ASTM D5920-96

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Designation: D 5920 – 96
Standard Test Method (Analytical Procedure) for
Tests of Anisotropic Unconfined Aquifers by Neuman
Method
This standard is issued under the fixed designation D5920; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope D4106 Test Method (Analytical Procedure) for Determin-
ing Transmissivity and Storage Coefficient of Nonleaky
1.1 This test method covers an analytical procedure for
Confined Aquifers by the Theis Nonequilibrium Method
determining the transmissivity, storage coefficient, specific
D4750 Test Method for Determining Subsurface Liquid
yield, and horizontal-to-vertical hydraulic conductivity ratio of
Levels in a Borehole or Monitoring Well
an unconfined aquifer. It is used to analyze the drawdown of
water levels in piezometers and partially or fully penetrating
3. Terminology
observation wells during pumping from a control well at a
3.1 Definitions:
constant rate.
3.1.1 aquifer, confined—an aquifer bounded above and
1.2 The analytical procedure given in this test method is
below by confining beds and in which the static head is above
used in conjunction with Guide D4043 and Test Method
the top of the aquifer.
D4050.
3.1.2 aquifer, unconfined—an aquifer that has a water table.
1.3 The valid use of the Neuman method is limited to
3.1.3 control well—awellbywhichtheheadandflowinthe
determination of transmissivities for aquifers in hydrogeologic
aquifer is changed by pumping, injecting, or imposing a
settings with reasonable correspondence to the assumptions of
constant change of head.
the theory.
3.1.4 drawdown—the vertical distance the static head is
1.4 The values stated in SI units are to be regarded as
lowered due to removal of water.
standard.
3.1.5 head, static—the height above a standard datum the
1.5 This standard does not purport to address all of the
surface of a column of water can be supported by the static
safety concerns, if any, associated with its use. It is the
pressure at a point.
responsibility of the user of this standard to establish appro-
3.1.6 hydraulic conductivity— field aquifer test, the volume
priate safety and health practices and determine the applica-
of water at the existing kinematic viscosity that will move in a
bility of regulatory limitations prior to use.
unit time under a unit hydraulic gradient through a unit area
2. Referenced Documents measured at right angles to the direction of flow.
3.1.7 observation well—a well open to all or part of an
2.1 ASTM Standards:
aquifer.
D653 Terminology Relating to Soil, Rock, and Contained
3.1.8 piezometer—a device used to measure static head at a
Fluids
point in the subsurface.
D4043 Guide for Selection of Aquifer-Test Method in
3.1.9 storage coeffıcient—the volume of water an aquifer
Determining Hydraulic Properties by Well Techniques
releases from or takes into storage per unit surface area of the
D4050 Test Method (Field Procedure) for Withdrawal and
aquifer per unit change in head.
Injection Well Tests for Determining Hydraulic Properties
3.1.10 transmissivity—the volume of water of the prevail-
of Aquifer Systems
ingkinematicviscositythatwillmoveinunittimeunderaunit
D4105 Test Method (Analytical Procedure) for Determin-
hydraulic gradient through a unit width of the aquifer.
ing Transmissivity and Storage Coefficient of Nonleaky
3.1.11 For definitions of other terms used in this test
Confined Aquifers by the Modified Theis Nonequilibrium
method, see Terminology D653.
Method
3.2 Symbols:Symbols and Dimensions:
3.2.1 b [L]—initial saturated thickness of the aquifer.
This test method is under the jurisdiction of ASTM Committee D-18 on Soil
3.2.2 d [L]—vertical distance between top of screen in
andRockandisthedirectresponsibilityofSubcommitteeD18.21onGroundWater
pumping well and initial position of the water table.
and Vadose Zone Investigations.
3.2.3 d [nd]—dimensionless d, equal to d/b.
Current edition approved Feb. 10, 1996. Published June 1996. D
Annual Book of ASTM Standards, Vol 04.08. 3.2.4 J (x)—zero-order Bessel function of the first kind.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5920
−1 2 2
3.2.5 K [LT ]—hydraulic conductivity in the plane of the 3.2.24 (t/r ) [T]—t/r correspondingtotheintersectionofa
r e
aquifer, radially from the control well. straight line through the early data with s 50 on semiloga-
−1 −2
rithmic paper [TL ].
