Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Permeability and seepage analysis
Question Statement:
The critical hydraulic gradient ($i_c$) at which quicksand condition (boiling) occurs in upward seepage through a sand stratum is expressed by:
Options:
(A) $i_c = \frac{G_s - 1}{1 + e}$
(B) $i_c = \frac{G_s + 1}{1 - e}$
(C) $i_c = \frac{1 + e}{G_s - 1}$
(D) $i_c = (G_s - 1)(1 + e)$
Answer Key:
A
Step-by-Step Solution & Explanation
Quicksand condition occurs when the upward seepage force balances the submerged weight of the soil particles, causing effective stress $\sigma'$ to become zero:
$\sigma' = \gamma' z - i \gamma_w z = 0 \implies i_c = \frac{\gamma'}{\gamma_w}$
Since $\gamma' = \frac{G_s - 1}{1 + e} \gamma_w$:
$i_c = \frac{G_s - 1}{1 + e}$
Option A is correct.