{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T16:10:30Z","timestamp":1776269430793,"version":"3.50.1"},"reference-count":81,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,25]],"date-time":"2023-09-25T00:00:00Z","timestamp":1695600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This study examines the potential of the soft computing technique, namely, multiple linear regression (MLR), genetic programming (GP), classification and regression trees (CART) and GA-ENN (genetic algorithm-emotional neuron network), to predict the ultimate bearing capacity (UBC) of cohesionless soils beneath shallow foundations. For the first time, two grey-box AI models, GP and CART, and one hybrid AI model, GA-ENN, were used in the literature to predict UBC. The inputs of the model are the width of footing (B), depth of footing (D), footing geometry (ratio of length to width, L\/B), unit weight of sand (\u03b3d or \u03b3\u2032), and internal friction angle (\u03d5). The results of the present model were compared with those obtained via two theoretical approaches and one AI approach reported in the literature. The statistical evaluation of results shows that the presently applied paradigm is better than the theoretical approaches and is competing well for the prediction of qu. This study shows that the developed AI models are a robust model for the qu prediction of shallow foundations on cohesionless soil. Sensitivity analysis was also carried out to determine the effect of each input parameter. The findings showed that the width and depth of the foundation and unit weight of soil (\u03b3d or \u03b3\u2032) played the most significant roles, while the internal friction angle and L\/B showed less importance in predicting qu.<\/jats:p>","DOI":"10.3390\/a16100456","type":"journal-article","created":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T02:31:29Z","timestamp":1695695489000},"page":"456","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Enhancing Ultimate Bearing Capacity Prediction of Cohesionless Soils Beneath Shallow Foundations with Grey Box and Hybrid AI Models"],"prefix":"10.3390","volume":"16","author":[{"given":"Katayoon","family":"Kiany","sequence":"first","affiliation":[{"name":"School of Design, University of Melbourne, Parkville, VIC 3052, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9151-4469","authenticated-orcid":false,"given":"Abolfazl","family":"Baghbani","sequence":"additional","affiliation":[{"name":"School of Engineering, Deakin University, Geelong, VIC 3216, Australia"},{"name":"Future Regions Research Centre (FRRC), Federation University, Gippsland, VIC 3842, Australia"}]},{"given":"Hossam","family":"Abuel-Naga","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, La Trobe University, Bundoora, VIC 3086, Australia"}]},{"given":"Hasan","family":"Baghbani","sequence":"additional","affiliation":[{"name":"School of Engineering, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran"}]},{"given":"Mahyar","family":"Arabani","sequence":"additional","affiliation":[{"name":"School of Engineering, Guilan University, Guilan 4199613776, Iran"}]},{"given":"Mohammad Mahdi","family":"Shalchian","sequence":"additional","affiliation":[{"name":"School of Engineering, Guilan University, Guilan 4199613776, Iran"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1186\/s40703-019-0105-7","article-title":"Improvement of bearing capacity of soil by using natural geotextile","volume":"10","author":"Panigrahi","year":"2019","journal-title":"Int. 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