Predicting the uniaxial compressive strength of different rock types using implementable stochastically modified artificial neural network and Shapley additive explanations

• Published in: Multiscale and Multidisciplinary Modeling, Experiments and Design Vol. 8; no. 10; p. 469
• Main Authors: Lawal, Abiodun Ismail, Mulenga, Francois
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.11.2025; Springer Nature B.V
• Subjects: Algorithms; Artificial intelligence; Artificial neural networks; Characterization and Evaluation of Materials; Civil engineering; Compressive strength; Datasets; Engineering; Gaussian process; Mathematical Applications in the Physical Sciences; Mechanical Engineering; Neural networks; Numerical and Computational Physics; Optimization; Original Paper; P waves; Particle swarm optimization; Porosity; Python; Rocks; Simulation; Soft computing; Solid Mechanics; User interface; Wave velocity; Arithmetic optimization algorithm; Artificial neural network; Sonic velocity; SHAP analysis; Particle swarm optimization; Uniaxial compressive strength
• ISSN: 2520-8160; 2520-8179; 2520-8179
• DOI: 10.1007/s41939-025-01050-4

The uniaxial compressive strength (UCS) is one prominent property of rocks because of its usefulness in different rock engineering applications. For a quick and easy assessment of the UCS of rocks, different empirical models have been proposed as experimental procedures are found to be tedious but many of them are found to be unable to capture the heterogeneous nature of the rocks. To obtain more accurate predictions, soft computing (SC) models have been proposed in the literature. They have been reported to yield more accurate predictions in many cases compared to empirical models. Nevertheless, SC models are considered as black boxes, and the possibility of their practical implementation are vague. This study proposed artificial neural network (ANN) models optimized with stochastic algorithms such as particle swarm optimization (PSO) and arithmetic optimization algorithm (AOA) implemented in MATLAB to predict the UCS using porosity, p-wave velocity, Schmidt rebound hardness value and point load index as the inputs. The study reported that the proposed PSO-ANN and AOA-ANN models gave overall R 2 values of 0.9974 and 0.9967 respectively which are better than 0.9955 for the Gaussian process regression (GPR) models. A graphic user interface (GUI) was then prepared using the extracted weights and biases from the proposed PSO-ANN and AOA-ANN models for easy implementation which is absent in the existing models. The gradient boost (GB) method was also tried and implemented in Python for the purpose of performing the Shapley additive explanations (SHAP) analysis. This analysis revealed that porosity and P-wave velocity have the highest influence on UCS. Finally, the proposed SC/artificial intelligence (AI) based models can give reliable predictions of UCS of rocks with easy practical implementation.