Soil mechanics fundamentals: The relationship between submerged unit weight (γ′) and saturated unit weight (γ_sat) of a soil is based on which physical principle?

Introduction / Context:
Submerged (buoyant) unit weight γ′ is the effective weight of saturated soil below the water table and is central to analyses of bearing capacity, slope stability, and earth pressure in submerged conditions. It reflects the reduction of soil self-weight due to buoyancy from the surrounding water.

Given Data / Assumptions:

• Saturated soil below groundwater level.
• γ_sat is the saturated unit weight; γ_w is the unit weight of water.
• Buoyant force acts upward on solids displacing water.

Concept / Approach:

Archimedes’ principle states that a body submerged in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. On a representative elemental volume of saturated soil, water occupies voids; the net vertical force on the soil skeleton is its saturated weight minus the buoyant force = γ_sat − γ_w, which defines the submerged unit weight γ′.

Step-by-Step Solution:

Verification / Alternative check:

Effective stress σ′ = σ − u mirrors the same physics: submerged unit weight is the incremental overburden that contributes to σ′ in hydrostatic conditions.

Why Other Options Are Wrong:

• Equilibrium of floating bodies: Related conceptually but Archimedes’ is the direct basis.
• Stokes’ law: Particle settling; unrelated to buoyant weight of soil mass.
• Darcy’s law: Flow through porous media; not weight relationships.
• Pascal’s law: Pressure transmission; again not the buoyancy-weight relation.

Common Pitfalls:

• Using γ′ above the water table (incorrect).
• For partially saturated soils, γ′ ≠ γ_sat − γ_w; the simple relation applies to full saturation.

Final Answer:

Archimedes' principle