# Model Uncertainty for Settlement Prediction on Axially Loaded Piles in Hydraulic Fill Built in Marine Environment

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## Abstract

**:**

## 1. Introduction

## 2. Site Geology

## 3. Soil Conditions

^{2}mesh. The operation is controlled until it is densified up to 90% of its maximum dry density.

#### Site Investigation Uncertainty

_{SPT}) are presented in the following Figure 1. SPT indexes have been corrected by hammer energy to achieve a homogeneous value corresponding to N

_{60}index and by groundwater, according to the following criterion (Equation (1)) [9,10,11].

_{i}is the N

_{60}average value at a depth i.

- The dispersion on SPT test is higher than that on CPT test, at least in the first 16 m. SPT test dispersion is varied between 0.4 and 0.7, while the CPT dispersion is around 0.2.
- In the last four meters, both dispersions are similar. Their values are in the range of 0.4 to 0.7.

## 4. Pile Analytical Model

- Relative density is related to the ultimate skin friction and base resistance according to API.
- The pile can be split in same-length slices. At each slice, an ultimate skin friction is associated depending om its depth. The deepest slice has additionally a base resistance.
- For each pile slice, it is calculated its t-z curve and for the deepest the base bearing capacity curve, according to the aforementioned code.
- That analytical model gives a load-settlement prediction curve which later can be compared to the real-scale load test

#### 4.1. Relative Density from SPT Index

_{v}is Vertical effective stress at the SPT test depth.

_{60}is SPT-index corrected by hammer energy and depth.

_{SPT}is the SPT value corrected only by groundwater table.

- From borehole top to 3.0 m deep, it is 0.75
- Below 3.0 m deep, z = 3.0 m Cr = (z − 3)/28 + 0.75 < 1.0

#### 4.2. Ultimate Skin Friction and Base Resistance

_{0}(z) Vertical effective pressure at z depth.

_{q}: non-dimensional parameter

_{0,tip}: effective vertical pressure at the base of the pile.

#### 4.3. Pile Model

_{i}). Each of them has a weight (P

_{i}) and ultimate skin friction (Rf

_{i}). The deepest slice has additionally a base resistance (Rp). At pile top, it is applied a load (F

_{0}).

_{i}), as a result of the application of the external load and weight. u

_{i}is positive downward. The following equation system solves the mathematical problem.

_{i}is the pile stiffness that takes the value:

_{i}pile cross-section area.

_{i}: slice length.

_{0}and displacement at the top pile (u

_{1}). Since skin friction Rf

_{i}(u

_{i}) and base resistance Rp(u

_{n}) are functions of displacement, the system is nonlinear and it has to be used an iterative algorithm to reach the solution.

#### 4.4. t-z Curve and Q-z Curve

_{i}functions are obtained from the t-z curve defined in standard ISO 19901-4:2003 (API RP 2GEO). Base resistance also follows the recommendations of this standard. The following Figure 8 shows the used functions.

#### 4.5. Load Application

_{0}is applied by steps as it is done in the large-scale load test. Positive load is downward. Model admits starting loads as tension (upwards) or compression (downwards).

## 5. Pile Load Test Outputs

- There is no correlation between the length of the pile and total settlement. This can be explained by the fact that all the piles have been punched to the dense sand layer, so their support conditions are similar.
- The tests with more frequent values are separated from other tests, which are considered special cases and are beyond the average behavior. Four out-of-average pile tests were removed, since it was suspected that their support conditions were different from others

## 6. Fitting the Analytical Model and Pile Load Test

## 7. Probabilistic Approach

- Artificial soil resistance profiles based on SPT tests are generated, so that they meet the expected mean and standard deviation previously defined at soil conditions section. It has been assumed a Norma Distribution for SPT values.
- For each of these artificial profiles, pile settlement is calculated using the same load pattern that in the load tests. Total bearing capacity is also calculated.
- Settlement distribution generated by artificial profile is compared to the pile load test distribution.
- Both distributions have the same mean, after reasonable and small adjustments are introduced on the model.
- However, dispersion in the pile load test outputs is larger than in the model. Therefore, it is necessary to introduce a statistical function that takes into account the uncertainty of the model itself.

#### 7.1. Artificial Soil Resistance Profiles Generation

#### 7.2. Pile Bearing Capacity

- The point resistance is hardly affected by the stochastic variation in soil strength. This result can be explained considering that soil strength and density are related. At the pile tip, density is always at its very high; therefore, base resistance is often taking the maximum value.
- However, shaft resistance shows a higher dispersion that is related to the dispersion of the input data.

#### 7.3. Pile Settlement Calculation

#### 7.4. Model Uncertainty

## 8. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**NSPT representation: (

**a**) Example of a statistical representation of the SPT-parameter corrected by method and statistical uncertainty; (

**b**) Artificial SPT profile generated by probabilistic Monte Carlo Method.

**Figure 6.**(

**a**) Relationship between relative density and skin friction; (

**b**) Relationship between relative density and resistance.

**Figure 13.**Numerical models outputs for each load step (

**a**) skin friction versus depth (

**b**) displacement distribution versus depth.

Property | Type 1 |
---|---|

Maximum particle size | 125 mm |

Maximum % greater 125 mm | 0 |

Minimum % passing 2 mm sieve | 35 |

Maximum % passing 75 micron | 20 |

Maximum % clay (<2 micron) | 2 |

Liquid Limit (%) | <35 |

Plasticity Index (%) | <10 |

Settlement | Values |
---|---|

Maximum settlement | 4.84 mm |

Minimum settlement | 1.22 mm |

Average | 2.05 mm |

Standard deviation | 0.68 mm |

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**MDPI and ACS Style**

Bueno Aguado, M.; Escolano Sánchez, F.; Sanz Pérez, E.
Model Uncertainty for Settlement Prediction on Axially Loaded Piles in Hydraulic Fill Built in Marine Environment. *J. Mar. Sci. Eng.* **2021**, *9*, 63.
https://doi.org/10.3390/jmse9010063

**AMA Style**

Bueno Aguado M, Escolano Sánchez F, Sanz Pérez E.
Model Uncertainty for Settlement Prediction on Axially Loaded Piles in Hydraulic Fill Built in Marine Environment. *Journal of Marine Science and Engineering*. 2021; 9(1):63.
https://doi.org/10.3390/jmse9010063

**Chicago/Turabian Style**

Bueno Aguado, Manuel, Félix Escolano Sánchez, and Eugenio Sanz Pérez.
2021. "Model Uncertainty for Settlement Prediction on Axially Loaded Piles in Hydraulic Fill Built in Marine Environment" *Journal of Marine Science and Engineering* 9, no. 1: 63.
https://doi.org/10.3390/jmse9010063