Estimation of ultimate bearing capacity of shallow foundations resting on cohesionless soils using a new hybrid M5'-GP model

Available methods to determine the ultimate bearing capacity of shallow foundations may not be accurate enough owing to the complicated failure mechanism and diversity of the underlying soils. Accordingly, applying new methods of artificial intelligence can improve the prediction of the ultimate bearing capacity. The M5' model tree and the genetic programming are two robust artificial intelligence methods used for prediction purposes. The model tree is able to categorize the data and present linear models while genetic programming can give nonlinear models. In this study, a combination of these methods, called the M5'-GP approach, is employed to predict the ultimate bearing capacity of the shallow foundations, so that the advantages of both methods are exploited, simultaneously. Factors governing the bearing capacity of the shallow foundations, including width of the foundation (B), embedment depth of the foundation (D), length of the foundation (L), effective unit weight of the soil (${\gamma}$) and internal friction angle of the soil (${\varphi}$) are considered for modeling. To develop the new model, experimental data of large and small-scale tests were collected from the literature. Evaluation of the new model by statistical indices reveals its better performance in contrast to both traditional and recent approaches. Moreover, sensitivity analysis of the proposed model indicates the significance of various predictors. Additionally, it is inferred that the new model compares favorably with different models presented by various researchers based on a comprehensive ranking system.