Intelligent modeling of unconfined compressive strength (UCS) of hybrid cement-modified unsaturated soil with nanostructured quarry fines inclusion

Gene expression programming (GEP) and multi-expression programming (MEP) have been employed to predict models for the unconfined compressive strength of soil under unsaturated (partially saturated to 60%) conditions. Due to the complexity and time consumed during the laboratory estimation of UCS for flexible pavement subgrade design, there is a great need to employ prediction models to overcome this setback. Soils are erratic and change from time to time and from season to season especially unsaturated soils. Therefore, this behavior poses a big problem to the design and performance monitoring of foundations subjected to hydraulically bound effects. The soil belonged to A-7–6 group in the AASHTO method of classification and poorly graded. It was also observed to be highly plastic with high clay content (CH). The soil was treated with hybrid cement (HC); a composite binder made from the blend of rice husk ash and hydrated lime as activator and nanostructured quarry fines (NQF); another binder sourced from pulverized quarry dust sieved with 200-nm sieves to achieve fineness. Multiple experiments were conducted to generate datasets of the selected parameters, which were the predictors of the model exercise. A baseline regression model was conducted using the MLR to ascertain the level of agreement between the target variable and its multiple predictors (HC, NQF, C, AC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{C}$$\end{document}, CC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{C}$$\end{document}, Cu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{u}$$\end{document}, δmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta }_{max}$$\end{document}, wmax\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w}_{max}$$\end{document},wL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w}_{L}$$\end{document},wP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w}_{P}$$\end{document},IP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I}_{P}$$\end{document},Nc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{c}$$\end{document},∅∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varnothing }^{^\circ }$$\end{document}, γunsat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\gamma }_{unsat}$$\end{document}). The results of this regression showed that only 6 predictor variables (HC,AC,Cu,wP,∅,γunsat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$HC,{ A}_{C},{ C}_{u},{ w}_{P},\varnothing , {\gamma }_{unsat}$$\end{document}) out of the 14 variables showed close-correlation between 0.987 and 0.995 to influence the behavior of the dependent variable (target). Therefore, these were further deployed in the GEP and MEP models. The outcome of the models showed that the GEP outclassed the MEP and MLR with a coefficient of determination (R2) of 0.99 and 0.988, relative root-mean-square error (RRMSE) of 0.0728 and 0.0741 and proximal performance indicators of 0.036 and 0.037 for training and validation, respectively. Moreover, the model with a minimum O’Brien and Fleming (OBF) of 0.31 was selected, which was GEP to show that there was no over-fitting. Finally, the sensitivity analysis showed that the parameters influenced the model in this order; wP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w}_{P}$$\end{document}˃ ∅∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varnothing }^{^\circ }$$\end{document} ˃ HC, ˃γunsat\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\gamma }_{unsat}$$\end{document} ˃ Cu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${C}_{u}$$\end{document} ˃AC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{C}$$\end{document}. Generally, GEP proved to be the better soft computing technique in this exercise, although MEP equally performed creditable.