Problem Statement
A soil has a bulk unit weight of 20.11 kN/m3 and a water content of 15%. Calculate the water content if the soil partially dries to a unit weight of 19.42 kN/m3, assuming the voids ratio remains unchanged.
Solution
1. Initial Dry Unit Weight
Before drying:
2. Final Water Content
Since the voids ratio \( e \) does not change, \( \gamma_d \) remains the same:
Rearranging for \( 1 + w \):
Water content:
Explanation
The dry unit weight \( \gamma_d \) represents the soil mass per unit volume excluding water content. It is calculated using the bulk unit weight \( \gamma \) and the water content \( w \). When the soil partially dries, its bulk unit weight decreases, but the voids ratio remains constant, implying that the dry unit weight stays unchanged.
By using the relationship \( \gamma = \gamma_d (1 + w) \), the new water content can be calculated directly from the ratio of the final bulk unit weight to the dry unit weight. This approach simplifies the calculation while ensuring consistency in the results.
Physical Meaning
This problem highlights the relationship between bulk unit weight, dry unit weight, and water content in soil mechanics. The voids ratio remaining unchanged means the soil structure and porosity are constant, and only the amount of water changes. The decrease in bulk unit weight reflects the loss of water, which reduces the overall mass of the soil. Understanding this relationship is critical for analyzing soil stability, compaction, and strength in geotechnical engineering applications.
