ASTM D6029/D6029M-20

Standard Practice for (Analytical Procedures) Determining Hydraulic Properties of a Confined Aquifer and a Leaky Confining Bed with Negligible Storage by the Hantush-Jacob Method

SIGNIFICANCE AND USE
5.1 Assumptions:  
5.1.1 The control well discharges at a constant rate, Q.  
5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer.  
5.1.3 The aquifer is homogeneous, isotropic, and areally extensive.
Note 2: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer).  
5.1.5 The aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness. It is assumed that there is no change of water storage in this confining bed and that the hydraulic gradient across this bed changes instantaneously with a change in head in the aquifer. This confining bed is bounded on the distal side by a uniform head source where the head does not change with time.  
5.1.6 The other confining bed is impermeable.  
5.1.7 Leakage into the aquifer is vertical and proportional to the drawdown, and flow in the aquifer is strictly horizontal.  
5.1.8 Flow in the aquifer is two-dimensional and radial in the horizontal plane.  
5.2 The geometry of the well and aquifer system is shown in Fig. 1.  
5.3 Implications of Assumptions:  
5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Section 8.1 of Test Method D4050 discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could result in misinterpretation of the water-level change data unless taken into consideration.  
5.3.2 The leaky confining bed problem considered by the Hantush-Jacob solution requires that the control well has an infinitesimal diameter and has no storage. Abdul Khader and Ramadurgaiah (5) developed graphs of a solution for the drawdowns in a large-diameter control well discharging at a constant rate from an aquifer confined...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer and the leakance value of an overlying or underlying confining bed for the case where there is negligible change of water in storage in a confining bed. This practice is used to analyze water-level or head data collected from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate.  
1.2 This analytical procedure is used in conjunction with Test Method D4050.  
1.3 Limitations—The valid use of the Hantush-Jacob method is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (Practice D4106) with the exception that in this case the aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness, and in which the gain or loss of water in storage is assumed to be negligible, and that bed, in turn, is bounded on the distal side by a zone in which the head remains constant. The hydraulic conductivity of the other bed confining the aquifer is so small that it is assumed to be impermeable (see Fig. 1).
FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1)3). The Confining and Impermeable Bed Locations Can Be Interchanged  
1.4 Units—The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. Reporting of results in units other than SI shall not...

General Information

• Status: Published
• Publication Date: 31-May-2020
• ICS: 13.060.10 - Water of natural resources
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Refers: ASTM D3740-23 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Nov-2023
• Refers: ASTM D4050-20 - Standard Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of Aquifer Systems
• Effective Date: 01-Jan-2020
• Refers: ASTM D3740-19 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Oct-2019
• Refers: ASTM D4106-15 - Standard Test Method for (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined Aquifers by the Theis Nonequilibrium Method
• Effective Date: 15-Apr-2015
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2014
• Refers: ASTM D4050-14 - Standard Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of Aquifer Systems
• Effective Date: 01-Jun-2014
• Refers: ASTM D3740-12a - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-May-2012
• Refers: ASTM D3740-12 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Mar-2012
• Refers: ASTM D653-11 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Sep-2011
• Refers: ASTM D3740-11 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Sep-2011
• Refers: ASTM D3740-10 - Standard Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• Effective Date: 01-Mar-2010
• Refers: ASTM D653-09 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jan-2009
• Refers: ASTM D653-08a - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Dec-2008
• Refers: ASTM D653-08 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2008
• Refers: ASTM D4050-96(2008) - Standard Test Method for (Field Procedure) for Withdrawal and Injection Well Tests for Determining Hydraulic Properties of Aquifer Systems
• Effective Date: 15-Sep-2008

Overview

ASTM D6029/D6029M-20 - Standard Practice for Determining Hydraulic Properties of a Confined Aquifer and a Leaky Confining Bed with Negligible Storage by the Hantush-Jacob Method provides analytical procedures for evaluating groundwater resources. This ASTM standard is designed for determining the transmissivity and storage coefficient of confined aquifers, as well as the leakance value of overlying or underlying confining beds where water storage changes in the confining bed are negligible. Its implementation is critical for hydrogeological site assessments, aquifer test analysis, and sustainable groundwater management.

Key Topics

• Constant-Rate Pumping and Well Configuration: The practice assumes a control well of minimal diameter, fully penetrating the aquifer, operating at a constant discharge rate. The aquifer is expected to remain saturated throughout the test.
• Aquifer and Confining Bed Properties: The method applies specifically to homogeneous, isotropic, and extensive confined aquifers overlain or underlain by a uniform confining bed with negligible storage. The other confining bed (if present) is assumed impermeable.
• Hydraulic Test Data Analysis: Water-level or head data are collected from observation wells or piezometers during pumping or injection at the control well. Type curve analysis techniques are used to interpret drawdown and estimate hydraulic properties.
• Vertical Leakage and Hydrostatic Boundaries: Leakage into the aquifer is assumed vertical and proportional to drawdown, while horizontal flow dynamics within the aquifer are considered.
• Limitations and Assumptions: Accurate use relies on field conditions closely matching the standard’s assumptions, especially regarding the geological setting and hydraulic boundaries.

Applications

This standard is widely applicable in the groundwater industry for:

• Aquifer Test Analysis: Applied to constant-rate pumping or injection tests to evaluate characteristics like transmissivity, storage coefficient, and leakance of confining beds.
• Hydrogeologic Site Characterization: Used by hydrogeologists and environmental consultants for assessing groundwater supplies and predicting well performance in confined aquifer systems with leaky confining layers.
• Groundwater Management and Remediation: Provides essential data for water resource management, contamination investigations, and sustainability planning in regions dependent on confined aquifers.
• Regulatory and Engineering Support: Supports compliance with regulatory requirements and aids in engineering decisions related to groundwater extraction, recharge, or containment.

The method is most suitable for settings where field assumptions match those of the Hantush-Jacob method, and it is not appropriate in fractured rock or carbonate environments. Careful attention to test setup, calibration of monitoring instruments, and nuanced analysis of drawdown data are required for reliable results.

Related Standards

Professionals using ASTM D6029/D6029M-20 should also consult:

• ASTM D4050 - Field procedures for withdrawal and injection well testing for determining hydraulic properties of aquifer systems.
• ASTM D4106 - Analytical procedures for determining transmissivity and storage coefficient of non-leaky confined aquifers using the Theis nonequilibrium method.
• ASTM D6026 - Practice for using significant digits in geotechnical data.
• ASTM D6028 - Analytical procedure for determining hydraulic properties of confined aquifers considering storage in leaky confining beds by the modified Hantush method.
• ASTM D653 - Terminology relating to soil, rock, and contained fluids.

These standards provide foundational methods, terminology, and data handling practices essential for the correct application of the Hantush-Jacob method and for comprehensive groundwater analyses.

