Assumptions:

Control well discharges at a constant rate, Q.

Control well is of infinitesimal diameter and partially penetrates the aquifer.

The nonleaky artesian aquifer is homogeneous, and aerially extensive. The aquifer may also be anisotropic and, if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively. The methods may be used to analyze tests on unconfined aquifers under conditions described in a following section.

Discharge from the well is derived exclusively from storage in the aquifer.

The geometry of the assumed aquifer and well conditions are shown in Fig. 2.

Implications of Assumptions-The vertical flow components in the aquifer are induced by a control well that partially penetrates the aquifer, that is, a well that is not open to the aquifer through its full thickness. The effects of vertical flow components are measured in piezometers near the control well, that is, within a distance, r, in which vertical flow components are significant, that is:

Application of Method to Unconfined Aquifers:

Although the assumptions are applicable to artesian or confined conditions, Weeks (1) has pointed out that the solution may be applied to unconfined aquifers if drawdown is small compared with the saturated thickness of the aquifer or if the drawdown is corrected for reduction in thickness of the aquifer, and the effects of delayed gravity response are small. The effects of gravity response become negligible after a time as given, for piezometers near the water table, by the equation:

for values of ar/b < 0.4 and by the equation:

for greater values of ar/b.

Drawdown in an unconfined aquifer is also affected by curvature of the water table or free surface near the control well, and by the decrease in saturated thickness, that causes the transmissivity to decline toward the control well. This test method should be applicable to analysis of tests on water-table aquifers for which the control well is cased to a depth below the pumping level and the drawdown in the control well is less than 0.2b. Moreover, little error would be introduced by effects of water-table curvature, even for a greater drawdown in the control well, if the term (s²/2 b) for a given piezometer is small compared to the δ s term.

The transmissivity decreases as a result of decreasing thickness of the unconfined aquifer near the control well. Jacob (4) has shown that the effect of decreasing transmissivity on the drawdown may be corrected by the equation:

where s is the observed drawdown and s′ is the drawdown in an equivalent confined aquifer.