Why is it essential for civil engineering operations to thoroughly understand the principles and applications of soil mechanics in the construction of foundations, and how do the various properties of soil, such as shear strength, compressibility, and permeability, influence the design and stability of different types of foundations in diverse geological settings? Discuss the impact of soil$-$structure interaction on the overall performance of civil engineering projects, particularly in relation to load$-$bearing capacity and settlement behavior. Additionally, explore the challenges posed by problematic soils such as expansive clays and loose sands, and the engineering solutions that can be employed to mitigate risks associated with these soils. Include in your discussion the role of advanced geotechnical investigations and testing methods in accurately characterizing soil properties, and how these methods contribute to more reliable and efficient foundation design. Consider also the environmental and economic implications of foundation failures due to inadequate understanding of soil mechanics.