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Keywords: ASTM D6029, Hantush-Jacob method, confined aquifer testing, hydraulic properties, transmissivity, storage coefficient, leakance, leaky confining bed, groundwater analysis, observation well, aquifer test, hydrogeology standard.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation:D6029/D6029M −20
Standard Practice for
(Analytical Procedures) Determining Hydraulic Properties of
a Confined Aquifer and a Leaky Confining Bed with
Negligible Storage by the Hantush-Jacob Method
This standard is issued under the fixed designation D6029/D6029M; the number immediately following the designation indicates the
year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last
reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* formance with the standard. Reporting of results in units other
than SI shall not be regarded as nonconformance with this
1.1 This practice covers an analytical procedure for deter-
standard.
mining the transmissivity and storage coefficient of a confined
aquifer and the leakance value of an overlying or underlying
1.5 All observed and calculated values shall conform to the
confining bed for the case where there is negligible change of
guidelines for significant digits and round established in
water in storage in a confining bed. This practice is used to
Practice D6026, unless superseded by this standard.
analyze water-level or head data collected from one or more
1.5.1 Theproceduresusedtospecifyhowdataarecollected/
observation wells or piezometers during the pumping of water
recorded or calculated, in this standard are regarded as the
fromacontrolwellataconstantrate.Withappropriatechanges
industry standard. In addition, they are representative of the
in sign, this practice also can be used to analyze the effects of
significant digits that generally should be retained. The proce-
injecting water into a control well at a constant rate.
dures used do not consider material variation, purpose for
obtaining the data, special purpose studies, or any consider-
1.2 This analytical procedure is used in conjunction with
ations for the user’s objectives; and it is common practice to
Test Method D4050.
increase or reduce significant digits of reported date to be
1.3 Limitations—The valid use of the Hantush-Jacob
commensuratewiththeseconsiderations.Itisbeyondthescope
method is limited to the determination of hydraulic properties
of this standard to consider significant digits used in analysis
for aquifers in hydrogeologic settings with reasonable corre-
method for engineering design.
spondence to the assumptions of the Theis nonequilibrium
method (Practice D4106) with the exception that in this case
1.6 This practice offers a set of instructions for performing
theaquiferisoverlain,orunderlain,everywherebyaconfining
one or more specific operations.This document cannot replace
bed having a uniform hydraulic conductivity and thickness,
educationorexperienceandshouldbeusedinconjunctionwith
and in which the gain or loss of water in storage is assumed to
professional judgment. Not all aspects of the practice may be
be negligible, and that bed, in turn, is bounded on the distal
applicable in all circumstances. This ASTM standard is not
side by a zone in which the head remains constant. The
intended to represent or replace the standard of care by which
hydraulic conductivity of the other bed confining the aquifer is
the adequacy of a given professional service must be judged,
so small that it is assumed to be impermeable (see Fig. 1).
nor should this document be applied without the consideration
ofaproject’smanyuniqueaspects.Theword“Standard”inthe
1.4 Units—The values stated in either SI units or inch-
title of this document means only that the document has been
pound units are to be regarded separately as standard. The
approved through the ASTM consensus process.
values stated in each system may not be exact equivalents;
therefore,eachsystemshallbeusedindependentlyoftheother.
1.7 This standard does not purport to address all of the
Combining values from the two systems may result in noncon-
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
1 priate safety, health, and environmental practices and deter-
This practice is under the jurisdiction of ASTM Committee D18 on Soil and
mine the applicability of regulatory limitations prior to use.
Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and
Vadose Zone Investigations.
1.8 This international standard was developed in accor-
Current edition approved June 1, 2020. Published June 2020. Originally
dance with internationally recognized principles on standard-
approved in 1996. Last previous edition approved in 2017 as D6029–17. DOI:
ization established in the Decision on Principles for the
10.1520/D6029_D6029M-20.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6029/D6029M−20
FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1) ). The Confining and Impermeable Bed Locations
Can Be Interchanged
Development of International Standards, Guides and Recom- 3.2.1.1 Discussion—The use of the symbol K for the term
mendations issued by the World Trade Organization Technical hydraulic conductivity is the predominant usage in groundwa-
Barriers to Trade (TBT) Committee. ter literature by hydrogeologists, whereas the symbol k is
commonly used for this term in soil and rock mechanics and
2. Referenced Documents
soil science.
2.1 ASTM Standards:
3.2.2 K'—vertical hydraulic conductivity of the confining
−1
D653Terminology Relating to Soil, Rock, and Contained
bed through which leakage can occur [LT ].
Fluids
3.2.3 L(u,v)—leakance function of u,v [nd]; equal to W(u,r/
D3740Practice for Minimum Requirements for Agencies
B).
Engaged in Testing and/or Inspection of Soil and Rock as
3 −1
3.2.4 Q—discharge [L T ].
Used in Engineering Design and Construction
3.2.5 S=bS —storage coefficient [nd].
D4050Test Method for (Field Procedure) for Withdrawal
S
−1
and Injection Well Testing for Determining Hydraulic
3.2.6 S —specific storage of the aquifer [L ].
s
Properties of Aquifer Systems
−1
3.2.7 S' —specific storage of the confining bed [L ].
s
D4106Practice for (Analytical Procedure) for Determining
2 −1
3.2.8 T—transmissivity [L T ].
Transmissivity and Storage Coefficient of Nonleaky Con-
r S
fined Aquifers by the Theis Nonequilibrium Method
3.2.9 u5 nd .
@ #
4Tt
D6026Practice for Using Significant Digits in Geotechnical
Data
3.2.10 W(u,r/B)—well function for leaky aquifer systems
D6028/D6028MPractice for (Analytical Procedure) Deter- with negligible storage changes in confining beds [nd].
miningHydraulicPropertiesofaConfinedAquiferTaking
3.2.11 b—thickness of aquifer [L]. b'—thickness of the
into Consideration Storage of Water in Leaky Confining
confining bed through which leakage can occur [L].
Beds by Modified Hantush Method
3.2.12 r—radial distance from control well [L].
3. Terminology
3.2.13 r —radius of the control well casing, or hole if
c
uncased [L].
3.1 Definitions:
3.1.1 Fordefinitionsofcommontechnicaltermsusedinthis 3.2.14 s—drawdown [L].
standard, refer to Terminology D653.
r r K'
3.2.15 v5 5 Œ ,v—defined by Eq 7 [nd].
3.2 Symbols and Dimensions:
2B 2 Tb'
−1
3.2.1 K—hydraulic conductivity of the aquifer [LT ].
Tb'
3.2.16 L .
Π@ #
K'
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.2.17 t—time since pumping or injection began [T].
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
3.2.18 K (x)—zero-order modified Bessel function of the
Standards volume information, refer to the standard’s Document Summary page on 0
the ASTM website. second kind [nd].
D6029/D6029M−20
r
r K'S'
S
where W u, was called the well function for leaky
S D
3.2.19 β5
Œ
B
4b KS
S
systems. Hantush tabulated values of this function for a
r
4. Summary of Practice
practical range of the parameters u and .
B
4.1 This practice involves pumping a control well that is
4.2.3 Cooper (4) opted to express the Hantush-Jacob solu-
fully screened through the confined aquifer and measuring the
tion in the following form:
water-level response in one or more observation wells or
piezometers. The well is pumped at a constant rate. The
Q
s 5 L~u, v! (6)
water-level response in the aquifer is a function of the
4πT
transmissivity and storage coefficient of the aquifer and the
r
leakancecoefficientofaconfiningbed.Theotherconfiningbed
where Cooper’s v=Hantush’s
2B
is assumed to be impermeable. Alternatively, the practice can
or
be performed by injecting water at a constant rate into the
control well.Analysis of buildup of water level in response to r r
v 5 5 (7)
injection is similar to analysis of drawdown of the water level 2B
Tb'
Œ
in response to withdrawal in a confined aquifer. The water-
K'
level response data may be analyzed in two ways. The time
4.2.4 Cooper prepared two families of type curves. One set
variation of the water-level response in any one well can be
