ASTM D5920-96(2005)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:D5920 −96(Reapproved 2005)
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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope erties of Aquifer Systems
D4105Test Method for (Analytical Procedure) for Deter-
1.1 This test method covers an analytical procedure for
mining Transmissivity and Storage Coefficient of Non-
determining the transmissivity, storage coefficient, specific
leaky ConfinedAquifers by the Modified Theis Nonequi-
yield, and horizontal-to-vertical hydraulic conductivity ratio of
librium Method
an unconfined aquifer. It is used to analyze the drawdown of
D4106Test Method for (Analytical Procedure) for Deter-
water levels in piezometers and partially or fully penetrating
mining Transmissivity and Storage Coefficient of Non-
observation wells during pumping from a control well at a
leaky Confined Aquifers by the Theis Nonequilibrium
constant rate.
Method
1.2 The analytical procedure given in this test method is
used in conjunction with Guide D4043 and Test Method
3. Terminology
D4050.
3.1 Definitions:
1.3 The valid use of the Neuman method is limited to
3.1.1 aquifer, confined—an aquifer bounded above and be-
determination of transmissivities for aquifers in hydrogeologic
lowbyconfiningbedsandinwhichthestaticheadisabovethe
settings with reasonable correspondence to the assumptions of
top of the aquifer.
the theory.
3.1.2 aquifer, unconfined—an aquifer that has a water table.
1.4 The values stated in SI units are to be regarded as
3.1.3 control well—awellbywhichtheheadandflowinthe
standard.
aquifer is changed by pumping, injecting, or imposing a
1.5 This standard does not purport to address all of the
constant change of head.
safety concerns, if any, associated with its use. It is the
3.1.4 drawdown—the vertical distance the static head is
responsibility of the user of this standard to establish appro-
lowered due to removal of water.
priate safety and health practices and determine the applica-
3.1.5 head, static—the height above a standard datum the
bility of regulatory limitations prior to use.
surface of a column of water can be supported by the static
pressure at a point.
2. Referenced Documents
2 3.1.6 hydraulic conductivity— field aquifer test, the volume
2.1 ASTM Standards:
of water at the existing kinematic viscosity that will move in a
D653Terminology Relating to Soil, Rock, and Contained
unit time under a unit hydraulic gradient through a unit area
Fluids
measured at right angles to the direction of flow.
D4043Guide for Selection of Aquifer Test Method in
3.1.7 observation well—a well open to all or part of an
Determining Hydraulic Properties by Well Techniques
aquifer.
D4050Test Method for (Field Procedure) for Withdrawal
and Injection Well Tests for Determining Hydraulic Prop-
3.1.8 piezometer—a device used to measure static head at a
point in the subsurface.
3.1.9 storage coeffıcient—the volume of water an aquifer
ThistestmethodisunderthejurisdictionofASTMCommitteeD18onSoiland
releases from or takes into storage per unit surface area of the
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
aquifer per unit change in head.
Vadose Zone Investigations.
Current edition approved Jan. 1, 2005. Published February 2005. originally
3.1.10 transmissivity—thevolumeofwateroftheprevailing
approved in 1996. Last previous edition approved in 1996 as D5920–96. DOI:
kinematic viscosity that will move in unit time under a unit
10.1520/D5920-96R05.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or hydraulic gradient through a unit width of the aquifer.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.11 For definitions of other terms used in this test
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. method, see Terminology D653.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5920−96 (2005)
3.2 Symbols and Dimensions: 3.2.20 t [nd]—dimensionless time with respect to S , equal
s s
3.2.1 b [L]—initial saturated thickness of the aquifer. to Tt/Sr .
3.2.2 d [L]—vertical distance between top of screen in 3.2.21 t [nd]—dimensionless time with respect to S , equal
y y
pumping well and initial position of the water table. to Tt/S r .
y
3.2.3 d [nd]—dimensionless d, equal to d/b. 3.2.22 t [T]—time, t, corresponding to intersection of a
D
β
horizontal line through the intermediate data with an inclined
3.2.4 J (x)—zero-order Bessel function of the first kind.
line through late data on semilogarithmic paper.
−1
3.2.5 K [LT ]—hydraulic conductivity in the plane of the
r
3.2.23 t [nd]—dimensionless time, t , corresponding to
yβ y
aquifer, radially from the control well.
the intersection of a horizontal line through intermediate data
−1
3.2.6 K [LT ]—hydraulicconductivitynormaltotheplane
Z
with an inclined line through late data in Fig. 1.
of the aquifer.
2 2
3.2.24 (t/r ) [T]—t/r correspondingtotheintersectionofa
3.2.6.1 Discussion—The use of the symbol K for the hy- e
straight line through the early data with s =0 on semilogarith-
draulic conductivity is the predominant usage in groundwater
−2
mic paper [TL ].
literature by hydrogeologists, whereas, the symbol k is com-
2 2
monly used for this term in soil and rock mechanics and soil
3.2.25 (t/r ) [T]—t/r correspondingtotheintersectionofa
l
science.
straight line through the late data with s =0 on semilogarith-
mic paper.
