Accurate projection of the ultimate bearing capacity ( \({Q}_{u})\) of rock-socketed piles is critical for safe and cost-effective foundation design in geotechnical engineering. Traditional testing tactics, such as static load tests, while reliable, are often time-consuming and expensive. The present study, therefore, envisions the projection of \({Q}_{u}\) by integrating the strength of the Radial Basis Function (RBF) model with two different optimizers, namely Northern Goshawk Optimization (NGO) and Mountain Gazelle Optimizer (MGO). The result of this research, in particular, shows the extraordinary performance of the RBF model when combined with an NGO and MGO. The R2 stands at a very high 0.994, thereby showing that the RBMG model provides an extremely good description of the database variability. Similarly, the RMSE of the RBMG model is very low at 830.319; thus, the model is quite accurate in determining Qu. These findings are practical and reliable in the RBMG approach, which establishes this as an auspicious and reliable tool in various engineering and construction applications. The predictive accuracy is also improved substantially in the critical area of Qu analysis in this research by seamlessly embedding advanced optimization approaches into the RBF model, benefiting the engineering and construction sectors considerably.
