Submerged (Buoyant) Unit Weight

Below the water table every grain is buoyed by the water it displaces, so the stress it hands down to the grain beneath is reduced by exactly γw per unit volume. A saturated soil at 19.5 kN/m³ therefore contributes only 19.5 − 9.81 = 9.69 kN/m³ to effective stress — barely half. Multiply γ′ by depth and you get effective stress directly, without the σ − u round trip, which is why field engineers carry γ′ in their heads (a handy 62.4 pcf subtraction: 128.8 − 62.4 = 66.4 pcf).

The trap is using γ′ for total stress, or γsat for effective stress. Total stress needs the full saturated weight, because the water is physically there and pressing; effective stress needs the buoyant weight. Get them backwards and a 10 m submerged profile is off by a factor of two. The second trap is that buoyancy applies to structures too: a below-grade parking garage with a high water table can float, and the Chicago and Boston waterfront basements that had to be tied down with tension piles are monuments to somebody forgetting that a box full of air weighs less than the water it displaces.