# Dynamic Response of Offshore Open-Ended Pile under Lateral Cyclic Loadings

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## Abstract

**:**

## 1. Introduction

## 2. Model Test Design

#### 2.1. Model Box and Soil Sample Preparations

#### 2.2. Model Pile and Sensor Layout

#### 2.3. Test Programme

_{R}) of a single pile foundation under the lateral static load conditions is the corresponding load when the pile top displacement reaches 0.1 times the pile diameter. Based on static the loading test, the lateral ultimate bearing capacity of the pipe pile is 1587 N. Leblanc et al. [13] defines two coefficients ${\zeta}_{\mathrm{b}}$ and ${\zeta}_{\mathrm{c}}$ to represent the characteristics of cyclic loading (Refer to Equations (1) and (2). ${\zeta}_{\mathrm{b}}$ is cyclic load ratio, ${\zeta}_{\mathrm{c}}$ is the ratio of minimum load P

_{min}to maximum load P

_{max}.

_{R}= 1587 N) are 0.126, 0.315, and 0.504, respectively. The uniaxial cyclic load ratio is 0.113.

## 3. Discrete Element Simulations

#### 3.1. Soil Sample Preparation

_{50}) and uneven coefficient (C

_{u}) are 3.52 mm, 2.25 mm, 2.92 mm and 1.26, respectively.

#### 3.2. Numerical Simulation Model

_{pp}(0.2 R) [30], as shown in Figure 7. In this simulation, the diameter of the particles forming the pile is much smaller than the diameter of the pile. Further, the distance between the particles is short. The roughness is close to the initial set value. The direction of the contact force between the particles and the pile is the same as the axial direction of the pile. With this, the axis resistance calculations are easier and more accurate. Since the proposed GM uses the explosive method for particle generation. Particles are created at their final radii in specify numbers to achieve the desired porosity and the number of every type size are calculated in advance. The following Equations (3)–(6) will be used for the calculation of the initial porosity e

_{initial}and particle number in every grid. A

_{m}is the area of the model, A

_{pi}and N

_{(i)}is the total particles area of the same specific diameter r

_{(i)}and the quantity of the corresponding diameter particles. The final selection of soil samples is shown in Table 2.

#### 3.3. Numerical Simulation Programme

## 4. Test Results and Discussions

#### 4.1. Measured Pile Top Cumulative Displacement under Lateral Cyclic Loadings

_{N}) of the pile under the cyclic load and the displacement y

_{1}of the pile after the first cycle and the number of cycles N are as follows:

_{N}is the horizontal displacement after N cycles, C

_{N}is the weakening coefficient. For cohesion-less soil, C

_{N}is usually 0.2. The weakening coefficients for M1, M2, M3 and M4 are found to be 0.159, 0.173, 0.181, and 0.186, respectively. The weakening coefficient is similar to that obtained by Zhu et al. [33].

#### 4.2. Measured Load-displacement Curve under Lateral Cycling Load

#### 4.3. Measured Surface Displacement under Lateral Cyclic Loading

#### 4.4. Measured Pile Friction under Lateral Cyclic Loading

#### 4.5. Measured Lateral Pressure of Pile under Lateral Cycling Load

#### 4.6. Measured Static p-y Curve under Lateral Cyclic Loadings

## 5. Numerical Simulation Results

#### 5.1. Computed Cumulative Displacement of Pile Top

#### 5.2. Computed Load-displacement Curves

#### 5.3. Computed Displacement Around Soil

#### 5.4. Computed Pile Side Friction

#### 5.5. Computed Lateral Pressure of the Pile Body

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Cyclic loading control (Note: 1–6 is the displacement meter number; and the displacement from the pile is 0.1 m, 0.25 m and 0.6 m).

