# Vibrations Induced by a Low Dynamic Loading on a Driven Pile: Numerical Prediction and Experimental Validation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling Approach

#### 2.1. Generalities

#### 2.2. Axisymmetric FEM-PML Approach: Modeling of the Pile–Ground System

#### 2.3. Impact Hammer Model and Hammer–Pile Interaction

## 3. Characterization of the Construction Site

^{3}. As expected, a large increase in the P-wave velocity occurred at the depth of the groundwater table.

^{3}). A hysteretic damping factor equal to 0.01 was considered for the pile and the value of 0.20 was assumed for the Poisson’s ratio. The piles had a total length varying from 8 to 15 m.

## 4. Experimental Validation of the Axisymmetric FEM-PML Approach in Low-Strain Conditions

#### 4.1. Experimental Setup

^{®}Impact Hammer Model 086D50), and the transient signal was recorded using unidirectional accelerometers with reference PCB603C01, with a measurement range of ±0.5 g and sensitivity of 10 V/g, placed in a straight line starting from the location of the pile. A total of 50 measurement points with intervals of 1 m were used. The collected signals (the ground response data and the applied load) were conditioned by an electronic system composed of a laptop connected to an acquisition system, with reference NI CDAQ-9172. A sampling rate of 2048 Hz was considered.

#### 4.2. Numerical Considerations

#### 4.3. Comparison between Experimental and Numerical Results

## 5. Is Linear Modeling Reasonable for Predicting Vibrations Induced by Pile Driving?

^{−4}(depending on the type of soil and the confining stress).

## 6. Conclusions

- (i)
- Given the uncertainties regarding the material damping of the soil, a parametric study was performed, allowing to discuss the relevant influence of this parameter on the dynamic response of the ground and finding an optimized value that fits the experimental results;
- (ii)
- The comparison between the experimental and numerical results shows a very satisfactory agreement. This general comment is valid not only in terms of the maximum levels of vibration but also in the frequency range of the response;
- (iii)
- Given the results obtained, the proposed numerical model can be used in the prediction of ground-borne vibrations for situations where low-strain deformations are expected.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Experimental test site: (

**a**) general view; (

**b**) geological–geotechnical profile; (

**c**) foundation plan and borehole’s location (S1–S7).

**Figure 6.**Dynamic characterization of the soil: (

**a**) setup for the experimental activities; (

**b**) experimental P-SV dispersion relationship.

**Figure 7.**Dynamic properties of the soil along the depth: (

**a**) S-wave velocity profile; (

**b**) P-wave velocity profile.

**Figure 12.**Peak particle velocity versus distance from the pile due to Ricker pulse: experimental (blue line) vs numerical results (red line—$\xi =0.05\left(firstlayer\right);0.025\left(remaininglayers\right)$; upper bound—${\xi}_{1}=0.01$; lower bound—${\xi}_{2}=0.05$).

**Figure 13.**Experimental velocities of vertical vibration measured at different distances from the pile compared to the numerical prediction for a material damping ratio equal to 0.025: (

**a**) 10 m; (

**b**) 20 m; (

**c**) 30 m; (

**d**) 40 m; (

**e**) 50 m (left: time history; right: frequency content).

**Table 1.**Elastodynamic properties of the pile–ground system (E—Young’s modulus; ν—Poisson’s ratio; ρ—mass density; ξ—hysteretic damping factor).

Element | h (m) | E (MPa) | ν (-) | ρ (kg/m^{3}) | ξ (%) |
---|---|---|---|---|---|

Soil | 2 | 154 | 0.25 | 1900 | 5 |

6 | 251 | 0.25 | 2.5 | ||

5 | 620 | 0.49 | |||

inf | 2200 | 0.49 | |||

Pile | L = 12 m | 30,000 | 0.20 | 2500 | 1 |

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**MDPI and ACS Style**

Colaço, A.; Costa, P.A.; Parente, C.; Abouelmaty, A.M.
Vibrations Induced by a Low Dynamic Loading on a Driven Pile: Numerical Prediction and Experimental Validation. *Vibration* **2022**, *5*, 829-845.
https://doi.org/10.3390/vibration5040049

**AMA Style**

Colaço A, Costa PA, Parente C, Abouelmaty AM.
Vibrations Induced by a Low Dynamic Loading on a Driven Pile: Numerical Prediction and Experimental Validation. *Vibration*. 2022; 5(4):829-845.
https://doi.org/10.3390/vibration5040049

**Chicago/Turabian Style**

Colaço, Aires, Pedro Alves Costa, Cecília Parente, and Ahmed M. Abouelmaty.
2022. "Vibrations Induced by a Low Dynamic Loading on a Driven Pile: Numerical Prediction and Experimental Validation" *Vibration* 5, no. 4: 829-845.
https://doi.org/10.3390/vibration5040049