ASTM D6028/D6028M-20

Standard 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

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 1: 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, or both, everywhere by confining beds individually having uniform hydraulic conductivities, specific storages, and thicknesses. The confining beds are bounded on the distal sides by one of the cases shown in Fig. 1.  
5.1.6 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. Paragraph 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.
Note 2: 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.  
5.3.2 The leaky confining bed problem considered by the modified Hantush method requires that the control well has an infinite...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer taking into consideration the change in storage of water in overlying or underlying confining beds, or both. 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 modified Hantush method (1)2 is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Practice D6029/D6029M) with the exception that in this case the gain or loss of water in storage in the confining beds is taken into consideration (see 5.1). All possible combinations of impermeable beds and source beds (for example, beds in which the head remains uniform) are considered on the distal side of the leaky beds that confine the aquifer of interest (see Fig. 1).
FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating Three Different Cases of Boundary Conditions (from Reed (2) )  
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026.  
1.4.1 The procedures used to specify how data are collected/recorded and calculated in the 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,...

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 D6028/D6028M-20 is a standard practice published by ASTM International for determining the hydraulic properties of a confined aquifer, specifically accounting for water storage in leaky confining beds using the modified Hantush method. This analytical procedure is essential for groundwater professionals and hydrogeologists seeking accurate assessment of aquifer transmissivity and storage coefficient under complex geological conditions, where interaction with confining layers significantly impacts aquifer behavior.

The standard guides the analysis of water-level (head) data from observation wells or piezometers during a controlled pumping or injection test. By incorporating the effect of water storage within overlying or underlying leaky confining beds, ASTM D6028/D6028M-20 enables a more comprehensive understanding of aquifer systems than assessments focused solely on the primary aquifer unit.

Key Topics

• Hydraulic Properties Assessment: The main focus of this standard is the determination of transmissivity and storage coefficient for confined aquifers considering the influence of confining bed storage.
• Modified Hantush Method: This method extends classical models by integrating the impact of water storage in leaky confining layers, resulting in more complete aquifer characterizations.
• Analytical Procedures: Groundwater data collected from constant-rate pumping or injection tests are analyzed using type curves and mathematical relationships to quantify aquifer and confining bed parameters.
• Assumptions and Limitations:
  • Aquifer is homogeneous, isotropic, and fully saturated.
  • The control well maintains a constant discharge and fully penetrates the aquifer.
  • Flow is two-dimensional and radial.
  • Not recommended for fractured rock or carbonate settings, where the porous medium assumption does not hold.
  • Applicable when confining beds have uniform conductivities and storages.
• Reporting and Data Quality: The standard requires thorough documentation of test procedures, equipment, well constructions, and an assessment of the test’s validity based on conformance to assumptions.

Applications

ASTM D6028/D6028M-20 provides practical value across groundwater management, environmental engineering, and water resource development, especially when:

• Designing Wellfields: Accurate transmissivity and storage estimates help optimize well locations, spacing, and sustainable pumping rates.
• Evaluating Aquifer Protection Measures: Understanding the leakage through confining beds informs vulnerability assessments and the effectiveness of barriers.
• Groundwater Modeling: Enhanced parameterization improves the reliability of groundwater flow models, particularly in regions with significant confining layer storage.
• Regulatory Compliance and Site Assessment: Satisfies requirements for aquifer testing in environmental site investigations and permits where leaky confined systems exist.

The procedure is also instrumental in scenarios involving recovery or injection wells, as it accommodates analysis for both withdrawal and recharge operations.

Related Standards

For a complete approach and compliance, users should consider the following ASTM standards closely associated with D6028/D6028M-20:

• ASTM D4050: Field procedure for withdrawal and injection well testing, essential for collecting appropriate test data.
• ASTM D6026: Practice for using significant digits in geotechnical data, ensuring proper data precision and reporting.
• ASTM D6029/D6029M: Practice for determining hydraulic properties using the Hantush-Jacob method for leaky aquifers with negligible confining bed storage.
• ASTM D4106: Practice for determining transmissivity and storage of nonleaky confined aquifers via the Theis nonequilibrium method.
• ASTM D3740: Minimum requirements for agencies engaged in testing and/or inspection of soil and rock, ensuring procedural quality.
• ASTM D653: Terminology relating to soil, rock, and contained fluids, supporting clarity and consistent communication.

