Presentation of machine learning methods and multi-objective optimization of fracture indices for asphalt rubber mixtures containing wax-based warm mix additives modified by nano calcium carbonate

Warm mix asphalt (WMA) additives have been proposed to overcome the high viscosity problem of crumb rubber modified asphalt (CRMA) binders. Various additives have been used to improve the low-temperature cracking performance of asphalt mixtures, but no study has been conducted to present the optimum additive content in CRMA binders in different loading modes. Therefore, this research aims to present the optimum content of nano calcium carbonate (NCC) to improve the fracture toughness and energy of asphalt rubber mixtures containing WMA additives (slack wax (SW) and polypropylene wax (PPW)). The semi-circular bend (SCB) fracture test was applied under pure mode I, mixed mode I-II, mixed mode II-I and pure mode II loadings at subzero temperature. Machine learning methods, including multivariate regression (MVR) and artificial neural network (ANN) models of group method of data handling (GMDH) and multilayer perceptron (MLP), were used to provide the prediction models of effective stress intensity factor (Keff) and fracture energy (Gf). Finally, the multi-objective optimization of Keff and Gf was performed to obtain optimum NCC content. The results indicated that in MVR model, the outputs had a small correlation with laboratory values, so that R value of MVR was 0.8406 and 0.8011 for Keff and Gf, respectively. Also, it was revealed in MVR that NCC had the highest impact on Keff and Gf significantly. GMDH model results showed that the relationships between predicted and laboratory values of Keff and Gf are appropriately described with R value of 0.9546 and 0.9229 for Keff and Gf models, respectively. In MLP model, different layer structures of the feed-forward neural network were developed to obtain the most accurate structure. It was indicated that MLP with 4–22–1 and 3–19–1 structures had a higher accuracy for Keff and Gf prediction models with R value of 0.9951 and 0.9978, respectively. Finally, by the use of the best model relationships, the results of the multi-objective optimization indicated that 4.91% and 6.37% NCC were the design optimum contents resulting in a maximum of Keff and Gf simultaneously for SW and PPW-modified CRMA mixtures. Moreover, the optimum NCC contents in loading modes of mode mixity Me of 1, 0.8, 0.4 and 0 were 3.62%, 5.12%, 4.08% and 3.42% for SW-modified CRMA mixtures and 4.35%, 6.51%, 7.19% and 2.84% for PPW-modified CRMA mixtures, respectively.