# Study on the Influence of Groundwater Variation on the Bearing Capacity of Sandy Shallow Foundation

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Tests

#### 2.1. Materials

#### 2.2. Experimental Setup

- (a)
- The model box with transparent glass: Its purpose is to hold the foundation soil. It has an inlet at the bottom to let water in and out. The size of the model box is 1.2 m × 0.6 m × 0.6 m. The bottom of the model is covered with 0.1 m gravel, and the layer above is 0.35 m thick. The water level in the soil can be seen through clear glass because saturated soil is darker than unsaturated soil. The glass is marked with a scale to measure the height from the bottom of the model box to the water level.
- (b)
- Air-pressure control system: It controls the air pressure in the pump to move water in and out of the model box
- (c)
- Water pump: Its purpose is to simulate groundwater.
- (d)
- Loading system. It can apply vertical load to the foundation soil through the loading plate. The loads can be controlled by the loading system.
- (e)
- PIV filming system: It can capture the displacements of foundation soil by using PIV technology.
- (f)
- Data-acquisition system: It shows the displacement change captured by PIV through the color change of the image, so that the final displacement can be calculated.

#### 2.3. Experiment Program

#### 2.4. Test Procedures

- First, lay the gravel blocks into the model box and spread a layer of permeable cloth on the gravel blocks to prevent the upper sand from falling into the gravel blocks. Adjust the water level to soak the gravel blocks [29]. Next, put sandy soil into the model box and compact it.
- Turn on the air-pressure control system and increase the air pressure to raise the water level to the specified height. Then control the air pressure to lower the water level to the initial level and repeat for the specified number of times.
- When the foundation is damaged, stop loading. Record the pressure and save the photos of the PIV shooting system.
- Finally, remove and dry the foundation soil for the next set of tests.

#### 2.5. Analysis of Results

## 3. Numerical Analysis

#### 3.1. Numerical Model

_{m}represents the mass source term. When there is no external flow supply, Q

_{m}= 0. ∇D represents a unit vector in the direction of gravity.

_{vs}is the consolidation or rebound coefficient of the calculation model. In this paper, the possible changes of the foundation permeability coefficient and volume compression coefficient in the process of dynamic change of groundwater level are not taken into consideration temporarily. To simplify the calculation, c

_{vs}is directly taken as the consolidation coefficient and a constant.

#### 3.2. Numerical Analysis Procedures

- Establish a two-dimensional model. In order to improve the convergence of calculation, a symmetric structure was adopted with a length of 0.6 m and a width of 0.45 m. The soil was divided into two layers: gravel in the lower layer and sandy soil in the upper layer.
- Input the material parameters of the soil which are shown in Table 1.
- Set the boundary conditions of the model. The left side of the model is sliding support. The right side is a symmetric boundary. The lower side is a fixed constraint, and the right end of the upper side is the applied boundary load.
- Add soil weight and pore water pressure. Set soil plasticity and enable Mohr–Coulomb strength criteria.
- Add the global control equation. Use the parameter solver to control the gradual increase in load and define the integral function to record the vertical displacement of the loading midpoint.
- Divide the finite element mesh. Use relatively dense mesh in the contact surface of two layers of soil and the fluctuation surface of the water level.
- Calculate and output the stress and deformation and plastic development of the model and the p–s curves at the midpoint of loading.

#### 3.3. Simulation Plan

- During the test, the water content of the soil layer above the water table increased due to the capillary phenomenon of the soil, which led to a decrease in the parameters of internal friction angle and cohesion and a decrease in the bearing capacity. The numerical simulation assumes that the water content of the soil above the water table is the initial water content. Therefore, the bearing capacity of the test result is smaller than that of the simulation result.
- The termination condition of loading during the test is according to the Geotechnical Test Procedure: the deformation of the foundation reaches 1/12 of the width of the loading plate. Then the foundation was considered to be damaged, and the loading was stopped. In contrast, the numerical simulation is loaded until the damage. Therefore, the test may not reach the ultimate bearing capacity of the foundation when the loading is stopped and the p–s curve has not reached the inflection point.

