Geotechnical Engineering

DHARM

128 GEOTECHNICAL ENGINEERING

rr 22

rr 11

rr

r 0

zz 22 zz zz 11 zz 00 HH Aquifer

Impervious boundary

Drawdown curve

d 2

dzdr

Observation

wells

d 1

dd 00

Central well

Original water table

Ground level

ImperviousImpervious stratumstratum

hh

Fig. 5.7 Flow toward a well in a confined aquifer

The notation in this case is precisely the same as that in the case of the unconfined

aquifer; in addition, H denotes the thickness of the confined aquifer, bounded by impervious

strata.

By Darcy’s law, the discharge q is given by :

q = k.A.dz/dr, as before.

But the cylindrical surface area of flow is given by A = 2πrH, in view of the confined

nature of the aquifer.

∴ q = k. 2 πrH.dz/dr

or k.dz =

q

H

dr

2 π r

..

Integrating both sides within the limits z 1 and z 2 for z, and r 1 and r 2 for r,

kz

q

H

r

z

z

e

r

r

L

NM

O

QP

=

L

N

M

M

O

Q

P

1 P

2

1

2

2 π

log

or k(z 2 – z 1 ) =

q

H

r

2 er

2

π 1

.log

or k =

q

Hz z

r

2 21 er

2

π () 1

.log

−

Since z 1 = (h – d 1 ) and z 2 = (h – d 2 ), (z 2 – z) = (d 1 – d 2 )

Substituting, we have :

k = q

Hd d

r

r

q

Hd d

r

2212 e 72 r

2

112

10

2

π () 1

.log

.( )

.log

−

=

−

...(Eq. 5.23)

Since the coefficient of transmissibility, T, by definition, is given by kH,

T =

q

dd

rr

272 .( 12 )^10 2 1

.log ( / )

− ...(Eq. 5.24)