Conclusion

ASTM D6028/D6028M-20 is an authoritative groundwater standard for evaluating confined aquifer systems impacted by leaky confining beds. Its adoption promotes accurate aquifer characterization, informed water resource management, and compliance with environmental regulations, making it invaluable for hydrogeology and environmental engineering professionals.

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:D6028/D6028M −20
Standard 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
This standard is issued under the fixed designation D6028/D6028M; 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* significant digits that generally should be retained. The proce-
dures used do not consider material variation, purpose for
1.1 This practice covers an analytical procedure for deter-
obtaining the data, special purpose studies, or any consider-
mining the transmissivity and storage coefficient of a confined
ations for the user’s objectives; and it is common practice to
aquifertakingintoconsiderationthechangeinstorageofwater
increase or reduce significant digits of reported data to be
in overlying or underlying confining beds, or both. This
commensuratewiththeseconsiderations.Itisbeyondthescope
practice is used to analyze water-level or head data collected
of these test methods to consider significant digits used in
from one or more observation wells or piezometers during the
pumping of water from a control well at a constant rate. With analysis methods for engineering data.
appropriate changes in sign, this practice also can be used to
1.5 The values stated in SI units or inch-pound units are to
analyze the effects of injecting water into a control well at a
be regarded separately as standard. The values stated in each
constant rate.
system may not be exact equivalents; therefore, each system
1.2 This analytical procedure is used in conjunction with
shall be used independently of the other. Combining values for
Test Method D4050.
the two systems may result in nonconformance with the
1.3 Limitations—The valid use of the modified Hantush
standard.ReportingofresultsinunitsotherthanSIshallnotbe
method (1) is limited to the determination of hydraulic
regarded as nonconformance with this standard.
properties for aquifers in hydrogeologic settings with reason-
1.6 This practice offers a set of instructions for performing
able correspondence to the assumptions of the Hantush-Jacob
one or more specific operations.This document cannot replace
method (Practice D6029/D6029M) with the exception that in
educationorexperienceandshouldbeusedinconjunctionwith
this case the gain or loss of water in storage in the confining
professional judgment. Not all aspects of the practice may be
beds is taken into consideration (see 5.1). All possible combi-
applicable in all circumstances. This ASTM standard is not
nations of impermeable beds and source beds (for example,
intended to represent or replace the standard of care by which
bedsinwhichtheheadremainsuniform)areconsidered on the
the adequacy of a given professional service must be judged,
distal side of the leaky beds that confine the aquifer of interest
nor should this document be applied without the consideration
(see Fig. 1).
ofaproject’smanyuniqueaspects.Theword“Standard”inthe
1.4 All observed and calculated values shall conform to the
title of this document means only that the document has been
guidelines for significant digits and rounding established in
approved through the ASTM consensus process.
Practice D6026.
1.4.1 Theproceduresusedtospecifyhowdataarecollected/
1.7 This standard does not purport to address all of the
recorded and calculated in the standard are regarded as the
safety concerns, if any, associated with its use. It is the
industry standard. In addition, they are representative of the
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
This practice is under the jurisdiction of Committee D18 on Soil and Rock and
1.8 This international standard was developed in accor-
is the direct responsibility of Subcommittee D18.21 on Groundwater and Vadose
dance with internationally recognized principles on standard-
Zone Investigations.
Current edition approved June 1, 2020. Published June 2020. Originally ization established in the Decision on Principles for the
approved in 1996. Last previous edition approved in 2010 as D6028–17. DOI:
