# Deformation and Force Analysis of Wood-Piled Island Cofferdam Based on Equivalent Bending Stiffness Principle

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Equivalent Bending Stiffness Principle

#### 2.1. Equivalent Representation of the Wood-Pile Cofferdam

#### 2.2. Equivalent of Wood Piles

_{w}is the diameter of wood piles; t

_{w}is the interval of two adjacent wood piles; l is the length of the dam calculated; n

_{w}is the number of single-row wood piles ‘l’ containing; h

_{w}is the equivalent thickness of a single row of stakes; E

_{w}is the stiffness of wood piles; also, D

_{w}and D

_{h}, are, respectively, the equal bending stiffness of stakes and sheet piles.

_{w}= D

_{h}, putting Equation (3) into Equation (2). According to Equation (4), the equivalent thickness of a single row of stakes (h

_{w}) is defined as follows:

_{w}/n

_{w}approaches 0, according to Equation (5), h

_{w}can be approximately expressed as follow:

#### 2.3. Equivalent Model of Steel Pipe Pile

_{s}is the outer diameter of steel pipe piles; d

_{si}is the inner diameter of steel pipe piles; t

_{s}is the interval of two adjacent steel pipe piles; h

_{s}is the equivalent thickness of a row of steel pipe piles; and E

_{s}is the stiffness of steel pipe piles.

_{m}(the stiffness of composite piles) is the only unknown parameter.

## 3. Project Overview

## 4. Numerical Analysis

#### 4.1. Model Setup

^{3D}, ITASCA, Minneapolis, MN, USA), providing a more efficient way of solving the fluid–mechanical interaction problems. Additionally, FLAC

^{3D}has been used in many deep excavation and cofferdam projects and proved to be greatly accurate and reliable [18,19].

#### 4.2. Simulation Results

## 5. Parametric Analysis

#### 5.1. Parameters Value

#### 5.2. The Effect of Pile Length

#### 5.3. The Effect of Dam Width

#### 5.4. The Effect of Tension Bars Interval

#### 5.5. The Effect of Wood Piles Interval

#### 5.6. Discussion

## 6. Steel Pipe Pile Reinforcement Effect

#### 6.1. Description of Steel Pipe Pile Reinforcement

#### 6.2. Analysis of Reinforcement Effect

^{5}MPa, as well the parameters of the lower half: the thickness of 118 mm, and the elastic modulus of 2 × 10

^{5}MPa.

## 7. Conclusions

- According to the analysis of the double-row wood-piled cofferdam scheme, the maximum horizontal deformation of the pile can be controlled at about 0.6% of pile length, either the peak values of the bending moment and tension bar stress in the construction process are both within the allowable range and still have large redundancy. In general, the original scheme of the wood-piled island cofferdam can meet the basic construction safety requirements.
- The width of the dam is an important parameter affecting the stability of the cofferdam and should be the primary consideration in the design. Other parameters, such as the pile length, the pile interval, and the tension bars interval, ought to be determined by the dam interval. Summarizing a large number of parameter sensitivity analyses, it is concluded that the axial force of tension bars in the wood-piled cofferdam is not large, and the wood piles bear most of the external force. In the design of the cofferdam structure, more attention should be paid to the deformation and bending moment of the wood piles.
- The steel pipe pile reinforcement scheme performed better than the double-row wood-piled cofferdam scheme. The deformation of the pile after reinforcement is brought down by more than half, but the reinforcement is useless in reducing the bending moment of wood piles. The scheme reinforced by steel pipe piles provides a new idea for island-type cofferdams with rigorous structural deformation control.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 26.**Comparison of the horizontal displacement between reinforced piles and double-row wood piles.

