# Load-Bearing Performance and Safety Assessment of Grid Pile Foundation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Construction of the Numerical Model

#### 2.1. Parameters of Numerical Models

_{0}between the pile and soil is calculated from the internal friction angle according to Equation (1).

#### 2.2. Numerical Model for SWF

#### 2.3. Numerical Model for GPF

## 3. Numerical Calculation and Analysis of GPF

#### 3.1. Settlement Curve Analysis

#### 3.2. Stress Analysis of Pile and Soil

#### 3.3. Analysis of Lateral Frictional Resistance of Pile

## 4. Impact of Change in GPF Size on Its Load-Bearing Performance

#### 4.1. Impact of Pile Length on Load-Bearing Performance

#### 4.2. Impact of Pile Side Length on Load-Bearing Performance

## 5. Simplification Algorithm and Safety Evaluation Method for GPF Settlement

#### 5.1. Simplification Algorithm for GPF Settlement Based on Mindlin Stress Solution

#### 5.2. Monte Carlo Method-Based Settlement Reliability Analysis of GPF

^{−5}and 3.754, respectively. The reliability of this study is greater than the threshold value (3.5) specified in the Specifications of the National Transportation Association of the USA [35]. Therefore, the GPF proposed in this study can be safely used under complex geological conditions.

## 6. Conclusions

- (1)
- Under identical grid sizes, the soil stress and frictional resistance of the GPF change less with the increasing load, thereby resulting in significant changes in the inner frictional resistance in the lower portion of the pile.
- (2)
- Along the depth, the inner frictional resistance of the GPF exhibits an exponential distribution pattern, whereas the outer frictional resistance shows an approximately triangular or trapezoidal distribution pattern.
- (3)
- The stress in the upper third of the pile length is higher. Therefore, the strength of the upper third of the pile should be strengthened during pile foundation designing.
- (4)
- The changes in the pile and side lengths have a small effect on the outer frictional resistance, and their reductions can improve the exertion of inner frictional resistance and reduce the tip resistance. Therefore, the GPF load-bearing performance can be enhanced.
- (5)
- The safety and reliability analyses indicate that the GPF proposed in this study can be safely used under complex geological conditions.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wu, J.; Cheng, Q.; Wen, H. Overview of the variety of diaphragm wall foundation developed in Japan in recent years. Ind. Constr.
**2013**, 43, 1. [Google Scholar] - Maheshwari, P. Analysis of combined footings on extensible geosyntheticstone column improved ground. J. Civ. Eng. Sci. Technol.
**2017**, 8, 57–71. [Google Scholar] [CrossRef] - Kumar, P.; Kumar, M.; Chandaluri, V.K.; Sawant, V.A. Uplift capacity of single and group of granular anchor pile system. J. Civ. Eng. Sci. Technol.
**2018**, 9, 34–40. [Google Scholar] [CrossRef] [Green Version] - A Rashid, A.S.; Black, J.; Kueh, A.B.H.; Mohamad, H.; Md Noor, N. Bearing capacity charts of soft soil reinforced by deep mixing. Inst. Civ. Eng.
**2017**, 170, 12–25. [Google Scholar] [CrossRef] - A Rashid, A.S.; Kueh, A.B.H.; Mohamad, H. Behaviour of soft soil improved by floating soil–cement columns. Inst. Civ. Eng.
**2018**, 18, 95–116. [Google Scholar] [CrossRef] - Wu, J.; Cheng, Q.; Wen, H.; Cao, J.-L. Vertical bearing behaviors of lattice shaped diaphragm walls and group piles as bridge foundations in soft soils. Chin. J. Geotech. Eng.
**2014**, 36, 1733–1744. [Google Scholar] - Wu, J.; Cheng, Q.; Wen, H.; Li, Y.; Zhang, J.; Wang, L. Comparison on the Horizontal Behaviors of Lattice-Shaped Diaphragm Wall and Pile Group under Static and Seismic Loads. Shock Vib.
**2016**, 2016, 1289375. [Google Scholar] [CrossRef] [Green Version] - Ou, Q.; Zhang, L.; Zhao, M.; Wang, Y. Lateral Displacement and Internal Force in Diaphragm Walls Based on Principle of Minimum Potential Energy. Int. J. Geomech.
**2019**, 19, 04019055. [Google Scholar] [CrossRef] - Lei, G.H.; Sun, H.S.; Ng, C.W.W. An Approximate Analytical Solution for Calculating Ground Surface Settlements Due to Diaphragm Walling. Comput. Geotech
**2014**, 61, 108–115. [Google Scholar] [CrossRef] - Yajnheswaran, B.; Akshay, P.R.; Rajasekaran, C.; Rao, S. Effect of stiffness on performance of diaphragm wall. Procedia Eng.
**2015**, 116, 343–349. [Google Scholar] - Liu, L.; Dai, G.; Gong, W. Numerical analysis about bearing characteristics of closed diaphragm wall under horizontal load. In Proceedings of the International Symposium on Innovation and Sustainability of Structures in Civil Engineering (ISISS 2011), Xiamen, China, 28–30 October 2011. [Google Scholar]
- Chen, Q.; Wu, J.; Song, Z.; Wen, H. The behavior of a rectangular closed diaphragm wall when used as a bridge foundation. Front. Struct. Civ. Eng.