Development of International Standards, Guides and Recom-
10.1520/D6028_D6028M-20.
2 mendations issued by the World Trade Organization Technical
The boldface numbers in parentheses refer to a list of references at the end of
this practice. Barriers to Trade (TBT) Committee.
*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
D6028/D6028M−20
FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating Three
Different Cases of Boundary Conditions (from Reed (2))
D6028/D6028M−20
2. Referenced Documents 3.2.14 b', b"—thicknesses of the confining beds through
3 which leakage can occur [L].
2.1 ASTM Standards:
3.2.15 r—radial distance from control well [L].
D653Terminology Relating to Soil, Rock, and Contained
Fluids
3.2.16 s—drawdown [L].
D3740Practice for Minimum Requirements for Agencies
Tb'
Engaged in Testing and/or Inspection of Soil and Rock as
3.2.17 B5 L .
Π@ #
K'
Used in Engineering Design and Construction
3.2.18 t—time since pumping or injection began [T].
D4050Test Method for (Field Procedure) for Withdrawal
and Injection Well Testing for Determining Hydraulic
r K'S' K"S"
3.2.19 β5 S 1D nd .
Π@ #
Œ
Properties of Aquifer Systems
4b b'KS b"KS
s s
D4106Practice for (Analytical Procedure) for Determining
Transmissivity and Storage Coefficient of Nonleaky Con- 4. Summary of Practice
fined Aquifers by the Theis Nonequilibrium Method
4.1 This practice involves pumping a control well that is
D6026Practice for Using Significant Digits in Geotechnical
fully screened through the confined aquifer and measuring the
Data
water-level response in one or more observation wells or
D6029/D6029MPractice for (Analytical Procedures) Deter-
piezometers. The well is pumped at a constant rate. The
mining Hydraulic Properties of a Confined Aquifer and a
water-level response in the aquifer is a function of the
Leaky Confining Bed with Negligible Storage by the
transmissivity and storage coefficient of the aquifer and the
Hantush-Jacob Method
leakance coefficients and storage coefficients of the confining
beds.Alternatively, the practice can be performed by injecting
3. Terminology
water at a constant rate into the control well. Analysis of
3.1 Definitions—For definitions of common technical terms
buildup of water level in response to injection is similar to
used in this standard, refer to Terminology D653.
analysis of drawdown of water level in response to withdrawal
3.2 Symbols and Dimensions: in a confined aquifer. The water-level response data are
3.2.1 H (u,β)—well function for leaky systems where water analyzed using a set of type curves.
storage in confining beds is important [nd].
4.2 Solution—Hantush (1) gave solutions applicable to each
−1
3.2.2 K—hydraulic conductivity of the aquifer [LT ]. of Cases 1, 2, and 3 shown in Fig. 1 for “relatively small”
3.2.2.1 Discussion—The use of the symbol K for the term
values of time and for “relatively large” values of time. The
hydraulic conductivity is the predominant usage in groundwa- solution applicable for each case for relatively small values of
ter literature by hydrogeologists, whereas the symbol k is
time can be written as follows
commonly used for this term in soil and rock mechanics and
Q
soil science. s 5 H ~u,β! (1)
4πT
3.2.3 K', K"—vertical hydraulic conductivities of the con-
−1 where:
fining beds through which leakage can occur [LT ].
3 −1
r S
3.2.4 Q—discharge [L T ].
u 5 (2)
4Tt
3.2.5 S=bS —storage coefficient of the aquifer [nd].
s
and
3.2.6 S'5b'S' —storage coefficients of the confining beds
s
[nd]. r K'S' K" S"
β 5 1 (3)
S D
S"5b"S" 4b b'KS b"KS
s
s s
−1
3.2.7 S —specific storage of the aquifer [L ]. 2y
s
` e β=u
H u,β 5 erfc dy (4)
~ ! *
u
3.2.8 S' S" —specific storages of the confining beds. y
s s
=y y 2 u
~ !
@L #
2 `
y2
2 −1 erfc ~x! 5 * e2 dy (5)
3.2.9 T—transmissivity [L T ]. u
= π
r s
3.2.10 u= nd .
@ # where y is the variable of integration.
4Tt
4.2.1 The “relatively small” times when Eq 1 is applicable
3.2.11 W(u,r/B)—well function for leaky aquifer systems
are when:
with negligible storage changes in confining beds [ nd].
b'S' b"S"
3.2.12 W(u)—well function for nonleaky aquifer systems
t, and t, (6)
10K' 10K"
[nd].
Equation 1 is applicable at early times for each of the cases
3.2.13 b—thickness of aquifer [ L].
shown in Fig. 1 even though the conditions on the distal sides
oftheconfiningbedsarequitedifferentbecauseforearlytimes
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
