Tripp Winters
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Anisotropy is a common feature in water laid
sedimentary deposits (fluvial, clastic lake,
deltaic and glacial outwash).
Water lain deposits may exhibit anisotropy on
the horizontal plain (X,Y if looking down from
above)
Hydraulic conductivity in the direction of flow
tends to be greater than that perpendicular to
flow, which causes lines of equal drawdown
to form ellipses rather than circles.
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Water laid sedimentary deposits are often
“stratified” (have layers of alternating stratum,
therefore alternating K’s)
Any layer with a low K will retard vertical flow,
but horizontal flow can occur easily through
any layer with relatively high K.
When Kh (parallel to the layer) is larger than
Kv (perpendicular to layer), the aquifer is said
to be “Vertically anisotropic”.
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When an aquifer exhibits both vertical and
horizontal anisotropy, it has 3-D anisotropy
The principal axes are:
 Kz: the vertical direction
 Kparallel: The direction parallel to stream flow
 Kperpendicular: The direction perpendicular to
stream flow
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The assumptions listed at the beginning of Chapter 3, with
the exception of the third assumption, which is replaced
by:
The aquifer is homogeneous, anisotropic on the
horizontal plane, and of uniform thickness over the
area influenced by the pumping test.
Some conditions are added:
The flow to the well is in unsteady state;
If the principal directions of anisotropy are known,
drawdown data from two piezometers on different rays
from the pumped well will be sufficient. If the principal
directions of anisotropy are not known, drawdown data
must be available from at least three rays of piezometers.
So, since the shape of equal drawdown is an ellipse in
anisotropic aquifers we need to look at the equation of
an ellipse in Cartesian coordinates is:
where:
a= major horizontal axis
b= minor horizontal axis
c= vertical axis (not used in this case)
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If we have one or more piezometers on a ray
that froms an angle with the X axis, methods
for isotropic aquifers can be applied to obtain
values for (KD)e and S/(KD)n.
Consequently, data is needed from more than
one ray of piezometers to calculate S and
(KD)n (Transmissivity along rays 0 to n
originating at the pumped well, plotting all of
these KDn’s corresponding to arrays 0 to n
will make an ellipse shape).
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If is defined as the angle between the first
ray of piezometers (n = 1) and the X axis, and
as the angle between the nth ray of
pizometers and the first ray of piezometers
(KD)n is given by:
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Method stated that when KDe, as, bs are
known the other hydraulic characteristics can
be calculated.
Hence, it is not necessary to have values of
S/(KD)n, provided that one has sufficient
observations to draw the ellipses of equal
drawdown.
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The Hantush-Thomas method can be applied
if the following assumptions and conditions
are satisfied:
- The assumptions listed at the beginning of
Chapter 3, with the exception of the third
assumption, which is replaced by:
◦ The aquifer is homogeneous, anisotropic on the
horizontal plane, and of uniform thickness over the
area influenced by the pumping test.
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The following condition is added:
◦ - The flow to the well is in unsteady state.
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As stated before, lines of equal drawdown in
an isotropic aquifer are circular around the
pumped well whereas the lines of equal
drawdown in a horizontally anisotropic
aquifer form ellipses. The equation of the an
ellipses is:
The assumptions listed at the beginning of Chapter
3, with the exception of the third assumption,
which is replaced by:
The aquifer is homogeneous, anisotropic on
the horizontal plane, and of uniform
thickness over the area influenced by the
pumping test.
 The following conditions are added:
-The flow to the well is in an unsteady state;
-The aquifer is penetrated by three wells,
which are not on one ray. Two of them are
pumped in sequence.
Where:
as and bs are the principal axes of the ellipse
of equal drawdown s at time Ts (Figure 8.1 C)
It can be shown that:
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In 1984, Neumann and others showed that
the Papadopulos can be used with drawdown
data from only three wells so long as two
pumping test performed in sequence with
two of the wells.
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HANTUSH’S METHOD
The flow to a well in a leaky aquifer which is
anisotropic on the horizontal plane can be
analyzed with a method that is essentially the
same as the Hantush method for confined
aquifers with anisotropy on the horizontal
plane.
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The leakage factor, L, is unknown which is
given by Hantush in
c is constant so equation 8.7 gives the relationship between Ln and L1
The Hantush method can be applied if the
following assumptions and conditions are
The assumptions listed at the beginning of Chapter
3, with the exception of the first and third
assumptions, which are replaced by:
 The aquifer is leaky;
 The aquifer is homogeneous, anisotropic on the
horizontal plane, and of uniform thickness over
the area influenced by the pumping test.
The following condition is added:
 The flow to the well is in an unsteady state.
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WEEKS’S METHOD
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Weeks’s Method
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Flow to a partially penetrating well in an unconfined
aquifer is considered 3-D during the time the delayed
watertable response occurs. 3-D flow is affected by
anisotropy in the vertical plane. Neumann’s curve
fitting method from section 5.1.1 takes this
anisotropy into account.
Two other methods can also be used that take
vertical plane anisotropy into account when the well
is partially penetrating:
◦ Streltsova’s curve-fitting method (Section 10.4.1)
◦ Neuman’s curve-fitting method (Section 10.4.2)
◦ Boulton-Streltsova’s curve-fitting method (Section 11.2.1).