Predicting the ultimate bearing capacity of shallow foundations on ethiopian cohesive soils using a hybrid grey wolf optimizer artificial neural network model

Accurate estimation of the ultimate bearing capacity of shallow foundations on cohesive soils remains a major challenge in geotechnical engineering, particularly in regions with expansive, heterogeneous clay deposits. In Ethiopia, the direct application of classical bearing capacity theories often leads to unreliable designs due to the complex behavior of local soils. This study develops and validates a hybrid Grey Wolf Optimizer Artificial Neural Network (GWO-ANN) model for predicting the ultimate bearing capacity of shallow foundations on cohesive soils in Ethiopia. A database of 408 records was established from laboratory tests on 34 soil samples and parametric variations in foundation geometry. The dataset covers cohesion (15–65 kPa), friction angle (5–25 \(^\circ\) ), natural moisture content (18–42%), porosity (0.35–0.52), foundation width (1.0–2.5 m), embedment depth (0.5–1.5 m), and aspect ratio (1.0–2.0). The model achieved high predictive accuracy (R \(^2\) = 0.981, RMSE = 28.1 kPa, MAE = 21.8 kPa) on an independent test set, outperforming standard machine learning models and classical methods. External validation using 150 independent records from six peer-reviewed studies across different countries, covering both small and large projects, achieved R \(^2\) = 0.935, RMSE = 31.6 kPa, and MAE = 25.1 kPa, confirming the model’s generalizability across diverse cohesive soil conditions. Sensitivity analysis identified cohesion, foundation width, and friction angle as dominant parameters, with porosity and natural moisture content exerting significant influence. The results demonstrate that incorporating soil state parameters substantially improves predictions, providing a reliable, data-driven tool for foundation design in expansive clay regions. Although the proposed model demonstrated excellent predictive performance for Ethiopian expansive cohesive soils and showed satisfactory performance during external validation within the investigated parameter ranges, its application to soils from different geological, mineralogical, or environmental conditions may require additional validation using region-specific datasets. The proposed hybrid GWO-ANN framework offers a novel, regionally tailored machine learning solution that effectively captures the nonlinear soil-foundation interaction in unsaturated expansive clays.