Ahmad Fahimifar

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.

As urbanization accelerates, the demand for efficient underground infrastructure has grown, with rectangular tunnels gaining prominence due to their enhanced space utilization and construction efficiency. However, ensuring the stability of shallow rectangular tunnel faces in undrained clays presents significant challenges due to complex soil behaviors, including anisotropy and non-homogeneity. This study addresses these challenges by developing a novel failure mechanism within the kinematic approach of limit analysis, integrating soil arching effects alongside anisotropic and non-homogeneous undrained shear strength. The mechanism's analytical solutions are rigorously validated against finite element simulations using PLAXIS 3D and existing models, demonstrating superior accuracy. Key findings show that the proposed model improves predictive performance for critical support pressure, with relative differences as low as 5% for wide rectangular tunnels compared to numerical simulations. Results reveal that limit support pressure decreases with increasing non-homogeneity ratios and rises with higher anisotropy factors. However, both effects diminish in wider tunnels, where increasing width in soils with high non-homogeneity and low anisotropy factors significantly enhances stability. Practical implications of this study are substantial, offering design formulas and dimensionless coefficients for estimating critical face pressures in shallow rectangular tunnels. These tools enable engineers to account for soil anisotropy and non-homogeneity, optimizing design and ensuring safety in urban environments. Furthermore, the proposed model’s applicability extends to circular tunnels, where it offers comparable accuracy. This study bridges a critical gap in understanding the stability of rectangular tunnels, providing a robust framework for tackling the challenges of modern urban construction.