# Study on the Horizontal Bearing Characteristic of a New Type of Offshore Rubber Airbag Branch Pile

^{1}

^{2}

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## Abstract

**:**

_{0}of the pile, size of rubber airbag branch and depth S

_{0}of rubber airbag branch embedded in soil on the horizontal bearing capacity of the pile, have been investigated using numerical simulations. Simulation results were used to modify the eigenvalue equations of the horizontal bearing capacity. The results also showed that reverse displacement and the bending moment of the rubber airbag branch pile were lower in pipe piles with larger diameters, and the horizontal bearing capacity was more stable. At small horizontal displacements of the pile top, horizontal bearing capacities of large-diameter pipe piles were slightly higher, while for the pile’s top horizontal displacements of above 10 mm, horizontal bearing capacities of rubber airbag branch piles became significantly greater than those of the large-diameter pipe piles. Based on assumptions, the calculation equations of vacuum negative pressure and friction force between the rubber airbag branch and soil were derived. The equations for calculating the characteristic horizontal bearing capacities of rubber airbag branch piles were also derived and were modified based on simulation results. The calculation results confirmed the improvement in the accuracy of the modified equations.

## 1. Introduction

_{0}, exposed lengths of pile above the soil surface L

_{0}and horizontal displacements of pile top. The results were compared with those obtained for large-diameter pipe piles. On this basis, the equations for calculating the characteristic values of the horizontal bearing capacity of rubber airbag branch piles were derived.

## 2. Horizontal Bearing Mechanism of Rubber Air Bag Branch Piles

## 3. Finite Element Numerical Simulation and Result Analysis

#### 3.1. Establishment of Finite Element Model of Rubber Airbag Branch Pile

_{0}were 0, 5, 10, 15 and 20 m. To decrease the amount of stress transferred from the pile to the soil boundary through a horizontal load, a cylindrical model with a radius of 25 m and depth of 70 m, where 0–50 m was a clay layer and 50–70 m was a rock layer, was adopted. The Mohr–Coulomb constitutive and linear elastic constitutive models were used for the simulation of the clay layer. A linear elastic constitutive model was applied for rock stratum, pile and rubber airbag branch. In order to avoid relative slippage, the pile-rubber airbag branch and pile bottom-rock layer contacts had to be bound. A penalty function was applied for the rubber airbag branch surface-soil body and pile body-soil body contacts. Pile-rock surface contact was considered to be a rough contact. To realize the transformation of pile top horizontal displacement from a small horizontal displacement to a large horizontal displacement, the horizontal displacement range of the pile top was considered as 0~50 mm with an interval of 2 mm. Table 1 summarizes the physical and mechanical parameters of the soil layer, rubber airbag branch and pile, and Figure 2 shows the mesh division of the model.

#### 3.2. Simulation Conditions

_{0}, rubber airbag branch size and buried depth S

_{0}in soil. In this section, these three influencing factors are compared and analyzed under the following combination of working conditions.

_{0}, the effect of L

_{0}on horizontal bearing capacities was explored when horizontal displacement deformation occurred on the pile top. Table 2 summarizes the specific combination of working conditions for this test.

_{0}and S

_{0}were fixed at 5 m. Table 3 and Table 4 summarize the combined working conditions of the test.

_{0}of rubber airbag branch in the soil also affected pile horizontal bearing capacity; especially, horizontal reactions of rubber airbag branch at various pile body positions affected pile bending performance. In order to explore the effects of rubber airbag branch on the two properties of the buried depth S

_{0}of rubber airbag branch and the length L

_{0}of pile above the soil surface, the relationship between pile top horizontal displacement and bearing capacity, and that between pile top horizontal displacement and pile body bending moment were compared and analyzed. Table 5 summarizes the combined conditions applied in this experiment.

#### 3.3. Result Analysis

#### 3.3.1. Comparative Analysis of Different Exposed Pile Lengths

_{0}of the straight pile and rubber airbag branch pile outside the pile were different, as shown in Figure 3. It was seen that an increase in L

_{0}decreased the pile horizontal bearing capacity. The pile top horizontal bearing capacity was increased with the increase in pile top horizontal displacement at a growth rate of an almost straight line; also, the growth rate of the horizontal bearing capacity of rubber airbag branch piles was greater than that of the large-diameter pipe piles. However, the horizontal bearing capacity of rubber airbag branch piles with small pile top horizontal displacements was smaller than that of the large-diameter pipe piles. In Figure 3a, at a pile top horizontal displacement of 12 mm, the horizontal bearing capacities of rubber airbag branches and straight piles were 2827 and 2880 kN, respectively. At a pile top horizontal displacement of 14 mm, the horizontal bearing capacities of rubber airbag branches and vertical piles were 3369 and 3364 kN, respectively. It was seen that the horizontal bearing capacity of the rubber airbag branch pile was higher than that of the large-diameter pipe piles at pile top displacements of 12–14 mm. In Figure 3b–e, the pile top horizontal displacements were 4~6, 4~6, 6~8 and 8~10 mm, respectively. The bearing capacities of the rubber airbag branch piles exceeded those of vertical piles. At L

