The study presents the investigation of the elastic behavior of the soil in the optimal design of continuous foundations according to the rigid solid case. For the investigation, the optimization algorithm that can find optimal section and reinforcement details of continuous foundations has been developed. The developed algorithm uses one of the well-known meta-heuristic methods named the artificial Bee Colony method to find the optimal design. The Winkler spring hypothesis (analytic solution) is used to calculate internal forces and stresses in elastic continuous foundations. We used the real-size design example previously used in the literature to test the elastic soil effect and algorithm performance. The obtained results show that the current algorithm performs well, and lower cost values are obtained in the elastic design.

This study focuses on determining stress distribution in elastic continuous beam foundations subjected to large eccentricities primarily induced by the overturning moments generated when horizontal forces, like those from earthquakes and wind, act on the superstructure. Traditional linear static solutions provide an incorrect stress distribution when a foundation loses partial contact with the ground, as they erroneously calculate tensile stress in the uplifted regions. This research aims to formulate a mathematical model that accurately calculates the corrected stress distribution. An optimization problem is defined to minimize the discrepancy between the external effects (loads and moments) from the superstructure and the internal resistance effects from the redistributed base stress under the condition of partial foundation uplift. To solve this, meta-heuristic optimization methods, including Artificial Bee Colony (ABC), Tree Seed Algorithm (TSA), and Biogeography-Based Optimization (BBO), are employed to derive accurate mathematical formulas. The performance of these methods is evaluated under varying soil conditions and loading scenarios. The Tree Seed Method has consistently delivered the most accurate results, with near-zero optimization errors. The findings provide the applicability of algorithmic methods and their potential for improving stress distribution modeling in elastic foundations.