Development of mathematically motivated hybrid soft computing models for improved predictions of ultimate bearing capacity of shallow foundations

Ultimate bearing capacity(UBC)is a key subject in geotechnical/foundation engineering as it determines the limit of loads imposed on the foundation.The most reliable means of determining UBC is through experiment,but it is costly and time-consuming which has led to the development of various models based on the simplified assumptions.The outcomes of the models are usually validated with the experimental results,but a large gap usually exists between them.Therefore,a model that can give a close prediction of the experimental results is imperative.This study proposes a grasshopper optimization algorithm(GOA)and salp swarm algorithm(SSA)to optimize artificial neural networks(ANNs)using the existing UBC experimental database.The performances of the proposed models are evaluated using various statistical indices.The obtained results are compared with the existing models.The proposed models outperformed the existing models.The proposed hybrid GOA-ANN and SSA-ANN models are then transformed into mathematical forms that can be incorporated into geotechnical/foundation engineering design codes for accurate UBC measurements.