3.2.6 K [LT ]—hydraulic conductivity normal to the
Z
2 2
plane of the aquifer. 3.2.25 (t/r ) [T]—t/r correspondingtotheintersectionofa
l
straight line through the late data with s 50 on semilogarith-
3.2.6.1 Discussion—The use of the symbol K for the hy-
draulic conductivity is the predominant usage in ground water mic paper.
2 −1
literature by hydrogeologists, whereas, the symbol k is com- 3.2.26 T[L T ]—transmissivity, K b.
r
monly used for this term in soil and rock mechanics and soil 3.2.27 z [L]—vertical distance above the bottom of the
science. aquifer.
3.2.7 l [L]—vertical distance between bottom of screen in 3.2.28 z [L]—vertical distance of the bottom of the obser-
control well and initial position of water table. vation well screen above the bottom of the aquifer.
3.2.8 l [nd]—dimensionless l, equal to l/b. 3.2.29 z [L]—verticaldistanceofthetopoftheobservation
D 2
3 −1
well screen above the bottom of the aquifer.
3.2.9 Q[L T ]—discharge rate.
3.2.30 z [nd]—dimensionless elevation, equal to z/b.
3.2.10 r [L]—radial distance from control well.
D
3.2.31 z [nd]—dimensionless elevation of base of screen,
3.2.11 s [L]—drawdown.
1D
equal to z /b.
3.2.12 s [L]—corrected drawdown.
c
3.2.32 z [nd]—dimensionless elevation of top of screen,
3.2.13 s [nd]—dimensionlessdrawdown,equalto4pTs/Q.
2D
D
equal to z /b.
3.2.14 s [L]—drawdown of the water table.
wt
3.2.33 a—degree of anisotropy, equal to K /K .
3.2.15 S [nd]—storage coefficient, equal to S b.
z r
s
2 2
−1
3.2.34 b [nd]—dimensionless parametera r /b .
3.2.16 S [L ]—specific storage.
s
3.2.35 Ds [L]—the difference in drawdown over one log
3.2.17 S [nd]—specific yield. e
y
cycle of time along a straight line through early data on
3.2.18 t [T]—time since pumping started.
semilogarithmic paper.
3.2.19 t [T]—time since recovery started.
r
3.2.36 Ds [L]—the difference in drawdown over one log
l
3.2.20 t [nd]—dimensionless time with respect to S , equal
s s
cycle of time along a straight line through late data on
to Tt/Sr .
semilogarithmic paper.
3.2.21 t [nd]—dimensionlesstimewithrespectto S ,equal
y y
3.2.37 s [nd]—dimensionless parameter S/S .
to Tt/S r . y
y
3.2.22 t [T]—time, t, corresponding to intersection of a
b
4. Summary of Test Method
horizontal line through the intermediate data with an inclined
line through late data on semilogarithmic paper.
4.1 Procedure—This test method describes a procedure for
3.2.23 t [nd]—dimensionless time, t , corresponding to analyzing data collected during a withdrawal well test. This
yb y
the intersection of a horizontal line through intermediate data test method should have been selected using Guide D4043 on
with an inclined line through late data in Fig. 1. the basis of the hydrologic characteristics of the site. The field
FIG. 1 Aquifer-Test Analysis, Example Two
D 5920
test(TestMethodD4050)requirespumpingacontrolwellthat 4.2.2 In the case in which the control well and observation
is open to all or part of an unconfined aquifer at a constant rate well fully penetrate the aquifer, the equations reduce to
for a specified period and observing the drawdown in piezom- Neuman’s (1) Eqs 2 and 3 as follows:
eters or observation wells that either partly or fully penetrate
2 2
$1– exp @–t b~y – g !#%tanh ~g !
s 0 0
the aquifer. This test method may also be used to analyze an u ~y! 5 (8)
2 2 2 2 2
y 1 11s! g – y – g ! /s g
$ ~ @~ #%
0 0 0
injection test with the appropriate change in sign. The rate of
and:
drawdown of water levels in the aquifer is a function of the
location and depths of screened open intervals of the control 2 2
1– exp –t b y 1g tan g
$ @ ~ !#% ~ !