of Cooper’s curves allow the head changes as a function of
analyzed using one set of type curves, or the water-level
time at a fixed distance to be analyzed for the aquifer
responses measured at the same time but in observation wells
parameters, and the other set of curves allow the head changes
at different distances from the control well can be analyzed
at different distances at some fixed time to be analyzed.
using another set of type curves.
NOTE 1—The quality of the result produced by this standard is
5. Significance and Use
dependent on the competence of the personnel performing it, and the
suitability of the equipment and facilities used. Agencies that meet the
5.1 Assumptions:
criteria of Practice D3740 are generally considered capable of competent
5.1.1 The control well discharges at a constant rate, Q.
and objective testing/sampling/inspection/etc. Users of this standard are
5.1.2 The control well is of infinitesimal diameter and fully
cautioned that compliance with Practice D3740 does not in itself assure
reliable results. Reliable results depend on many factors; Practice D3740 penetrates the aquifer.
provides a means of evaluating some of those factors.
5.1.3 The aquifer is homogeneous, isotropic, and areally
4.2 Solution—Hantush and Jacob (2) give two mathemati- extensive.
cally equivalent expressions for the solution which can be
NOTE 2—Slug and pumping tests implicitly assume a porous medium.
written as follows:
Fractured rock and carbonate settings may not provide meaningful data
`
and information.
Q 1 r
s 5 exp 2z 2 dz (1)
* S D
5.1.4 Theaquiferremainssaturated(thatis,waterleveldoes
4πT z 4B z
u
not decline below the top of the aquifer).
where z is the variable of integration and
5.1.5 The aquifer is overlain, or underlain, everywhere by a
`
confining bed having a uniform hydraulic conductivity and
Q r 1 r
s 5 2K 2 exp 2z 2 dz (2)
S D * S D thickness.Itisassumedthatthereisnochangeofwaterstorage
4πT B z 4B z
F G
r
in this confining bed and that the hydraulic gradient across this
4B u
bed changes instantaneously with a change in head in the
where:
aquifer. This confining bed is bounded on the distal side by a
r S uniform head source where the head does not change with
u 5 (3)
4Tt time.
5.1.6 The other confining bed is impermeable.
Tb'
B 5 (4)
5.1.7 Leakageintotheaquiferisverticalandproportionalto
K'
the drawdown, and flow in the aquifer is strictly horizontal.
4.2.1 Because a closed-form expression of the integrals that
5.1.8 Flow in the aquifer is two-dimensional and radial in
appear in Eq 1 or Eq 2 are not known, Hantush and Jacob
the horizontal plane.
developed equivalent expressions that involve infinite series
5.2 Thegeometryofthewellandaquifersystemisshownin
that can be numerically evaluated. The infinite series for Eq 1
Fig. 1.
converges more rapidly for early times and the infinite series
for Eq 2 converges more rapidly for late times.
5.3 Implications of Assumptions:
4.2.2 Hantush (3) expressed Eq 1 and Eq 2 as follows:
5.3.1 Paragraph 5.1.1 indicates that the discharge from the
control well is at a constant rate. Section 8.1 of Test Method
Q r
s 5 W u, (5)
S D
D4050 discusses the variation from a strictly constant rate that
4πT B
isacceptable.Acontinuoustrendinthechangeofthedischarge
rate could result in misinterpretation of the water-level change
The boldface numbers in parentheses refer to a list of references at the end of
this practice. data unless taken into consideration.
D6029/D6029M−20
5.3.2 The leaky confining bed problem considered by the
Hantush-Jacob solution requires that the control well has an
infinitesimal diameter and has no storage. Abdul Khader and
Ramadurgaiah (5) developed graphs of a solution for the
drawdowns in a large-diameter control well discharging at a
constant rate from an aquifer confined by a leaky confining
bed. Fig. 2 (Fig. 3 of Abdul Khader and Ramadurgaiah (5))
gives a graph showing variation of dimensionless drawdown
with dimensionless time in the control well assuming the
−3
aquiferstoragecoefficient, S=10 ,andtheleakageparameter,
r
w
Note that at early dimensionless times the curve for a
B FIG. 3 Schematic Diagram of Two-Aquifer System
large-diameter well in a non-leaky aquifer (BCE) and in a
leaky aquifer (BCD) are coincident. At later dimensionless
Abdul Khader and Ramadurgaiah (5)present graphs of dimen-
times, the curve for a large diameter well in a leaky aquifer
sionless time versus dimensionless drawdown in a discharging
coalesces with the curve for an infinitesimal diameter well
−1 −2 −3 −4 −5
control well for values of S=10 ,10 ,10 ,10 , and 10
(ACD)inaleakyaquifer.Theycoalesceaboutonelogarithmic
−2 −3 −4 −5 −6
rw
and ⁄B=10 ,10 ,10 ,10 ,10 ,and0.Thesegraphscan
cycle of dimensionless time before the drawdown becomes
−3
be used in an analysis prior to the aquifer test making use of
sensibly constant. For a value of r /B smaller than 10 , the
w
estimatesofthehydraulicpropertiestoestimatethetimeperiod
constant drawdown (D) would occur at a greater value of
during which well-bore storage effects in the control well
dimensionless drawdown and there would be a longer period
probablywillmaskothereffectsandthedrawdownswouldnot
during which well-bore storage effects are negligible (the
fit the Hantush-Jacob solution.
period where ACD and BCD are coincident) before a steady
drawdown is reached.
5.3.2.1 The time needed for the effects of control-well bore
r
w
−3
storage to diminish enough that drawdowns in observation
For values of greater than 10 , the constant drawdown (D)
B
wellsshouldfittheHantush-Jacobsolutionislessclear.Butthe
would occur at a smaller value of drawdown and there would
time adopted for when drawdowns in the discharging control
be a shorter period of dimensionless time during which
well are no longer dominated by well-bore storage affects
well-storage effects are negligible (the period whereACD and
probably should be the minimum estimate of the time to adopt
BCD are coincident) before a steady drawdown is reached.
for observation well data.
5.3.3 The assumption that the aquifer is bounded, above or
below,byaleakylayerononesideandanonleakylayeronthe
other side is not likely to be entirely satisfied in the field.
Neuman and Witherspoon (6, p. 1285) have pointed out that
because the Hantush-Jacob formulation uses water-level
changedataonlyfromtheaquiferbeingpumped(orrecharged)
it can not be used to distinguish whether the leaking beds are
aboveorbelow(orfrombothsides)oftheaquifer.Hantush (7)
presentsarefinementthatallowstheparametersdeterminedby
the aquifer field test analysis to be interpreted as composite
parameters that reflect the combined effects of overlying and
underlying confined beds. Neuman and Witherspoon (6) de-
scribe a method to estimate the hydraulic properties of a
confining layer by using the head changes in that layer.
5.3.4 The Hantush-Jacob theoretical development requires
that the leakage into the aquifer is proportional to the
drawdown,andthatthedrawdowndoesnotvaryinthevertical
in the aquifer. These requirements are sometimes described by
statingthattheflowintheconfiningbedsisessentiallyvertical
and in the aquifer is essentially horizontal. Hantush’s (8)
analysisofanaquiferboundedonlybyoneleakyconfiningbed
suggested that this approximation is acceptably accurate wher-
ever
K b
.100 (8)
K' b'
5.3.5 The Hantush-Jacob method requires that there is no
change in water storage in the leaky confining bed. Weeks (9)
FIG. 2 Time—Drawdown Variation in the Control Well for
−3
S= δ=10 (from Abdul Khader and Ramadurgaiah (5)) states that if the “leaky” confining bed is thin and relatively
D6029/D6029M−20
permeable and incompressible, the solution of Hantush and the level of which does not change with time, was considered
Jacob (2) will apply, whereas the solution of Hantush (7), by Neuman and Witherspoon (11, p. 810). They considered a
which is described in Practice D6028/D6028M, that considers confined system of two aquifers separated by a confining bed
storage in confining beds will apply in most cases if one asshownschematicallyinFig.3.Theiranalysisconcludedthat
confining bed is thick, of low permeability, and highly com- the drawdowns in an aquifer in response to discharging from a
pressible. For the case where one layer confining the aquifer is well in that aquifer would not be affected by the properties of
sensiblyimpermeable,andtheotherconfiningbedisleakyand the other, unpumped, aquifer for times that satisfy
bounded on the distal side by a layer in which the head is 2
S' b'
s
t# 0.1 (16)
constantitfollowsfromHantush (7)thatwhentime, t,satisfies
K'
5 b' S'
~ !
s
t. (9)
6. Apparatus
K'
6.1 Analysis of data from the field procedure (see Test
the drawdowns in the aquifer will be described by the
Method D4050) by this practice requires that the control well
equation
and observation wells meet the requirements specified in the
Q K' following paragraphs.
