# Numerical Analysis of Passive Piles under Surcharge Load in Extensively Deep Soft Soil

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Field Test

^{2}). Figure 2 shows the layout of the field test and the positions calculated in the numerical model, which included the profile view, plan view, and the instrumentations. The detailed information of the field test and the measurement results can be found in Yi, et al. [33] and was not introduced in here for purposes of brevity.

## 3. Numerical Modelling

#### 3.1. General

^{9}Pa.

#### 3.2. Soil and Structure Properties

^{3}, 2.18 × 10

^{9}Pa, and 0.60, respectively. The permeability of the 2nd, 3rd, 4th, and 5th soil layers were determined as 1 × 10

^{−10}, 1 × 10

^{−8}, 1 × 10

^{−2}, and 1 × 10

^{−2}m/s, respectively. The initial fluid balance was achieved within the allowable convergence value. The interface element was not introduced for the pile-soil interaction in the study. The steel pipe pile and its surrounding soft soil always stuck together even in situations involving large deformations. The flow and cohesion characteristics of the silt and mud were difficult to capture in the numerical modeling.

^{7}Pa, 1940 kg/m

^{3}, and 0.3, respectively. The surcharge loading was then carried out by activating each plain fill layer in the same sequence of the field construction. The whole model was calculated to reach a balance state (i.e., both the force and fluid balance) after the placement of each new fill layer. Each lift was kept for three days, and then the next lift was placed. The gravity force of the fill layers was transferred to the underlying foundation soil and the steel pipe pile. The deformation of the foundation soil and the structure, the excess pore water pressure, and the earth pressure acting at the surface of the pile were recorded by writing the fish function and history command.

## 4. Results and Discussion

#### 4.1. Model Verification

#### 4.2. The Vertical Displacement of the Foundation Soil

#### 4.3. The Lateral Displacement of the Pile and the Foundation Soil

#### 4.4. Excess Pore Water Pressure

#### 4.5. Lateral Earth Pressure

#### 4.6. Variation of the m Value

^{3}); ${x}_{z}$ was the horizontal displacement of the soil at a depth of z; and $m$ was the proportion coefficient of the horizontal resistance coefficient of soil (kN/m

^{4}).

^{4}. It was clear that the values of $m$ decreased with the increase in depth. The $m$ value in the shallow soil layer was typically smaller than the lower limit of the recommended value (e.g., 2 MN/m

^{4}) due to the large lateral displacement of the foundation soil. The $m$ value in the deep soil layer was significantly higher than the upper limit of the recommended value (e.g., 4.5 MN/m

^{4}) because of the small lateral displacement and the high earth pressure of the foundation soil. The design code may overestimate the horizontal resistance of the shallow foundation soil, which was dangerous for the laterally loaded structures.

^{4}) until the depth reached 25 m. The average $m$ values along the depth were 11.4, 3.5, and 2.2 MN/m

^{4}, respectively, at the end of the 1st, 3rd, and 5th loadings. The horizontal resistance of the shallow foundation soil at a high surcharge load (i.e., caused large lateral displacement) was further overestimated by the design code. Attention should be given for the design and analysis of the laterally loaded structures in such geotechnical situations.

## 5. Conclusions

- (1)
- The corner of the loading area developed large uplift deformation. The uplift deformation only happened within a shallow depth of 6 m for the foundation soil at the short edge of the loading area. The foundation soil at the center section always developed downward displacement at different depths.
- (2)
- The pile developed large lateral displacement for a shallow depth of 10 m. The lateral displacement decreased sharply with the increase in depth and increased with the placement of the new lift loading. The foundation soil developed the maximum lateral displacement at depths varying from 1 to 4 m in different cases instead of the ground surface. The lateral displacement of the soil was slight when the depth exceeded 30 m.
- (3)
- The EPWP initially increased significantly after the placement of the 1st lift loading. The increment of the EPWP was not linear with the increase of the surcharge load. The value of the EPWP continued to increase and accumulated with the placement of the new lift loading.
- (4)
- The lateral earth pressure typically increased with the increase in depth at the end of the 1st lift loading. The distribution of the lateral earth pressure in the shallow soil layer was complicated and a negative value was observed under a high surcharge load. The suction effect could be dominant at the soil-pile interface in the situation of high surcharge load and large soil movement.
- (5)
- The m value in the shallow soil layer was typically smaller than the lower limit of the recommended value, while the m value in the deep soil layer was significantly higher than the upper limit of the recommended value. The value of m decreased with the increase of the surcharge load. The design code overestimated the horizontal resistance of the shallow foundation soil at a high surcharge load and large lateral displacement.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The layout of the field test and the positions calculated in the numerical model: (

**a**) profile view; (

**b**) plan view. (Unit: m).

**Figure 5.**The comparison of the measured and calculated horizontal displacement of the pile at the ground surface.

**Figure 6.**The horizontal displacements along the steel pipe pile obtained by the field test and numerical model.

**Figure 7.**The vertical displacement curves of the foundation soil at different depths at: (

**a**) A-A section; (

**b**) B-B section.

Materials | Cohesion | Friction Angle | Density | Young’s Modulus | Poisson | Constitutive Model |
---|---|---|---|---|---|---|

(kPa) | (°) | (g/cm^{3}) | (Pa) | |||

1st layer | 0 | 37 | 1.65 | 1.0 ×10^{7} | 0.37 | Mohr-Coulomb |

2nd layer | 8.81 | 0.06 | 1.59 | 1.5 × 10^{6} | 0.45 | Drucker-Prager |

8.81 | 0.07 | 1.59 | 1.6 × 10^{6} | 0.45 | ||

3rd layer | 5.46 | 0.08 | 1.69 | 8 × 10^{6} | 0.30 | |

7.46 | 0.12 | 1.69 | 9 × 10^{6} | 0.30 | ||

10.46 | 0.20 | 1.69 | 1 × 10^{7} | 0.30 | ||

20.46 | 0.45 | 1.69 | 2 × 10^{7} | 0.30 | ||

4th layer | 3.0 | 32 | 2.05 | 5.2 × 10^{8} | 0.30 | Mohr-Coulomb |

5th layer | 60 | 45 | 2.25 | 1 × 10^{9} | 0.30 | |

Steel pipe pile | - | - | - | 2.0 × 10^{11} | 0.31 | Elastic |

Inclinometer tube | - | - | - | 4.28 × 10^{8} | 0.30 | Elastic |

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**MDPI and ACS Style**

Gu, M.; Cai, X.; Fu, Q.; Li, H.; Wang, X.; Mao, B.
Numerical Analysis of Passive Piles under Surcharge Load in Extensively Deep Soft Soil. *Buildings* **2022**, *12*, 1988.
https://doi.org/10.3390/buildings12111988

**AMA Style**

Gu M, Cai X, Fu Q, Li H, Wang X, Mao B.
Numerical Analysis of Passive Piles under Surcharge Load in Extensively Deep Soft Soil. *Buildings*. 2022; 12(11):1988.
https://doi.org/10.3390/buildings12111988

**Chicago/Turabian Style**

Gu, Meixiang, Xiaocong Cai, Qiang Fu, Haibo Li, Xi Wang, and Binbing Mao.
2022. "Numerical Analysis of Passive Piles under Surcharge Load in Extensively Deep Soft Soil" *Buildings* 12, no. 11: 1988.
https://doi.org/10.3390/buildings12111988