Limit equilibrium and swarm intelligence solutions in analyzing shallow footing's bearing capacity located on two-layered cohesionless soils

The research findings of two nonlinear machine learning and soft computing models- the Cuckoo optimization algorithm (COA) and the Teaching-learning-based optimization (TLBO) in combination with artificial neural network (ANN)- are presented in this article. Detailed finite element modeling (FEM) of a shallow footing on two layers of cohesionless soil provided the data sets. The models are trained and tested using the FEM outputs. Additionally, various statistical indices are used to compare and evaluate the predicted and calculated models, and the most precise model is then introduced. The most precise model is recommended to estimate the solution after the model assessment process. When the anticipated findings are compared to the FEM data, there is an excellent agreement, which indicates that the TLBO-MLP solutions in this research are reliable (R2=0.9816 for training and 0.99366 for testing). Additionally, the optimized COA-MLP network with a swarm size of 500 was observed to have R2 and RMSE values of (0.9613 and 0.11459) and (0.98017 and 0.09717) for both the normalized training and testing datasets, respectively. Moreover, a straightforward formula for the soft computing model is provided, and an excellent consensus is attained, indicating a high level of dependability for the suggested model.