Question $2$

$($a$)$ State Darcy's Law as it applies to flow of water through soil, explaining all relevant

terms. Distinguish between Darcy velocity and true seepage velocity.

$($b$)$ Use a clear labelled diagram to explain the principle of the well pumping test. State

Dupuit's assumption and derive a relationship between the quantity of water

pumped from a well in an unconfined layer and the drawdown in groundwater level

in two observation wells.

$($c$)$ A pumping test was performed in permeable sands and gravels extending to a depth

of $15\mathrm{.}8m,$ where a bed of clay was encountered. The normal ground water level

was $550mm$ below the ground surface. Observation wells were located at distances

of $3\mathrm{.}5m($W$1)$ and $8\mathrm{.}2m($W$2)$ from the pumping well. A steady state was reached

after $24$ hours at a discharge of $19\mathrm{.}4\frac{m^3}{m}in$ from the pumping well. Calculate the

permeability $($in $\frac{m}{s})$ if the drawdown was $1750mm$ at $W1$ and $350mm$ at W$2.$

Comment on the value obtained.

$($d$)$ What other methods can be used to estimate soil permeability? Given an example

of how soil permeability values are used in geotechnical engineering practice.