifcally, the horizontal displacement along the side of the sand was released frst during cyclic loading, and then the vertical displacement along the side of the sand was restrained.At the same time, the horizontal bearing reaction force under static load was applied.Finally, the preset time history of acceleration was introduced into the bottom of the sand to complete the static-dynamic coupling boundary.

Results and Interpretation
4.1.Acceleration.Figure 5 shows the test results of the time histories of accelerations for the three diferent connection forms of the pile-raft systems, and the calculated results are shown in Figure 6.
Because of the pile-soil-raft interaction, the accelerations recorded on the raft and sand difered from those input from the shaking table or the ground bottom of the numerical models.Te amplifcation factor of acceleration was usually used to study this law.Equation ( 1) was used to normalize the peak acceleration, and the amplifcation factors at different positions were obtained, as shown in Table 5.
where λ denotes the amplifcation factor of acceleration, x is the peak acceleration recorded on the accelerometer, and y is the peak acceleration input from the shaking table.
Te peak acceleration measured on the top of the raft and the surface of the sand apparently exceeded the values input from the shaking table at the bottom under the three types of connection conditions, as shown in Figure 5. Table 5 shows that the amplifcation coefcients of the experimental results ranged from 1.5 to 2.8.Tese results were consistent with the previously reported fndings of Zhang et al. [29] showing that soils could obviously amplify ground motions.Moreover, the peak soil and raft accelerations of CLPRS and CBPRS were found to be lower than those of PRF, implying that the disconnection between the pile and the raft could weaken the amplifcation efect of soil on acceleration.Tis was also reported by Ha et al. [30].Importantly, the amplifcation factor on the top of the CBPRS raft was lower than that on the surface of sand, which was contrary to PRF [31].In addition, the reduction in acceleration on the top of the raft weakened the inertial force of the superstructure caused by the horizontal cycle load.Tis meant that the compressible block played a signifcant isolation role under the test conditions in this study.
Table 5 also shows that the calculated peak acceleration amplifcation factors of the three types of pile-raft systems were consistent with those measured using the shaking table test.For example, compared with the results in PRF, the experimental and calculated peak accelerations of the raft top could be reduced by 42% and 45%, respectively, after the embedment of the compressible block, while the  Shock and Vibration experimental and calculated peak accelerations of the sand surface were reduced by 8% and 9%, respectively, after the embedment of the cushion layer.Tis verifed the feasibility of numerical simulation in this study.Tis also implied that the isolation efect of the compressible block was relatively obvious.
Te amplifcation factors of peak acceleration to reveal the acceleration response of the ground at diferent depths along the pile are shown in Figure 7. Te amplifcation factors increased from bottom to top during sine wave transmission from the bottom of the site.Moreover, the amplifcation factors of CBPRS and CLPRS along the pile were lower than those of PRF.Te reason was that the ground was obviously afected by the dynamic interaction of the larger stifness with the connection of the pile and raft.When the pile top and raft were separated by a cushion layer or compressible block, the ground was less afected by the inertia efect and the acceleration response of the ground was also weakened [18,32].