s 5 WS uδ, r D (10)
Œ
4πT Tb'
6.2 Construction of Control Well—Installthecontrolwellin
theaquiferandequipwithapumpcapableofdischargingwater
where
fromthewellataconstantrateforthedurationofthefieldtest.
S'
Preferably, the control well should be open throughout the full
δ 5 11 (11)
3S
thickness of the aquifer. If the control well partially penetrates
the aquifer, take special precaution in the placement or design
Note that in Hantush’s (7) solution, the term
of observation wells.
2 2
S' r S S' r S'
uδ 5 u 11 5 11 5 S1 (12)
S D S D S D
6.3 Construction and Location of Observation Wells and
3S 4Tt 3S 4Tt 3
Piezometers—Construct one or more observation wells or
appearsinsteadoftheexpressiongivenfor uinEq3,namely
piezometers screened only in the pumped aquifer at a distance
from the control well. Observation wells may be open through
r S
u 5 (13)
all or part of the thickness of the aquifer. Hantush (12, p. 350)
4Tt
indicates that the effects of a partially penetrating control well
The implication being from Hantush (7) that after the time
can be neglected for
criterion given by Eq 9 is satisfied, the apparent storage
coefficient of the aquifer will include the aquifer storage K
r
r.1.5bΠ(17)
coefficient and one third of the storage coefficient for the
K
z
confining bed. If the storage coefficient of the confining bed is
where K and K are the aquifer hydraulic conductivities in
r z
very much less than that of the aquifer, then the effect of
the horizontal and vertical directions, respectively. If an
storage in the confining bed will be very small or sensibly nil.
observation well fully penetrates the aquifer, its drawdown is
To illustrate the use of Hantush’s time criterion, suppose a
not affected by a partially penetrating control well and it reacts
confining bed is characterized by b'=3m, K'=0.001 m/day,
−6 −1 as if the control well completely penetrated the aquifer
and S' =3.6×10 m , then the Hantush-Jacob solution Eq
s
(Hantush, 12, p. 351).
10 would apply everywhere when
2 2 26 21
5~b'! S' 5~3m! ~3.6 310 m !
s 7. Procedure
t. 5 (14)
K' 0.001 m/day
~ !
7.1 Field pretest preparations are described in detail in Test
Method D4050.The overall process consists of (1) conducting
or
the field procedure for withdrawal or injection well tests
t.0.162 day 5 233min (15)
(described in Test Method D4050) and (2) analysis of the field
data, which is addressed in Section 8.
If the vertical hydraulic conductivity of the confining bed
was an order of magnitude larger, K'=0.01 m/day, then the
8. Calculation and Interpretation of Test Data
Hantush-Jacob (2) solution would apply when t > 23 min.
5.3.5.1 It should be noted that the Hantush (7) analysis
8.1 Aquifer field-test data may be plotted in two ways
assumes that well bore storage is negligible.
(Cooper (4), p. C51). Cooper (4) prepared two families of type
5.3.5.2 Moench (10) presents numerical results that give
curves that are plots of L(u,v) versus 1/u. Fig. 4 is a plot of a
insight into the effects of control well storage and changes in
family of solid-type curves involving the parameter v (recall
storage in the confining bed on drawdowns in the aquifer for
r K'
Eq7, v5 ) thatareusefulforaplotofdrawdownversus
Œ
various parameter values. However, Moench does not offer an
2 Tb'
explicit formula for when those effects diminish enough for
time at some constant distance, r. For the other family of type
subsequent drawdown data to fit the Hantush-Jacob solution.
curves, v /u (this is equal to K't/Sb') there is the parameter for
5.3.6 The assumption stated in 5.1.5, that the leaky confin- which type curves having different values are plotted (see Fig.
ingbedisboundedontheothersidebyauniformheadsource, 4, the dashed-line curves are the v /u curves).These curves are
D6029/D6029M−20
FIG. 4Type Curve of L(u,v) versus 1/u (from Cooper (4)). The type curves for the region v# 1.2 are based on data computed by H. H.
Cooper, Jr., and Yvonne Clarke of the U.S. Geological Survey; th
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: D6029 − 17 D6029/D6029M − 20
Standard Test Method (Analytical Procedure) Practice for
(Analytical Procedures) Determining Hydraulic Properties of
a Confined Aquifer and a Leaky Confining Bed with
Negligible Storage by the Hantush-Jacob Method
This standard is issued under the fixed designation D6029;D6029/D6029M; the number immediately following the designation indicates
the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last
reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This test method covers an analytical procedure for determining the transmissivity and storage coefficient of a confined
aquifer and the leakance value of an overlying or underlying confining bed for the case where there is negligible change of water
in storage in a confining bed. This test method is used to analyze water-level or head data collected from one or more observation
wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this
test method also can be used to analyze the effects of injecting water into a control well at a constant rate.
1.2 This analytical procedure is used in conjunction with Test Method D4050.
1.3 Limitations—The valid use of the Hantush-Jacob method is limited to the determination of hydraulic properties for aquifers
in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (Test Method
D4106) with the exception that in this case the aquifer is overlain, or underlain, everywhere by a confining bed having a uniform
hydraulic conductivity and thickness, and in which the gain or loss of water in storage is assumed to be negligible, and that bed,
in turn, is bounded on the distal side by a zone in which the head remains constant. The hydraulic conductivity of the other bed
confining the aquifer is so small that it is assumed to be impermeable (see Fig. 1).
1.4 The values stated in SI units are to be regarded as standard. The values given in parentheses are mathematical conversions
to inch-pound units, which are provided for information only and are not considered standard.
1.4.1 The converted inch-pound units use the gravitational system of units. In this system, the pound (lbf) represents a unit of
force (weight), while the unit for mass is slugs. The converted slug unit is not given, unless dynamic (F = ma) calculations are
involved.
1.5 All observed and calculated values shall conform to the guidelines for significant digits and round established in Practice
D6026, unless superseded by this standard.
1.5.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industry
standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not
consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objectives;
and it is common practice to increase or reduce significant digits of reported date to be commensurate with these considerations.
It is beyond the scope of this standard to consider significant digits used in analysis method for engineering design.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in
Engineering Design and Construction
This test method practice is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater
and Vadose Zone Investigations.
Current edition approved Jan. 1, 2017June 1, 2020. Published January 2017June 2020. Originally approved in 1996. Last previous edition approved in 20102017 as
ɛ1
D6029–96(2010)D6029 .–17. DOI: 10.1520/D6029-17.10.1520/D6029_D6029M-20.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6029/D6029M − 20
FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1) ). The Confining and Impermeable Bed Locations
Can Be Interchanged
D4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of
Aquifer Systems
D4106 Practice for (Analytical Procedure) for Determining Transmissivity and Storage Coefficient of Nonleaky Confined
Aquifers by the Theis Nonequilibrium Method
D6026 Practice for Using Significant Digits in Geotechnical Data
D6028 Practice for (Analytical Procedure) Determining Hydraulic Properties of a Confined Aquifer Taking into Consideration
Storage of Water in Leaky Confining Beds by Modified Hantush Method
3. Terminology
3.1 Definitions:
3.1.1 For definitions of common terms used in this test method, see Terminology D653.
3.2 Symbols and Dimensions:
−1
3.2.1 K—hydraulic conductivity of the aquifer [LT ].
3.2.1.1 Discussion—
The use of the symbol K for the term hydraulic conductivity is the predominant usage in groundwater literature by hydrogeologists,
whereas the symbol k is commonly used for this term in soil and rock mechanics and soil science.
−1
3.2.2 K'—vertical hydraulic conductivity of the confining bed through which leakage can occur [LT ].
3.2.3 L(u,v)—leakance function of u,v [nd]; equal to W(u,r/B).
3 −1
3.2.4 Q—discharge [L T ].
3.2.5 S = bS —storage coefficient [nd].
S
−1
3.2.6 S —specific storage of the aquifer [L ].
s
−1
3.2.7 S' —specific storage of the confining bed [L ].
s
2 −1
3.2.8 T—transmissivity [L T ].
