Question

A clay sample has a void ratio of 0.5 in dry state. The specific gravity of soil solids is 2.5. What is the shrinkage limit of the soil?

• A. 15%
• B. 20%
• C. 12%
• D. 2%

Hint:

At the shrinkage limit, soil is always considered $100%$ saturated. Use the "Se-waG" formula ($Se = wG$) for quick calculations!

Answer 1

The Correct Option is B

Concept: The shrinkage limit ($w_s$) is the maximum water content at which a reduction in water content will not cause a decrease in the volume of the soil mass. At the shrinkage limit, the soil is just saturated ($S = 100% = 1$), and the volume of voids remains constant even as the soil dries further.

Step 1: Identify given parameters.
Given:
• Void ratio ($e$) = 0.5 (at dry state/shrinkage limit)
• Specific gravity ($G$) = 2.5
• Degree of saturation at shrinkage limit ($S$) = 1

Step 2: Apply the relationship between $e, w, G,$ and $S$.
We use the fundamental soil mechanics equation: \[ Se = wG \] At the shrinkage limit: \[ (1) \times 0.5 = w_s \times 2.5 \] \[ w_s = \frac{0.5}{2.5} = \frac{1}{5} \] \[ w_s = 0.20 \text{ or } 20% \]