# The Influence Depth of Pile Base Resistance in Sand-Layered Clay

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{c}S

_{u}, where N

_{c}is the coefficient of pile base resistance. Wilson [14] suggested that N

_{c}should be taken as 8.0 by the pile base resistance tests in clay. To measure pile base resistance, six tests were conducted by Meigh [15] and Yassin [16] in undisturbed soil and remolded soil in Imperial College London, and Skempton [17] suggested that N

_{c}should be taken as 9.0 based on six test results and the theoretical analysis of Meyerhof and Mott–Gibson. Randoplh et al. [18], who combined with the empirical coefficient of deep foundation base resistance of Skempton and the theoretical solution of base resistance coefficient established by Vesic based on cavity expansion theory, recommended N

_{c}as 9.0. This coefficient was introduced into the American Petroleum Institute (API), which is a standard method widely used in offshore pile foundation engineering for determining unit pile base resistance based on undrained shear strength. The end is at least three diameters above the bottom of the layer to preclude punch-through in layered soils, and the unit pile base resistance should be corrected if this distance cannot be reached.

## 2. Difference in Calculation Formula of Pile Base Resistance

#### 2.1. Engineering Example

#### 2.2. Results of Pile Base Resistance

_{u}or cone resistance) and the empirical coefficients are different in these methods. Because the pile base resistance has a certain range of influence above and below the pile end, the depth range of the soil at the pile end is different when calculating the pile base resistance by various methods, and the comparison is shown in Table 3.

## 3. Numerical Simulation on Influence Range of Pile Base Resistance

#### 3.1. Numerical Model and Verification

_{0}= 85.29 m, the length of the embedded L = 82.29 m, and the length–diameter ratio L/D = 30. The Mohr–Coulomb model is adopted for soil, the effective The relationship between mass and mobility is often expressed with the effective density, which is defined as the mass of the particle divided by its mobility equivalent volume, of soil is taken, Poisson’s ratio is taken as 0.49, and the elastic modulus is taken as 500 S

_{u}. The parameters of FEM are shown in Table 5.

#### 3.2. Results in Homogeneous Clay

#### 3.3. Results when the Clay Is above the Sand

#### 3.3.1. Influence of Distance between Sand and the Pile End

_{1}is taken as 0.5 D, 1.0 D, 1.5 D, 1.7 D, and 2.0 D, respectively. The results are shown in Figure 10b.

#### 3.3.2. Influence of Sand Thickness

_{1}is shown in Figure 11a, and the result is shown in Figure 11b.

#### 3.4. Results when the Clay Is under the Sand

#### 3.4.1. Influence of Distance between Sand and the Pile End

_{2}is taken as 0.1 D, 0.2 D, 0.5 D, 1.0 D, and 1.5 D, respectively. The results are shown in Figure 12.

#### 3.4.2. Influence of Sand Thickness

_{2}is shown in Figure 13a, and the result is shown in Figure 13b.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Base resistance at representative depth. (

**a**) Based on the parameters at the pile end, (

**b**) based on the average of parameters below the pile end, (

**c**) and based on the average of parameters above and below the pile end.

**Figure 8.**Distribution of plastic zone at pile end under the different distance between the pile end and the soil bottom boundary.

**Figure 9.**Ultimate bearing capacity. (

**a**) Load–displacement curve, (

**b**) relationship between ultimate bearing capacity and distance.

**Figure 10.**Influence of the distance between the pile end and top of the sand on pile base resistance.

Pile Length (m) | Length of Embedded Pile (m) | Diameter (m) | Thickness (mm) |
---|---|---|---|

171 | 134 | 2.743 | 70 |

Stratum | Soil Description | Thickness (m) | Submerged Unit Weight γ′ (kN/m ^{3}) | Internal Friction Angle φ (°) | Design Shear Strength S _{u} (kPa) |
---|---|---|---|---|---|

1 | Very soft sandy clay | 0.8 | 8.2 | — | 11 |

2 | Soft calcareous silty clay | 5.8 | 7.7 | — | 12–24 |

3 | Slightly hard calcareous sandy clay | 2.5 | 7.0 | — | 28–38 |

4 | Slightly hard to hard calcareous silty clay | 36.4 | 7.6 | — | 30–75 |

5 | Hard to very hard calcareous sandy clay | 3.9 | 9.8 | — | 90–120 |

6 | Loose to medium dense clayey sand | 2.2 | 9.3 | 25 | — |

7 | Hard to very hard calcareous silty clay | 21.1 | 8.6 | — | 80–130 |

8 | Medium dense carbonate silty fine sand | 6.1 | 6.5 | 30 | — |

9 | Very hard to hard calcareous silty clay | 91.4 | 9.6 | — | 160–400 |

Method | Formula | Kernel Parameter | Range of Soil |
---|---|---|---|

API/ISO | $q=9{S}_{u}^{}$ | Design Shear Strength, S_{u} | Pile end |

NGI | $q=9{S}_{u}^{\mathrm{UU}}$ | UU Shear Strength, S_{u}^{UU} | Pile end |

Lehane | $q={q}_{t}\left[0.2+0.6{D}^{*}/D\right]$ | q_{t} | 20 times the pile wall thickness below the pile end |