r S
3.2.9 u5 @nd#.
4Tt
3.2.10 W(u,r/B)—well function for leaky aquifer systems with negligible storage changes in confining beds [nd].
3.2.11 b—thickness of aquifer [L]. b'—thickness of the confining bed through which leakage can occur [L].
3.2.12 r—radial distance from control well [L].
3.2.13 r —radius of the control well casing, or hole if uncased [L].
c
D6029/D6029M − 20
3.2.14 s—drawdown [L].
r r K'
3.2.15 v5 5 ,v—defined by Eq 7 [nd].
Œ
2B 2 Tb'
Tb'
3.2.16 Π@ L#.
K'
3.2.17 t—time since pumping or injection began [T].
3.2.18 K (x)—zero-order modified Bessel function of the second kind [nd].
r K'S'
S
3.2.19 β5
Œ
4b KS
S
4. Summary of Test Method
4.1 This test method involves pumping a control well that is fully screened through the confined aquifer and measuring the
water-level response in one or more observation wells or piezometers. The well is pumped at a constant rate. The water-level
response in the aquifer is a function of the transmissivity and storage coefficient of the aquifer and the leakance coefficient of a
confining bed. The other confining bed is assumed to be impermeable. Alternatively, the test method can be performed by injecting
water at a constant rate into the control well. Analysis of buildup of water level in response to injection is similar to analysis of
drawdown of the water level in response to withdrawal in a confined aquifer. The water-level response data may be analyzed in
two ways. The time variation of the water-level response in any one well can be analyzed using one set of type curves, or the
water-level responses measured at the same time but in observation wells at different distances from the control well can be
analyzed using another set of type curves.
NOTE 1—The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of the
equipment and facilities used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objective
testing/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself assure reliable results. Reliable
results depend on many factors; Practice D3740 provides a means of evaluating some of those factors.
4.2 Solution—Hantush and Jacob (2) give two mathematically equivalent expressions for the solution which can be written as
follows:
`
Q 1 r
s 5 exp 2z 2 dz (1)
* S D
4πT z 4B z
u
where z is the variable of integration and
`
Q r 1 r
s 5 2K 2 exp 2z 2 dz (2)
S D * S D
0 2
4πT B z 4B z
F 2 G
r
4B u
where:
r S
u 5 (3)
4Tt
Tb'
B 5 (4)
K'
4.2.1 Because a closed-form expression of the integrals that appear in Eq 1 or Eq 2 are not known, Hantush and Jacob developed
equivalent expressions that involve infinite series that can be numerically evaluated. The infinite series for Eq 1 converges more
rapidly for early times and the infinite series for Eq 2 converges more rapidly for late times.
4.2.2 Hantush (3) expressed Eq 1 and Eq 2 as follows:
Q r
s 5 W u, (5)
S D
4πT B
r
where W u, was called the well function for leaky systems. Hantush tabulated values of this function for a practical range
S D
B
r
of the parameters u and .
B
4.2.3 Cooper (4) opted to express the Hantush-Jacob solution in the following form:
Q
s 5 L~u, v! (6)
4πT
The boldface numbers in parentheses refer to a list of references at the end of this test method.practice.
D6029/D6029M − 20
r
where Cooper’s v = Hantush’s
2B
or
r r
v 5 5 (7)
2B
Tb'
2Œ
K'
4.2.4 Cooper prepared two families of type curves. One set of Cooper’s curves allow the head changes as a function of time
at a fixed distance to be analyzed for the aquifer parameters, and the other set of curves allow the head changes at different
distances at some fixed time to be analyzed.
5. Significance and Use
5.1 Assumptions:
5.1.1 The control well discharges at a constant rate, Q.
5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer.
5.1.3 The aquifer is homogeneous, isotropic, and areally extensive.
5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer).
5.1.5 The aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and
thickness. It is assumed that there is no change of water storage in this confining bed and that the hydraulic gradient across this
bed changes instantaneously with a change in head in the aquifer. This confining bed is bounded on the distal side by a uniform
head source where the head does not change with time.
5.1.6 The other confining bed is impermeable.
5.1.7 Leakage into the aquifer is vertical and proportional to the drawdown, and flow in the aquifer is strictly horizontal.
5.1.8 Flow in the aquifer is two-dimensional and radial in the horizontal plane.
5.2 The geometry of the well and aquifer system is shown in Fig. 1.
5.3 Implications of Assumptions:
5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Section 8.1 of Test Method D4050
discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could
result in misinterpretation of the water-level change data unless taken into consideration.
5.3.2 The leaky confining bed problem considered by the Hantush-Jacob solution requires that the control well has an
infinitesimal diameter and has no storage. Abdul Khader and Ramadurgaiah (5) developed graphs of a solution for the drawdowns
in a large-diameter control well discharging at a constant rate from an aquifer confined by a leaky confining bed. Fig. 2 (Fig. 3
of Abdul Khader and Ramadurgaiah (5)) gives a graph showing variation of dimensionless drawdown with dimensionless time in
r
w
−3
the control well assuming the aquifer storage coefficient, S = 10 , and the leakage parameter, Note that at early dimensionless
B
times the curve for a large-diameter well in a non-leaky aquifer (BCE) and in a leaky aquifer (BCD) are coincident. At later
dimensionless times, the curve for a large diameter well in a leaky aquifer coalesces with the curve for an infinitesimal diameter
well (ACD) in a leaky aquifer. They coalesce about one logarithmic cycle of dimensionless time before the drawdown becomes
−3
sensibly constant. For a value of r /B smaller than 10 , the constant drawdown (D) would occur at a greater value of
w
dimensionless drawdown and there would be a longer period during which well-bore storage effects are negligible (the period
where ACD and BCD are coincident) before a steady drawdown is reached.
r
w
−3
For values of greater than 10 , the constant drawdown (D) would occur at a smaller value of drawdown and there would be
B
a shorter period of dimensionless time during which well-storage effects are negligible (the period where ACD and BCD are
coincident) before a steady drawdown is reached. Abdul Khader and Ramadurgaiah (5)present graphs of dimensionless time versus
−1 −2 −3 −4 −5 −2 −3 −4
rw
dimensionless drawdown in a discharging control well for values of S = 10 , 10 , 10 , 10 , and 10 and ⁄B = 10 , 10 , 10 ,
−5 −6
10 , 10 , and 0. These graphs can be used in an analysis prior to the aquifer test making use of estimates of the hydraulic
properties to estimate the time period during which well-bore storage effects in the control well probably will mask other effects
and the drawdowns would not fit the Hantush-Jacob solution.
5.3.2.1 The time needed for the effects of control-well bore storage to diminish enough that drawdowns in observation wells
should fit the Hantush-Jacob solution is less clear. But the time adopted for when drawdowns in the discharging control well are
no longer dominated by well-bore storage affects probably should be the minimum estimate of the time to adopt for observation
well data.
5.3.3 The assumption that the aquifer is bounded, above or below, by a leaky layer on one side and a nonleaky layer on the other
side is not likely to be entirely satisfied in the field. Neuman and Witherspoon (6, p. 1285) have pointed out that because the
Hantush-Jacob formulation uses water-level change data only from the aquifer being pumped (or recharged) it can not be used to
distinguish whether the leaking beds are above or below (or from both sides) of the aquifer. Hantush (7) presents a refinement that
allows the parameters determined by the aquifer test analysis to be interpreted as composite parameters that reflect the combined
D6029/D6029M − 20
−3
FIG. 2 Time—Drawdown Variation in the Control Well for S = δ = 10 (from Abdul Khader and Ramadurgaiah (5))
FIG. 3 Schematic Diagram of Two-Aquifer System
effects of overlying and underlying confined beds. Neuman and Witherspoon (6) describe a method to estimate the hydraulic
properties of a confining layer by using the head changes in that layer.
5.3.4 The Hantush-Jacob theoretical development requires that the leakage into the aquifer is proportional to the drawdown, and
that the drawdown does not vary in the vertical in the aquifer. These requirements are sometimes described by stating that the flow
in the confining beds is essentially vertical and in the aquifer is essentially horizontal. Hantush’s (8) analysis of an aquifer bounded
only by one leaky confining bed suggested that this approximation is acceptably accurate wherever
