Hybrid machine learning-based triaxial jointed rock mass strength

Rock mass is a complex structure and its mechanical behavior is significantly influenced by the joint frequency and orientation. The evaluation of rock mass strength is a key element in rock mechanics applications. In accordance with the advancement of computer aids in this field, the functionality of various machine-learning (ML) models needs to be explored for triaxial rock mass strength estimation. To bridge this gap in research, hybrid surrogate models, i.e., lazy locally weighted learning (LWL) method combined with Gaussian process regression (GPR) and support vector regression (SVR) algorithms are developed to estimate the triaxial strength of rock mass. An experimental published database of triaxial compressive strength of jointed rock is used for constructing the ML models, whose input parameters contain the joint frequency, joint orientation, and confining stress. Subsequently, the ML models of GPR and SVR, an instance of kernel-based algorithms, are first constructed and analyzed. The effect of the different kernel functions namely radial basis function kernel (RBF), Pearson VII function-based universal kernel (PUK), and polynomial kernel function on the performance of the GPR and SVR models is also analyzed. Then, these probabilistic and stochastic algorithms are considered as a classifier in the LWL-based model to predict triaxial rock mass strength. Finally, the comparison is performed to evaluate the performance of proposed surrogate models. The results demonstrate that the computational hybrid LWL-SVR and LWL-GPR models based on RBF, PUK, and polynomial kernels as well as individual GPR and SVR models based on RBF and PUK kernels (root mean squared error (RMSE) < 1.54 MPa, coefficient of determination (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}) > 0.996, mean absolute error (MAE) < 1.32 MPa, and relative absolute error (RAE) < 7.75% for the training and testing datasets) can be successfully applied for estimation of triaxial compressive strength of jointed rock. The sensitivity analysis results of the proposed models indicate that the confining pressure is the most influential variable on the triaxial strength of the jointed rock in all ML models.