Coatings 2022, 12, 1944. https://doi.org/10.3390/coatings12121944 www.mdpi.com/journal/coatings Article Development of a Road Pavement Structure Diagnostic Procedure Based on the Virtual Inertial Point Method Csaba Tóth * and Péter Primusz Department of Highway and Railway Engineering, Budapest University of Technology and Economics, 1111 Budapest, Hungary * Correspondence: toth.csaba@emk.bme.hu Abstract: Falling weight deflectometers (FWD) are utilised worldwide to analyse the condition and the load-bearing capacity of road pavement structures. One of the FWD measurement results, the deflection bowl, may provide surplus information that is suitable for better road pavement structure diagnostics, based on the novel approach presented in this paper. This study presents a computa- tional method that can calculate the layer thicknesses from the deflection data recorded by the non- destructive FWD device. The motivation for this research is that FWD and GPR equipment are often not available at the same time. However, the back-calculation of the pavement layer moduli from the deflections requires knowledge of the exact thicknesses. The developed method is based on the inertia point principle and provides not only the total pavement thickness but also the total asphalt thickness at each FWD drop point. From 25,200 linear elastic layered pavement models, 350 virtual inertia points could be identified. To describe the relationship between the structural model charac- teristics of the pavement (thickness and subgrade modulus) and the virtual inertia points, we chose the Gaussian process regression, a widely used method in machine learning. In addition to the thick- nesses, the point of inertia can also be used to calculate the bearing modulus of the subgrade with high accuracy. Based on the data from the experimental road section, the radius value of the inertia point   is not sensitive to the stiffness of the layers that compose the pavement structure, depend- ing only on the total pavement thickness and the bearing capacity of the subgrade. The calculation was compared with the AASHTO (1993) procedure, and very similar values for the subgrade-bear- ing capacity were obtained. Moreover, in the near future, the method can be further developed to provide an estimation of layer thicknesses, together with a deflection measurement, especially adapted to continuous deflection measurement devices (Curviameter and Rolling Wheel Deflec- tometer). Keywords: layer thickness; deflection bowl; inertial point; Gaussian process regression; falling weight deflectometer; ground-penetrating radar 1. Introduction In practice, condition surveys of the structure of road pavement are conducted in two main ways: destructive and non-destructive. Destructive surveys utilise core or sawed samples for the laboratory analysis. Alt- hough these methods provide exact results (i.e., thickness measurements), they have sev- eral disadvantages, such as the damage to the pavement structure, the impossibility of real-time measurement, or the traffic disturbance during sample taking. Currently, non- destructive surveys are the method of choice for in-site road condition assessment. These non-destructive surveys do not cause any damage to the surveyed structure; moreover, a high volume of measured data can be obtained quickly and without disturbances. A detailed review of non-destructive surveys for road pavement structure diagnos- tics can be found in the work of Goel and Das [1]. There are many devices delineated in Citation: Tóth, C.; Primusz, P. Development of a Road Pavement Structure Diagnostic Procedure Based on the Virtual Inertial Point Method. Coatings 2022, 12, 1944. https://doi.org/10.3390/ coatings12121944 Academic Editors: Valeria Vignali and Qiao Dong Received: 21 October 2022 Accepted: 5 December 2022 Published: 10 December 2022 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and institu- tional affiliations. Copyright: © 2022 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https://cre- ativecommons.org/licenses/by/4.0/).