Environmental Engineering Reference
In-Depth Information
7.
Shape of the cone of depression during pumping is determined from measuring the
depth to the water table in a number of observation wells or piezometers dis-
tributed about the well. (At least two should be located along each of several sets
of perpendicular lines extending from the well). From the shape of the cone and
the distance R it extends from the well, the hydraulic behavior of the well and the
permeability of the aquifer penetrated by the well can be calculated.
Gravity Wells: Analysis
Because of the heterogeneity of formations, calculations of quantities before data are avail-
able from pumping tests are only rough approximations. Well yields are best determined
from pumping tests, and observation wells provide important additional data on draw-
down. Because of the low velocities of groundwater flow, true equilibrium conditions usu-
ally occur only after some time interval of pumping.
Quantity of flow to a fully penetrating gravity well ( Figure 8.31a) at equilibrium may be
expressed in terms of permeability ( k mean because of stratification effects) and the depres-
sion cone characteristics as
Q w π
k ( H 2
h w 2 )/log e ( R / r w )
(8.10)
where H is the height to the original groundwater table.
Permeability can be computed by rearrangement of Equation 8.10 from
K mean
Q log e ( r 2 / r 1 )/
π
( h 2 2
h 1 2 )
(8.11)
where k mean represents the overall stratum permeability, h 1 and h 2 are the heights of the
phreatic surface referenced to an impermeable stratum, and r 1 and r 2 are the distances
from the well to monitoring piezometers where h 1 and h 2 were measured.
Drawdown, H - h , is used in dewatering problems to evaluate system effectiveness as
well as to estimate the possible effects of overextraction and ground subsidence. It may be
determined by calculating the head h at a distance r from the well with the expression
h
( Q w /
π
k ) log e [( r / r w )
h w 2 ]
(8.12)
At distances from the well exceeding approximately 1.0 to 1.5 times the height H to the
original groundwater table, the drawdown will be equal to that computed from Equation
8.12. At closer distances to the well, the drawdown will be less than that computed, with
the difference increasing in magnitude with decreasing distance. It is significant that in a
frictionless gravity well, the water level in the well will be lower than the piezometric sur-
face at the periphery of the well as shown in Figure 8.31b. The difference h ' in the two
water levels is the height of free discharge. Equation 8.10 provides an accurate estimate for
Q if the height of water ( t s ) is used for h w .
Artesian Wells
Flow from a confined aquifer to a fully penetrating artesian well is illustrated in Figure 8.32.
Quantity and permeability are related by the expression
Q w
2
π
kD ( H
h w )/log e ( R / r w )
(8.13)
Drawdown, H - h , at any distance r from the well, may be computed from the following
expression for the head at distance r :
H
( Q w /2
π
kD ) log e ( r / r w h w )
(8.14)
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