Schmertmann | $q=\frac{{q}_{c1}+{q}_{c2}}{2}$ | q_{c} | 8 D above the pile end, 0.7 D–4 D below the pile end |

European | $q=9{C}_{u}\le 15\mathrm{MPa}{C}_{u}={q}_{c}/{N}_{k}$ | q_{c} | 0.7 D–4 D below the pile end |

ICP | Closed: q = 0.8 q_{c} (undrained) q = 0.8 q _{c} (drained)Open (fully plugged): q = 0.4 q _{c} (undrained) q = 0.65 q_{c} (drained)Open (unplugged): q = 1.0 q _{c} (undrained) q = 1.6 q_{c} (drained) | q_{c} | ±1.5 D at the pile end |

LCPC | $q=k{q}_{c}$ | q_{c} | ±1.5 D at the pile end |

Penpile [29] | $q=0.25{q}_{c}$ | q_{c} | Pile end |

Takesue [30] | $q={q}_{t}-{u}_{2}$ | q_{t} | Pile end |

Fugro | $q=0.7{q}_{n,av}$ | q_{n} | ±1.5 D at the pile end |

_{u}is design shear strength; S

_{u}

^{UU}is shear strength determined by UU test; D is the out diameter of pile, ${D}^{*}={\left({D}^{2}-{D}_{i}^{2}\right)}^{0.5}$, D

_{i}is the inner diameter of pile; q

_{c}

_{1}is average cone resistance within the range of 8 D above the pile end, q

_{c}

_{2}is average cone resistance within the range of 0.7–4 D below the pile end; C

_{u}is the shear strength of soil, N

_{k}is empirical coefficient; q

_{c}is cone resistance; q

_{t}is corrected cone resistance, q

_{t}= q

_{c}+ (1 − a)u

_{2}; q

_{n}is net cone resistance, q

_{n}= q

_{c}+ (1 − a) u

_{2}− σ

_{v0}; u

_{2}is pore pressure; k is empirical coefficient; and q

_{n,av}is the average net cone resistance within the 1.5 D above and below the pile end.

Depth (m) | Maximum (MN) | Minimum (MN) | Mean (MN) | Variance | COV |
---|---|---|---|---|---|

33 | 7.4 | 1.9 | 3.9 | 1.6 | 0.41 |

49 | 13.4 | 2.5 | 7.9 | 3.8 | 0.48 |

80 | 22.9 | 5.3 | 12.2 | 5.9 | 0.49 |

130 | 36.0 | 9.5 | 19.6 | 8.3 | 0.42 |

Model | Effective Density (kg/m ^{3}) | Elastic Modulus (kPa) | Poisson’s Ratio | Shear Strength (kPa) | Internal Friction Angle (°) |
---|---|---|---|---|---|

Pile | 6850 | 210 × 10^{6} | 0.25 | — | — |

Clay | 600 | 500 S_{u} | 0.49 | 20–100 | — |

Sand | 900 | 50,000 | 0.3 | — | 30 |

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**MDPI and ACS Style**

Fu, D.; Li, S.; Zhang, H.; Jiang, Y.; Liu, R.; Li, C.
The Influence Depth of Pile Base Resistance in Sand-Layered Clay. *Sustainability* **2023**, *15*, 7221.
https://doi.org/10.3390/su15097221

**AMA Style**

Fu D, Li S, Zhang H, Jiang Y, Liu R, Li C.
The Influence Depth of Pile Base Resistance in Sand-Layered Clay. *Sustainability*. 2023; 15(9):7221.
https://doi.org/10.3390/su15097221

**Chicago/Turabian Style**

Fu, Dianfu, Shuzhao Li, Hui Zhang, Yu Jiang, Run Liu, and Chengfeng Li.
2023. "The Influence Depth of Pile Base Resistance in Sand-Layered Clay" *Sustainability* 15, no. 9: 7221.
https://doi.org/10.3390/su15097221