**2012**, 6, 398–420. [Google Scholar] - Wu, J.; Chen, Q.; Wen, H.; Wang, L.; Li, Y.; Zhang, J. A load transfer approach to rectangular closed diaphragm walls. Inst. Civ. Eng.
**2016**, 169, 509–526. [Google Scholar] [CrossRef] - Wen, H.; Chen, Q.; Meng, F.; Chen, X. Diaphragm wall-soil-cap interaction in rectangular-close diaphragm-wall bridge foundations. Front. Archit. Civ. Eng.
**2009**, 3, 93–100. [Google Scholar] [CrossRef] - Guo, P.; Gong, X.; Wang, Y. Research on performance of cellular diaphragm wall in deep excavation considering nonlinear contact between wall and soil. Chin. J. Geotech. Eng.
**2021**, 43, 1201–1209. (In Chinese) [Google Scholar] - Wu, J.; Chen, Q.; Tang, W. Numerical Analysis of the Chamber Effect of Lattice Shaped Diaphragm Wall as Bridge Foundation in Sand. Constr. Technol.
**2016**, 45, 60–63. (In Chinese) [Google Scholar] - Hou, Y. Study on Retaining Structure Behavior of Lattice Diaphragm Wall in Soft Soil Stratum. Ph.D. Thesis, Shanghai Jiaotong University, Shanghai, China, 2010. (In Chinese). [Google Scholar]
- (JGJ94-2008); Technical Code for Building Pile Foundations. China Architecture and Building Press: Beijing, China, 2008. (In Chinese)
- (GB50007—2011); Code for design of building foundation. China Architecture and Building Press: Beijing, China,, 2012. (In Chinese)
- Ding, X.; Zhang, T.; Li, P.; Cheng, K. A Theoretical Analysis of the Bearing Performance of Vertically Loaded Large-Diameter Pipe Pile Groups. J. Ocean Univ. China
**2016**, 15, 57–68. [Google Scholar] [CrossRef] - Liu, H.; Fei, K.; Zhou, Y.; Gao, Y. Numerical simulation of inner frictional resistance of cast-in-situ concrete thin-wall pipe pile. Rock Soil Mech.
**2004**, 25, 211–216. (In Chinese) [Google Scholar] - Mindlin, R.D. Force at a point in the interior of a semi-infinite solid. Physics
**1936**, 7, 195–202. [Google Scholar] [CrossRef] - Zhu, M.; Wang, J.; Zhu, X. Performance analysis of cast-in-place tubular pile composite ground under embankment load. J. Zhejiang Univ. (Eng. Sci.)
**2006**, 40, 2186–2190. (In Chinese) [Google Scholar] - Wang, Z.; Zhang, Y. Analytical analysis of vertical load-transfer of large-diameter cast-in-situ concrete tubular piles. Chin. J. Geotech. Eng.
**2007**, 29, 1488–1492. (In Chinese) [Google Scholar] - Liu, H.; Wu, C.; Yu, F.; Xia, T. Dynasty Improved algorithm for settlement of cylindrical pile composite foundation under embankment load. J. Geotech. Eng.
**2013**, 35, 638–642. (In Chinese) [Google Scholar] - Pang, Y.; Meng, R.; Li, C.; Li, C. A probabilistic approach for performance-based assessment of highway bridges under post-earthquake induced landslides. Soil Dyn. Earthq. Eng.
**2022**, 155, 107207. [Google Scholar] [CrossRef] - Pang, Y.; Wei, K.; He, H.; Wang, W. Assessment of lifetime seismic resilience of a long-span cable-stayed bridge exposed to structural corrosion. Soil Dyn. Earthq. Eng.
**2022**, 157, 107275. [Google Scholar] [CrossRef] - Yang, H.; Pang, Y.; Tian, S.; Dang, X.; Yuan, W. Case study of the seismic response of an extra-dosed cable-stayed bridge with cable-sliding friction aseismic bearing using shake table tests. Struct. Des. Tall Spec. Build.
**2017**, 26, e1398. [Google Scholar] [CrossRef] - Shen, Z.; Wei, K. Stochastic model of tropical cyclones along China coast including the effects of spatial heterogeneity and ocean feedback. Reliab. Eng. Syst. Saf.
**2021**, 216, 108000. [Google Scholar] [CrossRef] - Pang, Y.; Wang, X. Cloud-IDA-MSA conversion of fragility curves for efficient and high-fidelity resilience assessment. J. Struct. Eng.
**2021**, 147, 04021049. [Google Scholar] [CrossRef] - Pang, Y.; Wang, X. Enhanced endurance-time-method (EETM) for efficient seismic fragility, risk and resilience assessment of structures. Soil Dyn. Earthq. Eng.
**2021**, 147, 106731. [Google Scholar] [CrossRef] - Zhong, J.; Ni, M.; Hu, H.; Yuan, W.; Yuan, H.; Pang, Y. Uncoupled multivariate power models for estimating performance-based seismic damage states of column curvature ductility. Structures
**2022**, 36, 752–764. [Google Scholar] [CrossRef] - Wei, K.; Arwade, S.R.; Myers, A.T.; Valamanesh, V. Directional effects on the reliability of non-axisymmetric support structures for offshore wind turbines under extreme wind and wave loadings. Eng. Struct.
**2016**, 106, 68–79. [Google Scholar] [CrossRef] [Green Version] - Zhong, J.; Yang, T.; Pang, Y.; Yuan, W. A novel structure-pulse coupled model for quantifying the column ductility demand under pulse-like GMs. J. Earthq. Eng.
**2021**, 1–19. [Google Scholar] [CrossRef] - American Association of State Highway and Transportation Officials. LRFD Bridge Design Specifications, 8th ed.; American Association of State Highway and Transportation Officials: Washington, DC, USA, 2017. [Google Scholar]

