Estimating the Maximum Dry Density of Soil via Least Square Support Vector Regression Individual and Hybrid Forms

Maximum dry density (MDD) holds pivotal importance in geotechnical engineering as it signifies the ideal soil mass per unit volume given particular circumstances. It is important in determining the stability and effectiveness of various earthworks, such as embankments and foundations. MDD is subject to variation based on factors including soil type, distribution of grain sizes, level of compaction, and moisture content. Typically, increasing compaction efforts result in higher MDD values, leading to a denser structure, while elevated moisture levels tend to decrease it. The precise estimation of MDD is indispensable for engineers to make well-founded decisions, ensuring the longevity and safety of civil engineering structures over time. This paper introduces a novel method for predicting maximum dry density \(({\text{MDD}})\) $(\text{MDD})$ by utilizing the least square support vector regression (LSSVR) algorithm. The approach involves utilizing the LSSVR technique to develop precise models that connect the MDD of stabilized soil with several intrinsic soil characteristics such as particle size distribution, plasticity, linear shrinkage, and the composition and amount of stabilizing agents used. In this study, a comprehensive dataset comprising 187 samples of various soil types sourced from previously published stabilization test results is utilized to formulate and evaluate the predictive models. Furthermore, the accuracy of the LSSVR model in this research is augmented through the incorporation of meta-heuristic techniques, specifically Leader Harris Hawk's optimization (LHHO) and generalized normal distribution optimization (GNDO). The R² values for the training, validation, and testing data for the LSLH model were 99.55%, 98.51%, and 99.32%, respectively. Additionally, LSLH had the most suitable RMSE of 15.72  \({\text{kN}}/{\text{m}}\) $\text{kN}/\text{m}$ ³. Generally, the LSLH model demonstrated acceptable predictive and generalization capabilities compared to the LSGN model developed in this study.