# Research on the Load Transfer Law of Cross-Sections of Pile-Supported Reinforced Embankments Based on the Finite Element Method

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## Abstract

**:**

## 1. Introduction

## 2. Field Test

#### 2.1. Introduction of Field Test

#### 2.2. Test Results and Discussion

#### 2.2.1. Variation Law of the Pile–Soil Stress Ratio

#### 2.2.2. Load Variation Law of Subgrade Cross-Sections

## 3. Numerical Simulation

#### 3.1. Numerical Model

#### 3.1.1. Model Establishment and Parameter Selection

_{w}, is zero on the top of the groundwater simulating the free drainage boundary. The finite element calculation model is shown in Figure 7. In the numerical model, the unit type of the embankment and pile is CPE4, the unit type of the soft soil foundation above groundwater level is CPE4, and the unit type of the soft soil foundation below groundwater level is CPE4P. The geogrid adopts the Truss element, and the element type is T2D2.

#### 3.1.2. Model Validation

#### 3.2. Analysis of the Numerical Simulation Results

#### 3.2.1. Variation Law of Load Transfer Efficacy

#### 3.2.2. Load Variation Law of Subgrade Cross-Sections

#### Pile Length

#### Pile Spacing

#### Pile Cap Width

#### Embankment Height

#### 3.2.3. Sensitivity Analysis of the Influencing Factors

_{AF}represents the sensitivity of the influence factors such as pile length and pile spacing to the evaluation index (the load transfer efficacy E). The calculation formula is shown below. The larger the |S

_{AF}| is, the more sensitive the evaluation index A is to the influencing factor F, as follows:

_{0}represents the corresponding parameters in model 1, ${\Delta {A}_{i}/A}_{0}$ is the corresponding change rate of the evaluation index, A, when the influencing factor F changes in $\Delta {F}_{i}$, $\Delta {A}_{i}$ is the amount of change in the evaluation index, and ${A}_{0}$ is the value of the evaluation index in model 1.

#### 3.3. Comparison between Theoretical Value and Calculated Value

#### 3.3.1. Analysis of Calculation Methods

^{3}).

^{3}), $H$ is the height of the embankment (m), and $a$ is the size of the pile caps (m).

^{3}), $S$ is the pile spacing between adjacent piles (m), $b$ is the size of the pile caps (m), $\delta $ is the ratio of pile cap width to pile spacing ($\delta =b/S$), and $\alpha $ is the undetermined coefficient.

^{2}), ${A}_{E}$ is the influence range of single pile (m

^{2}), ${K}_{crit}$ is the critical principle stress ratio, ${\gamma}_{k}$ is the unit weight of the embankment fill (kN/m

^{3}), ${P}_{K}$ is the characteristic value of the permanent distributed load on the top of the reinforced earth structure (kN/m

^{2}), ${h}_{g}$ is the arch height (m),

#### 3.3.2. Analysis of Calculation Results

## 4. Conclusions

- (1)
- Analysis of influencing factors: Increasing the pile length, pile cap width, and embankment height and reducing the pile spacing will increase the pile load transfer efficacy, that is, a single pile’s bearing capacity will be improved. The pile cap’s width has the greatest influence on the load transfer efficacy, followed by pile spacing, while the pile length and embankment height have less influence on the load transfer efficacy.
- (2)
- Variation law of the load sharing ratio of subgrade cross-sections: Macroscopically, increasing the pile length, pile spacing, and embankment height and reducing the pile cap width can improve the soil arch effect’s load sharing ratio. The load sharing ratio of the soil arch effect at the shoulder is smaller than that at the center of the subgrade, indicating that the deformation of the geogrid at the shoulder is large and the membrane effect is significant. Comparing the load sharing ratio of the soil arch effect of each calculation model, the load ratio of the embankment center is 65–90% and that of the shoulder is 51–88%. It can be seen that the load transfer of the embankment is mainly based on the soil arch effect and supplemented by the tensile membrane effect.
- (3)
- Load variation law of subgrade cross-sections: Compared with the center of subgrade, the load transfer efficacy at 10 m on the right side of the central line decreases by 0.1–1.6% and the load transfer efficacy at the shoulder decreases by 2.5–7.5%. This shows that the variation of the load transfer efficacy of subgrade cross-sections is related to the position of the observation point. From the center of the subgrade to the shoulder, the load transfer efficacy decreases gradually and the load transfer efficacy at the shoulder decreases significantly.
- (4)
- Compared with other codes, the load transfer efficacy calculated according to the Chinese specification and BS8006-1-1 is in good agreement with the simulated value.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The geographical location of the test site. (