K b
.100 (8)
K' b'
5.3.5 The Hantush-Jacob method requires that there is no change in water storage in the leaky confining bed. Weeks (9) states
that if the “leaky” confining bed is thin and relatively permeable and incompressible, the solution of Hantush and Jacob (2) will
apply, whereas the solution of Hantush (7), which is described in Test Method D6028, that considers storage in confining beds will
apply in most cases if one confining bed is thick, of low permeability, and highly compressible. For the case where one layer
confining the aquifer is sensibly impermeable, and the other confining bed is leaky and bounded on the distal side by a layer in
which the head is constant it follows from Hantush (7) that when time, t, satisfies
5~b'! S'
s
t. (9)
K'
D6029/D6029M − 20
the drawdowns in the aquifer will be described by the equation
Q K'
s 5 WS uδ, rŒ D (10)
4πT Tb'
where
S'
δ5 11 (11)
3S
Note that in Hantush’s (7) solution, the term
2 2
S' r S S' r S'
uδ5 u 11 5 11 5 S1 (12)
S D S D S D
3S 4Tt 3S 4Tt 3
appears instead of the expression given for u in Eq 3, namely
r S
u 5 (13)
4Tt
The implication being from Hantush (7) that after the time criterion given by Eq 9 is satisfied, the apparent storage coefficient
of the aquifer will include the aquifer storage coefficient and one third of the storage coefficient for the confining bed. If the storage
coefficient of the confining bed is very much less than that of the aquifer, then the effect of storage in the confining bed will be
very small or sensibly nil. To illustrate the use of Hantush’s time criterion, suppose a confining bed is characterized by b' = 3 m,
−6 −1
K' = 0.001 m/day, and S' = 3.6 × 10 m , then the Hantush-Jacob solution Eq 10 would apply everywhere when
s
2 2 26 21
5~b'! S' 5~3 m! ~3.6 310 m !
s
t. 5 (14)
K' 0.001 m/day
~ !
or
t.0.162 day 5 233min (15)
If the vertical hydraulic conductivity of the confining bed was an order of magnitude larger, K' = 0.01 m/day, then the
Hantush-Jacob (2) solution would apply when t > 23 min.
5.3.5.1 It should be noted that the Hantush (7) analysis assumes that well bore storage is negligible.
5.3.5.2 Moench (10) presents numerical results that give insight into the effects of control well storage and changes in storage
in the confining bed on drawdowns in the aquifer for various parameter values. However, Moench does not offer an explicit
formula for when those effects diminish enough for subsequent drawdown data to fit the Hantush-Jacob solution.
5.3.6 The assumption stated in 5.1.5, that the leaky confining bed is bounded on the other side by a uniform head source, the
level of which does not change with time, was considered by Neuman and Witherspoon (11, p. 810). They considered a confined
system of two aquifers separated by a confining bed as shown schematically in Fig. 3. Their analysis concluded that the drawdowns
in an aquifer in response to discharging from a well in that aquifer would not be affected by the properties of the other, unpumped,
aquifer for times that satisfy
S' b'
s
t # 0.1 (16)
K'
6. Apparatus
6.1 Analysis of data from the field procedure (see Test Method D4050) by this test method requires that the control well and
observation wells meet the requirements specified in the following paragraphs.
6.2 Construction of Control Well—Install the control well in the aquifer and equip with a pump capable of discharging water
from the well at a constant rate for the duration of the test. Preferably, the control well should be open throughout the full thickness
of the aquifer. If the control well partially penetrates the aquifer, take special precaution in the placement or design of observation
wells.
6.3 Construction and Location of Observation Wells and Piezometers—Construct one or more observation wells or piezometers
screened only in the pumped aquifer at a distance from the control well. Observation wells may be open through all or part of the
thickness of the aquifer. Hantush (12, p. 350) indicates that the effects of a partially penetrating control well can be neglected for
K
r
r.1.5bΠ(17)
K
z
where K and K are the aquifer hydraulic conductivities in the horizontal and vertical directions, respectively. If an observation
r z
well fully penetrates the aquifer, its drawdown is not affected by a partially penetrating control well and it reacts as if the control
well completely penetrated the aquifer (Hantush, 12, p. 351).
D6029/D6029M − 20
7. Procedure
7.1 Pretest preparations are described in detail in Test Method D4050. The overall test procedure consists of (1) conducting the
field procedure for withdrawal or injection well tests (described in Test Method D4050) and (2) analysis of the field data, which
is addressed in Section 8.
8. Calculation and Interpretation of Test Data
8.1 Aquifer-test data may be plotted in two ways (Cooper (4), p. C51). Cooper (4) prepared two families of type curves that
are plots of L(u,v) versus 1/u.Fig. 4 is a plot of a family of solid-type curves involving the parameter v (recall
r K'
Eq 7, v5 ) that are useful for a plot of drawdown versus time at some constant distance, r. For the other family of type
Œ
2 Tb'
curves, v /u (this is equal to K't/Sb') there is the parameter for which type curves having different values are plotted (see Fig. 4,
2 2
the dashed-line curves are the v /u curves). These curves are useful for a plot of drawdown versus 1/r at some constant time, t.
Note that the parent curve of both families of curves is the Theis nonequilibrium type curve that corresponds to a nonleaky confined
aquifer. Either family of type curves can be used to compute values of T, S, and K'/b'.
8.2 Except for a change in the notation used for the leakage coefficient, change of the equation numbers, and deletion of a small
amount of text, the following description of the method of use of type curves is taken directly from Cooper (4, p. C51–C53).
r K'
8.2.1 To compute T, S, and K'/b' by use of the v5 Πcurves (solid-line type curves on Fig. 4), proceed as follows:
2 Tb'
8.2.1.1 Plot s versus t/r for each observation well on logarithmic graph paper having the same scale as the graph of the type
curves.
8.2.1.2 Superpose this time-drawdown plot on the v curves and, keeping the coordinate axes of the two graphs parallel, translate
the data plot to the position where the earliest data approach the limiting curve labeled W(u) and the remaining data for each well
fall either between one pair of the curves labeled v = 2.2, v = 2.0, and so forth, or along one of them.
8.2.1.3 Select a convenient match point and note its coordinates (s, t/r , L(u,v), and 1/u).
8.2.1.4 Determine the value of v that corresponds to the value of r for each observation well. If the later data do not lie along
one of the v-curves, estimate the value of v by interpolation.
8.2.1.5 Compute the hydraulic constants of the aquifer by making appropriate substitutions in the following equations:
Q L u,v
~ !
T 5 (18)
4π s
~t/r !
S 5 4T (19)
1/u
and
FIG. 4 Type Curve of L(u,v) versus 1/u (from Cooper (4)). The type curves for the region v # 1.2 are based on data computed by H. H.
Cooper, Jr., and Yvonne Clarke of the U.S. Geological Survey; those for the regionv$ 1.4 are based on data graphically interpolated
from a table computed by Hantush ((3), p. 707–711)
D6029/D6029M − 20
K' v
5 4T (20)
b' r
v
8.2.2 To compute T, S, and K'/b' by use of curves (the dashed-line type curves on Fig. 4), proceed as follows:
u
8.2.2.1 Plot values of s, each from a different observation well but for identical values of t, versus t/r on logarithmic graph
paper having the same scale as the graph of the type curves.
8.2.2.2 Superpose this distance-drawdown plot on the v /u type curves and, keeping the coordinate axes of the two graphs
parallel, translate the data plot to the position where the data fall between one pair of the type curves or along one of them.
8.2.2.3 Select a convenient match point and note its coordinates (s, t/r ,L(u,v), and 1/u).
8.2.2.4 Determine the value of v /u that corresponds to the value of t at which the drawdowns occurred. If the data do not lie
along one of the type curves, estimate the value of v /u by interpolation.
8.2.2.5 Compute the values of T and S from Eq 17 and Eq 18. If the value is to be expressed in units consistent with those for
T and S in Eq 17 and Eq 18, use
K' v /u
5 S (21)
b' t
2 2 −2
If, when superposed on the v /u (dashed-line) type curves, the plotted data fall in the region v /u≥ 8 and L(u,v) ≥ 10 , steady
state conditions have been reached and the method of analysis suggested by Jacob (13) and described by Ferris et al (14, p.
112–115) is applicable.
8.2.3 Type curves of the Hantush-Jacob solution in the form developed by Cooper are available in numerous publications at
scales convenient for matching against data plots. Some available sources of those type curves are Cooper (4), Lohman (15), and
