Role of constrained modulus in predicting resilient modulus of RAP-included granular materials via ML and conventional methods

Conventional regression and modern machine learning (ML) models were developed and evaluated to estimate the resilient modulus (M_R) of unbound granular materials. Recycled asphalt pavement (RAP) content and constrained modulus (M_c) values were included as pivotal input variables. The predictive accuracy of ML models like artificial neural networks (ANN), recurrent neural networks (RNN), random forests (RF), and decision trees (DT) with traditional multilinear regression (MLR) and nonlinear regression (NLR) models was assessed using standard statistical invariants, including R², MSE, and residual error (RE). The MLR model had R² values of 0.894 (training) and 0.886 (testing), whereas the corresponding values for the NLR models were 0.959 and 0.958. For ANN-based algorithms, a single-hidden-layer model with 12 neurons performed best, with R² values of 0.908 and 0.900 and MSE of 682 and 708 during training and testing phases. RNN models were fairly accurate but not as excellent as ANN-based models. RF and DT both achieved an R² of 0.999 for the training dataset, and for the testing datasets, this index remained 0.936 and 0.961 for the best performing structure with ‘N-Estimator = 9' and at a ‘Tree Depth = 11', respectively. Various sensitivity analysis techniques identified varying degrees of relative importance for the input variables, practically depending upon the modeling techniques. However, collectively, σ₃ and gravel content proved to be the most and least contributing factors in the model’s development and accuracy. Closed-form predictive models based on ANN internal structures yielded R² = 0.884∼0.903 and outperformed RNN algorithms with R² = 0.596∼0.641.