Uniaxial compressive strength prediction in rocks: a comprehensive review from empirical equations to AI methods

Abstract Uniaxial compressive strength (UCS) is one of the most fundamental parameters in rock mechanics, widely used in the design and stability assessment of geotechnical and mining structures. However, its direct determination requires high-quality samples, sophisticated laboratory facilities, and significant time and cost, which often limit its applicability in practice. As a result, a broad spectrum of indirect estimation techniques has been developed, ranging from simple empirical correlations to advanced artificial intelligence (AI) models. This review provides a comprehensive synthesis of the methods employed in UCS estimation, with a particular focus on both conventional index tests and machine learning approaches. Traditional methods such as the Schmidt rebound hammer (SRH), ultrasonic pulse velocity (UPV), point load test (PLT), and Brazilian tensile strength (BTS) have demonstrated considerable utility, though their predictive accuracy is highly dependent on lithology, rock anisotropy, and site-specific conditions. On the other hand, AI-based techniques, including artificial neural networks (ANN), adaptive neuro-fuzzy inference systems (ANFIS), and optimization-enhanced hybrid models, have achieved superior predictive performance by capturing nonlinear and multivariate relationships, often yielding coefficients of determination ( R 2 ) above 0.95. Despite their promise, AI methods require large and representative datasets, and issues of model interpretability and overfitting remain challenges. The comparison highlights that no single approach is universally applicable; rather, the integration of empirical knowledge with computational intelligence appears to be the most effective strategy. The study concludes that future research should prioritize the development of hybrid models and standardized open-access databases to enhance the accuracy, robustness, and practical applicability of UCS prediction in diverse geological settings.