Expression for permeability of an Unconfined Aquifer.

Hi,

In pumping out test, the water is pumped out through a tube well, until a steady state is reached. The water table around the well turns into a cone of depression. The maximum depression along the centre line of the well is known as the drawdown(d).

Following assumptions are made:

1. Flow follows the Darcy's law.
2. Flow is laminar.
3. Soil mass is isotropic and homogeneous.
4. Well penetrates the aquifer to reach the impervious bed.
5. Steady flow along the soil.
6. Co-efficient of permeability is constant throughout.
7. Natural water ground regime doesn't change.

Also it is assumed that the slope of the hydraulic line is small and so it can be taken as the tangent of the angle, in place of sine of the angle. 

  

or i = dz/dr

Consider flow through a cylindrical surface at a distance of 'r' and of depth 'z'. Further equation are given in the image below.

Flow can be estimated to a rough value using the influence radius of the well. Influence radius is the radius of the circle along which the effect of the pumping are observed. It varies from 150m to 300m. According the Sichardt, it can be found as follows. 

  R = 3000*d*(k)^0.5    , here d = Drawdown, k = permeability.

Further, permeability can be calculated using the influence radius as given in the formula in the image below.

Thanks!

Reference :  Buy the book online from the link given below.  Book Title: "Soil Mechanics and Foundation Engineering" by Dr. K R Arora.