**3. Results**

Deflections from two different sites are presented. Each of these sites was measured three times for repetition. In Figure 5a, *x* axis represents the position of the load and *y* axis represents deflections measured by the laser over the joint in microns. The deflection is measured on the slab under *G* 0 from the negative axis is the approaching side, while the other part of the laser *G* <sup>0</sup> after the joint is marked as leaving side. The joint is approximately positioned at *x* = 0 m in all cases. In plots, selected load positions to range from −8 m to 8 m which includes the effect of the loaded wheel. Measured deflections range approximately over −100 microns to 50 microns. The symmetric peaks in the deflection signal at x = −4 m and 4 m appear due to contribution from the load crossing the other edge and then approach the beam's support. Deflection values at the edge of the slab as a function of the load position is ultimately measured. In Figure 5b, the deflection difference of the signal shown in Figure 5a, is shown with respect to the load position and it can be observed that the model compares well to this difference as inherent noise is canceled.

As the information about the moduli, structure, subgrade and load transfer is unknown. By assuming a set of realistic values of these parameters as shown in the Figure 5a, the model can generate deflections. This set of parameters is kept constant for the repetitions while comparing modelled deflections to measurements for the same site. A comparison of the measured signal to the

modelled signal shows the match of the peaks. Modelled deflections to the left and right of the joint match the trend in the measured data with a load transfer efficiency of 75%.

This comparison demonstrates that the model can predict the response due to a moving load closer to the edge. Given some structural information of the pavement, it is obvious that this model can be used to back-calculate the properties of the slabs from the measurements and eventually the load transfer capability of the slabs. This experiment also demonstrates the capability of the measurement system and associated sensors to capture deflection in order of microns without embedding the sensors inside the structure. It's a simple demonstration of nondestructive evaluation by a slow-moving load. A more advanced measurement system based on the setup used in this study forms the Dynatest Rolling wheel Deflectometer technology platform.

**Figure 5.** Comparing Experimental data to Modelled quantities (**a**) Deflection below laser *G* 0 (**b**) Deflection Difference ∆*P*12.

### **4. Discussion**

To use a novel measurement technique based on an RWD technology, a model predicting the deflection outside of load plane is required. To obtain a vertical deflection field for jointed rigid pavements with a deflection-based load transfer mechanism, a simple 3D semi-analytical solution is obtained. The model is reliable in predicting deflections as good as a FEM based model solution. It solves for deflection with a static loading condition in load's vicinity and across joint on slabs forming it. Due to its simple and yet accurate formulation, it requires a smaller number of inputs compared to a FEM solution. In a back-calculation process, these advantages will help to calculate the load transfer adequately. Next steps were to build the understanding of the measurements and how it can be used. Measurements are based on a simple beam setup where the measuring device is fixed, and the load is a rolling wheel. This technique relies on measuring equipment with its accuracy and precision. It also requires data processing which is tailored to the measurement technique. After processing of the high-frequency raw measurements, a comparison to deflections from the model is done. The trends in comparison of measured deflection to the modelled deflections mean that it is possible to measure the deflections with a moving load on a rigid pavement with some uncertainty. If the layer and subgrade properties are known, then model can be used to fit the measured data leading to calculation of load transfer efficiency. However further research is required as at this time there are still some improvements that could be potentially achieved. The deflection values decrease sharply further out of the load plane and if the measurement system could be closer to the load, the measured signal would be larger. Variation in the moving load speed could be used to understand how this affects the experiment. Additional steps to reduce the noise in the data by putting additional weights on the beam could be one idea. The aim is to have a large signal to noise ratio.

Overall results from this experiment support the objectives that were set up. This development is foundational and preliminary for the use of RWD technology on jointed pavement. It has been demonstrated that the load transfer efficiency can be calculated and given the layer and subgrade properties by a moving load, where the measuring instrument is stationary. However, there are limitations in the sense that the load transfer mechanism such as dowels and other types of jointed structures are not modelled separately. These separate jointed structures influence the shape of the deflection profile and thus will pose challenge in load transfer evaluation. Improvements in the modelling with these ideas need to be researched in future.

With this built up understanding, next steps would require using the model to simulate the Rolling wheel, where measurement setup mounting lasers on a beam is fixed inside the trailer with the loading wheel with RWD technology. Further development of this setup in the modelling and the resulting deflection needs to be investigated.

## **5. Conclusions**

The study demonstrates that by using an analytical model, a faster prediction of the rigid pavement response across joints can be done. The model is a three-dimensional model and analytical in its formulation. Use of this model will be effective in the development of analysis for RWD based measurement technologies for a static load. Along with the model being faster, it uses more structural parameters than a simple analytical model, thus can provide more information than a traditional back-calculation. Thus, by analyzing high-frequency measurements from RWD technology, information about the pavement can be inferred and understood better. This application of a three-dimensional analytical formulation for a discontinuity in rigid pavements combined with an experimental demonstration by use of RWD technology is a novel development.

**Author Contributions:** Conceptualization, P.D., M.B.A., N.T. and D.L.P.; methodology, P.D. and M.B.A.; software, P.D.; validation, P.D.; formal analysis, P.D. and M.B.A.; investigation, P.D.; resources, P.D. and M.B.A.; writing—original draft preparation, P.D.; writing—review and editing, P.D.; visualization, P.D.; supervision, M.B.A., N.T. and D.L.P.; project administration, M.B.A., N.T. and D.L.P.; funding acquisition, D.L.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project has received funding from the European Union's H2020 Programme for research, technological development and demonstration under grant agreement number 721493.

**Acknowledgments:** This work is carried out in collaboration with Dynatest International A/s and NTEC at the University of Nottingham. The research presented in this report/paper/deliverable was carried out as part of the H2020-MSCA-ETN-2016.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