#### 3.4. Analysis of Simulation Results

#### 3.5. Discussion

## 4. Conclusions

- The height of water level and the frequency of water-level fluctuation are negatively correlated with the bearing capacity of the foundation, and the relationship of change is nonlinear. The water-level fluctuation can strengthen the capillary effect and expand the range of saturated soil in the foundation.
- In this study, the influence of the water-level fluctuation was added to the traditional calculation of the foundation bearing capacity. A new expression form of pore water pressure was derived for sinusoidal fluctuation. The average error between the calculated bearing capacity and the test results is less than 8%. It shows that this theory can be used to calculate the bearing capacity of a foundation under water-level fluctuation.
- This model can well predict the change in the foundation bearing capacity due to the water-level change. It has a good early warning function for an engineered foundation that has been under a high groundwater level for a long time.
- This model also has some limitations. It is currently only applicable to sandy shallow foundations. In the future, the model will be expanded to apply to more types of foundations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 7.**Schematic diagram of water level fluctuation form: (

**a**) straight line, (

**b**) sine wave and (

**c**) random function.

**Figure 10.**Comparison of test and simulation results at different water-level heights: (

**a**) initial water level, (

**b**) 50 mm water level and (

**c**) 100 mm water level.

**Figure 11.**The p–s curves under different water level fluctuation ranges: (

**a**) 50 mm water level, (

**b**) 100 mm water level and (

**c**) 150 mm water level.

**Figure 12.**The p–s curves under different forms of water-level fluctuations: (

**a**) 50 mm water level, (

**b**) 100 mm water level and (

**c**) 150 mm water level.

Parameter | Density, ρ (g/cm ^{3}) | Cohesive Force, c (kPa) | Angle of Internal Friction, φ (°) | Young’s Modulus, E (MPa) | Poisson’s Ratio, Μ | |
---|---|---|---|---|---|---|

Soil Sample | ||||||

Silty sand (natural) | 1.92 | 12.7 | 20.1 | 15.0 | 0.25 | |

Silty sand (saturated) | 2.05 | 8.4 | 18.3 | 9.4 | 0.25 | |

Gravel | 2.20 | 3.2 | 38.7 | 150 | 0.3 |

Factors | Hight of Water Level (mm) | Times of Water-Level Cycle | |
---|---|---|---|

Number | |||

1 | 0 | 0 | |

2 | 50 | 1 | |

3 | 50 | 15 | |

4 | 50 | 30 | |

5 | 100 | 1 | |

6 | 100 | 15 | |

7 | 100 | 30 | |

8 | 150 | 1 | |

9 | 150 | 15 | |

10 | 150 | 30 |

Factors | Elevation of Water Level (mm) | Water-Level Fluctuation Range (mm) | Water-Level Fluctuation Form | |
---|---|---|---|---|

Number | ||||

1 | 50 | 10 | sine wave | |

2 | 50 | 20 | sine wave | |

3 | 50 | 30 | sine wave | |

4 | 50 | 40 | sine wave | |

5 | 100 | 10 | sine wave | |

6 | 100 | 20 | sine wave | |

7 | 100 | 30 | sine wave | |

8 | 100 | 40 | sine wave | |

9 | 150 | 10 | sine wave | |

10 | 150 | 20 | sine wave | |

11 | 150 | 30 | sine wave | |

12 | 150 | 40 | sine wave | |

13 | 50 | 30 | straight line | |

14 | 100 | 30 | straight line | |

15 | 150 | 30 | straight line | |

16 | 50 | 30 | random function | |

17 | 100 | 30 | random function | |

18 | 150 | 30 | random function |

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## Share and Cite

**MDPI and ACS Style**

Chen, W.; Xia, W.; Zhang, S.; Wang, E.
Study on the Influence of Groundwater Variation on the Bearing Capacity of Sandy Shallow Foundation. *Appl. Sci.* **2023**, *13*, 473.
https://doi.org/10.3390/app13010473

**AMA Style**

Chen W, Xia W, Zhang S, Wang E.
Study on the Influence of Groundwater Variation on the Bearing Capacity of Sandy Shallow Foundation. *Applied Sciences*. 2023; 13(1):473.
https://doi.org/10.3390/app13010473

**Chicago/Turabian Style**

Chen, Wenfeng, Weishu Xia, Shanshan Zhang, and Erlei Wang.
2023. "Study on the Influence of Groundwater Variation on the Bearing Capacity of Sandy Shallow Foundation" *Applied Sciences* 13, no. 1: 473.
https://doi.org/10.3390/app13010473