the solution in the aquifer is essentially independent of
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
conditions on the distal side of the confining beds. The effects
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. of those distant boundary conditions are not felt in the aquifer
D6028/D6028M−20
forawhile.Eq1-5arethebasisforthetypecurvesolutionthat 5b'S' 10b"S"
t. and t. (14)
is described by this practice. K' K"
4.2.2 For relatively large values of time the solutions given
are both satisfied, then
by Hantush (1) can be written as:
Q K' Q
4.2.2.1 Case 1—Heads in zones on the distal side of the
s 5 WS uδ , r D 5 W uδ ,r/B (15)
Π~ !
3 3
confiningbedsremainconstantandareunaffectedbydischarge 4πT Tb' 4πt
of the pumped well. For times when
where:
b'S' b"S"
δ 5 11~S " 1 S'⁄3!S (16)
t.5 and t.5 (7)
K' K"
and W(u,r/B) is defined in Case 1 (see Eq 11).
are both satisfied, then
Hantush (1) did not develop expressions for the solutions to
Q
these cases for intermediate times (between“ small” and
s 5 W ~uδ , α! (8)
4πT
“large” times). Reed ((2) p. 26) notes that Neuman and
Witherspoon ((5), p. 250) developed a complete (that is,
where:
applicableforalltimes)solutionforCase1(sourcebedsonthe
~S'1S"! K' K" distal sides of both confining beds) but did not tabulate it.
δ 5 11 and α 5 r 1 (9)
Œ
3S Tb' Tb"
5. Significance and Use
Hantush (1) notes that if K", S', and S" are taken as zero in
5.1 Assumptions:
the flow systems shown in Fig. 1 as Case 1 or Case 3, the
resulting flow system is that of a confined aquifer overlying an 5.1.1 The control well discharges at a constant rate, Q.
impermeable bed and the aquifer being overlain by a confining 5.1.2 The control well is of infinitesimal diameter and fully
bed in which the storage is negligible. Hantush gives the penetrates the aquifer.
solution for that special case as follows: 5.1.3 The aquifer is homogeneous, isotropic, and areally
extensive.
Q
s 5 W ~u,r/B! (10)
4πT
NOTE 1—Slug and pumping tests implicitly assume a porous medium.
Fractured rock and carbonate settings may not provide meaningful data
where:
and information.
5.1.4 Theaquiferremainssaturated(thatis,waterleveldoes
r K'
5 rŒ
not decline below the top of the aquifer).
B Tb'
5.1.5 The aquifer is overlain or underlain, or both, every-
Note that W(u,r/B) is the well function for leaky systems
wherebyconfiningbedsindividuallyhavinguniformhydraulic
with negligible storage in the confining beds given by Hantush
conductivities, specific storages, and thicknesses. The confin-
and Jacob (3) and described in Practice D6029/D6029M. That
ing beds are bounded on the distal sides by one of the cases
function is defined as follows:
shown in Fig. 1.
` dy
5.1.6 Flow in the aquifer is two-dimensional and radial in
2 2
W u,r/B 5 exp 2y 2 r / 4B y (11)
~ ! * ~ ~ !!
u
y the horizontal plane.
5.2 Thegeometryofthewellandaquifersystemisshownin
4.2.2.2 Case 2—The materials in the zones on the distal
Fig. 1.
sides of the confining beds are impermeable. For times when
5.3 Implications of Assumptions:
b'S' b"S"
t.10 and t.10 (12)
5.3.1 Paragraph 5.1.1 indicates that the discharge from the
K' K"
control well is at a constant rate. Paragraph 8.1 ofTest Method
are both satisfied, then
D4050 discusses the variation from a strictly constant rate that
Q
isacceptable.Acontinuoustrendinthechangeofthedischarge
s 5 W u,δ (13)
~ !
4πT rate could result in misinterpretation of the water-level change
data unless taken into consideration.
where:
NOTE 2—The quality of the result produced by this standard is
S'1S"
~ !
dependent on the competence of the personnel performing it, and the
δ 5 11
S
suitability of the equipment and facilities used. Agencies that meet the
criteria of Practice D3740 are generally considered capable of competent
and where the function W(u) is the well function for
and objective testing/sampling/inspection/etc. Users of this standard are
non-leaky aquifers that appears in the solution given by Theis
cautioned that compliance with Practice D3740 does not in itself assure
reliable results. Reliable results depend on many factors; Practice D3740
(4) described in Practice D4106 for drawdowns in response to
provides a means of evaluating some of those factors.
a well pumped at a constant rate from a non-leaky aquifer.
4.2.2.3 Case 3—The materials on the distal side of one 5.3.2 The leaky confining bed problem considered by the
