Meta-Heuristic Optimization Model for Base Stress Distribution in Elastic Continuous Foundations with Large Eccentricity

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.