Optimization of ANN using metaheuristic algorithms for predicting failure envelope of ring foundations on anisotropic clay

• Developing hybrid ANN-based models for V-H-M failure envelope of ring foundations on anisotropic clay. • Novel limit state solutions for ring foundations under combined V-H-M loading. • Three optimization methods used for hybrid machine learning models including the artificial bee colony, the imperialist competitive algorithm, and the artificial lion optimization. • Examining predictive precision, robustness, and efficiency in score analysis of all hybrid machine learning models. This paper is concerned with the assessment of V-H-M failure envelopes of ring foundations subjected to general loadings on anisotropic clay using adaptive three-dimensional finite element limit analysis (3D AFELA). The 3D analysis involves calculations of the bearing capacity of ring surface foundations for individual vertical force ( V ), horizontal force ( H ), and moment ( M ) using the well-known anisotropic undrained shear (AUS) failure criterion to study the effect of clay anisotropy. Accordingly, the combinations of V-H, V-M , and H-M load spaces are examined with the use of normalized output parameters ( V/s uTC A, H/s uTC A , and M/s uTC AB ) and two dimensionless input parameters, including the radius coefficient ( r i /r o ) and the anisotropic factor ( r e ). Furthermore, the various characteristics of the failure mechanisms are examined. The study continues with artificial neural network (ANN) models, aiming to evaluate the correlation between input parameters and their corresponding outcomes. Three optimization methods based on metaheuristic algorithms are considered: artificial bee colony (ABC), imperialist competitive algorithm (ICA), and artificial lion optimization (ALO). The ANN-ICA model stands out for its exceptional predictive precision, robustness, and top-ranking efficiency in score analysis. The outcome of the study proves to be both effective and efficient for evaluating the 3D failure envelope of ring foundations on anisotropic clay subjected to combined loadings ( V-H-M ).