of unconfined ground-water movement. For determination of ground-water parameters there is an alternative, namely to assume that recharge to the unconfined ground-water régime is either zero ( W = O) or constant during two computation intervals of time.
For two-dimensional flow and the distribution of observation wells shown in Figure 6.2.1 with A x
=
Ay and W = O we have:6.2(5) Av
At
2
Di- - -
KHw a = - S
$=I
where Av = A H a v AX)^ is the change in volume of the saturated zone in the flow element of area AX)^ for the interval of time At, and Di is defined by the relation:
where :
is the ground-water level in one of the numbered peripheral wells, i, at the first period of observation;
is the same, at the nth period of observation;
are the ground-water levels in the middle well m at the first and the nth periods of observations, respectively;
H?)
m , H(l) H m
6.2 page 2
Determining hydrodynamic parameters of ground-water flow
H,?, Hj”’ are the ground-water levels in the middle, m, and peripheral wells, i, respect- n
A H a v
ively at any period of observation;
is number of periods of observations in equal intervals of time At;
is the ground-water level averaged over the area in the flow element for the interval of time At.
For the interval At the following equation willbe true:
6.2(7)
where Hi,H, are the ground-water levels in the outer and middle wells respectively at the mean of the time interval At, other symbols being as above.
+ Y
-Y
Legend
1. Observation well or computation point.
2. Streamflow line.
3. F l o w element.
FIG. 6.2.1. Element of two-dimensional unconfined ground-water flow.
The change of ground-water level, AHav, averaged over the area of the flow element, used in the calculation of Av, is determined with greater accuracy when more obser- vation wells are located in the flow element.
W h e n W and S are constant:
-
6.2(8)(z1
-
22) A x a =2‘ [(y
- HZ- ”)
At]l- $ [(
HI-
HZ-
HZ - H3)12 I2 2
1
6.2 page 3
Ground-water studies
where :
z1 and z2 are summed variations of unconfined ground-water level ( C A H ) , for the
nl nz
periods of time At and At respectively;
1 1
ni, n2 are numbers of intervals of time, such that in the two periods the total values of recharge Z w A t are equal;
HI, Hz, H3 are levels of ground water in wells 1, 2, 3 respectively, taken at mid- intervals of time At;
11, 12 are distances between the wells 1 and 2, 2 and 3, so that:
11
+
12A X =
-
2 .
Before using Equation 6.2 (8) one must check whether the following condition is ob- served :
where :
HI
-
H2Il = , I2 = HZ - H3.
11 12 '
n3
23 = A h for the time At, in which the value of w A t is the same as for the
1 n1
time At.
1
The rest of the notations are as above.
Note that all finite-difference equations indicated above can be applied only for a homogeneous water-bearing stratum; where the stratum is appreciably heterogeneous, corrections should be applied (Shestakov, 1965).
W h e n a stratum of low permeability lies immediately above one of high permeability, and there are vertical components of potential gradient, the upper stratum exhibits mainly ascending or descending water while horizontal confined flow may take place in the lower.
If a piezometer is installed in the upper layer and another in the roof of the lower, observations of their water levels m a y be used to compute the diffusivity of the poorly permeable upper layer from the formula:
h f A h K -
S HI
-
HI'-
At 6.2(10)where :
K is the hydraulic conductivity of the upper layer;
S is the specific yield of this layer;
h' is the vertical distance between the piezometer locations;
HI, H' are water heads in the lower and upper piezometers, respectively;
A h is variation of the saturated thickness (unconfined ground water) in the upper layer during the time At.
The conditions for using this method are: (a) measurement of unconfined ground-water level in the upper layer for the computation of A h should.be carried out by specially
6.2 page 4
Determining hydrodynamic parametera of ground-water flow
located piezometers, the screens of which must be near the water table; (b) during the period of observation there should be no infiltration recharge or evaporation; (c) while installing piezometers there should be no leakage of water from one part of the layer to another. This is usually ensured by the use of drive-point screens.
6.2.2
Determining speciJic yield from moisture measurements in zone of aeration
This parameter may be directly determined from the observation of moisture storage in the lower part of the zone of aeration during the period of time At during which the unconfined ground-water level changes by the value AH.
The initial level of water in a shallow well (depth to water not exceeding 5-6 m> is observed, together with the neighbouring moisture profile by sampling at vertical inter- vals of 0.1 m . W h e n the ground-water level has risen by AH the soil sampling for deter- mination of the moisture profile is repeated on the same site.
Having drawn the volume moisture profile as shown in Figure 6.2.2, the difference between the areas enclosed by them represents the increment of gravity water reserves pAH for a water-level rise AH.
Portion of soil moisture profile prior to water-level rise.
Portion of soil-moisture profile after water-level rise.
-
Initial water-table position.---
Final water-table position after a steady rise.FIG. 6.2.2. Soil-moisture profles for the zone of aeration.
6.2 page 5
Groimrl-wuter stirdies
The increment of this moisture storage is given by the expression
/ l A H = C Z A Z V ~
-
CIAZV,, 6.2(11) where :A Z is vertical interval of soil sampling;
Vo is the volume moisture content of soil in the middle of that interval (expressed as a decimal fraction).
The subscript 1 in Equation 6.2 (11) indicates the initial soil sampling for moisture content and the subscript 2 the later soil sampling.
Volume moisture content (expressed as a fraction of the soil volume) equals the gravity moisture content multiplied by the volume weight of the soil skeleton. Having divided Equation 6.2 (1 1) by A H one finds the parameter
6.2( 1 2)