Question

Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of the water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the coefficient of permeability of the second specimen is 5-times that of the first, the ratio of initial to final water heads in the tests involving the second specimen is

• A. 3.05
• B. 3.80
• C. 4.00
• D. 6.25

Answer 1

The correct option is A 3.05

In a falling head permeability test, Coefficient of permeability,

$K=\frac{aL}{At}ln\left(\frac{h_1}{h_2}\right)$

For first specimen,

$K_1=\frac{aL}{At}ln\left(1.25\right)...\left(i\right)$

For second specimen,

$K_2=5K_1$

Given,

$\therefore 5K_1=\frac{aL}{At}ln\frac{h_1}{h_2}...\left(2\right)$

Equation (2) divided by (1)

$5=\frac{ln\left(\frac{h_1}{h_2}\right)}{ln\left(1.25\right)}$

$\Rightarrow \frac{h_1}{h_2}=3.052$