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

Du, Juan; Lei, Xiao-Peng; Ren, Di-Fan; Wang, Zai-Cheng; Zhang, Yang

doi:https://doi.org/10.1155/2023/3775654

Shock and Vibration

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Abstract Introduction Numerical Simulation Results Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 3775654 | https://doi.org/10.1155/2023/3775654

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

Juan Du,¹Xiao-Peng Lei,¹Di-Fan Ren,¹Zai-Cheng Wang,¹and Yang Zhang¹

Academic Editor: Sandro Carbonari

Received19 Jun 2023

Revised01 Oct 2023

Accepted24 Oct 2023

Published03 Nov 2023

Abstract

This study aimed to examine the aseismic performance of the pile-raft systems with various connection forms. The related shaking table test and numerical simulation were performed for in-depth investigation. The acceleration response spectra on the top of the soil layer and raft were obtained and plotted for contrastive analysis based on the model test at a reduced scale of 1 : 30 and finite element numerical simulation. Accordingly, the working mechanisms of the pile-raft systems in conventional connections with the embedment of the compressible blocks and cushion layers under cyclic loading were explored. The results showed that the embedment of the cushion layer on the pile top could most significantly mobilize the potential of the foundation soil, effectively reduce the bending moment peak of the pile, and reduce the acceleration amplification effect on the top of the soil layer and raft. The embedment of the compressible block on the pile top most markedly reduced the bending moment peak of the pile and effectively mobilized the potential of the foundation soil, which was most favorable for lowering the amplification effect of acceleration on the top of the soil layer and raft.

1. 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 [1–4]. 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. Therefore, 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. [8–10] 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 effectively dropped under static load conditions [11, 12]. This was attributed to the cushion layer effectively 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 stiffness of the foundation [13–15]. As for CBPRS, researches have dedicated that the appropriate stiffness of compressible blocks can be selected to adjust the reaction force distribution at the pile head and obtain the specified settlement [16, 17].

The 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 affected 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 fixity of the piles with the raft. The crossover point in the bending moment profile 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 effectively 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 difference in the seismic responses of PRF and CLPRS and found that the seismic absorption effect of a cushion was good, with an absorption ratio of approximately 0.85.

While it has been confirmed 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 effect, 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, finite element software was used for numerical simulations and supplementary analysis of the model tests. The 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.

2. Shaking Table Test Set-Up

2.1. Testing Apparatus

All the experiments in the present study were carried out using the shaking table at Hainan University, as shown in Figure 1. The 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. The rubber membrane was applied inside the model box, which could effectively weaken the reflection and scattering effects of dynamic waves on the boundary.

2.2. Model Configuration

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 × 10⁴ MPa was modeled by 3 × 10³ 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 × 10³ kg/cm³ was modeled by 1.18 × 10³ kg/cm³. Furthermore, the similarity ratios of other physical model parameters, such as time (t) and acceleration (a), were deduced from the Buckingham π theorem [23]. The similarity ratios of the model system are shown in Table 1. The properties of elements used in the pile-raft systems are shown in Table 2. Three types of the pile-raft systems are shown in Figure 2.

(a)

(b)

(c)

2.3. Soil Sample

The 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-Pacific 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. The soil was packed layer by layer to ensure the uniformity of the soil in the model box. The soil was divided into six layers; each layer was 60 mm, and the total height was 300 mm. The surface of each layer was scraped to ensure good contact between the layers filled 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. The 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. The accelerometers were set on the shaking table, the top of the raft, and the surface of the soil.

The 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.

The 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.

The 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.

The 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 electrical signals. The accelerometer acquisition device uses the WS-5921/U60216-DA1 vibration table control and signal acquisition device inside the shaking table, with 8 channels, directly connected to the accelerometer sensor through a wire, and outputs acceleration values.

2.5. 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 effect of the earthquake intensity of the northern region on Hainan Island. In combination with the test conditions, the test samples were divided into different groups according to the test contents, as shown in Table 4.

3. Numerical Simulation

Based on the aforementioned experimental results, the finite element software ABAQUS was used to provide more insight into the dynamic load-bearing mechanism of the pile-raft systems.

3.1. Finite Element Modeling

First, a three-dimensional model was adopted in the Part module, including three types of pile-raft systems, as shown in Figure 4. The dimensions of the pile, raft, compressible block, and cushion layer were used as the prototypes, as shown in Table 2. The ground was generated with a size of 10 × 10 × 30 m³. Then, the material and section properties were assigned to the elements of the pile-raft systems in the property module. An elastic, perfectly plastic model using the Mohr‒Coulomb failure criterion was adopted in this study with a nonassociated flow rule. The 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 finite element software. This element was capable of effectively simulating the 3D pile-soil model. The 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. The elements on the contact surface had different material properties; hence, the soil closer to the pile was more densely divided to ensure the convergence of the calculation.