Material | Silt | Clay | Solidifies Soil | Backfill Soil | Wood Pile | Tension Bar |
---|---|---|---|---|---|---|

Model | Mohr- Coulomb | Mohr- Coulomb | Mohr- Coulomb | Mohr- Coulomb | Elastic | Elastic |

Element | Brick | Brick | Brick | Brick | Liner | Cable |

Thickness/m | 20.0 | 5.0 | 2.0 | 4.5 | - | - |

Density/kg·m^{−3} | 1700 | 1900 | 1800 | 1800 | 800 | 7800 |

Young’s modulus/MPa | 2.4 | 6.6 | 5.2 | 4.6 | 6.0 × 10^{3} | 2.0 × 10^{5} |

Friction angle/° | 10 | 15 | 12 | 10 | - | - |

Cohesion/kPa | 1.4 × 10^{4} | 5.6 × 10^{4} | 1.5 × 10^{4} | 1.0 × 10^{4} | - | - |

Poisson’s ratio | 0.35 | 0.3 | 0.3 | 0.3 | 0.3 | 0.2 |

Permeability coefficient/m·s^{−1} | 10^{−6} | 10^{−8} | 10^{−7} | - | - | - |

Stage No. | Description | Model Operation |
---|---|---|

1 | Initializing stress field and seepage field balance | Activating the soil layer (silt and clay), setting seepage boundary |

2 | Dam construction | Activating the cofferdam structure (liner and cable elements) |

3 | Dewatering inside the cofferdam | Lowering the cofferdam water level from 4.0 m to the riverbed |

4 | Grouting to reinforce silty foundations | Modifying the silt (2.0 m below the riverbed) parameter to solidified soil |

5 | Backfilling | Activating the backfilling soil |

Number of Cases | Length of Piles/m | Width of the Dam Body/m | Interval of Adjacent Tension Bars/m | Interval of Adjacent Wood Piles/m |
---|---|---|---|---|

1 | 7.0 m | 2.5 m | 1.0 m | 0.5 m |

2 | 8.0 m | 2.5 m | 1.0 m | 0.5 m |

3 | 9.0 m | 2.5 m | 1.0 m | 0.5 m |

4 | 10.0 m | 2.5 m | 1.0 m | 0.5 m |

5 | 11.0 m | 2.5 m | 1.0 m | 0.5 m |

6 | 9.0 m | 2.0 m | 1.0 m | 0.5 m |

7 | 9.0 m | 3.0 m | 1.0 m | 0.5 m |

8 | 9.0 m | 3.5 m | 1.0 m | 0.5 m |

9 | 9.0 m | 4.0 m | 1.0 m | 0.5 m |

10 | 9.0 m | 2.5 m | 0.5 m | 0.5 m |

11 | 9.0 m | 2.5 m | 1.5 m | 0.5 m |

12 | 9.0 m | 2.5 m | 2.0 m | 0.5 m |

13 | 9.0 m | 2.5 m | 2.5 m | 0.5 m |

14 | 9.0 m | 2.5 m | 1.0 m | 0.3 m |

15 | 9.0 m | 2.5 m | 1.0 m | 0.7 m |

16 | 9.0 m | 2.5 m | 1.0 m | 1.0 m |

17 | 9.0 m | 2.5 m | 1.0 m | 1.2 m |

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**MDPI and ACS Style**

Chen, S.; Wang, Y.; Li, Y.; Li, X.; Guo, P.; Hou, W.; Liu, Y. Deformation and Force Analysis of Wood-Piled Island Cofferdam Based on Equivalent Bending Stiffness Principle. *Buildings* **2022**, *12*, 1104.
https://doi.org/10.3390/buildings12081104

**AMA Style**

Chen S, Wang Y, Li Y, Li X, Guo P, Hou W, Liu Y. Deformation and Force Analysis of Wood-Piled Island Cofferdam Based on Equivalent Bending Stiffness Principle. *Buildings*. 2022; 12(8):1104.
https://doi.org/10.3390/buildings12081104

**Chicago/Turabian Style**

Chen, Shi, Yixian Wang, Yonghai Li, Xian Li, Panpan Guo, Weichao Hou, and Yan Liu. 2022. "Deformation and Force Analysis of Wood-Piled Island Cofferdam Based on Equivalent Bending Stiffness Principle" *Buildings* 12, no. 8: 1104.
https://doi.org/10.3390/buildings12081104