# Definition of Optimized Indicators from Sensors Data for Damage Detection of Instrumented Roadways

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background of the Optimized Indicators Method (OIM)

_{R}calculated from a reference signal ${\epsilon}_{R}\left(x\right)$. This reference signal was obtained through numerical modeling (or a real measurement) of the considered structure.

## 3. Description of the Experiment

#### 3.1. The Pavement Fatigue Carousel

#### 3.2. Tested Instrumented Structure

^{−6}) with a sensitivity of 0.11 N/µstrain and capable of withstanding the high temperature of the hot asphalt concrete during construction (up to 150 °C) [19]. In addition, some temperature sensors (not represented in Figure 3 for readability purposes) were also embedded at 0 and 10 cm depth in the bituminous layer so that this parameter could be monitored during this experimental campaign. All signals were recorded as a function of time at a frequency of 600 Hz.

#### 3.3. Loading Characteristics and Data Acquisition

^{−6}) consists of a measurement as a function of time of the strain that reached its maximal value (peak, indicating an extension of the gauge) each time that a dual-wheel load passed above the sensor, as pictured in Figure 4.

## 4. Modelling

#### 4.1. Huet-Sayegh Model

#### 4.2. VISCOROUTE© Software

## 5. Calculation of the Optimized Indicators and the Weighting Functions

#### 5.1. Choice of the Construction Parameters of the Optimized Indicators

^{©}software to check the influence of each pavement parameters on the shape of the modeled signal. The parametric study consists of separately applying a ±10% variation on each parameter of the model (indicated in Table 1) by considering the other parameters as constants. With respect to the previously proposed model and considering the values of parameters listed in Table 1 as references, each of these variations differently affects the shape of the signal and the value of the equivalent module (|E*|). The aim of this parametric study was identifying the two most influential parameters usable to determine separately the characteristics and/or the damage level for two different layers. The determination of these influential parameters consists of a first step in a numerical integration of the simulated reference signal to calculate its surface (${S}_{ref}$). In a second step, after applying the ±10% variation on a chosen parameter, a second surface (${S}_{param}$) was deduced by integration of the simulated signal. Then, the difference between these two surfaces over ${S}_{ref}$ allowed the calculation of a relative surface variation $\%S$ as given by the following equation:

#### 5.2. Choice of the Construction Parameters of the Optimized Indicators

^{©}and by separately making a ±10% variation of the two selected parameters. Using Equation (6), a 2 × 2 ${b}_{jk}$ matrix was constructed from the simulated data, and the orthogonality between ${b}_{jk}$ and ${a}_{jk}$ allowed for calculating the latter (Equations (7) and (8)); then, the weighting function associated with the selected parameters and for each position of x was deduced (Equation (3)). Figure 9 shows the weighting functions calculated from the reference signal for the two selected parameters, labeled as ${P}_{{E}_{\infty}}$ and ${P}_{{E}_{UGM}}$.

## 6. Data Processing of the Carousel Test

#### 6.1. Evolution of Signals’ Values with Loadings

#### 6.2. Implementation of the OIM

#### 6.3. Data Processing through Regular Recalibration of the OIM

_{ref}= 245,600) was selected and used as a new reference signal for the recalibration of the weighting functions. All steps described in Section 4 and Section 5 were repeated to calibrate new weighting functions that were then applied on all remaining signals recorded from 245,600 to 881,600 loadings, allowing the plotting of new values for the optimized indicators as a function of the number of loads. With these recalibrated weighting functions, another deviation greater than 10% was observed for ${I}_{{E}_{\infty}}$ at 450,400 loadings. The evaluated values of ${E}_{\infty}$ and ${E}_{UGM}$ obtained from 245,400 to 429,600 loadings were saved, and a third calibration was conducted with the signal recorded at N = 450,400 loadings as the new reference. This procedure was repeated each time one of the deduced optimized indicators had a relative variation greater than ±10%. In this study, three recalibration procedures were required to proceed all gauge signals with the OIM, and were performed at 245,600, 450,400, and 652,000 loadings.

#### 6.4. Discussion and Prospects

- -
- The bituminous layer is progressively damaged during the complete experimental campaign, this damage leading to a decrease of its instantaneous elastic modulus. After a regular decrease from 152,200 to 536,000 loadings, this characteristic remained nearly constant in the range of 652,000 to 789,200 loadings and noticeably decreased at 820,000 loadings.
- -
- The base layer, composed of unbound granular materials, kept a nearly constant 120 MPa elastic modulus from 151,200 to 688,400 loadings, before a net increase evaluated up to 130 MPa at N = 789,200. As the elastic modulus of the bituminous layer is reduced due to the repeated 65 kN-loadings, we assume that a slight compaction of the base layer may occur through compressive stress transmission. Afterwards, the damaging of the bituminous layer continued at 820,000 loadings, while the base layer was unaffected.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flowchart for the determination of weighting functions and optimized indicators of a structure parameter.

