Settlement Calculation of Semi-Rigid Pile Composite Foundation on Ultra-Soft Soil under Embankment Load
Abstract
:1. Introduction
2. Analytical Model
2.1. Basic Assumptions
- (1)
- The embankment filling is simplified as a uniform load p, and after the adjustment of the cushion layer, it acts on the top surface of the pile and the surrounding soil in the form of a uniform load pp and ps.
- (2)
- The pile and the surrounding soil are isotropic linear elastomers. The elastic modulus, Poisson’s ratio, and diameter of the pile are constant. The compression modulus and Poisson’s ratio of the surrounding soil are constant.
- (3)
- The pile stress distribution is uniform, and the settlement is the same in the same horizontal plane of composite foundation. The stress and settlement of the surrounding soil at the same horizontal plane are nonuniform. Only vertical deformation occurs in the pile and surrounding soil, and lateral deformation is negligible. Only one-dimensional uniform compression occurs in the underlying layer.
- (4)
- Pile top load and upward penetration deformation conform to a linear relationship. The relationship between pile end resistance and downward penetration deformation is hyperbolic.
2.2. Model of the Unit Cell
2.3. Mechanism of Pile–Soil–Cushion Interaction
3. Analysis of Pile–Soil Interaction
3.1. Skin Friction Distribution Model
3.2. Pile End Load Transfer Model
4. Settlement Calculation of Composite Foundation
4.1. Compressive Deformation of Reinforcement Area
4.1.1. Vertical Displacement Model of Surrounding Soil
4.1.2. Establishment and Solution of Differential Equations for the Unit Cell
4.2. The Upward and Downward Penetrations of Pile
4.3. Settlement of the Underlying Layer of Composite Foundation
5. Determination of Calculation Parameters
5.1. Pile–Soil Load Sharing
5.2. Elastic and Plastic Zone Play Depth l1, l0, l2 and τ1, τ2
6. Example Validation
6.1. Field Test Validation
6.2. Model Test Validation
6.2.1. Introduction to Model Tests
6.2.2. Analysis of Model Test Results
6.3. Analysis of Influencing Factors of Pile End Penetration
7. Conclusions
- (1)
- For ultra-soft soil composite foundation reinforced by semi-rigid piles, by assuming a linear distribution model in the elastic zone and nonuniform one in plastic zone of skin friction, the upward and downward penetrations of pile, and the pile–soil sliding characteristics are considered. An analytical expression for the settlement calculation of semi-rigid pile composite foundation under embankment loading is derived by using the differential equation for pile–soil load transfer of the unit cell.
- (2)
- The validity of the settlement calculation formula of semi-rigid pile composite foundation is verified through in-site measurement and model tests. The theoretical calculation results are in good agreement with the results of field tests and model tests.
- (3)
- The test results show that the settlement stability time of the ultra-soft soil composite foundation is longer, and the settlement is large. Through model tests, it was found that the semi-rigid pile end is penetrated in the ultra-soft soil composite foundation. The relationship between pile end resistance and pile end penetration is hyperbolic.
- (4)
- Through the analysis of the influencing factors of the different compression moduli of the underlying layer and pile diameters on the pile end penetration, it was found that the compression modulus of the underlying layer has a great influence on the pile end penetration. The lower the compression modulus of the underlying layer, the larger the pile end penetration. The larger the pile diameter, the smaller the pile end penetration.
- (5)
- In the design work for composite foundations, increasing the pile diameter and placing the pile end in a high compression modulus soil layer can be used to reduce the pile end penetration, so as to reduce the compression deformation of the surrounding soil.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Embankment | Cushion Layer | Crust Layer | Ultra-Soft Soil | Underlying Layer | |
---|---|---|---|---|---|
Thickness, h (m) | 4 | 0.3 | 1.5 | 13.5 | 10 |
Unit weight, γ (kN/m3) | 20 | 21 | 17 | 15.3 | 18.5 |
Compression modulus, Es1–2 (MPa) | - | 150 | 3.4 | 1.3 | 7.2 |
Poisson’s ratio, ν | - | - | 0.3 | 0.4 | 0.3 |
Cohesion, c (kPa) | - | - | 12.3 | 6 | 28.1 |
Friction angle, φ (degree) | - | - | 4.2 | 3.5 | 12.3 |
Projects | CSF (mm) | Relative Error of CSF | Reinforced Area | Underlying Layer | PSSR | Relative Error of PSSR | ||
---|---|---|---|---|---|---|---|---|
Settlement (mm) | Percentage of CSF | Settlement (mm) | Percentage of CSF | |||||
Measured value | 533.97 | - | - | - | - | - | 1.75 | - |
Calculated value | 563.00 | 5.44% | 453.60 | 80.57% | 109.40 | 19.43% | 1.25 | 28.57% |
Soils | γ (kN/m3) | w (%) | wL (%) | wp (%) | e | Es (MPa) | φ (°) | cq (kPa) |
---|---|---|---|---|---|---|---|---|
Clay | 17.2 | 55.3 | 62.4 | 27.3 | 1.558 | 0.581 | 4.2 | 12.2 |
Mucky | 15.3 | 83.7 | 62.4 | 27.3 | 2.173 | 0.516 | 3.5 | 6.0 |
Silty clay | 18.0 | 16.1 | 29.6 | 16.1 | 0.735 | 0.8/1 * | 12.3 | 28.1 |
Water–Gypsum Ratio | Pult (kN) | fult (MPa) | f50 (MPa) | E50 (MPa) |
---|---|---|---|---|
0.6 | 9.3 | 4.7 | 2.4 | 607 |
0.7 | 6.1 | 3.1 | 1.6 | 509 |
0.8 | 5.7 | 2.9 | 1.5 | 347 |
1.0 | 4.1 | 2.1 | 1.0 | 180 |
1.2 | 1.7 | 0.8 | 0.4 | 115 |
2.0 | 0.8 | 0.4 | 0.2 | 90 |
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Cao, F.; Ye, C.; Wu, Z.; Zhao, Z.; Sun, H. Settlement Calculation of Semi-Rigid Pile Composite Foundation on Ultra-Soft Soil under Embankment Load. Buildings 2024, 14, 1954. https://doi.org/10.3390/buildings14071954
Cao F, Ye C, Wu Z, Zhao Z, Sun H. Settlement Calculation of Semi-Rigid Pile Composite Foundation on Ultra-Soft Soil under Embankment Load. Buildings. 2024; 14(7):1954. https://doi.org/10.3390/buildings14071954
Chicago/Turabian StyleCao, Fengxu, Chaoliang Ye, Zhenxu Wu, Zitong Zhao, and Hao Sun. 2024. "Settlement Calculation of Semi-Rigid Pile Composite Foundation on Ultra-Soft Soil under Embankment Load" Buildings 14, no. 7: 1954. https://doi.org/10.3390/buildings14071954