Finite Element Method in Geotechnical Engineering: The Finite Element Method $($FEM$)$ has revolutionized the field of geotechnical engineering by providing a powerful tool for analyzing complex soil$-$structure interactions. Elaborate on the theoretical underpinnings of FEM, including the discretization of soil and structure into finite elements and the formulation of governing equations. Discuss how FEM enables civil engineers to simulate various geotechnical problems such as slope stability, foundation settlement, and soil$-$structure interaction with high accuracy. Furthermore, explore the challenges and limitations associated with implementing FEM in geotechnical analyses and propose potential advancements or alternative methods to address these limitations$.$