This study investigates the bearing capacity of a sloping rock foundation beneath rectangular and, in particular, square footings. Additionally, the study proposes a novel hybrid machine learning approach, namely MPA-XGBoost, and develops a Graphical User Interface (GUI) that enables end-users to predict the bearing capacity of foundations without requiring any complex computations. Numerical simulations are conducted via PLAXIS 3D software, which incorporates the finite element method and the Hoek-Brown failure criterion. Through a series of design charts, the correlation between the bearing capacity factor and six input parameters is explored: slope angle (β), intact rock yield (mi), geological strength index (GSI), compressive strength ratio (γB/σci), dimension ratio (L/B), and setback ratio (b/B). Regarding the machine learning part, the study employs the XGBoost model integrated with the Marine Predators Algorithm (MPA) as an optimization technique. The obtained results demonstrate that the design charts clearly illustrate the influence of various parameters on the bearing capacity. Furthermore, in the failure mechanism analysis when investigating the effect of the geological strength index (GSI) parameter, the incremental displacements show both decreasing and increasing trends, which can be attributed to the indirect influence of the parameters E and ν. Finally, the machine learning results indicate that the application of the Marine Predators Algorithm (MPA) improved the model's accuracy to 99.93%, compared to 99.87% achieved by the default XGBoost model. In addition, a Graphical User Interface (GUI) was proposed to facilitate practical applications.
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