Application of Calculus of Variation in the Optimization of Functional Parameters of Compacted Modified Soils: A Simplified Computational Review

Fixed endpoint problems (FEPPs) in constrained systems like the effect of curing time or the effect of certain additives in soil stabilization operations have been reviewed illustratively for sustainability purposes in geotechnics. The calculus of variation (CoV) technique of Hamilton’s problem was demonstrated using a typical case in geotechnics; the effect of curing time on the unconfined compressive strength of expansive soils is utilized as foundation materials. The era of smart technologies is evolving, and to key into this fast-moving area to help the field of geotechnics, it is required that these new areas are deployed to study their usefulness. The use of CoV in modeling or simulating geotechnical properties of soil behavior is not prominent and has been played down due to the uncertainties surrounding it. However, this work has identified that if any geotechnical system can be demonstrated in graphs, then the use of CoV becomes easy with the mathematical concept that curves are elements of straight paths. The results of this work show that CoV is a powerful tool to achieving sustainable optimization of quality properties of stabilized for sustainable and optimal materials handling, design, and construction.