## Transientstate

Hantush and Jacob (1955) showed that the drawdown in a semiconfined aquifer is described by s so c where

22w K

r2S 4Tt

Equation 9.8(36) is similar to Equation 9.7(20) for a confined aquifer except that the well function contains the additional term r/A. The values of W(u, r/A) are given in Table 9.8.2.

### Walton Method

Walton's solution (1962) of Equation 9.8(36) is similar to the Theis method for a confined aquifer. Plotting s versus t/r2 gives the data curve. Plotting W(u, r/A) versus u for various values of r/A gives several type curves. Figure 9.8.8 shows the type curves. The data curve is superimposed on the type curves to get the best fitting curve. Again, four coordinates of a match point are read on both graphs. The resulting values of W(u, r/A) and s are substituted into Equation 9.8(36) to calculate T. The value of S is obtained from Equation 9.8(37) when u, t/r2, and T are substituted. The value c is calculated from c = A2/T where A is obtained from the r/A value of the best fitting curve.

Hantush's Inflection Point Method

Hantush's procedure (1956) for calculating T, S, and c from pumping test data utilizes the halfway point or inflection point on a curve relating s to log t. The inflection point is the point where the drawdown s is one-half the final or equilibrium drawdown as

The value u at the inflection point is

^ = = r2S 22 = u = 4Tt, where ti is t at the inflection point. The ratio between the drawdown and the slope of the curve at the inflection point As expressed as the drawdown per unit log cycle of t is derived as

The values of function er/A • Ko(r/A) versus r/A are in Table 9.8.1.

To determine T, S, and c from pumping test data, follow the following procedure:

1. Plot drawdown-time on semilog paper (s-log t).

2. Locate the inflection point P where s = 1/2 X final drawdown.

3. Draw a line tangent to the curve at point P, and determine the corresponding value of ti and the slope As.

4. Substitute s and As values into Equation 9.8(40) to obtain er/A • Ko(r/A), and determine the corresponding value of r/A and Ko r/A from Table 9.8.1.

5. Determine T from Equation 9.8(38).

6. Determine S from Equation 9.8(39).