Determining ultimate bearing capacity of shallow foundations by using multi expression programming (MEP)

Abstract

This study presents an artificial intelligence approach, namely multi expression programming (MEP), for determining ultimate bearing capacity of shallow foundations on cohesionless soils. Five governing parameters (i.e., internal friction angle, soil unit weight, the length to width ratio of foundation, foundation depth and foundation width) were used as input variables to develop the MEP model. Through the determination of the optimal parameter setting of MEP, a group of expressions were proposed. Then, the MEP model was compared with linear multiple regression, non-linear multiple regression and several previous models, and three statistical indices (i.e., coefficient of determination (R2), root mean squared error (RMSE) and mean absolute error (MAE)) were employed to evaluate the prediction accuracy of these models. The results show that the proposed model has higher prediction precision than the other models, with higher R2 value and lower RMSE and MAE values. Additionally, a monotonicity analysis was performed to verify the correct relationship between ultimate bearing capacity and various factors. From the monotonicity analysis, the ultimate bearing capacity increases with the increase of internal friction angle (φ), soil unit weight (γ), foundation width (B) and foundation depth (D), whereas it decreases with the increase of the length to width ratio of foundation (L/B). Then, a sensitivity analysis was performed. Through the sensitivity analysis, the effect rank of the five input parameters on ultimate bearing capacity is φ>B >D >γ>L/B. Finally, a graphical user interface (GUI) of the MEP model is developed for practical application.