Reed (1). Cooper (4) illustrates the type curve procedure using hypothetical field data involving drawdowns at selected times for
observation points at three different distances from a control well (see Note 4).
8.2.3.1 A procedure for analyzing data for steady-state conditions is described in 8.3.
8.2.3.2 Table 1 gives a tabulation of selected values of W(u, r/B). If a set of type curves are not available these data can be used
to develop a type curve plot. More detailed tabulations of the Hantush-Jacob solution are available from Hantush (3,12), and
Walton (16).
TABLE 1 Values of W(u,r/B)for Selected Values ofuandr/B(from Hantush(12))
r/B
u
0.001 0.003 0.01 0.03 0.1 0.3 1 3
−6
1 × 10 13.0031 11.8153 9.4425 7.2471 4.8541 2.7449 0.8420 0.0695
2 12.4240 11.6716
3 12.0581 11.5098 9.4425
5 11.5795 11.2248 9.4413
7 11.2570 10.9951 9.4361
−5
1 × 10 10.9109 10.7228 9.4176
2 10.2301 10.1332 9.2961 7.2471
3 9.6288 9.7635 9.1499 7.2470
5 9.3213 9.2618 8.8827 7.2450
7 8.9863 8.9580 8.6625 7.2371
−4
1 × 10 8.6308 8.6109 8.3983 7.2122
2 7.9390 7.9290 7.8192 7.0685
3 7.5340 7.5274 7.4534 6.9068 4.8541
5 7.0237 7.0197 6.9750 6.6219 4.8530
7 6.6876 6.6848 6.6527 6.3923 4.8478
−3
1 × 10 6.3313 6.3293 6.3069 6.1202 4.8292
2 5.6393 5.6383 5.6271 5.5314 4.7079 2.7449
3 5.2348 5.2342 5.2267 5.1627 4.5622 2.7448
5 4.7260 4.7256 4.7212 4.6829 4.2960 2.7428
7 4.3916 4.3913 4.3882 4.3609 4.0771 2.7350
−2
1 × 10 4.0379 4.0377 4.0356 4.0167 3.8150 2.7104
2 3.3547 3.3546 3.3536 3.3444 3.2442 2.5688
3 2.9591 2.9590 2.9584 2.9523 2.8873 2.4110 0.8420
5 2.4679 2.4679 2.4675 2.4642 2.4271 2.1371 0.8409
7 2.1508 2.1508 2.1506 2.1483 2.1232 1.9206 0.8360
−1
1 × 10 1.8229 1.8229 1.8227 1.8213 1.8050 1.6704 0.8190
2 1.2226 1.2226 1.2226 1.2220 1.2155 1.1602 0.7148 0.0695
3 0.9057 0.9057 0.9056 0.9053 0.9018 0.8713 0.6010 0.0694
5 0.5598 0.5598 0.5598 0.5596 0.5581 0.5453 0.4210 0.0681
7 0.3738 0.3738 0.3738 0.3737 0.3729 0.3663 0.2996 0.0639
1 × 10 0.2194 0.2194 0.2194 0.2193 0.2190 0.2161 0.1855 0.0534
2 0.0489 0.0489 0.0489 0.0489 0.0488 0.0485 0.0444 0.0210
3 0.0130 0.0130 0.0130 0.0130 0.0130 0.0130 0.0122 0.0071
5 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0011 0.0008
7 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001
D6029/D6029M − 20
NOTE 2—Commercial software is available to calculate and plot these values and curve.
8.2.3.3 Because the v curves represent different values of r/B, there is an advantage to having more than one observation well
and for such wells to be at different distances from the control well so that a composite data-matching process can be used. Weeks
(9) states of a composite data-curve matching process that:
Such a match should be made when data from more than one
observation well are available, and single values of
transmissivity, storage coefficient, and other hydraulic properties
are to be determined from that match. The ability or lack thereof
of the data from observation wells at different distances to fit
type curves having proportional distance-based parameters, will
do much to confirm or deny the validity of the selected type-
curve model. Moreover, the time-drawdown plot for a given
observation well is affected by many extraneous factors, such as
storage and inertial effects in the observation well, deviations of
natural water-level fluctuations from those predicted from the
pretest trend, barometric or loading effects on the water levels,
and effects of local aquifer heterogeneity. Because most type-
curve families include curves exhibiting a wide range of shapes,
the chance of fortuitously fitting one of them is high when data
for only a single well are matched. Thus, the composite data-
curve matching process is useful both in confirming the validity
of the selected model and in screening the data for extraneous
effects.
NOTE 3—Spane and Wurstner (17) discussed the advantage of supplementing the type-curve plots of drawdown versus time by plots of the derivative
of drawdown (with respect to an appropriate time function) versus time as an aide in selecting an aquifer interpretation model and in estimating the aquifer
parameters. To apply the derivative methods requires that measurements be spaced closely enough that numerically developed time derivatives can be
reasonably approximated.
8.2.4 Cooper (4) expressed some reservations about the use of this test method to determine values of the leakance, K'/b', for
confining beds other than those that are sufficiently thin and for which the confining bed diffusivity K'/S' is sufficiently large. He
s
noted that for confining beds that have a relatively large specific storage, much of the water yielded to the aquifer for a certain
period of time would be derived from storage in the confining bed. For these reasons, the values of leakance obtained by this test
method should be scrutinized considering independent geologic and hydrologic information.
NOTE 4—Following is an application of the type-curve method that Cooper (4) presented using “postulated” measurements of water-level drawdowns
in observation wells at 100, 500, and 1000 ft from a well being pumped at a constant rate of 1000 gal/min for 1000 min. The aquifer in which the pumped
well is screened is confined by a thin bed of materials whose lithologic character suggests that its ability to transmit water vertically through it may be
an important factor that should be estimated. Fig. 5 is a log-log plot of the postulated drawdown data for each observation well plotted against values
of t/r . Cooper’s hypothetical “data” plot is superposed on a plot of the type curves (see Fig. 4) of L(u,v) versus 1/u.
8.2.4.1 For convenience, a match point is selected on the type-curve plot where L(u,v) = 1.0 and 1/u = 1.0. For that choice, the
2 −9 2
corresponding point on the data plot gives s = 1.15 ft and t/r of 1.87 × 10 (day/ft ). Substitution of those values into Eq 17 and
Eq 18 is as follows:
2 2
FIG. 5 Data Plot of Drawdown sversus Corresponding Values oft/r (time/distance ) Superposed on the Type Curves Plot ofL(u,v) ver-
sus 1/u
D6029/D6029M − 20
Q L u,v
~ !
T 5
4π s
1000 gal/min 3~1440min/day!
4π37.48 gal/ft
~ !
1.0
1.15 ft
5 13 320 ft /day (22)
and
2 2 29 2
t/r 4 13 320 ft /day 1.87 310 day/ft
~ ! ~ ! ~ !
S 5 4T 5 5 0.0001 (23)
1/u 1.0
For the match position selected, Cooper estimated that the v curves that best fit the drawdown data are v = 0.025 for Observation
Well 1 (r = 100 ft), v = 0.125 for Observation Well 2 (r = 500 ft), and v = 0.25 for Observation Well 3 (r = 1000 ft).
Considering the data at Observation Well 1, using Eq 19 the following is obtained:
2 2
K' v 0.025
~ !
2 23 21
5 4T 5 4~13 320 ft /day! 5 3.3~10 ! day (24)
2 2
b' r ~100 ft!
The same value for K'/b' would be calculated for Observation Wells 2 and 3 because note that the ratios of v/r for Observation
Wells 1, 2, and 3 turn out to be
v 0.025
5 5 0.00025 ft (25)
r 100 ft
v 0.125
5 5 0.00025 ft
r 500 ft
v 0.25
5 5 0.00025 ft
r 1000 ft
respectively. This exact agreement reflects that the data used for the illustration are hypothetical and idealized. That the ratio of
the v’s selected for the observation wells are in the same proportion as the distances to the observation wells is a desirable property
to seek as Weeks (9) stresses because it is useful “in confirming the validity of the selected model and in screening the data for
extraneous effects.”
8.3 For the case where drawdowns in the vicinity of a control well have essentially reached a steady state, Jacob (13, p. 204)
suggested a graphical type-curve method to analyze drawdowns at different distances to obtain an estimate of transmissivity and
the coefficient of leakage. The steady-state drawdown is given by the following equation (Jacob, 13,Eq 16):
Q
s 5 K x (26)
~ !
2πT
where
r K'
x 5 5 rΠ(27)
B Tb'
and where K (x) is the zero-order modified Bessel function of the second kind.
8.3.1 The graphical type-curve procedure used to calculate aquifer test results is based on the functional relations between K (x)
and s and between x and r.
8.3.1.1 Plot values of K (x) versus x on logarithmic paper (see Table 2 and Fig. 6). This plot is referred to as the type-curve plot.
TABLE 2 Values of the Bessel Function K (x) for Selected Values
ofx (from Hantush (3, p. 704))
−2 −1
N N × 10 10 1
1 4.7212 2.4271 0.4210
1.5 4.3159 2.0300 0.2138
2 4.0285 1.7527 0.1139
3 3.6235 1.3725 0.0347
4 3.3365 1.1145 0.0112
5 3.1142 0.9244 0.0037
6 2.9329 0.7775 .
7 2.7798 0.6605 .
8 2.6475 0.5653 .
9 2.5310 0.4867 .
D6029/D6029M − 20
FIG. 6 Type Curve of the Bessel Function K , (x) as a Function ofx(from Reed (1))
For convenience plot values of K (x) on the vertical coordinate.
8.3.1.2 On logarithmic tracing paper of the same scale and size as the K (x) versus x type curve, plot values of drawdown, s,
on the vertical coordinate versus the distance r on the horizontal coordinate.
