# Effect of Scour on the Natural Frequency Responses of Bridge Piers: Development of a Scour Depth Sensor

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Materials and Cross-Sections of the Rod-Sensor

#### 2.2. Experimental Procedures

#### 2.2.1. Sandy Soil

#### 2.2.2. Clayey Soil

## 3. Numerical Model

#### 3.1. Theoretical Formulation

#### 3.2. Model Description

## 4. Results and Discussion

#### 4.1. Experimental Results

#### 4.1.1. Effect of Soil Aging

#### 4.1.2. Repeatability Analysis

#### 4.1.3. Effect of Scour

#### 4.1.4. Effect of the Embedded Length

#### 4.1.5. The Effect of Soil Type

#### 4.2. Numerical Results

#### 4.2.1. Model Validation

#### 4.2.2. The Effect of Water

#### 4.3. Proposed Calibration Technique of the Sensor

#### 4.3.1. Equivalent Cantilever Beam

#### 4.3.2. Wet Frequencies and Equivalent Cantilever Beam

#### 4.4. Sensitivity Study

#### 4.4.1. The Effect of the Elasticity of the Rod-Sensor ${E}_{r}$

#### 4.4.2. The Effect of the Density of the Rod-Sensor ${\rho}_{r}$

#### 4.4.3. The Effect of the Elasticity of the Soil ${E}_{s}$

#### 4.5. General Discussion about the Findings

## 5. Concluding Remarks and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

D | = | Embedded length of the rod (m); |

${D}_{50}$ | = | Average grain diameter (mm); |

E | = | Young modulus of the cantilever (MPa); |

${E}_{m}$ | = | Ménard modulus of the soil (MPa); |

${E}_{r}$ | = | Young modulus of the rods (MPa); |

${E}_{s}$ | = | Young modulus of the soil (MPa); |

f | = | First frequency (Hz); |

${f}_{dry}$ | = | First frequency in air (Hz); |

${f}_{wet}$ | = | First frequency in water (Hz); |

f | = | First frequency (Hz); |

H | = | Exposed length of the rod (m); |

${H}^{\prime}$ | = | Adjustment length (m); |

${H}_{c}$ | = | Free length of the cantilever (m); |

I | = | Inertia of the rod in the vibration direction (m${}^{4}$); |

L | = | Total length of the rod (m); |

M | = | Mass of the rod (kg); |

${M}_{a}$ | = | Added mass of water (kg); |

m | = | Mass of the accelerometer (kg); |

S | = | Section of the rod (m${}^{2}$); |

$\alpha $ | = | Rheological parameter of the soil (-); |

${\rho}_{s}$ | = | Bulk density of the soil (kg.m${}^{-3}$); |

${\rho}_{r}$ | = | Bulk density of the rods (kg.m${}^{-3}$); |

$\rho $ | = | Bulk density of the cantilever (kg.m${}^{-3}$). |

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**Figure 1.**Laboratory set-up in dry sand, where the tank at the bottom has a volume of 1 m × 1 m × 1 m and can be filled up to 0.7 m by sand.

**Figure 3.**Finite elements scour model. (

**a**) Three-dimensional numerical model of the rod-soil system and mesh details; (

**b**) Scour simulation with the numerical model.

**Figure 4.**Variation of first frequency with exposed length H in the clayey soil after 3, 10 and 45 resting days.

**Figure 8.**Comparison of experimental and numerical first frequencies of the tested rods (correlation coefficient of ${R}^{2}=0.9905$).

**Figure 9.**Equivalent cantilever of CA rod-sensors in sand: experimental first frequency for road-sensors CA-80 and CA-60, and first frequency of equivalent cantilever beam ${f}_{th}={\displaystyle \frac{1}{2\pi}}\times \sqrt{{\displaystyle \frac{3EI}{{{H}_{c}}^{3}(0.24M+m)}}}$.

**Figure 10.**Equivalent cantilever of rectangular aluminium (RA) rod-sensors in sand and clayey soil: experimental first frequency for road-sensor RA-80 and RA-60 in both sand and clayey soil, and first frequency of equivalent cantilever beam ${f}_{th}={\displaystyle \frac{1}{2\pi}}\times \sqrt{{\displaystyle \frac{3EI}{{{H}_{c}}^{3}(0.24M+m)}}}$.

**Figure 11.**Equivalent cantilever of circular PVC (CP) rod-sensor in sand and clayey soil: experimental first frequency for road-sensor CP-80 and RA-60 in both sand and clayey soil, and first frequency of cantilever beam ${f}_{th}={\displaystyle \frac{1}{2\pi}}\times \sqrt{{\displaystyle \frac{3EI}{{{H}_{c}}^{3}(0.24M+m)}}}$.

