Question

A strata of 3 m thick fine sand has a void ratio of 0.5 and specific gravity of 2.5. For a quick sand condition to develop in this strata, the flowing in upward direction would require a head of:

• A. 7 m
• B. 3 m
• C. 3.5 m
• D. 4.5 m

Hint:

For many typical soils where $(G-1) \approx (1+e)$, the critical hydraulic gradient $i_c$ is approximately 1.0. This means quick sand condition often occurs when the head is equal to the thickness of the soil layer.

Answer 1

The Correct Option is B

Concept: Quick sand condition occurs when the upward seepage pressure becomes equal to the submerged weight of the soil, causing the effective stress to become zero. This happens when the hydraulic gradient ($i$) reaches the critical hydraulic gradient ($i_c$).

Step 1: Calculate the critical hydraulic gradient ($i_c$).
The formula for critical hydraulic gradient is: \[ i_c = \frac{G - 1}{1 + e} \] Given:
• Specific gravity ($G$) = 2.5
• Void ratio ($e$) = 0.5 Substituting the values: \[ i_c = \frac{2.5 - 1}{1 + 0.5} = \frac{1.5}{1.5} = 1.0 \]

Step 2: Calculate the required head ($h$).
The hydraulic gradient is defined as the head loss per unit length of flow: \[ i = \frac{h}{L} \] Where:
• $i = i_c = 1.0$ (for quick sand condition)
• $L = 3 \text{ m}$ (thickness of the strata) \[ 1.0 = \frac{h}{3} \quad \Rightarrow \quad h = 3 \text{ m} \]