Numerical characterization of high modulus asphalt concrete containing RAP: A comparison among optimized shallow neural models

Knowing the relationship between the stiffness modulus and the empirical mechanical characteristics of asphalt concrete, road engineers may predict the expected results of costly laboratory tests and save both time and financial resources in the mix design phase. In fact, such a model would make it possible to assess a priori whether the stiffness of a specific mixture, characterised in the laboratory only by the common Marshall test, is suitable for the level of service required by the road pavement under analysis. In this study, 54 Marshall test specimens of high modulus asphalt concrete were prepared and tested in the laboratory to determine an empirical relationship between the stiffness modulus and Marshall stability by means of shallow artificial neural networks. Part out of these mixtures was characterised by different types of bitumen (20/30 or 50/70 penetration grade) and percentages of used reclaimed asphalt (RAP at 20% or 30%); a polymer modified bitumen was used in the preparation of the remaining Marshall test specimens, which do not contain RAP. For the complex and laborious identification of the neural model hyperparameters, which define its architecture and algorithmic functioning, the Bayesian optimization approach has been adopted. Although the results of this methodology depend on the predefined hyperparameters variability ranges, it allows an unbiased definition of the optimal neural model characteristics to be performed by minimizing (or maximizing) a loss function. In this study, the mean square error on 5 validation folds was used as a loss function, in order to avoid a poor performance evaluation due to the small number of samples. In addition, 3 different neural training algorithms were applied to compare results and convergence times. The procedure presented in this study is a valuable guide for the development of predictive models of asphalt concretes' behaviour, even for different types of bitumen and aggregates considered here.