**Figure 14.**Variation of the adjustment length ${H}^{\prime}$ with the Young modulus of the rod ${E}_{r}$.

**Figure 15.**Variation of the adjustment length ${H}^{\prime}$ with the bulk density of the rod ${\rho}_{r}$.

**Figure 16.**Variation of the adjustment length ${H}^{\prime}$ with the Young modulus of the soil ${E}_{s}$.

Tested Rods | Outer Diameter/Width (mm) | Thickness (mm) | Young Modulus (GPa) | Bulk Density (kg/m${}^{3}$) | Flexural Rigidity (N.m${}^{2}$) |
---|---|---|---|---|---|

CA-80, CA-60 | 12 | 1 | 59 | 2700 | 31.1 |

RA-80, RA-60 | 19 | 2 | 59 | 2700 | 0.8 |

CP-80 | 20 | 2 | 3.5 | 1425 | 11.0 |

${\mathit{D}}_{50}$ (mm) | ${\mathit{\rho}}_{\mathit{s}}$ (Kg/m${}^{3}$) | ${\mathit{\nu}}_{\mathit{s}}$ | ${\mathit{E}}_{\mathit{m}}$ (MPa) | ${\mathit{E}}_{\mathit{s}}$ (MPa) |
---|---|---|---|---|

0.7 | 1700 | 0.3 | 0.5 | 1.5 |

Tested Rods | Min H (cm) | Max H (cm) |
---|---|---|

CA-80 | 35.0 | 65.0 |

CA-60 | 15.0 | 45.0 |

RA-80 | 35.0 | 70.0 |

RA-60 | 15.0 | 50.0 |

CP-80 | 35.0 | 70.0 |

Tested Rods | Min H (cm) | Max H (cm) |
---|---|---|

RA-80 | 40.0 | 60.0 |

RA-60 | 20.0 | 50.0 |

CP-80 | 40.0 | 65.0 |

Exposed Length | CA-80 | RA-80 | CP-80 | |||
---|---|---|---|---|---|---|

Measured Freq. (Hz) | Average Freq. (Hz) | Measured Freq. (Hz) | Average Freq. (Hz) | Measured Freq. (Hz) | Average Freq. (Hz) | |

9.52 | 1.55 | 6.58 | ||||

H = 65 cm | 9.98 | 9.64 ± 0.30 | 1.56 | 1.55 ± 0.01 | 6.50 | 6.51 ± 0.07 |

9.42 | 1.55 | 6.45 | ||||

25.33 | 4.21 | 16.94 | ||||

H = 35 cm | 26.28 | 25.71 ± 0.50 | 4.11 | 4.14 ± 0.06 | 16.18 | 16.58 ± 0.38 |

25.53 | 4.10 | 16.61 |

Tested Rods | Flexural Rigidity N.m${}^{2}$ | Frequencies in Sand | Frequencies in Clayey Soil | ||||
---|---|---|---|---|---|---|---|

H = 60 cm | H = 40 cm | Change Rate $\mathit{p}$ (%) | H = 60 cm | H = 40 cm | Change Rate $\mathit{p}$ (%) | ||

CA-80 | 31.1 | 11.31 | 19.50 | 42 | - | - | - |

CP-80 | 11.0 | 7.50 | 13.90 | 46 | 6.6 | 10.78 | 39 |

RA-80 | 0.8 | 1.78 | 3.45 | 48 | 1.53 | 2.8 | 45 |

Exposed Length | Dry Frequency | Wet Frequency | Percentage Change of the Frequency |
---|---|---|---|

(cm) | (Hz) | (Hz) | Between Air and Water (%) |

55 | 12.8 | 11.6 | 9 |

50 | 14.6 | 13.3 | 9 |

45 | 16.8 | 15.5 | 8 |

40 | 19.7 | 18.3 | 7 |

35 | 23.4 | 21.9 | 6 |

30 | 28.3 | 26.8 | 5 |

25 | 35.2 | 33.6 | 4 |

Tested Rod | Corrected Length in Sand (cm) | Corrected Length in Clayey Soil (cm) |
---|---|---|

CA-80, CA-60 | 8.8 | No results |

RA-80, RA-60 | 4 | 11 |

CP-80 | 4.6 | 11 |

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## Share and Cite

**MDPI and ACS Style**

Boujia, N.; Schmidt, F.; Chevalier, C.; Siegert, D.; Pham van Bang, D.
Effect of Scour on the Natural Frequency Responses of Bridge Piers: Development of a Scour Depth Sensor. *Infrastructures* **2019**, *4*, 21.
https://doi.org/10.3390/infrastructures4020021

**AMA Style**

Boujia N, Schmidt F, Chevalier C, Siegert D, Pham van Bang D.
Effect of Scour on the Natural Frequency Responses of Bridge Piers: Development of a Scour Depth Sensor. *Infrastructures*. 2019; 4(2):21.
https://doi.org/10.3390/infrastructures4020021

**Chicago/Turabian Style**

Boujia, Nissrine, Franziska Schmidt, Christophe Chevalier, Dominique Siegert, and Damien Pham van Bang.
2019. "Effect of Scour on the Natural Frequency Responses of Bridge Piers: Development of a Scour Depth Sensor" *Infrastructures* 4, no. 2: 21.
https://doi.org/10.3390/infrastructures4020021