3.2.7 l [L]—vertical distance between bottom of screen in
2 −1
control well and initial position of water table.
3.2.26 T[L T ]—transmissivity, K b.
r
3.2.8 l [nd]—dimensionless l, equal to l/b.
3.2.27 z [L]—vertical distance above the bottom of the
D
3 −1
aquifer.
3.2.9 Q[L T ]—discharge rate.
3.2.28 z [L]—vertical distance of the bottom of the obser-
3.2.10 r [L]—radial distance from control well.
vation well screen above the bottom of the aquifer.
3.2.11 s [L]—drawdown.
3.2.29 z [L]—verticaldistanceofthetopoftheobservation
3.2.12 s [L]—corrected drawdown.
c
well screen above the bottom of the aquifer.
3.2.13 s [nd]—dimensionless drawdown, equal to 4πTs/Q.
D
3.2.30 z [nd]—dimensionless elevation, equal to z/b.
D
3.2.14 s [L]—drawdown of the water table.
wt
3.2.31 z [nd]—dimensionless elevation of base of screen,
1D
3.2.15 S [nd]—storage coefficient, equal to S b.
s
equal to z /b.
−1
3.2.16 S [L ]—specific storage.
s
3.2.32 z [nd]—dimensionless elevation of top of screen,
2D
3.2.17 S [nd]—specific yield.
equal to z /b.
y
3.2.18 t [T]—time since pumping started.
3.2.33 α—degree of anisotropy, equal to K /K .
z r
2 2
3.2.34 β [nd]—dimensionless parameterα r /b .
3.2.19 t [T]—time since recovery started.
r
FIG. 1 Aquifer-Test Analysis, Example Two
D5920−96 (2005)
2 2
3.2.35 ∆s [L]—the difference in drawdown over one log σγ sin γ 1 y 1γ cos γ 50 (5)
~ ! ~ ! ~ !
n n n n
e
cycle of time along a straight line through early data on
~2n21!~π/2!,γ ,nπ n$ 1
semilogarithmic paper. n
3.2.36 ∆s [L]—the difference in drawdown over one log
l
4.2.1 The drawdown in an observation well is the average
cycle of time along a straight line through late data on
over the screened interval, of which u (y) and u (y) are
0 n
semilogarithmic paper.
described by Neuman’s (1) Eqs 29 and 30:
3.2.37 σ [nd]—dimensionless parameter S/S .
y
2 2
12exp 2t β y 2γ sinh γ z 2sinh γ z
$ @ ~ !#% @ ~ ! ~ !#
s 0 0 2D 0 1D
sinh γ 12d 2sinh γ 12l
$ @ ~ !# @ ~ !#%
0 D 0 D
4. Summary of Test Method
u ~y!5 (6)
0 2 2 2 2 2
$y 1~11σ! γ 2~y 2γ ! /σ%cosh~γ !·
0 0 0
4.1 Procedure—This test method describes a procedure for
~z 2z !γ l 2d sinh~γ !
~ !
2D 1D 0 D D 0
analyzing data collected during a withdrawal well test. This
test method should have been selected using Guide D4043 on
2 2
12exp 2t β~y 1γ ! @sin~γ z !2sin~γ z !#
$ @ #%
s n n 2D n 1D
the basis of the hydrologic characteristics of the site. The field
$sin@γ ~12d !#2sin@γ ~12l !#%
test (Test Method D4050) requires pumping a control well that
n D n D
u ~y!5 (7)
2 2 2 2 2
n
y 2 11σ γ 2 y 1γ /σ cos γ ·
$ ~ ! ~ ! % ~ !
is open to all or part of an unconfined aquifer at a constant rate
n n n
for a specified period and observing the drawdown in piezom- z 2z γ ~l 2d !sin~γ !
~ !
2D 1D n D D n
eters or observation wells that either partly or fully penetrate
4.2.2 In the case in which the control well and observation
the aquifer. This test method may also be used to analyze an
well fully penetrate the aquifer, the equations reduce to
injection test with the appropriate change in sign. The rate of
Neuman’s (1) Eqs 2 and 3 as follows:
drawdown of water levels in the aquifer is a function of the
2 2
12exp 2t β~y 2γ ! tanh~γ !
$ @ #%
location and depths of screened open intervals of the control s 0 0
u ~y!5 (8)
2 2 2 2 2
y 1 11σ γ 2 y 2γ /σ γ
well, observation wells, and piezometers. The drawdown may $ ~ ! @~ ! #%
0 0 0
beanalyzedtodeterminethetransmissivity,storagecoefficient,
and:
specific yield, and ratio of vertical to horizontal hydraulic
2 2
$12exp@2t β~y 1γ !#%tan γ
~ !
conductivity of the aquifer. The accuracy with which any s n n
u y 5 (9)
~ !
2 2 2 2 2
n
y 2 11σ γ 2 y 1γ /σ γ
~ !
property can be determined depends on the location and length $ ~ ! %
n n n
of the well screen in observation wells and piezometers. Two
5. Significance and Use
methods of analysis, a type curve method and a semilogarith-
mic method, are described.
