# Study Method of Pile near Cohesionless Slope under Reversed Lateral Load Considering Sand Strength State and Lateral Deflection of Pile

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## Abstract

**:**

## 1. Introduction

## 2. Analysis of Proposed Method

#### 2.1. Basic Assumptions

#### 2.2. Force Analysis of Active Wedge

#### 2.3. Force Analysis of Passive Wedge

#### 2.4. Internal Friction Angle of Cohesionless Soil Related to Stress-Dilatancy Shear Strength State

## 3. Solution of Proposed Method

#### 3.1. P-Y Curve Model

#### 3.2. The Solution Flow Chart of the Proposed Method

## 4. Validation

#### 4.1. Centrifuge Test Pile

^{3}, the relative density ${D}_{r}$ = 65%. So, the value of ${n}_{h}$ is 42 MN/m

^{3}. The results of the load-lateral deflection curve of the centrifugal experiment and the results of the calculation method in this paper are shown in Figure 8.

#### 4.2. 3D FE Test Pile

^{3}. As can be seen from Figure 11, the prediction results of the proposed method are in good agreement with the FE results, which indicates the rationality of the proposed method. In addition, by considering the influence of both the lateral deflection of pile $y$ and the initial mean effective stress ${p}_{0}^{\prime}$ on the internal friction angle $\phi $, the predicted results of the proposed method are closer to the FE analysis results. It can be seen that the initial mean effective stress and the change of sand stress state caused by pile displacement are important influences on the sand internal friction angle, and this effect needs to be taken into account in pile foundation design.

## 5. Discussion

#### 5.1. Mean Effective Stress-Internal Friction Angle State of Sand

#### 5.1.1. Correlation between y and Mean Effective Stress-Internal Frictional Angle State of Sand

#### 5.1.2. Correlation between Relative Density ${D}_{r}$ and Mean Effective Stress-Internal Friction Angle State of Sand

#### 5.2. Pile Lateral Characteristic

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The direction of the lateral load acting on the pile foundation: (

**a**) forward loading; (

**b**) reverse loading.

**Figure 2.**Passive wedge and active wedge formed in front of and behind the pile under lateral load: (

**a**) The active wedge does not develop to the slope; (

**b**) The active wedge has developed to the slope.

**Figure 3.**Post-pile active wedge failure mode above critical depth ${z}_{c}$ and the system of forces.

**Figure 4.**Post-pile active wedge failure mode below critical depth ${z}_{c}$ and the system of forces.

**Figure 12.**The influence of lateral deflection $\mathrm{y}$ of pile on mean effective stress-internal friction angle state of sand: (

**a**) $\phi -{\phi}_{c}/\phi -{\phi}_{{c}_{y=0}}$ at different depths; (

**b**) ${p}_{0}^{\prime}/{{p}_{0}^{\prime}}_{y=0}$ at different depths; (

**c**) The relationship between $\phi -{\phi}_{c}$ and ${p}_{0}^{\prime}$.

**Figure 13.**The influence of relative density ${D}_{r}$ on mean effective stress-internal friction angle state of sand: (

**a**) $\phi -{\phi}_{c}/\phi -{\phi}_{{c}_{y=0}}$ at different depths; (

**b**) ${p}_{0}^{\prime}/{{p}_{0}^{\prime}}_{y=0}$ at different depths; (

**c**) The relationship between $\phi -{\phi}_{c}$ and ${p}_{0}^{\prime}$ (ignoring the influence of $y$); (

**d**) The relationship between $\phi -{\phi}_{c}$ and ${p}_{0}^{\prime}$ (considering the influence of $y$).

**Figure 14.**Influence of the sand state considering lateral deflection $y$ on the pile lateral characteristic: (

**a**) Curve of bending moment of pile versus depth; (

**b**) Curve of lateral deflection of pile versus depth.

$\mathit{E}\left(\mathbf{p}\mathbf{a}\right)$ | $\mathit{\upsilon}$ | $\mathit{\gamma}\left(\mathbf{k}\mathbf{N}/{\mathbf{m}}^{3}\right)$ | $\mathit{c}\left(\mathbf{k}\mathbf{P}\mathbf{a}\right)$ | $\mathit{\phi}$ | $\mathit{\psi}$ | $\mathit{L}\left(\mathbf{m}\right)$ | $\mathit{D}\left(\mathbf{m}\right)$ | |
---|---|---|---|---|---|---|---|---|

Pile | $2.52\times {10}^{10}$ | 0.3 | 68 | / | / | / | 21 | 0.61 |

Soil | $1.65\times {10}^{7}$ | 0.3 | 9 | 0.2 | 39 | 9 | / | / |

$\mathit{E}\left(\mathbf{p}\mathbf{a}\right)$ | $\mathit{L}\left(\mathbf{m}\right)$ | $\mathit{\gamma}\left(\mathbf{k}\mathbf{N}/{\mathbf{m}}^{3}\right)$ | $\mathit{D}\left(\mathbf{m}\right)$ | ${\mathit{\phi}}_{\mathit{c}}$ | $\mathit{b}$ | $\mathit{\theta}$ | $\mathit{h}$ (m) | ${\mathit{D}}_{\mathit{r}}$ | |
---|---|---|---|---|---|---|---|---|---|

Pile | $2.52\times {10}^{10}$ | 21 | / | 1 | / | 0.3 | |||

Soil | $/$ | / | 9 | / | 28.5° | $b=4D$ | 30° | / | 90% |

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**MDPI and ACS Style**

Jiang, C.; Liu, J.; Lin, M.
Study Method of Pile near Cohesionless Slope under Reversed Lateral Load Considering Sand Strength State and Lateral Deflection of Pile. *J. Mar. Sci. Eng.* **2023**, *11*, 741.
https://doi.org/10.3390/jmse11040741

**AMA Style**

Jiang C, Liu J, Lin M.
Study Method of Pile near Cohesionless Slope under Reversed Lateral Load Considering Sand Strength State and Lateral Deflection of Pile. *Journal of Marine Science and Engineering*. 2023; 11(4):741.
https://doi.org/10.3390/jmse11040741

**Chicago/Turabian Style**

Jiang, Chong, Jing Liu, and Mingke Lin.
2023. "Study Method of Pile near Cohesionless Slope under Reversed Lateral Load Considering Sand Strength State and Lateral Deflection of Pile" *Journal of Marine Science and Engineering* 11, no. 4: 741.
https://doi.org/10.3390/jmse11040741