How does a decrease in void ratio impact the dry unit weight of a fully saturated soil when the specific gravity remains constant?

The dry unit weight of a fully saturated soil is the weight of the solid particles divided by the total volume of the soil mass, which includes both the volume of solids and the volume of voids. The void ratio, denoted as 'e', is a measure of the empty spaces within the soil, defined as the ratio of the volume of voids to the volume of solid particles. Specific gravity of solids, 'Gs', is the ratio of the density of the soil solid particles to the density of water. The unit weight of water, 'γw', is the weight of water per unit volume. For a fully saturated soil, all void spaces are completely filled with water, meaning there is no air. The dry unit weight (γd) can be expressed by the fundamental relationship: γd = (Gs γw) / (1 + e). This formula is derived from the definitions: the weight of solids (Ws) equals Gs multiplied by the unit weight of water and the volume of solids (Vs), and the total volume (V) equals the volume of solids plus the volume of voids (Vv). Since the void ratio e = Vv / Vs, it follows that Vv = e Vs, making the total volume V = Vs + e Vs = Vs (1 + e). Substituting these into γd = Ws / V yields the given formula. When the void ratio 'e' decreases, the value of the denominator (1 + e) in the formula also decreases. Since the specific gravity of solids (Gs) and the unit weight of water (γw) are stated to remain constant, a smaller denominator in the fraction (Gs γw) / (1 + e) results in a larger overall value for the dry unit weight (γd). Conceptually, a decrease in void ratio signifies that the soil particles are packed more densely. This means that for a given total volume, there is less empty space and therefore a greater mass of solid particles occupying that volume. Since dry unit weight quantifies the weight of these solids within a total volume, a denser packing directly translates to an increase in the dry unit weight.