**Figure 11.**Unit side friction for case M1 (refer to Table 1).

**Figure 12.**Variation of lateral soil pressures with depth for various loading conditions of Pile M1-M4.

**Figure 14.**Displacement of the pile top According to Equation (7), the weakening coefficients of P2, P4, P5, and P6 after fitting are 0.22, 0.24, 0.26, and 0.27, respectively. It can be seen that as the cyclic load ratio increases, the weakening coefficient also increases gradually. The axial cyclic load-weakening coefficient reaches its peak value at a much faster rate with an increase in the cyclic load ratio.

**Figure 19.**Distribution of lateral outside and inside pressure of Pile P2 ((

**a**) outer pressure; (

**b**) inside pressure).

**Figure 20.**Comparison of computed unit lateral pressure distribution with cycles between P2, P4, P5 and P6.

**Figure 21.**Comparison of simulated static load curves between P2, P4, P5 and P6 after cyclic loading.

**Figure 22.**Comparison of measured and computed normalized static loads between various loading conditions.

Test Number | Pile Diameter/mm | Pile End | Loading Method | Amplitude/N |
---|---|---|---|---|

M1 | 140 | open | two-way | 200 |

M2 | 140 | open | two-way | 500 |

M3 | 140 | open | two-way | 800 |

M4 | 140 | open | one-way | 200 |

Physical Parameter | Value |
---|---|

Sand particle density (kg/m^{3}) | 2650 |

Pile density (kg/m^{3}) | 66.65 |

Acceleration of gravity (m/s^{2}) | 9.8 |

Median grain size of particle, d_{50} (mm) | 5.85 |

Model pile diameter d_{pile} (mm) | 45 |

Model pile length (mm) | 500 |

Model pile wall thickness d_{pw} (mm) | 2.475 |

Model box width (mm) | 2400 |

Model box depth D (mm) | 2400 |

Friction coefficient between particles, μ | 0.5 |

Young’s modulus of particles, E_{p} (Pa) | 4 × 10^{7} |

Contact normal stiffness of particles, k_{n}(N/m) | 8 × 10^{7} |

contact shear stiffness of particles, k_{s} (N/m) | 2 × 10^{7} |

particle stiffness ratio (k_{s}/k_{n}) | 0.25 |

Wall normal contact stiffness, k_{n} (N/m) | 6 × 10^{12} |

Initial average porosity | 0.25 |

Final average porosity (Ultimate balance) | 0.185 |

Test Number | Pile Diameter /mm | Buried Depth/m | Loading Method | Amplitude /N | Frequency /Hz | Cycle |
---|---|---|---|---|---|---|

P2 | 45 | 0.4 | two-way | 1000 | 40 | 100 |

P4 | 45 | 0.4 | two-way | 3000 | 40 | 100 |

P5 | 45 | 0.4 | two-way | 5000 | 40 | 100 |

P6 | 45 | 0.4 | one-way | 1000 | 40 | 100 |

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**MDPI and ACS Style**

Liu, J.; Guo, Z.; Zhu, N.; Zhao, H.; Garg, A.; Xu, L.; Liu, T.; Fu, C.
Dynamic Response of Offshore Open-Ended Pile under Lateral Cyclic Loadings. *J. Mar. Sci. Eng.* **2019**, *7*, 128.
https://doi.org/10.3390/jmse7050128

**AMA Style**

Liu J, Guo Z, Zhu N, Zhao H, Garg A, Xu L, Liu T, Fu C.
Dynamic Response of Offshore Open-Ended Pile under Lateral Cyclic Loadings. *Journal of Marine Science and Engineering*. 2019; 7(5):128.
https://doi.org/10.3390/jmse7050128

**Chicago/Turabian Style**

Liu, Junwei, Zhen Guo, Na Zhu, Hui Zhao, Ankit Garg, Longfei Xu, Tao Liu, and Changchun Fu.
2019. "Dynamic Response of Offshore Open-Ended Pile under Lateral Cyclic Loadings" *Journal of Marine Science and Engineering* 7, no. 5: 128.
https://doi.org/10.3390/jmse7050128