**Figure 2.**The pavement fatigue carousel at Univ. Eiffel Nantes [16].

**Figure 3.**(

**a**) Schematic representation in front view of the pavement’s structure, (

**b**) top view illustrating the orientation of the strain gauge along the dual-wheel load direction, (

**c**) picture of a DYNATEST

^{®}strain gauge.

**Figure 4.**Example of µ strain signals recorded from the sensor as a function of time during spinning charging cycles.

**Figure 5.**Mean temperatures and date of acquisition recorded inside the bituminous layer as a function of the number of loads.

**Figure 6.**Huet–Sayegh model [22].

**Figure 8.**Fitting of the proposed numerical model to the reference signal with (

**a**) ±10% variation for ${E}_{\infty}$, (

**b**) ±10% variation for ${E}_{UGM}$.

**Figure 9.**Weighting functions as a function of distance of ${E}_{\infty}$ (blue axis in the center) and ${E}_{UGM}$ (red axis in the right) obtained from the reference signal.

**Figure 10.**Evolution of gauge signals with the loading, from 151,200 loadings (beginning of the test) to 881,600 loadings (end of test).

**Figure 13.**Evaluation of ${E}_{\infty}$ and ${E}_{UGM}$ as a function of loadings through the OIM with recalibration steps proceeding at numbers of loadings labeled as N

_{ref}with ±10% variation windows (

**a**) for ${E}_{\infty}$ and (

**b**) for ${E}_{UGM}$.

E_{0}(MPa) | ${\mathit{E}}_{\mathit{\infty}}$ (MPa) | ${\mathit{E}}_{\mathit{U}\mathit{G}\mathit{M}}$ (MPa) | δ | h | k | τ | A_{0} | A_{1} | A_{2} |
---|---|---|---|---|---|---|---|---|---|

150 | 19,000 | 120 | 1.35 | 0.54 | 0.11 | 1.30 | 8.9 | −0.44 | 0.0016 |

**Table 2.**Relative surface variation $\%S$ calculated after a ±10% variation for each parameter of the Huet–Sayegh model.

Parameter | E_{0} | ${\mathit{E}}_{\mathit{\infty}}$ | ${\mathit{E}}_{\mathit{U}\mathit{G}\mathit{M}}$ | δ | h | k | A_{0} | A_{1} | A_{2} |
---|---|---|---|---|---|---|---|---|---|

$\%S$ (%) | 0 | 11 | 10 | 3 | 1 | 3 | 3 | 3 | 0 |

${\mathit{E}}_{\mathit{\infty}}$ | ${\mathit{E}}_{\mathit{U}\mathit{G}\mathit{M}}$ | |||
---|---|---|---|---|

${\mathit{I}}_{{\mathit{E}}_{\mathit{\infty}}}$ | Deviation of the Indicator (%) | ${\mathit{I}}_{{\mathit{E}}_{\mathit{U}\mathit{G}\mathit{M}}}$ | Deviation of the Indicator (%) | |

Reference signal | −18,098.81 | 0 | −133.90 | 0 |

−10% ${E}_{\infty}$ | −20,161.25 | −11.46 | −133.57 | +0.25 |

+10% ${E}_{\infty}$ | −16,361.25 | +9.67 | −133.57 | +0.25 |

−10% ${E}_{UGM}$ | −18,075.03 | +0.13 | −146.71 | −9.34 |

+10% ${E}_{UGM}$ | −18,075.03 | +0.13 | −122.71 | +8.19 |

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**MDPI and ACS Style**

Souriou, D.; Simonin, J.-M.; Schmidt, F.
Definition of Optimized Indicators from Sensors Data for Damage Detection of Instrumented Roadways. *Sensors* **2022**, *22*, 5572.
https://doi.org/10.3390/s22155572

**AMA Style**

Souriou D, Simonin J-M, Schmidt F.
Definition of Optimized Indicators from Sensors Data for Damage Detection of Instrumented Roadways. *Sensors*. 2022; 22(15):5572.
https://doi.org/10.3390/s22155572

**Chicago/Turabian Style**

Souriou, David, Jean-Michel Simonin, and Franziska Schmidt.
2022. "Definition of Optimized Indicators from Sensors Data for Damage Detection of Instrumented Roadways" *Sensors* 22, no. 15: 5572.
https://doi.org/10.3390/s22155572