Improvement of the Approximate Method for Determining the Average Vertical Stress Increase Below the Rectangular Foundation Using Differential Evolution Algorithm

External loads transferred from the structure's foundations to the soil induce stress increases in the soil stratum. Since stress increases within the soil mass vary with depth and across the plane at a given depth, approaches that estimate the average stress increase under foundations can be advantageous for effective foundation design. This study aims to develop optimization-based approximate methods for calculating average vertical stress increases with higher accuracy than the conventional 2V:1H method for rectangular foundations with different L/B ratios. For this purpose, vertical stress increases within the foundation projection at 120 different depths for 12 different L/B ratios were numerically calculated using Boussinesq’s stress expressions. The model parameters of the proposed approximate models, such as expansion slopes (k or k₁, k₂) and normalized critical depth (z_cr/B), for each L/B ratio were optimized using the differential evolution algorithm. The proposed three-parameter approximate method achieved the highest accuracy, reducing the RMSE values by an average of 53% compared to the conventional method, while the one-parameter model reduced the RMSE by 9%. The maximum absolute errors in the three-parameter model remained between 0.0217 and 0.0283, with R² values greater than 0.9972. Building upon and improving the conventional method, this study presents a practical and novel three-parameter method that provides a more reliable and accurate estimation of the average vertical stress increase under flexible rectangular foundations, significantly reducing errors. This study contributes to geotechnical engineering by improving the accuracy of stress increase prediction models, potentially leading to more economical and safer foundation designs.