_{0}values of 0, 5, 10, 15 and 20 m, the horizontal displacements of rubber airbag branches and large-diameter pipe piles reached 50 mm and the difference in the horizontal loads they were able to carry were 1510, 1891, 1090, 656 and 410 kN, respectively. The obtained results showed that by increasing L

_{0}, the horizontal bearing capacity of the rubber airbag branch pile was first increased and then decreased under large pile top displacements.

_{0}on horizontal displacement was generated from the fact that when the pile top was exposed to horizontal loads, the flexural rigidity of the pile first played a role and then transferred to the soil under the constraint of the soil reaction around the pile. However, the length L

_{0}of the pile above the soil surface directly depended on flexural strength, which resulted in a decreased horizontal bearing capacity of the pile. As the length of the pile’s exposed part was increased, the distance of horizontal load transfer to soil was increased and the extension of time for the reaction of soil around the pile to exert its effect along with the horizontal bearing capacity of the pile was also decreased. When the rubber airbag branch entered the soil along with the pile, some parts of the soil and pile were separated. In the process of pile top horizontal load transfer, part of the soil reaction around the pile was missing. Therefore, when the pile top horizontal load was transferred to the rubber airbag branch, the rubber airbag branch first produced tensile deformation with pile body displacement direction and, then, extrusion deformation occurred in the opposite direction of the pile body horizontal displacement. In this process, the horizontal load-bearing capacity of rubber airbag branch piles was not high enough to make up for the loss of soil reaction around the pile and the horizontal bearing capacity of rubber airbag branch piles was less than those of large-diameter pipe piles. However, as pile top horizontal displacement occurred, the tensile and extrusion deformations of rubber airbag branches gradually reached their limit values. Pile horizontal bearing capacity was increased due to the horizontal load resistance generated by rubber airbag branches.

#### 3.3.2. Comparative Analysis of Different Sizes of Rubber Airbag Branches

#### 3.3.3. Comparative Analysis of Different Rubber Airbag Branch Buried Depths S_{0}

_{0}values. It can be seen in Figure 7 that the maximum pile bearing capacities of 8767, 8502 and 8343 kN were obtained for the S

_{0}values of 5, 10 and 20 m, respectively. It was concluded that deeper rubber airbag branches decreased pile bearing capacities. When pile top horizontal displacement was within 4 mm, straight pile bearing capacity was greater than that of the rubber airbag branch. Pile top horizontal displacement was within 18 mm and pile bearing capacity was smaller than that of the pile at a buried depth of rubber airbag branch at 5 m. It was seen that the soil reaction loss around the pile, due to different buried depths of rubber airbag branches, affected the improvement of pile horizontal bearing capacity.

_{0}. Compared with Figure 8, the maximum bending moment of rubber airbag branch piles was lower than those of large-diameter pipe piles and the maximum bending moment was increased by increasing the pile top horizontal displacement. At a pile top horizontal displacement of 30 mm and with S

_{0}values of 5 and 10 m, the maximum pile body bending moments were greater than those of large-diameter pipe piles. At a pile top horizontal displacement of 50 mm and with S

_{0}values of 5 to 20 m, the maximum bending moments of the rubber airbag branch pile bodies exceeded those of the large-diameter pipe piles. However, from the overall curve change in the pile bending moment, the variation range of the rubber airbag branch pile curve is smaller, and the horizontal bearing performance of the rubber airbag branch pile is more stable than that of large-diameter pipe piles.

## 4. The Horizontal Bearing Capacity Characteristic Value of Rubber Airbag Branch Piles

#### 4.1. Formula Correction for Bearing Capacity Characteristic Value of Large Diameter Tubular Piles

_{ha}is the horizontal bearing capacity characteristic value; “a” is the pile horizontal deformation coefficient; EI is pile bending stiffness; X

_{0a}is the allowable pile top horizontal displacement; V

_{x}is the pile top horizontal displacement coefficient; m is the counterforce growth coefficient of horizontal foundation; b

_{0}is the pile calculation width.

