^{1}

^{2}

^{1}

^{1}

^{1}

^{1}

^{1}

^{2}

Lateral displacement of pile foundation is crucial to the safety of an overall structure. In this study, a numerical simulation on the lateral displacement of pile foundation under stacking loads was conducted to determine its relation with different influencing factors. Simulation results demonstrated that stacking loads at the pile side mostly influence the lateral displacement of pile foundation. The lateral displacement of pile foundation increases by one order of magnitude when the stacking loads increase from 100 kPa to 300 kPa. Other influencing factors are less important than stacking loads. Lateral displacements of the pile body and at the pile top can be reduced effectively by increasing the deformation modulus of surface soil mass, reducing the thickness of soft soil, and expanding pile diameter. Our analysis indicates that a nonlinear relationship exists between the lateral displacement at the pile top and the pile diameter. The lateral resistance of the pile body can be enhanced by coupling the stacking load along piles and the axial force at the pile top. An actual large-scale engineering project was chosen to simulate the effects of postconstructed embankment on lateral displacement and axial force of bridge pile foundation under different construction conditions and to obtain the lateral displacement of the pile body and the negative frictional resistance caused by soft soil compression under stacking loads. On the basis of the calculated results, engineering safety and stability were evaluated, and a guide for the design and construction was proposed.

Pile foundations in bridge, housing construction, and wharf construction engineering mainly bear axial loads. However, pile foundation is inevitably affected by the lateral movement of soil mass in actual construction and use due to excavation, current scouring, adjacent stacking loads, or other reasons, according to Liang et al. [

Currently, few studies focus on multilayer soil mass and negative frictional resistance surrounding piles caused by stacking loads. To further discuss the effects of lateral movement of soil mass on pile under complex terrain conditions, this paper discussed the effects of lateral displacement of soil mass on pile by using finite element numerical simulation and studied the lateral resistances of pile foundation under stacking loads in different construction stages in actual engineering.

In this study, the large commercial finite element software MIDAS (Geotechnical and Tunnel Analysis System) was applied for numerical simulation analysis. MIDAS organically combines the universal finite element analysis core and professional requirements of rock tunnel structure. MIDAS integrates the advantages of existing rock tunnel analysis software and solves the displacement field and stress field of the whole structure well, including displacement distribution, size, positions of stress concentration, area, and scope of plastic region. The operation process mainly includes the definition of attributes, establishment of geometric model, meshing, setting of analysis conditions, analysis, and result examination. Six calculation steps are performed.

The relation formula of element stress can be deduced from the physical equation and (

When defining material attributes, the selection of a constitutive model of soil mass is crucial to the results. Currently, common yield criteria in the geotechnical engineering world include Tresca yield criterion, von Mises yield criterion, Drucker–Prager yield criterion, Mohr–Coulomb yield criterion, and double-shear stress yield criterion. All these yield criteria have certain adaptive norms. The Mohr–Coulomb yield criterion model can reflect the strength difference effect (S-D effect) of soil mass with different levels of compressive strength and sensitivity to hydrostatic pressure. The yield has the following three expressions:

The Mohr–Coulomb yield criterion is expressed as

Yield condition is expressed by principle stress:

If expressed by invariants,

Rock material is a granular material and mainly bears load through frictions of particles. The displacement and failure of rock materials are influenced by friction. Particles overcome frictions and cause relative slippage failure as a result of the combined effects of shear stress and vertical stress. Therefore, the Mohr–Coulomb yield criterion is relatively applicable to rock mass. In the principal stress space, the Mohr–Coulomb yield surface considering influences of hydrostatic pressure is an irregular pyramid surface with a hexagonal section and is projected into a hexagon with unequal angles in the

Mohr–Coulomb yield surface.

The finite element model is shown in Figure ^{3}, and 40 GPa, respectively. To study the effect of pile size on lateral displacement, pile diameter is set to 0.8, 1.0, and 1.2 m. The mature Mohr–Coulomb model is chosen for rock and soil masses. Solid elements are used. Initial deformation modulus, Poisson’s ratio, cohesion, and specific parameters are listed in Table

Information of soil.

Name | Thickness of soil | Deformation modulus | Poisson’s ratio | Unit weight ^{3}) | Cohesive | Internal friction angle |
---|---|---|---|---|---|---|

Filling | | 10 | 0.35 | 18 | 15 | 15 |

Mucky soil | | 9 | 0.43 | 16.4 | 25 | 14.5 |

Clay | | 60 | 0.25 | 18 | 35 | 25 |

Pile | | 40000 | 0.2 | 25 |

Numerical model of pile and soil.

Profile of the soil mode

Three-dimensional model of soil

Vertical and lateral (

Soil displacement under 100 kPa of stacking loads.

Soil displacement (

Soil displacement (

Relationship between lateral displacement of pile and stacking loads.

Relationship between lateral displacement and stacking loads at different positions.

As is shown in Figures

Relationship between lateral displacement of pile and

Relationship between lateral displacement and

The lateral displacement distribution cloud chart of the pile body under different pile diameters is shown in Figure

The lateral displacement distribution cloud chart of pile body under different pile diameters.

Relationship between lateral displacement of pile and pile diameters.