3.2. Numerical Modeling Procedure

The numerical modeling analysis had three steps: geostress equilibrium, vertical static load, and dynamic load. The vertical static load, a total of 450 kN, was applied to the center of the raft in five stages. The cyclic loading in the sinusoidal waveform was used on the bottom of the sand, which lasted 20 s.

The dynamic boundary condition adopted static-dynamic coupling boundary processing technology [28]. Specifically, the horizontal displacement along the side of the sand was released first 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.

4. Results and Interpretation

4.1. Acceleration

Figure 5 shows the test results of the time histories of accelerations for the three different connection forms of the pile-raft systems, and the calculated results are shown in Figure 6.

(a)

(b)

(c)

(d)

(e)

(f)

(a)

(b)

(c)

(d)

(e)

(f)

Because of the pile-soil-raft interaction, the accelerations recorded on the raft and sand differed from those input from the shaking table or the ground bottom of the numerical models. The amplification factor of acceleration was usually used to study this law. Equation (1) was used to normalize the peak acceleration, and the amplification factors at different positions were obtained, as shown in Table 5.where λ denotes the amplification factor of acceleration, x is the peak acceleration recorded on the accelerometer, and y is the peak acceleration input from the shaking table.

The 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 amplification coefficients of the experimental results ranged from 1.5 to 2.8. These results were consistent with the previously reported findings 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 amplification effect of soil on acceleration. This was also reported by Ha et al. [30]. Importantly, the amplification 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. This meant that the compressible block played a significant isolation role under the test conditions in this study.

Table 5 also shows that the calculated peak acceleration amplification 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 experimental and calculated peak accelerations of the sand surface were reduced by 8% and 9%, respectively, after the embedment of the cushion layer. This verified the feasibility of numerical simulation in this study. This also implied that the isolation effect of the compressible block was relatively obvious.

The amplification factors of peak acceleration to reveal the acceleration response of the ground at different depths along the pile are shown in Figure 7. The amplification factors increased from bottom to top during sine wave transmission from the bottom of the site. Moreover, the amplification factors of CBPRS and CLPRS along the pile were lower than those of PRF. The reason was that the ground was obviously affected by the dynamic interaction of the larger stiffness 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 affected by the inertia effect and the acceleration response of the ground was also weakened [18, 32].

4.2. Bending Moment along the Pile

The bending moments were calculated using equation (2) according to the pile flexural 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, ε₁ and ε₂ 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.

(a)

(b)

(c)

(d)

The 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 closer to the shaking table, consistent with the results of Banerjee et al. [33] and Wang et al. [34]. The 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 different connections. The maximum bending moment of the PRF was closer to the pile head and decreased gradually along the pile. This 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 first increased and then decreased along the pile, as reported by Kumar et al. Rasouli and Fatahi, and Ko et al. [18, 36, 37]. The maximum bending moments of CBPRS and CLPRS decreased by 71.7% and 46.8%, respectively, due to the separation of the pile and raft. These results showed that the flexure performance of the compressible block and cushion layer was better than that of PRF, thus effectively avoiding the shear failure of the pile head. It was concluded that the compressible block performed better overall.

4.3. Computed Results of Dynamic Contact Pressure

The dynamic response of the pile-raft systems was affected by the dynamic interaction between the pile and soil [38]. Hence, the dynamic contact pressure between the pile and soil was recorded, as shown in Figure 10. The distribution of the dynamic contact pressure of the PRF along the pile was K-shaped, 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. This 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 beneficial to the use of pile strength. Meanwhile, the dynamic soil pressure at the pile head was reduced by approximately 50%, which could effectively avoid pile head failure.

5. Conclusions

This 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 differences under cyclic loading. The following conclusions were drawn by comparing the model test and numerical simulation data.(1)The disconnection between the pile and the raft could weaken the amplification effect of the raft top and soil surface on acceleration. The 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, effectively avoiding shear failure of the pile head.(3)The embedment of the cushion layer and the compressible block could well mobilize the potential of the ground around the pile, which was more beneficial to the use of pile strength. Meanwhile, the dynamic soil pressure at the pile head was reduced by approximately 50%, which could effectively avoid pile head failure.(4)The 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. The acceleration amplification effect 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. Therefore, the test condition of this paper indicated that the isolation effect of the compressible block was relatively obvious.

Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This research was supported by the Hainan Province Science and Technology Special Fund (ZDYF2022SHFZ277), the National Natural Science Foundation of China (52268056), and the Hainan Research Institute of China Engineering Science and Technology Development Strategy (21-HN-ZD-02).

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Copyright © 2023 Juan Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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