Finite Element Analysis $($FEA$)$ in Geotechnical Engineering:

Finite element analysis $($FEA$)$ is a powerful numerical method widely used in geotechnical engineering for analyzing the behavior of soil$-$structure interaction systems. Discuss the theoretical principles underlying FEA in the context of geotechnical engineering applications. Explain how FEA models are developed to simulate complex soil behavior, including nonlinearities, anisotropy, and time$-$dependent properties. Describe the process of discretizing soil$-$structure systems into finite elements and nodes, and how governing equations are formulated to solve for displacement, stress, and pore pressure distributions. Furthermore, discuss the challenges and limitations associated with FEA in geotechnical engineering, such as mesh sensitivity$,$ boundary conditions, and material model selection. Finally, explore recent advancements in FEA techniques that aim to enhance the accuracy and efficiency of analyzing geotechnical problems, such as coupled hydro$-$mechanical modeling and multi$-$scale simulations.