Variable head test, two soils

Principle

For a variable head test, $k = \dfrac{aL}{A\,t}\ln\dfrac{h_1}{h_2}$, so for given $a$, $A$, $h_1$, $h_2$, the time is $t = \dfrac{aL}{Ak}\ln\dfrac{h_1}{h_2}$, proportional to $L/k$. When the second soil is placed on the first, the two act in series, so the flow resistances ($L/k$) add and the total time is the sum of the times for each soil taken alone.

Given

$h_1 = 900$ mm, $h_2 = 135$ mm, $a = 130$ mm², $A = 4560$ mm², $L_2 = 60$ mm.

• Soil 1 alone: $t_1 = 5$ s
• Soil 1 + soil 2: $t = 150$ s
• Time due to soil 2 alone: $t_2 = 150 - 5 = 145$ s

$$\ln\frac{h_1}{h_2} = \ln\frac{900}{135} = \ln 6.667 = 1.897$$

Permeability of soil 2

$$k_2 = \frac{a\,L_2}{A\,t_2}\ln\frac{h_1}{h_2} = \frac{130 \times 60}{4560 \times 145} \times 1.897 = 0.0224\ \text{mm/s}$$

Answer: $k_2 = 0.0224$ mm/s $= 2.24\times10^{-5}$ m/s.