^{4}. After calculation, it can be seen in the figure that the normative equation was more suitable for pipe piles with short exposed lengths and small pile diameters, but not for large-diameter pipe piles.

_{0}of a large-diameter pipe pile was taken as the most influential parameter. A correction factor was added to the canonical equation, as expressed in Equation (2):

_{0}is the pile exposed length; t, u, v and w are undetermined coefficients; and ζ

_{1}is the correction coefficient of the equation for large-diameter piles.

_{0}values of 0, 5, 10, 15 and 20 m were analyzed in a pile top displacement range of 2–50 mm. It was seen from the figure that pile horizontal bearing capacity was linearly changed with the increase in pile top horizontal displacement. It was also seen from the figure that by increasing pile top horizontal displacement, the horizontal bearing capacity of the pile was changed almost linearly. By analyzing the difference between the calculated and simulated values, the variation law of the horizontal bearing capacity for large-diameter pipe piles with exposed length was derived. As shown in Figure 12, the relationship between the calculated value-simulated value ratio and pile exposed length was fitted; it was also seen that the error after fitting was lower and the values of undetermined coefficients t, u, v and w were obtained. The modified calculation equation of large-diameter pipe pile bearing capacity was stated as Equation (3).

_{0}values of 0, 4, 12 and 20 m. As shown in Figure 13, it can be seen that the modified characteristic value of horizontal bearing capacity of large-diameter pipe piles was reasonable.

#### 4.2. The Characteristic Value of Bearing Capacity for Large-Diameter Rubber Airbag Branch Piles

#### 4.2.1. The Equation of the Resistance of Horizontal Load for Rubber Airbag Branch Piles

_{1}is negative vacuum pressure; F

_{2}is horizontal friction; P is pressure; R is the outer radius of the rubber airbag branch; r is pile radius; h is the rubber airbag branch dish height; ψ is the rubber airbag branch horizontal plane and surface projection angle, ψ = arctan[h/(R + r)]; k is the coefficient of soil side pressure, k = υ/(1 + υ); υ is Poisson’s ratio; γ is the soil weight, take the value of 19.23 kN/m

^{3}; δ is the soil internal friction angle, take the value of 14; c is the soil mass cohesive force, take the value of 25 kN/m

^{2}. Other coefficients can be obtained from the text or conversion.

#### 4.2.2. Establishment of the Characteristic Value of Horizontal Bearing Capacity

_{2}and ζ

_{3}are correction factors related to pile exposed length L

_{0}and rubber airbag branch buried depth S

_{0}in the equation of rubber airbag branch pile, respectively. Other parameters are the same as above.

_{2}and ζ

_{3}correction coefficients could be obtained, as stated in Equations (9) and (10), respectively.

_{0}is the rubber airbag branch pile’s buried depth.

#### 4.3. Verification of Bearing Capacity Eigenvalue Equation of Rubber Airbag Branch Pile

_{0}values of 0, 5, 10, 15 and 20 m, the differences between corresponding, uncorrected, calculated, and simulated values were 19,100, 22,663, 25,881, 27,802 and 28,978 kN, and those between the corrected, calculated, and simulated values were 1389, 803, 588, 378 and 351 kN, respectively. At S

_{0}values of 5, 10 and 20 m, the corresponding differences were 22,663, 21,992 and 23,087 kN, respectively. The differences between the modified calculated and simulated values were 803, 936 and 830 kN, respectively. By analyzing the difference values, the corrected calculated values were found to be close to the simulated values and the corrected error was controlled within the range of 10%. Due to the complexity of soil mass’ physical and mechanical parameters, there were too many influencing factors, making it impossible to accurately calculate the contact force between the pile–soil and rubber airbag branch pile–soil mass interfaces. Moreover, the correction coefficient of fitting ζ

_{1}, ζ

_{2}, ζ

_{3}had certain errors. By multiplying corrected coefficients ζ

_{1}, ζ

_{2}and ζ

_{3}, the overall error was amplified and it was concluded that the horizontal bearing capacity characteristic value of the modified rubber airbag branch pile was greater than the simulated value. However, a comparison of the calculation and comparison results revealed that the calculated values after the addition of the correction coefficients ζ

_{2}and ζ

_{3}were closer to the simulation values, and their accuracy was higher than the calculated values before adding correction coefficients, which played a certain role in the accuracy of the calculation results.