**Figure 2.**Settlement curve of SWF A [17].

**Figure 3.**Stress nephogram of numerical models: (

**a**) The stress nephogram of single-width UGDW, (

**b**) the stress nephogram of GPF.

**Figure 6.**Additional stress curves of soil inside and outside GPF: (

**a**) Additional stress curves of soil outside pile, (

**b**) additional stress curves of pile core soil.

**Figure 7.**Distribution curves of lateral frictional resistance of GPF: (

**a**) Distribution curves of outer friction resistance, (

**b**) distribution curves of inner friction resistance.

**Figure 10.**Lateral friction resistance of piles ①, ④, and ⑤: (

**a**) The outer frictional resistance of piles ①, ④, and ⑤, (

**b**) the inner frictional resistance of piles ①, ④, and ⑤.

**Figure 13.**Lateral friction resistance of piles ①, ②, and ③: (

**a**) The outer frictional resistance of piles ①, ②, and ③, (

**b**) the inner frictional resistance of piles ①, ②, and ③.

Foundation Type | SWF | GPF | |||||
---|---|---|---|---|---|---|---|

A | B | ① | ② | ③ | ④ | ⑤ | |

Length of side (m) | 5 | 6 | 6 | 7.2 | 4.8 | 6 | 6 |

Thickness (m) | 0.8 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 |

Length (m) | 27 | 30 | 30 | 30 | 30 | 33 | 27 |

Density (kg/m ^{3}) | Elasticity Modulus (E/MPa) | Internal Friction Angle φ/(°) | Cohesive Force (c/kPa) | Poisson’s Ratio (v) | Initial Void Ratio e_{0} | Coefficient of Lateral Pressure k_{0} | |
---|---|---|---|---|---|---|---|

Pile | 2500 | 30,000 | - | - | 0.2 | - | - |

Soil layer 1 | 1860 | 60 | 27.5 | 10 | 0.3 | 0.71 | 0.54 |

Soil layer 2 | 1720 | 30 | 18 | 18 | 0.3 | 0.76 | 0.69 |

Random Variables | Distribution Pattern | Upper Limit | Lower Limit |
---|---|---|---|

E/MPa | Uniform distribution | 60 | 40 |

$\nu $ | Uniform distribution | 0.4 | 0.2 |

P/MN | Uniform distribution | 60 | 50 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tang, R.; Wang, Y.; Zhang, W.; Jiao, Y.
Load-Bearing Performance and Safety Assessment of Grid Pile Foundation. *Sustainability* **2022**, *14*, 9477.
https://doi.org/10.3390/su14159477

**AMA Style**

Tang R, Wang Y, Zhang W, Jiao Y.
Load-Bearing Performance and Safety Assessment of Grid Pile Foundation. *Sustainability*. 2022; 14(15):9477.
https://doi.org/10.3390/su14159477

**Chicago/Turabian Style**

Tang, Rui, Yongyi Wang, Weili Zhang, and Yuyong Jiao.
2022. "Load-Bearing Performance and Safety Assessment of Grid Pile Foundation" *Sustainability* 14, no. 15: 9477.
https://doi.org/10.3390/su14159477