Stacking Ensemble Machine Learning-Based Shear Strength Model for Rock Discontinuity

Accurate estimation of shear strength (SS) of rock discontinuities is crucial in rock engineering applications such as slope stability. This study proposes a stacking ensemble support vector machine (SVM)-M5P-random forest (RF) algorithms-based SS model for discontinuities with different joint wall compressive strength (DDJCS). SVM, M5P, and RF models are first constructed and investigated separately for predicting SS ratio (tau(i)/tau(s) ). tau(i) and tau(s) indicate the peak SS of DDJCS and discontinuities with identical joint wall compressive strength, respectively. Then, this study uses the stacking ensemble framework SVM-M5P-RF as a base model and linear regression as a meta model to combine the predictions of base models for the shear model. Out of the total 168 experimental data samples from the literature, 134 randomly chosen samples were used for training and the remaining 34 were used for testing the models. Normal stress (sigma(n)), compressive strength ratio of joint walls (sigma(ch) /sigma(cs)), and joint roughness coefficient (JRC) have been adopted as inputs of SVM, M5P, RF, and stacked ensemble learning models. The output of SVM with three kernel functions (radial basis function (RBF), Pearson VII universal kernel function (PUK), and polynomial function), M5P, RF, and stacked ensemble models is the SS ratio. Comparisons of results propose that stacked ensemble and SVM (based on RBF and PUK kernel functions) modeling strategies work well and achieve the best overall performances. Moreover, sensitivity analysis to determine the importance of each predictor on SS ratio revealed that sigma(ch) /sigma(cs) JRC, and sigma(n) are the most effective predictor in all established models, respectively. This study shows that the developed models with stacked ensemble learning and individual SVM, M5P, and RF methods are robust models for predicting the SS ratio.