*7.2. Estimation of Pavement Layer Moduli*

To evaluate the back-calculation method, measurements made during the APT test at a speed of 20 m/s, a temperature of 19 ◦C and for position 6 (sensor placement between the wheels) were used. The initial moduli and thicknesses of the pavement layers used for the calculations are defined in Table 2. The loading considered was the 65 kN dual wheel load of the APT tests. The deflection signals are those presented in Figure 16. For the back-calculations with Alize, only half of the deflection basins are considered, and the deflection basin of each sensor has been described by a series of points, represented by the red dots in Figure 20. Points located at the same distance are considered for the geophones and accelerometers, and for the deflectometer. In the calculations, the maximum and minimum attainable modulus values have been limited for each layer, as shown in Table 4. These limits are needed to facilitate the convergence, and avoid getting unrealistic solutions. The final back-calculated moduli obtained for all the sensors are defined in Table 5.

**Table 5.** Back-calculated pavement layer moduli obtained with ALIZE for the different sensors, and comparison with reference values.


Figure 21a–e represent the fitted deflection basins obtained with Alize, and compare them with the measured deflections. On each figure, the green lines represent the measured values, and the red lines the adjusted calculated deflection curves. For the two geophones and the two accelerometers, a very good fit is obtained between the measured and calculated deflections. For the anchored deflectometer, however, a larger difference between the measured and calculated basin is obtained after the optimization.

following:

Alize

the software

is obtained.

experimental pavement (Table 2) under the APT dual wheel loading, and the corresponding deflection basin. This theoretical deflection basin is then compared with the measured basin, and an iterative method is used to adjust the layer moduli, until the best match between the calculated and measured response is obtained. The methodology used for the optimization of the layer moduli is the

• The initial characteristics of the pavement (layer thicknesses, initial layer moduli) are entered in

• The measured deflection basin is discretized into a certain number of points to be inputted in

• lower and upper limits are defined for the moduli of each layer, for the optimization process

• Successive pavement response calculations are carried out until the best match between the calculated and measured deflections, and thus the best estimate of the pavement layer moduli

> **Table 4.** Limit values of layer moduli defined for the back calculation. **Pavement Layer Lower Modulus Limit (MPa) Upper Modulus Limit (MPa)**  E1 8000 12000 E2 100 200 E3 50 150

To evaluate the back-calculation method, measurements made during the APT test at a speed of 20 m/s, a temperature of 19 °C and for position 6 (sensor placement between the wheels) were used. The initial moduli and thicknesses of the pavement layers used for the calculations are defined in Table 2. The loading considered was the 65 kN dual wheel load of the APT tests. The deflection signals are those presented in Figure 16. For the back-calculations with Alize, only half of the deflection basins are considered, and the deflection basin of each sensor has been described by a series of points, represented by the red dots in Figure 20. Points located at the same distance are considered for the geophones and accelerometers, and for the deflectometer. In the calculations, the maximum and minimum attainable modulus values have been limited for each layer, as shown in Table 4. These

• The characteristics of the wheel load are entered in Alize.

(the values used are given in Table 4).

*7.2. Estimation of Pavement Layer Moduli* 

**Figure 20.** Deflection points selected on the deflection basin for the back calculation with Alize. **Figure 20.** Deflection points selected on the deflection basin for the back calculation with Alize. after the optimization.

**Figure 21.** (**a**): Deflection fitting for Accelerometer CX Figure 21(**b**): Deflection fitting for Accelerometer SD. (**c**): Deflection fitting for Geophones ION. (**d**): Deflection fitting for Geophones GS11D. (**e**): Deflection fitting for anchored deflectometer **Figure 21.** (**a**): Deflection fitting for Accelerometer CX Figure 21(**b**): Deflection fitting for Accelerometer SD. (**c**): Deflection fitting for Geophones ION. (**d**): Deflection fitting for Geophones GS11D. (**e**): Deflection fitting for anchored deflectometer.

reference is about 1400 MPa. For the granular layer and soil, the maximum difference with the reference is 40 MPa. These first results are encouraging, and show that, with the developed signal

The pavement layer moduli back-calculated for each transducer are given in Table 5, and

The pavement layer moduli back-calculated for each transducer are given in Table 5, and compared with the reference modulus values obtained previously, from laboratory tests and FWD measurements (Table 2). In this first example, all the sensors give realistic modulus values, which are close to the reference moduli. For the Asphalt layer modulus, the maximum difference with the reference is about 1400 MPa. For the granular layer and soil, the maximum difference with the reference is 40 MPa. These first results are encouraging, and show that, with the developed signal treatment method, realistic deflection values, and realistic back-calculated moduli can be obtained using the geophones and accelerometers.

### **8. Conclusions**

The most common methods for measuring pavement deflections are dynamic or rolling devices, such as the FWD or deflectograph. However, these methods present some drawbacks: The measurements require to close the road to traffic, and cannot be made continuously. Typically, measurements are made only once every one or two years. The objective of this study was to evaluate an alternative solution for measuring deflections, using embedded sensors. This method offers the possibility to make continuous measurements, under real traffic, and thus to monitor daily and seasonal variations of deflection, and to detect rapidly any pavement deterioration. For this purpose, two types of sensors have been selected: Geophones and accelerometers. These sensors measure respectively the vertical velocity and the vertical acceleration, and deflections can be obtained by a single or double integration of the measurements.

To evaluate the accuracy of deflection measurements obtained with these sensors, two types of accelerometers and two types of geophones have been selected, and tested in the laboratory, on a vibrating table, under simulated pavement deflection signals. The results have shown that a straightforward integration of the results does not give realistic deflection values, but an original signal treatment procedure has been proposed, to correct the measurements. This procedure includes filtering, amplification and integration of the signals, and then application of the Hilbert transform. After this treatment, accurate deflection measurements have been obtained.

In a second step, the sensors have been tested under real moving wheel loading, on the IFSTTAR accelerated pavement testing facility. They have been tested under different test conditions (wheel loads, speeds, and wheel positions). The same signal treatment method has been applied as in the laboratory, and the measurements have been compared with those of an anchored deflectometer, taken as reference. In all cases, a good match has been obtained between deflection values measured with the geophones and accelerometers, and the reference, proving that the four types of sensors are suitable for the measurement of deflections on real pavements. Finally, the deflection basins obtained from the accelerometer and geophone measurements have been used to back-calculate pavement layer moduli, using the Alize pavement design software, which includes a back-calculation tool. Realistic back-calculated moduli have been obtained, indicating that the measured deflection basins are sufficiently accurate to carry this type of analysis, and to monitor pavement layer moduli.

Following this study, it is planned to use the accelerometers and geophones to instrument a real pavement section, to test continuous monitoring of deflections under real road traffic.

**Author Contributions:** N.B., J.B. and P.H. have conceptualize this project of the pavement instrumentation, performed the experiments and analysis the collected data. The laboratory experiments and signal processing aspects of the work were conducted and finalized by F.M. and N.B. All the authors have contributed in shaping the research and providing feedback for the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research presented in this paper was carried out as part of the H2020-MSCA-ETN-2016. This project has received funding from the European Union's H2020 Program for research, technological development and demonstration under grant agreement number 721493.

**Conflicts of Interest:** The authors declare no conflict of interest with research conducted.