5.1 Assumptions:
5.1.1 The control well discharges at a constant rate, Q.
4.2 Solution—The solution given by Neuman (1) can be
5.1.2 The control well, observation wells, and piezometers
expressed as:
are of infinitesimal diameter.
`
Q `
1/2
5.1.3 The unconfined aquifer is homogeneous and really
s~r, z, t!5 * 4yJ ~yβ ! u ~y!1 u ~y! dy (1)
F G
0 0 ( n
4πT
n51
extensive.
5.1.4 Discharge from the control well is derived initially
where, for piezometers, Neuman’s (1) Eqs 27 and 28 are as
from elastic storage in the aquifer, and later from gravity
follows:
drainage from the water table.
2 2
$12exp$2t β~y 2γ !]%cosh~γ z !
s 0 0 D
u y 5 (2) 5.1.5 The geometry of the aquifer, control well, observation
~ !
0 2 2 2 2 2
y 1 11σ γ 2 y 2γ /σ cosh γ
$ ~ ! ~ ! % ~ !
0 0 0
wells,andpiezometersisshowninFig.2.Thegeometryofthe
sinh@γ ~12d !#2sinh@γ ~12l !#
0 D 0 D
·
~l 2d !sinh~γ !
D D 0
and:
2 2
$12exp@2t β~y 1γ !#%cos~γ z !
s n n D
u y 5 (3)
~ !
2 2 2 2 2
n
y 2 11σ γ 2 y 1γ /σ γ
$ ~ ! ~ ! %
n n n
sin γ 12d 2sin γ 12l
@ ~ !# @ ~ !#
n D n D
·
~l 2d !sin γ
~ !
D D n
and the terms γ and γ are the roots of the following
0 n
equations:
2 2
σγ sinh γ 2~y 2γ !cosh~γ !50 (4)
~ !
0 0 0 0
2 2
γ ,y
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
D5920−96 (2005)
test wells should be adjusted depending on the parameters of Table 1 and Table 2 may be used to prepare the type curves, as
interest. shown in Fig. 3. For piezometers, or tests in which the control
well or observation wells do not effectively penetrate the full
5.2 Implications of Assumptions:
thickness of the aquifer, the values of s corresponding to
D
5.2.1 Use of the Neuman (1) method assumes the control
values of t and t for a range of values ofβ must be computed
s y
wellisofinfinitesimaldiameter.Thestorageinthecontrolwell
using computer programs such as those of Dawson and Istok
may adversely affect drawdown measurements obtained in the
(2), or Moench (3) . The program requires that values for the
early part of the test. See 5.2.2 of Test Method D4106 for
dimensionlessparameters l and d besuppliedforthecontrol
D D
assistance in determining the duration of the effects of well-
well, and values of z be supplied for the piezometers, or that
D
bore storage on drawdown.
the values of z and z be supplied for observation wells.
1D 2D
5.2.2 If drawdown is large compared with the initial satu-
Onlydrawdownsforwhichthesedimensionlessparametersare
rated thickness of the aquifer, the late-time drawdown may
similar may be analyzed using the same family of type curves.
need to be adjusted for the effect of the reduction in saturated
Prepare as many data plots and families of type curves as
thickness. Section 5.2.3 of Test Method D4106 provides
necessary to analyze the test.
guidance in correcting for the reduction in saturated thickness.
8.1.1.2 Holding the axes parallel, overlay the data plot on
According to Neuman (1) such adjustments should be made
the type curves. Match as many of the early time-drawdown
only for late-time values.
data as possible to the left-most part of the type curve (TypeA
curves).Selectanearly-timematchpoint,andrecordthevalues
6. Apparatus
of s, t/r ,s and t .Movingthedataplothorizontally,matchas
D s
6.1 Analysis—Analysisofdatafromthefieldprocedure(see
many as possible of the late-time data to the right-most part of
Test Method D4050) by this test method requires that the
the type curves (Type B curves) and select a late-time match
control well and observation wells meet the requirements
point. Record the values of s, s , t/r , and t for this match
D y
specified in the following subsections.
point.Thevaluesofsands shouldbethesameforeachmatch
D
6.2 Construction of Control Well—Installthecontrolwellin
point, that is, the data curves should be shifted only horizon-
the aquifer, and equip with a pump capable of discharging
tally, not vertically, on the type curve, and the values of β for
water from the well at a constant rate for the duration of the
each observation well should be the same for early and late
test.
times.
8.1.1.3 Repeat the procedure in 8.1.1.2 for all additional
6.3 Construction of Observation Wells— Construct one or
dataplotsandtypecurves.Thevaluesof sand s shouldbethe
more observation wells or piezometers at a distance from the
D
same for all plots in a single test. If necessary, repeat the
control well. For this test method, observation wells may be
analysisforeachplotuntilaconsistentsetofvaluesisobtained
open through all or part of the thickness of the aquifer.
betweenallplots.Calculatethevalueofthetermβ/r forevery
6.4 Location of Observation Wells— Wells may be located
observation well or piezometer. Because the remaining terms
at any distance from the control well within the area of
in the definition of β, α/b , shou
...