Drawdown In Unconfined Aquifer Calculator

by Glenn M. Duffield, President, HydroSOLVE, Inc.

Water-level drawdown produced by pumping withdrawal from an unconfined aquifer causes a reduction in the aquifer's saturated thickness and hence its transmissivity. A correction proposed by Jacob (Kruseman and de Ridder 1994) transforms drawdown measured in an unconfined aquifer to drawdown in an equivalent nonleaky confined aquifer:

$s^{'} = s - s^{2} / 2 b (1)$

where s′ is drawdown in an equivalent nonleaky confined aquifer [L], s is drawdown in unconfined aquifer [L] and b is aquifer saturated thickness before pumping [L].

Drawdown in the equivalent nonleaky confined aquifer is computed with the Theis Equation (Theis 1935):

$s^{'} = \frac{Q}{4 π T} w (u) (2)$

$w(u) = -0.5772 - ln(u) + u - \frac{u^{2}}{2 \cdot 2!} + \frac{u^{3}}{3 \cdot 3!} - \frac{u^{4}}{4 \cdot 4!} + \cdot\cdot\cdot (3)$

$u = \frac{r^{2} S}{4 T t} (4)$

where Q is pumping rate [L³/T], r is radial distance from pumping well to observation well [L], S is storativity in equivalent nonleaky confined aquifer [-], T is transmissivity in equivalent nonleaky confined aquifer [L²/T] and t is elapsed time since start of pumping [T].

After computing s′ with (2), the following equation for s is found from (1) by means of the quadratic formula:

$s = b - b \sqrt{1 - 2 s^{'} / b} (5)$