## Explore the principles and theoretical frameworks behind the design and analysis of geotechnical structures, such as foundations, retaining walls, and slopes. Discuss the importance of understanding soil mechanics, including soil classification, stress$-$strain behavior, and shear strength parameters, in geotechnical engineering design. How do different soil properties influence the stability and performance of geotechnical structures? Consider the methods used for subsurface investigation and the role of laboratory and field testing in obtaining reliable soil data. Additionally, analyze the impact of external factors, such as groundwater conditions and seismic activity, on the stability of geotechnical structures. Evaluate the various design methodologies, such as limit equilibrium, finite element analysis, and reliability$-$based design, emphasizing their theoretical basis and practical applications. What are the current challenges and emerging trends in geotechnical engineering research that aim to enhance the safety and sustainability of geotechnical structures?