Probability prediction of true-triaxial compressive strength of intact rocks based on the improved PSO-RVM model

Abstract

In deep underground engineering design, the true-triaxial compressive strength of intact rocks is a critical evaluation index. Traditional methods for acquiring true-triaxial strength data are hampered by labor-intensive manual operations. To mitigate the time-consuming nature of true-triaxial experiments, this study leverages the unique capabilities of the relevance vector machine (RVM) to develop machine learning prediction models. These models aim to streamline the process and enhance predictive accuracy, thereby offering a more efficient alternative to conventional experimental approaches. The proposed models establish a correlation between the major principal stress (σ₁) and the material constants, alongside other Hoek–Brown (H–B) strength parameters. A comprehensive data set, encompassing 408 sets of true-triaxial experimental data from 12 different rock types, was collated from previous studies. This true-triaxial strength data set was systematically divided into three groups based on the intact rock material content (m_i), facilitating subsequent validation efforts. To enhance prediction accuracy and generalization capability, particle swarm optimization (PSO) is employed to optimize the hybrid kernel function parameters of the RVM. This study introduces a dynamic inertia weight decreasing method, demonstrating superior prediction accuracy compared to conventional PSO improvement techniques. In comparison with five three-dimensional H–B type criteria and two other machine learning models, the improved PSO-RVM model demonstrated superior performance across three distinct m_i groups. Additionally, the proposed model is capable of generating probabilistic predictions, thereby effectively capturing the inherent uncertainty associated with rock strength. The probability distribution of model prediction errors closely aligns with that indicated by the generalized Zhang–Zhu criterion, underscoring the improved PSO-RVM model's ability to capture the uncertainty in true-triaxial compressive strength. Furthermore, this study explores sample selection for combined tests integrating true-triaxial experiments and the proposed improved PSO-RVM model, providing a tentative optimal ratio for predicting the true-triaxial compressive strength of intact rocks.

Keywords

intact rock / particle swarm optimization / probabilistic prediction / relevance vector machine / true-triaxial compressive strength

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2025 The Author(s). Deep Underground Science and Engineering published by John Wiley & Sons Australia, Ltd on behalf of China University of Mining and Technology.