s n n
u ~y! 5 (9)
well, observation wells, and piezometers. The drawdown may
n 2 2 2 2 2
y – ~11s! g – ~y 1g ! /s g
$ %
n n n
beanalyzedtodeterminethetransmissivity,storagecoefficient,
specific yield, and ratio of vertical to horizontal hydraulic
5. Significance and Use
conductivity of the aquifer. The accuracy with which any
5.1 Assumptions:
property can be determined depends on the location and length
5.1.1 The control well discharges at a constant rate, Q.
of the well screen in observation wells and piezometers. Two
methods of analysis, a type curve method and a semilogarith- 5.1.2 The control well, observation wells, and piezometers
mic method, are described. are of infinitesimal diameter.
4.2 Solution—The solution given by Neuman (1) can be
5.1.3 The unconfined aquifer is homogeneous and really
expressed as:
extensive.
` 5.1.4 Discharge from the control well is derived initially
Q
` 1/2
s~r, z, t! 5 4yJ ~yb !@u ~y! 1 u ~y!#dy (1)
* (
0 0 0 n from elastic storage in the aquifer, and later from gravity
4pT
n51
drainage from the water table.
where, for piezometers, Neuman’s (1) Eqs 27 and 28 are as
5.1.5 The geometry of the aquifer, control well, observation
follows:
wells, and piezometers is shown in Fig. 2.The geometry of the
2 2
1– exp —t b~y – g !# cosh ~g z !
$ $ %
s 0 0 D test wells should be adjusted depending on the parameters of
u ~y! 5 (2)
0 2 2 2 2 2
$y 1 ~11s! g – ~y – g ! /s%cosh ~g ! interest.
0 0 0
5.2 Implications of Assumptions:
sinh g 1– d –sinh g 1– l
@ ~ !# @ ~ !#
0 D 0 D
·
5.2.1 Use of the Neuman (1) method assumes the control
~l – d !sinh ~g !
D D 0
wellisofinfinitesimaldiameter.Thestorageinthecontrolwell
and:
may adversely affect drawdown measurements obtained in the
2 2
$1– exp @–t b~y 1g !#%cos ~g z !
s n n D early part of the test. See 5.2.2 of Test Method D4106 for
u y 5 (3)
~ !
n
2 2 2 2 2
$y – ~11s!g – ~y 1g ! /s% g
assistance in determining the duration of the effects of well-
n n n
bore storage on drawdown.
sin @g ~1– d !#–sin @g ~1– l !#
n D n D
·
5.2.2 If drawdown is large compared with the initial satu-
~l – d !sin ~g !
D D n
rated thickness of the aquifer, the late-time drawdown may
and the terms g and g are the roots of the following
0 n
need to be adjusted for the effect of the reduction in saturated
equations:
thickness. Section 5.2.3 of Test Method D4106 provides
2 2
sg sinh ~g !– ~y – g !cosh ~g ! 50 (4)
0 0 0 0 guidance in correcting for the reduction in saturated thickness.
2 2
According to Neuman (1) such adjustments should be made
g , y
only for late-time values.
2 2
sg sin ~g ! 1 ~y 1g !cos ~g ! 50 (5)
n n n n
~2n–1!~p/2!,g , np n$1
n
4.2.1 The drawdown in an observation well is the average
over the screened interval, of which u (y) and u ( y) are
0 n
described by Neuman’s (1) Eqs 29 and 30:
u ~y! 5
2 2
$1– exp @–t b~y – g !#% @sinh ~g z !–sinh ~g z !#
s 0 0 2D 0 1D
sinh g 1– d – sinh g 1– l
$ @ ~ !# @ ~ !#%
0 D 0 D
2 2 2 2 2
y 1 ~11s! g – ~y – g ! /s cosh ~g !·
$ %
0 0 0
z – z g l – d sinh g (6)
~ ! ~ ! ~ !