**a**) Location of test section. (

**b**) Local magnification of the test section location.

**Figure 2.**Schematic diagram of the monitoring element. (

**a**) The layout of an earth pressure box in the test section. (

**b**) An earth pressure box in the field test.

**Figure 4.**Earth pressure distribution of subgrade cross-sections. (

**a**) Earth pressure distribution of Section I. (

**b**) Earth pressure distribution of Section III.

**Figure 7.**The meshing of the numerical model. (

**a**) The meshing of the whole model. (

**b**) Local amplification of the model.

**Figure 8.**Numerical model verification. (

**a**) Cloud image of the embankment settlement. (

**b**) Comparison of field-measured values and the numerical simulation results of the subgrade settlement.

**Figure 11.**Load transfer law under the influence of pile length. (

**a**) Variation law of the load transfer efficacy. (

**b**) Variation law of the load sharing ratio.

**Figure 12.**Load transfer law under the influence of pile spacing. (

**a**) Variation law of the load transfer efficacy. (

**b**) Variation law of the load sharing ratio.

**Figure 13.**Load transfer law under the influence of pile cap width. (

**a**) Variation law of the load transfer efficacy. (

**b**) Variation law of the load sharing ratio.

**Figure 14.**Load transfer law under the influence of embankment height. (

**a**) Variation law of the load transfer efficacy. (

**b**) Variation law of the load sharing ratio.

**Figure 15.**Calculation and theoretical value of the load transfer efficacy under varied pile spacing.

**Figure 16.**Calculation and theoretical value of the load transfer efficacy under different pile cap widths.

**Figure 17.**Calculation and theoretical value of the load transfer efficacy under the embankment height.

Section Number | Foundation Treatment Method | Cushion Thickness (m) | Embankment Height (m) | Pile Length (m) | Pile Diameter (m) | Pile Spacing (m) |
---|---|---|---|---|---|---|

Section I | prestressed pipe pile and gravel cushion | 0.3 | 7.2 | 14 | 0.4 | 2.0 |

Section II | prestressed pipe pile and gravel cushion | 0.3 | 7.2 | 14 | 0.4 | 2.5 |

Section III | prestressed pipe pile, geogrid, and gravel cushion | 0.3 | 5.3 | 14 | 0.4 | 2.0 |

Section IV | prestressed pipe pile and gravel cushion | 0.3 | 5.0 | 14 | 0.4 | 2.5 |

No. | End of Construction Period | End of Observation Period | Decreasing Rate (%) |
---|---|---|---|

Section I | 4.7 | 4.3 | 8.5 |

Section II | 6.7 | 6.3 | 6 |

Section III | 7.7 | 6.9 | 10.5 |

Section IV | 4.3 | 4 | 6.9 |

Material | Thickness (Length) (m) | Volume Weight (kN/m ^{3}) | E (MPa) | Poisson Ratio | Internal Friction Angle (°) | Cohesion (kPa) | Moisture Content (%) | Void Ratio | Permeability Coefficient (10 ^{−5} m/d) |
---|---|---|---|---|---|---|---|---|---|

Pile | 12–20 | 25 | 20,000 | 0.2 | - | - | - | - | - |

Geogrid | - | - | 10 | 0.2 | - | - | - | - | - |

Cushion | 0.3 | 20 | 20 | 0.3 | 37 | 6 | - | - | - |

Embankment | 3–7 | 18.5 | 15 | 0.35 | 30 | 6 | - | - | - |

1. silty clay | 4 | 19.2 | 6.3 | 0.34 | 13.8 | 24.5 | 24.9 | 0.778 | 6.1 |

2. silt | 6 | 19.1 | 8.7 | 0.28 | 20.8 | 11.5 | 21.2 | 0.718 | 5.9 |

3. silty clay | 3 | 19.6 | 5.9 | 0.28 | 12.9 | 24.7 | 24.2 | 0.737 | 5.8 |

4. silty clay | 9 | 18.9 | 4.1 | 0.28 | 15.5 | 18.5 | 33.5 | 0.932 | 6.3 |

5. silt | 8 | 20.4 | 8.8 | 0.28 | 21.3 | 12.8 | 19.8 | 0.588 | 6.2 |

NO. | Influencing Factor | Declaration | |||
---|---|---|---|---|---|

Embankment Height (m) | Pile Spacing (m) | Pile Cap Width (m) | Pile Length (m) | ||

