Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 159

which is tabulated in various hydrogeological textbooks (e.g. Herth & Arndts 1973). S 0
is the specifi c storage coeffi cient of the aquifer. Equation (6.67) is valid if the lowering
of the water table is small compared with the thickness H of the aquifer penetrated by
the well. In this case the vertical component of the seepage velocity can be neglected. If
u < 0.01, (6.67) can be approximated as

(6.67a)

Setting h(r,t) = 0 and solving (6.67a) for r provides the radius of the drawdown cone,

that is, the radius of infl uence of the well, at time t:

Δ

(6.68)

To estimate the radius of infl uence R of the well when the required drawdown of
Δ

h 0 = 2 m is reached the well formula derived by Dupuit (1863) and Thieme (1870) can
be used, which is valid at steady state under the same assumptions as Equation (6.67):

(6.69)

10 -6 m/s and r 0 = 0.2 m into (6.69) where h 0 = H - Δ h 0 = 8 m. Inserting H = 10 m, k = 1 ⋅

and solving for R yields R 50 m. Setting r(t) = R and solving (6.68) for t gives the

duration t 0 in which the water table in the well is lowered by

≈

Δ h 0 = 2 m:

(6.70)

Equation (6.70) documents the important result that S 0 is proportional to the drawdown
time and thus controls the duration of groundwater lowering. This result can be general-
ized to each solution of the transient seepage fl ow equation (6.49). In most practical cases
transient fl ow has a fi nite duration so that S 0 also controls the duration of transient fl ow.
The evaluation of (6.70) for the two aquifers under consideration yields

t 0 = 40000 s ≈ 11 h

for the joint aquifer and

t 0 = 1.1 · 10 7 s

≈ 130 d

for the pore aquifer.