Relationship between lateral displacement and pile diameters at different positions.

To discuss the effects of relative thickness of soft soil, the deformation modulus of surface soil in the model is determined to be twice the deformation modulus of soft soil. Figures

Relationship between lateral displacement of pile and relative thickness of soft soil.

Lateral displacement at different positions.

The effects of deformation modulus ratio of the adjacent hard soft layer and soft soil layer (

Relationship between lateral displacement of pile and

Relationship between lateral displacement and

On the basis of Section

Lateral displacement of pile under coupling effect of stacking load and axial force.

Lateral displacement of pile at different positions under coupling effect.

In this section, the lateral displacement of the pile body and the negative frictional resistance of soft soil caused by stacking loads under different working conditions in different construction stages are discussed by combining a real engineering case. The engineering case is a newly constructed embankment with a height of approximately 6-7 m and runs through an existing bridge project. To avoid adverse impacts of the new embankment on the running safety of the original bridge structure, the embankment body applied a U-type-reinforced concrete integrated section, which runs through the whole section in a span of one bridge. To eliminate the compressive displacement of the foundation soil layer by the upper embankment load, the pile foundation was processed by using a small single-tube high-pressure jet grouting pile with simple equipment and small disturbance to the basic soil layer. The geological distribution is shown in Figure

Information of soil and pile.

Name | Thickness of soil | Deformation modulus | Poisson’s ratio | Unit weight ^{3}) | Cohesive | Internal friction angle | |
---|---|---|---|---|---|---|---|

| Filling | 0–2 | 10 | 0.35 | 18 | 15 | 15 |

| Silty clay | 0.4–3.9 | 18 | 0.38 | 19.1 | 25 | 14.5 |

| Coarse sand | 0.5–4 | 20 | 0.25 | 18 | 0 | 25 |

| Sand and gravel | 4–6 | 21 | 0.28 | 21 | 0 | 35 |

| Sludge | 4.5–5.0 | 9.25 | 0.43 | 16.4 | 11 | 1.5 |

| Completely weathered | 0.5–8 | 60 | 0.27 | 18.6 | 90 | 25 |

| Intense weathering | 30 | 200 | 0.23 | 19.5 | 180 | 35 |

| Embankment backfill | 6-7 | 20 | 0.25 | 18 | 0 | 25 |

| Jet-grouted pile foundation | 5 | 400 | 0.3 | 20 | 450 | 30 |

| Pile/column | 20/20 | 40000 | 0.2 | 25 | ||

| U-shaped concrete tank | 40000 | 0.2 | 25 |

Soil layer distribution and calculation model.

Numerical simulation of postconstructed embankment (m).

The lateral displacements of the bridge pile and pile column under different working conditions are shown in Figure

Lateral displacement of bridge piles and columns under different working condition.

Working condition 2

Working condition 3

Working condition 4

Working condition 5

The lateral displacement of the pile along the depth is shown in Figure

Lateral displacement of left and right bridge piles and columns.

The profiles of the lateral displacement under working condition 5 are shown in Figure

Profiles of bridge pile columns and lateral displacement of foundation soil-working condition 5.

Limited by article length and actual calculation results, only vertical displacements (

Longitudinal displacement of bridge piles.

Working condition 1

Working condition 5

To understand the effects of stacking load on the vertical displacement of bridge piles and columns, the vertical displacements of working conditions 1 and 5 of bridge piles and columns were extracted (Figure

Vertical displacement of bridge piles and columns.

Working condition 1

Working condition 5

Variations of axial forces of bridge piles and columns under five working conditions are shown in Figure

Axial forces of bridge piles and columns.

Vertical sedimentation of bridge pile and columns.

According to calculation results, a large lateral displacement will be generated under the postconstructed embankment and pedestrian loads. To ensure the safety of a bridge structure, spinning pile processing was adopted by combining the parameter analysis results in Section

Vertical settlement of foundation after spinning pile processing.

Working condition 2

Working condition 3

Working condition 4

Working condition 5

Soil mass will generate lateral displacement under stacking loads, and piles generate lateral displacement due to pile-soil interaction. However, soil mass surrounding piles is restricted by piles from free displacement. The lateral displacement of piles (

Maximum principal plastic strain of foundation soil under different working conditions.

Working conditions 1, 2

Working condition 3

Working condition 4

Working condition 5

To understand the plastic region size of soil mass, the vertical and plane views of the maximum principal plastic strain of soil mass under working condition 5 are shown in Figures

Maximum principal plastic strain of foundation soil-vertical view.

Maximum principal plastic strain of foundation soil-plane view.

On the basis of the above numerical analysis, attention is given to the monitoring of lateral displacement and axial force of bridge columns in actual construction to ensure the safety and stability of the original bridge pile foundation. The construction shall be stopped immediately if the lateral displacement of pile columns is too large, the displacement rate is high, or the displacement exceeds a certain value. The causes of such occurrences shall be analyzed. Considering the analysis results for the lateral displacement of the pile body in Section

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (51679093 and 51774147), the Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), China (SKLGP2018K008), the Natural Science Foundation of Fujian Province of China (2017J01094), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University, China (ZQN-PY112 and ZQN-PY311).