Geotechnical Engineering

DHARM

126 GEOTECHNICAL ENGINEERING

d 0 , d 1 and d 2 be the depths of water level after pumping from the initial level of

water table, or the drawdowns at the central well and the two observation wells

respectively,

h be the initial height of the water table above the impervious layer (h = z 0 + d 0 ,

obviously) and,

R be the radius of influence or the radial distance from the central well of the point

where the drawdown curve meets the original water table.

Impervious boundary

rr 22

rr

rr 11

r 0

hh zz 22 zz zz 11

zz 00

d (^2) d
dz^1
dr
Observation
wells
dd 00
RR
Original water table
Drawdown curve
Central well Ground level
q
Fig. 5.6 Flow toward a well in an unconfined aquifer
Let r and z be the radial distance and height above the impervious boundary at any
point on the drawdown curve.
By Darcy’s law, the discharge q is given by :
q = k.A.dz/dr,
since the hydraulic gradient, i, is given by dz/dr by Dupuit’s assumption.
Here,
k is the coefficient of permeability.
But A = 2πrz.
∴ q = k. 2 πrz.dz/dr
or k.zdz =
qdr
2 π r
F
HG
I
KJ
.
Integrating between the limits r 1 and r 2 for r and z 1 and z 2 for z,
k z
z
2 z
2
1
R^2
S
T
U
V
W
= (q/2π) loge
r
r
r
R
S
|
T|
U
V
|
W| 1
2