Machine Learning-Based Prediction of Bearing Capacity of Shallow Foundations on Rock Masses

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Abstract
The ultimate bearing capacity of square shallow foundations resting on jointed rock masses represents one of the most complex and fundamental problems in rock mechanics and geotechnical design, primarily due to the inherent heterogeneity of the medium and the highly nonlinear nature of failure mechanisms, which are associated with significant uncertainty. In this study, a combined framework of advanced numerical modelling and machine learning algorithms is employed to develop a robust and accurate predictive approach. To this end, a comprehensive dataset comprising 150 three-dimensional finite element simulations was generated using PLAXIS 3D. The generalized Hoek-Brown failure criterion was adopted for the rock mass, while the Mohr-Coulomb criterion was applied to discontinuity surfaces. The numerical results indicated that bearing capacity is governed by a complex interaction among rock mass quality parameters, intact rock properties, discontinuity characteristics, and the geometry and orientation of joints. Failure behaviour is primarily controlled by joint planes and is characterized by stress concentration, asymmetric deformation patterns, and localized plastic zones along discontinuities. Correlation analysis identified the Geological Strength Index (GSI), the intact rock parameter mi, and the uniaxial compressive strength (UCS) as the most influential variables affecting bearing capacity. In the machine learning phase, a comparative assessment of several models demonstrated that ensemble-based methods, particularly Gradient Boosting Regressor and Poisson Regressor, achieved the highest predictive performance, significantly outperforming conventional linear regression approaches. Feature importance analysis further confirmed the dominant roles of GSI and mi. Notably, the developed models, achieved a prediction accuracy of approximately 96% with low error levels. Overall, the results demonstrate that machine learning provides a powerful and reliable framework for modelling the highly nonlinear behavior of shallow foundations on jointed rock masses, offering valuable support for geotechnical design and reducing epistemic uncertainty in engineering practice.

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