Understanding the relationship between different soil unit weights is crucial in geotechnical engineering. Let's break down the concept of submerged unit weight.

Submerged Unit Weight Definition

When soil is fully submerged in water, its weight appears less due to the upward buoyant force exerted by the water. This apparent unit weight is called the submerged unit weight or buoyant unit weight.

Calculating Submerged Unit Weight

The submerged unit weight of soil ($\gamma_{sub}$) is calculated by considering the saturated unit weight of the soil ($\gamma_{sat}$) and the unit weight of water ($\gamma_w$). Specifically, it represents the reduction in the soil's unit weight due to the water displacement (buoyancy).

The relationship is expressed by the following formula:

$$ \gamma_{sub} = \gamma_{sat} - \gamma_w $$

In this formula:

• $ \gamma_{sub} $ represents the submerged unit weight of the soil.
• $ \gamma_{sat} $ represents the unit weight of the soil when it is fully saturated with water.
• $ \gamma_w $ represents the unit weight of water.

From the formula, it's clear that the submerged unit weight is obtained by subtracting the unit weight of water from the unit weight of the saturated soil. Therefore, the submerged unit weight is the difference between the unit weight of saturated soil and the unit weight of water.

Why It's the Difference

Imagine a saturated soil sample. Its total weight per unit volume is $ \gamma_{sat} $. When this sample is submerged, the surrounding water exerts an upward buoyant force equal to the weight of the water displaced by the soil volume. This buoyant force per unit volume is exactly $ \gamma_w $. The effective weight per unit volume that the soil exerts in its submerged state is its actual weight minus the buoyant force, hence the difference:

Effective Unit Weight = Total Unit Weight - Buoyant Force per Unit Volume

$$ \gamma_{sub} = \gamma_{saturated} - \gamma_{water} $$