Question

The critical hydraulic gradient \(i_c\) for a soil with a grain specific gravity \(G\) and a void ratio \(e\) is given by

• A. \(\displaystyle i_c=\frac{G-1}{1+e}\)
• B. \(\displaystyle i_c=\frac{G+1}{1+e}\)
• C. \(\displaystyle i_c=\frac{G+e}{1+e}\)
• D. \(\displaystyle i_c=\frac{G-1}{1-e}\)

Hint:

For the quick condition, \[ \boxed{ i_c=\frac{G-1}{1+e}. } \] This is one of the most frequently asked formulas in Soil Mechanics.

Answer 1

The Correct Option is A

Step 1: Recall the definition of critical hydraulic gradient. The critical hydraulic gradient is the hydraulic gradient at which the upward seepage force becomes equal to the submerged weight of soil, producing the quick condition.

Step 2: Write the standard expression. The critical hydraulic gradient is given by \[ \boxed{ i_c=\frac{G-1}{1+e} } \] where \[ G=\text{specific gravity of soil solids}, \] and \[ e=\text{void ratio}. \] Hence, \[ \boxed{(A)} \] is the correct answer.