## 5. Conclusions

- (1)
- The horizontal bearing capacities of piles with large pile top displacements were obviously higher than those of the pipe piles under the action of a rubber airbag branch bearing tray, which indicated that the rubber airbag branch bearing had a transverse constraint on the pile. As L
_{0}was increased, pile horizontal bearing capacity was also rapidly decreased. - (2)
- The increase in the rubber airbag branch height and radius did not increase pile horizontal bearing capacity, however, an increase in pile top horizontal displacement enhanced the increase rate of horizontal bearing capacity compared to that of the large-diameter pipe piles. Under the lateral constraint of the rubber airbag branch pile, the reverse displacement position and reverse pile bending moment were decreased and pile horizontal bearing capacity was more stable.
- (3)
- A buried depth of rubber airbag branch also increased pile horizontal bearing capacity. The horizontal bearing capacity was increased with an increase in the buried depth from 5 to 10 m.
- (4)
- The equation for the rubber airbag branch bearing capacity characteristic value was also derived. After modification, the modified equation of the horizontal bearing capacity characteristic value of the rubber airbag branch pile could be applied as a reference in designs.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Pile grid division; (

**b**) rubber airbag branch grid division; (

**c**) component grid division.

**Figure 3.**(

**a**) 0 m external exposure of pile L

_{0}; (

**b**) 5 m external exposure of pile L

_{0}; (

**c**) 10 m external exposure of pile L

_{0}; (

**d**) 15 m external exposure of pile L

_{0}; (

**e**) 20 m external exposure of pile L

_{0}.

**Figure 5.**(

**a**) 10 mm pile top horizontal displacement; (

**b**) 20 mm pile top horizontal displacement; (

**c**) 30 mm pile top horizontal displacement; (

**d**) 40 mm pile top horizontal displacement; (

**e**) 50 mm pile top horizontal displacement.

**Figure 8.**(

**a**) 10 mm horizontal pile top displacement; (

**b**) 20 mm horizontal pile top displacement; (

**c**) 30 mm horizontal pile top displacement; (

**d**) 40 mm horizontal pile top displacement; (

**e**) 50 mm horizontal pile top displacement.

**Figure 13.**(

**a**) 0 m external pile exposure; (

**b**) 4 m external pile exposure; (

**c**) 12 m external pile exposure; (

**d**) 20 m external pile exposure.

**Figure 17.**(

**a**) 0 m external pile exposure; (

**b**) 5 m external pile exposure; (

**c**) 10 m external pile exposure; (

**d**) 15 m external pile exposure; (

**e**) 20 m external pile exposure.

**Figure 18.**(

**a**) 5 m burial depth of rubber airbag branch; (

**b**) 10 m burial depth of rubber airbag branch; (

**c**) 20 m burial depth of rubber airbag branch.

**Table 1.**Physical parameters of each component [16].

Modulus | Poisson Ration | Cohesion | Severe | Internal Friction Angle | |
---|---|---|---|---|---|

Clay layer | 30 MPa | 0.3 | 25 kPa | 19.23 kN/m | 14° |

Rock stratum | 400 GPa | 0.3 | —— | 27 kN/m | —— |

Rubber airbag branch | 10 MPa | 0.3 | —— | 10 kN/m | —— |

Pile | 38 GPa | 0.3 | —— | 25 kN/m | —— |

R (m) | Height (m) | S_{0} (m) | L_{0} (m) |
---|---|---|---|

5 | 2 | 5 | 0/5/10/15/20 |

R (m) | Height (m) | S_{0} (m) | L_{0} (m) |
---|---|---|---|

5 | 1/1.5/2 | 5 | 5 |

R (m) | Heigh (m) | S_{0} (m) | L_{0} (m) |
---|---|---|---|

3.125/3.75/5 | 2 | 5 | 5 |

R (m) | Height (m) | S_{0} (m) | L_{0} (m) |
---|---|---|---|

5 | 2 | 5/10/20 | 5 |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Wang, Z.; Yuan, C.; Liu, L.
Study on the Horizontal Bearing Characteristic of a New Type of Offshore Rubber Airbag Branch Pile. *Sustainability* **2022**, *14*, 7331.
https://doi.org/10.3390/su14127331

**AMA Style**

Wang X, Wang Z, Yuan C, Liu L.
Study on the Horizontal Bearing Characteristic of a New Type of Offshore Rubber Airbag Branch Pile. *Sustainability*. 2022; 14(12):7331.
https://doi.org/10.3390/su14127331

**Chicago/Turabian Style**

Wang, Xiaolei, Zeyuan Wang, Changfeng Yuan, and Libo Liu.
2022. "Study on the Horizontal Bearing Characteristic of a New Type of Offshore Rubber Airbag Branch Pile" *Sustainability* 14, no. 12: 7331.
https://doi.org/10.3390/su14127331