State Archimedes' principle and its application in geotechnical engineering.

• A. The buoyant force equals the weight of displaced fluid; used to analyze submerged objects, foundation buoyancy, and pore-water effects in soils.
• B. The buoyant force equals the hydrostatic pressure integrated over an immersed surface.
• C. The buoyant force equals friction along a submerged surface.
• D. The buoyant force equals the normal reaction on a submerged body.

Answer: (A)

Archimedes' principle states that the buoyant force on a body immersed in a fluid equals the weight of the fluid it displaces, acting upward. In geotechnical engineering this principle is used to understand how submerged or water-saturated conditions affect foundations and soil-structure interactions. The buoyant force reduces the effective load of submerged elements, which is captured by the submerged unit weight γ_sub = γ − γ_w (where γ is the total unit weight of the material and γ_w the unit weight of water). This influences uplift checks for underwater or partially submerged foundations, piles, and cofferdams, as well as calculations of the submerged weight of soils in saturated conditions and the resulting impact on bearing capacity, stability, and settlement. The other descriptions describe related concepts (like deriving buoyancy from hydrostatic pressure) or refer to forces that are not buoyant lift (friction, normal reaction), so they do not define Archimedes' principle.