Bending Moment along the Pile.
Te bending moments were calculated using equation ( 2) according to the pile fexural rigidity, and its measured strain value was derived from the strain gauge recorded along the instrumented pile, as shown in Figure 8.
where M is the peak bending moment, ε 1 and ε 2 are tensile and compressive strains of each test section, respectively, E is Young's modulus of the model pile, I is the inertia moment of the pile section against the neutral axis, and b is the side length of the model pile.
Te time history of the bending moment along the pile of the PRF was basically the same under cyclic loading conditions, showing sinusoidal regulation, as shown in Figures 8(a)-8(c).Figure 8(d) shows the peak bending moment along the pile of PRF.It was apparent that the bending moment closer to the pile top was greater than that   Shock and Vibration closer to the shaking table, consistent with the results of Banerjee et al. [33] and Wang et al. [34].Te peaks of the positive and negative bending moments were approximately symmetrically distributed along the pile.Figure 9 shows the calculated peak bending moment along the pile in diferent connections.Te maximum bending moment of the PRF was closer to the pile head and decreased gradually along the pile.Tis was consistent with the bending moment measured using the shaking table test, as reported by this paper and Baziar et al. [35].However, the bending moments of CBPRS and CLPRS were nearly equal to zero at the pile head; they frst increased and then decreased along the pile, as reported by Kumar et al.Rasouli and Fatahi, and Ko et al. [18,36,37].Te maximum bending moments of CBPRS and CLPRS decreased by 71.7% and 46.8%, respectively, due to the separation of the pile and raft.Tese results showed that the fexure performance of the compressible block and cushion layer was better than that of the dynamic contact pressure between the pile and soil was recorded, as shown in Figure 10.Te distribution of the dynamic contact pressure of the PRF along the pile was Kshaped, which was consistent with the results of the shaking table test conducted by Qing et al. [39].However, the dynamic contact pressures of CBPRS and CLPRS in the range of 30-50 kPa were distributed more evenly than those of PRF.Tis indicated that the bearing capacity of the soil around the pile was more uniformly mobilized when the pile and raft were disconnected, which was more benefcial to the use of pile strength.Meanwhile, the dynamic soil pressure at the pile head was reduced by approximately 50%, which could efectively avoid pile head failure.

Conclusions
Tis study mainly dealt with the aseismic performances of the three types of pile-raft systems under the cyclic loading of the horizontal sine wave.Overall, the systems with different connection forms showed certain variation rules and diferences under cyclic loading.Te following conclusions were drawn by comparing the model test and numerical simulation data.
(1) Te disconnection between the pile and the raft could weaken the amplifcation efect of the raft top and soil surface on acceleration.Te peak acceleration of the raft top could be reduced by more than 40%, after the embedment of the compressible block, while the peak acceleration of the soil surface could be reduced by 8%, after the embedment of the cushion layer.(2) Due to the separation of the pile and raft, the maximum bending moments of the CBPRS and CLPRS decreased by 71.7% and 46.8%, respectively, efectively avoiding shear failure of the pile head.(3) Te embedment of the cushion layer and the compressible block could well mobilize the potential of the ground around the pile, which was more benefcial to the use of pile strength.Meanwhile, the dynamic soil pressure at the pile head was reduced by approximately 50%, which could efectively avoid pile head failure.(4) Te results of the shaking table test and numerical simulation showed that the dynamic response of the pile-raft systems was closely related to the elastic modulus of the connecting material between the pile and the raft.Te acceleration amplifcation efect on the top of the raft decreased, and the peak bending moment at the pile head decreased with the decrease in the elastic modulus.Moreover, the distribution of the dynamic contact pressure between the pile and soil became more uniform.Terefore, the test condition of this paper indicated that the isolation efect of the compressible block was relatively obvious.

Figure 5 :Figure 6 :
Figure 5: Time histories of acceleration acquired by tests (a) on the top of raft, PRF; (b) on the surface of sand, PRF; (c) on the top of raft, CBPRS; (d) on the surface of sand, CBPRS; (e) on the top of raft, CLPRS; and (f ) on the surface of sand, CLPRS.

Figure 7 :Figure 8 :
Figure 7: Calculated amplifcation factor of the peak acceleration along the pile.

Figure 8 :Figure 9 :Figure 10 :
Figure 8: Dynamic bending moment of PRF acquired by the following tests: (a) time history at 5 cm below the pile top; (b) time history at 12.5 cm below the pile top; (c) time history at 20 cm below the pile top; and (d) peak bending moment along the pile.

Table 1 :
Similarity ratio of the model system.
Figure 1: Schematic drawing of the shakingtable test system.* Adopted similarity ratio Young's modulus, E S E � E m /E p 1/10 Density, ρ S ρ � ρ m /ρ p 1/2 Length, L S l � L m /L p a � S E /(S p × S l ) 6 * S refers to the ratio of the model to the prototype, m in the subscript refers to the model, and p refers to the prototype.

Table 2 :
Properties of the elements.

Table 5 :
Te amplifcation factor of peak acceleration.