Shear Strength Criterion for Rock Discontinuities: A Comparative Study of Regression Approaches

Shear strength criterion for rock discontinuities is a greatly important issue to most geoengineering analyses and designs. This paper aims to develop criteria and make a comparative study using statistical, lazy, and ensemble learning methods for fast predicting the shear strength of rock discontinuities. To do so, simple linear regression (SLR), multiple linear regression (MLR), least median squared regression (LMSR), isotonic regression (IR), pace regression (PR), k-nearest neighbors (kNN), and extreme gradient boosting (XGBoost) learning models are developed using compiled experimental data from direct shear tests based on commonly used variables in criteria. Statistical indices (RMSE, R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document}, and MAE) and comparative analyses indicate that the adopted XGBoost model has a good generalization performance than other models. However, MLR- and PR-based-derived linear equations with R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^{2}$$\end{document} = 0.98 and 0.96 for training and testing datasets are also promising new practical criteria. Interpretability and explainability of the proposed XGBoost model are demonstrated using feature important rank, partial dependence plots (PDPs), feature interaction, and local interpretable model-agnostic explanations (LIME) techniques. The Taylor diagram is also included to substantiate the capability of the developed data-driven surrogate models. Moreover, the proposed models provide satisfactory performance and comparable results to existing prediction models. Findings of this study will assist the geoengineers in estimating shear strength of rock discontinuities.