1 | 5.3 | 2 | 1 | 14 | Model validation |

2 | 5.3 | 2 | 1 | 12 | Models 1, 2, 3, 4, and 5 analyze the effect of pile length |

3 | 5.3 | 2 | 1 | 16 | |

4 | 5.3 | 2 | 1 | 18 | |

5 | 5.3 | 2 | 1 | 20 | |

6 | 5.3 | 2.2 | 1 | 14 | Models 1, 6, 7, 8, and 9 analyze the effect of pile spacing |

7 | 5.3 | 2.4 | 1 | 14 | |

8 | 5.3 | 2.6 | 1 | 14 | |

9 | 5.3 | 2.8 | 1 | 14 | |

10 | 5.3 | 2 | 0.8 | 14 | Models 1, 10, 11, 12, and 13 analyze the effect of pile cap width |

11 | 5.3 | 2 | 1.2 | 14 | |

12 | 5.3 | 2 | 1.4 | 14 | |

13 | 5.3 | 2 | 1.6 | 14 | |

14 | 3.3 | 2 | 1 | 14 | Models 1, 14, 15, 16, and 17 analyze the effect of embankment height |

15 | 4.3 | 2 | 1 | 14 | |

16 | 6.3 | 2 | 1 | 14 | |

17 | 7.3 | 2 | 1 | 14 |

Pile Length (m) | Pile–Soil Differential Settlement (mm) | ||
---|---|---|---|

Subgrade Center | Right of Centerline | Road Shoulder | |

12 | 6 | 5 | 1 |

14 | 6 | 5 | 2 |

16 | 6 | 5 | 1 |

18 | 7 | 6 | 1 |

20 | 7 | 6 | 1 |

Pile Spacing (m) | Pile–Soil Differential Settlement (mm) | ||
---|---|---|---|

Subgrade Center | Right of Centerline | Road Shoulder | |

2 | 6 | 5 | 2 |

2.2 | 8 | 7 | 3 |

2.4 | 10 | 8 | 2 |

2.6 | 11 | 9 | 4 |

2.8 | 13 | 11 | 5 |

Pile Cap Width (m) | Pile–Soil Differential Settlement (mm) | ||
---|---|---|---|

Subgrade Center | Right of Centerline | Road Shoulder | |

0.8 | 8 | 7 | 2 |

1 | 6 | 5 | 2 |

1.2 | 5 | 4 | 2 |

1.4 | 4 | 3 | 1 |

1.6 | 3 | 2 | 1 |

Embankment Height (m) | Pile–Soil Differential Settlement (mm) | ||
---|---|---|---|

Subgrade Center | Right of Centerline | Road Shoulder | |

3.3 | 4 | 3 | 1 |

4.3 | 5 | 4 | 1 |

5.3 | 6 | 5 | 2 |

6.3 | 7 | 6 | 2 |

7.3 | 9 | 8 | 2 |

Influencing Factor | Evaluation Scope | Sensitivity Coefficient |S_{AF}| |
---|---|---|

Pile length (m) | 12–20 | 0.17 |

Pile spacing (m) | 2.2–2.8 | 1.43 |

Pile cap width (m) | 0.8–1.6 | 2.03 |

Embankment height (m) | 3.3–7.3 | 0.27 |

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**MDPI and ACS Style**

Wang, X.; Wang, X.; Yang, G.; Yang, X.; Zhang, D.
Research on the Load Transfer Law of Cross-Sections of Pile-Supported Reinforced Embankments Based on the Finite Element Method. *Sustainability* **2022**, *14*, 7831.
https://doi.org/10.3390/su14137831

**AMA Style**

Wang X, Wang X, Yang G, Yang X, Zhang D.
Research on the Load Transfer Law of Cross-Sections of Pile-Supported Reinforced Embankments Based on the Finite Element Method. *Sustainability*. 2022; 14(13):7831.
https://doi.org/10.3390/su14137831

**Chicago/Turabian Style**

Wang, Xin, Xizhao Wang, Guangqing Yang, Xiang Yang, and Da Zhang.
2022. "Research on the Load Transfer Law of Cross-Sections of Pile-Supported Reinforced Embankments Based on the Finite Element Method" *Sustainability* 14, no. 13: 7831.
https://doi.org/10.3390/su14137831