2D 1D 0 D D 0
u ~y! 5
n
2 2
$1– exp @–t b~y 1g !#% @sin ~g z !–sin ~g z !#
s n n 2D n 1D
sin g 1– d ! – sin g 1– l !
$ @ ~ # @ ~ #%
n D n D
2 2 2 2 2
$y – ~11s!g – ~y 1g ! /s%cos ~g !·
n n n
z – z g l – d sin g (7)
~ ! ~ ! ~ !
2D 1D n D D n
The boldface numbers in parentheses refer to a list of references at the end of FIG. 2 Cross Section Through a Discharging Well Screened in
the text. Part of an Unconfined Aquifer
D 5920
6. Apparatus 7.2 Analysis—Analyze the field test data by plotting the
data and recording parameters as specified in Section 8.
6.1 Analysis—Analysisofdatafromthefieldprocedure(see
Test Method D4050) by this test method requires that the
8. Calculation and Interpretation of Results
control well and observation wells meet the requirements
specified in the following subsections.
8.1 Methods—The drawdown data collected during the
6.2 Construction of Control Well—Installthecontrolwellin
aquifer test may be analyzed by either the type-curve method
the aquifer, and equip with a pump capable of discharging
orthesemilogarithmicmethod.Anyconsistentsetofunitsmay
water from the well at a constant rate for the duration of the
be used.
test.
8.1.1 Type-Curve Method—Plot drawdown, s, on the verti-
6.3 Construction of Observation Wells— Construct one or
calaxisandtimedividedbythesquareoftheradiustothewell
more observation wells or piezometers at a distance from the
or piezometer, t/r , on the horizontal axis using log-log paper.
control well. For this test method, observation wells may be
Group data for all wells or piezometers that have screened
open through all or part of the thickness of the aquifer.
intervals the same elevation above the base of the aquifer, z
D
6.4 Location of Observation Wells— Wells may be located
(for piezometers), or z and z (for observation wells).
1D 2D
at any distance from the control well within the area of
8.1.1.1 Prepare a family of type curves for different values
influence of pumping.
of b. For tests in which both the control well and the
observation wells fully penetrate the aquifer, the values in
7. Procedure
Table 1 andTable 2 may be used to prepare the type curves, as
7.1 Procedure—The procedure consists of conducting the shown in Fig. 3. For piezometers, or tests in which the control
field procedure for withdrawal well tests (see Test Method well or observation wells do not effectively penetrate the full
D4050), and analyzing the field data as addressed in this test thickness of the aquifer, the values of s corresponding to
D
method. values of t and t for a range of values of b must be computed
s y
A
TABLE 1 Values of S for the Construction of Type A Curves for Fully Penetrating Wells (1)
D
t b5 0.001 b5 0.004 b5 0.01 b5 0.03 b5 0.06 b5 0.1 b5 0.2 b5 0.4 b5 0.6
a
−1 −2 −2 −2 −2 −2 −2 −2 −2 −2
1 3 10 2.48 3 10 2.43 3 10 2.41 3 10 2.35 3 10 2.30 3 10 2.24 3 10 2.14 3 10 1.99 3 10 1.88 3 10
−1 −1 −1 −1 −1 −1 −1 −1 −1 −2
2 3 10 1.45 3 10 1.42 3 10 1.40 3 10 1.36 3 10 1.31 3 10 1.27 3 10 1.19 3 10 1.08 3 10 9.88 3 10
−1 −1 −1 −1 −1 −1 −1 −1 −1 −1
3.5 3 10 3.58 3 10 3.52 3 10 3.45 3 10 3.31 3 10 3.18 3 10 3.04 3 10 2.79 3 10 2.44 3 10 2.17 3 10
−1 −1 −1 −1 −1 −1 −1 −1 −1 −1
6 3 10 6.62 3 10 6.48 3 10 6.33 3 10 6.01 3 10 5.70 3 10 5.40 3 10 4.83 3 10 4.03 3 10 3.43 3 10
0 0 −1 −1 −1 −1 −1 −1 −1 −1
1 3 10 1.02 3 10 9.92 3 10 9.63 3 10 9.05 3 10 8.49 3 10 7.92 3 10 6.88 3
...