Random Forests and Cubist Algorithms for Predicting Shear Strengths of Rockfill Materials

The shear strength of rockfill materials (RFM) is an important engineering parameter in the design and audit of geotechnical structures. In this paper, the predictive reliability and feasibility of random forests and Cubist models were analyzed by estimating the shear strength from the relative density, particle size, distribution (gradation), material hardness, gradation and fineness modulus, and confining (normal) stress. For this purpose, case studies of 165 rockfill samples have been applied to generate training and testing datasets to construct and validate the models. Thirteen key material properties for rockfill characterization were selected to develop the proposed models. Validation and comparison of the models have been performed using the root mean square error (RMSE), coefficient of determination (R²), and mean estimation error (MAE) between the measured and estimated values. A sensitivity analysis was also conducted to ascertain the importance of various inputs in the prediction of the output. The results demonstrated that the Cubist model has the highest prediction performance with (RMSE = 0.0959, R² = 0.9697 and MAE = 0.0671), followed by the random forests model with (RMSE = 0.1133, R² = 0.9548 and MAE= 0.0665), the artificial neural network (ANN) model with (RMSE = 0.1320, R² = 0.9386 and MAE = 0.0841), and the conventional multiple linear regression technique with (RMSE = 0.1361, R² = 0.9345 and MAE = 0.0888). The results indicated that the Cubist and random forests models are able to generate better predictive results of the shear strength of RFM than ANN and conventional regression models. The Cubist model was considered to be more promising for interpreting the complex relationships between the influential properties of RFM and the shear strengths of RFM to some extent, which can be extremely helpful in estimating the shear strength of rockfill materials.