8.3.1.3 Overlay the data plot on the type-curve plot and, while holding the coordinate axes of the two plots parallel, translate
the data plot to a position that gives the best match to the type curve. Select and record the values of x, K (x), r, and s at an arbitrary
match point anywhere on the overlapping part of the two matched plots. It is convenient to select a match point where x and K (x)
are integers.
8.3.1.4 Using the coordinates of the arbitrarily selected point, the transmissivity and leakance are computed from Eq 21 and Eq
22:
Q
T 5 K ~x! (28)
2πs
K' x T
5 (29)
b' r
r
8.3.2 Hantush (3, see p. 703) notes that where r/B ≤ 0.05 the Bessel function K is well approximated by a logarithmic
S D
B
function. Thus, in that range, a semilogarithmic plot of drawdown, s, versus distance, r, with r on the logarithmic scale, will give
a straight-line relationship. The slope of that line,Δ s/Δlog r, is equal to (2.303Q)/(2πT), from which the transmissivity, T, can be
calculated. This relationship indicates that in the region r/B ≤ 0.05, the shape of the drawdown curve is not affected by the effects
of leakage. Hantush also noted that the intercept, r , of this straight line at the zero-drawdown axis, has the property that B
Tb' K'
5 from which the leakance can be calculated.
Œ
K' b'
8.4 Qualitatively assess the test results considering the correspondence of the hydrogeologic conditions to the assumptions
associated with the Hantush-Jacob (2) solution and the adequacy of the measurements of discharge and water-level changes.
D6029/D6029M − 20
9. Report: Test Data Sheet(s)/Form(s)
9.1 Record as a minimum the following general iformation (data).
9.1.1 Introduction—The introductory section presents the scope and purpose of the Hantush-Jacob method. Summarize the field
hydrogeologic conditions and the field equipment and instrumentation including the construction of the control well and
observation wells and piezometers, or both, the method of measurement of discharge and water levels, and the duration of the test
and pumping rate. Discuss the rationale for selecting the Hantush-Jacob formulation which assumes that although water moves
through the confining bed(s) the gain or loss of water in storage in the confining bed(s) is negligible.
9.1.2 Hydrogeologic Setting—Review the information available on the hydrogeology of the site. Include the driller’s logs and
geologist’s description of drill cuttings. Interpret and describe the hydrogeology of the site as it pertains to the selection of the
methods for conducting and analyzing an aquifer test. Compare the hydrogeologic characteristics of the site as it conforms and
differs from the assumptions in the solution to the test method.
9.1.3 Equipment—Report the field installation and equipment for the aquifer test, including the construction, diameter, depth of
screened interval, and location of control well and pumping equipment, and the construction, diameter, depth, and screened interval
of observation wells or piezometers and their distances from the control well.
9.1.4 Instrumentation—Report the field instrumentation for observing water levels, pumping rate, barometric changes, and other
environmental conditions pertinent to the test. Include a list of measuring devices used during the test; the manufacturer’s name,
model number, and basic specifications for each major item; and pertinent information on the method, including date, of the last
calibration, if applicable.
9.1.5 Testing Procedures—State the steps taken in conducting pretest, drawdown, and recovery phases of the test. Include the
frequency of measurements of discharge rate, water level in observation wells, and other environmental data recorded during the
test procedure.
9.1.6 Presentation and Interpretation of Test Results:
9.1.6.1 Data—Present tables (and charts for graphically recorded data) of data collected during the test (pretest and recovery
included). Show methods of adjusting water levels for barometric changes, tidal changes, or other background water level changes
(interference with other operations and boundary conditions) and calculation of drawdown.
9.1.6.2 Data Plots—Present data plots used in analysis of the data. Show overlays of data plots and type curves with match
points and corresponding values of parameters at match points.
9.1.6.3 Calculations—Show calculations of transmissivity, storage coefficient, and coefficient of leakage. Show the calculation
of transmissivity and storage coefficient in accordance with Practice D6026.
9.1.7 Evaluate qualitatively the overall accuracy of the test method on the basis of the adequacy of instrumentation and
observations of stress and response, and the conformance of site assumptions to test results.
10. Precision and Bias
10.1 Precision—Test data on precision is not presented due to the nature of this test method. It is either not feasible or too costly
at this time to have ten or more agencies participate in an in situ testing program at a given site.
10.1.1 The subcommittee D18.21 is seeking any data for the users of this test method that might be used to make a limited
statement on precision.
10.2 Bias—There is no accepted reference value for this test method, therefore bias cannot be determined.
11. Keywords
11.1 aquifers; aquifer tests; confined aquifers; confining beds; control wells; groundwater; hydraulic properties; leakance; leaky
aquifers; observation wells; storage coefficient; transmissivity
REFERENCES
(1) Reed, J. E., “Type Curves for Selected Problems of Flow to Wells in Confined Aquifers,” U.S. Geological Survey Techniques of Water-Resources
Investigation Book 3, Chapter B3, 1980.
(2) Hantush, M. S., and Jacob, C. E., “Non-Steady Radial Flow in an Infinite Leaky Aquifer,” Transactions, American Geophysical Union, Vol 36, No.
1, 1955, pp. 95–100.
(3) Hantush, M. S., “Analysis of Data From Pumping Tests in Leaky Aquifers,” Transactions, American Geophysical Union, Vol 37, No. 6, 1956, pp.
702–714.
(4) Cooper, H. H., Jr., “Type Curves for Nonsteady Radial Flow in an Infinite Leaky Artesian Aquifer,” in Shortcuts and Special Problems in Aquifer
Tests, Ray Bentall, Compiler, U.S. Geological Survey Water-Supply Paper 1545-C, 1963, pp. C48–C55.
(5) Abdul Khader, M. H., and Ramadurgaiah, D., “Flow Towards a Well of Large Diameter in a Leaky Confined Aquifer,” 6th Australasian Hydraulics
and Fluid Mechanics Conference, Adelaide, Australia, December 5–9, 1977, pp. 84–87.
D6029/D6029M − 20
(6) Neuman, S. P., and Witherspoon, P. A., “Field Determination of the Hydraulic Properties of Leaky Multiple Aquifer Systems,” Water Resources
Research, Vol 8, No. 5, 1972, pp. 1284–1298.
(7) Hantush, M. S., “Modification of the Theory of Leaky Aquifers,” Journal of Geophysical Research, Vol 65, No. 11, 1960, pp. 3713–3725.
(8) Hantush, M. S., “Flow of Ground Water in Relatively Thick Leaky Aquifers,” Water Resources Research, Vol 3, No. 2, 1967, pp. 583–590.
(9) Weeks, E. P., “Aquifer Tests—The State of the Art in Hydrology,” Proceedings of the Invitational Well-Testing Symposium, Berkeley, California,
October 19–21, 1977, LBL7027, Lawrence Berkeley Laboratory, pp. 14–26.
(10) Moench, A. F., “Transient Flow to a Large-Diameter Well in an Aquifer With Storative Semiconfining Layers,” Water Resources Research, Vol 21,
No. 8, pp. 1121–1131.
(11) Neuman, S. P., Witherspoon, P. A., “Theory of Flow in a Confined Two Aquifer System,” Water Resources Research, Vol 5, No. 4, 1969, pp.
803–816.
(12) Hantush, M. S., “Hydraulics of Wells,” in Chow, Ven Te, Ed., Advances in Hydroscience, Vol 1, New York, Academic Press, 1964, pp. 281–432.
(13) Jacob, C. E., “Radial Flow in a Leaky Artesian Aquifer,” Transactions American Geophysics Union, Vol 27, No. 2, 1946, pp. 198–205.
(14) Ferris, J. G., Knowles, D. B., Brown, R. H., and Stallman, R. W.,“Theory of Aquifer Tests,” U.S. Geological Survey Water-Supply Paper 1536-E,
1962 .
(15) Lohman, S. W.,“Ground-Water Hydraulics,” U.S. Geological Survey Professional Paper 708, 1972.
(16) Walton, W. C., “Selected Analytical Methods for Well and Aquifer Evaluation,” Illinois State Water Survey Bulletin 49, 1962.
(17) Spane, F. A., Jr., and Wurstner, S. K., “DERIV: A Computer Program for Calculating Pressure Derivatives for Use in Hydraulic Test Analysis,”
Ground Water, Vol 31, No. 5, 1993, pp. 814–822.
SUMMARY OF CHANGES
In accordance with Committee D18 policy, this section identifies the location of changes to this standard since
ɛ1
the last edition (1996 (2010) ) that may impact the use of this standard. (January 1, 2017)
(1) Added references, notes for D3740 and D6026.
(2) Removed terminology that was not used in the text or is already available in D653.
(3) Removed/revised jargon.
(4) Removed wording for dated technology.
(5) Updated precision and bias to current D18 wording.
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1. Scope*
1.1 This
...