confiningbedareimpermeableandtheheadsonthedistalsides modified Hantush method requires that the control well has an
of the other confining bed remain constant and are unaffected infinitesimal diameter and has no storage. Moench (6) gener-
by discharge of the pumped well. For times when alizedthefieldsituationaddressedbythemodifiedHantush (1)
D6028/D6028M−20
method to include the well bore storage in the pumped well. 6.3 Construction and Location of Observation Wells and
Themathematicalapproachthatheusedtoobtainasolutionfor Piezometers—Construct one or more observation wells or
that more general problem results in a Laplace transform piezometers screened only in the pumped aquifer at a distance
solutionwhoseanalyticalinversionhasnotbeendevelopedand from the control well. Observation wells may be open through
probably would be very complicated, if possible, to evaluate. all or part of the thickness of the aquifer. Hantush ((9) p. 350)
Moench (6) used a numerical Laplace inversion algorithm to indicates that the effects of a partially penetrating control well
develop type curves for selected situations. The situations can be neglected for
considered by Moench indicate that large well bore storage
K
r
may mask effects of leakage derived from storage changes in
r.1.5bΠ(19)
K
z
the confining beds. The particular combinations of aquifer and
confining bed properties and well radius that result in such
where K and K are the aquifer hydraulic conductivities in
r z
masking is not explicitly given. However, Moench ((6),p.
the horizontal and vertical directions, respectively. Although
1125) states “Thus observable effects of well bore storage are
that relationship was developed for an aquifer confined by a
maximized, for a given well diameter, when aquifer transmis-
leaky confining bed in which storage is neglected, it may be a
sivity Kbandthestoragecoefficient S baresmall.”Moench(p.
s useful guideline for the cases where storage in the confining
1129) notes that “.one way to reduce or effectively eliminate
beds is important. If an observation well fully penetrates the
the masking effect of well bore storage is to isolate the aquifer
aquifer, it’s drawdownis not affected by a partiallypenetrating
of interest with hydraulic packers and repeat the pump test
control well and it reacts as if the control well completely
underpressurizedconditions.Becausewellborestorage Cwill
penetrated the aquifer (Hantush (9) p. 351).
then be due to fluid compressibility rather than changing water
levels in the well”.“the dimensionless well bore storage 7. Procedure
parameter may be reduced by 4 to 5 orders of magnitude.”
7.1 Pretest preparations are described in detail in Test
5.3.3 The modified Hantush method assumes, for Cases 1
Method D4050. The overall test procedure consists of (1)
and 3 (see Fig. 1), that the heads in source layers on the distal
conducting the field procedure for withdrawal or injection well
side of confining beds remain constant. Neuman and Wither-
tests (described in Test Method D4050) and (2) analysis of the
spoon (7)developedasolutionforacasethatcouldcorrespond
field data, which is addressed in Section 8.
to Hantush’s Case 1 with K"= O = S" except that they do not
require the head in the unpumped aquifer to remain constant.
8. Calculation and Interpretation of Test Data
For that case, they concluded that the drawdowns in the
8.1 Aquifer—Field test data for “relatively small” values of
pumped aquifer would not be affected by the properties of the
time are analyzed using Eq 1-3. The graphical procedure used
other, unpumped, aquifer when (Neuman and Witherspoon (7)
to calculate test results is based on the functional relations
p. 810) time satisfies:
between H(u,β) and s and between u and t/r .
S'b'
t# 0.1 (17) NOTE 3—Because the H(u,β) type curve method is based on the
K'
assumption that the duration of the test is such that the boundary
conditions on the distal sides of the confining beds have not yet affected
5.3.4 Implicit in the assumptions are the conditions that the
drawdowns in the pumped aquifer, only the relatively early-time draw-
flow in the confining beds is essentially vertical and in the
down data should be used in fitting the H(u,β) curves. “Relatively
aquifer is essentially horizontal. Hantush’s (8) analysis of an
late-time”drawdowndatacanbeanalyzedusingEq8,Eq13,orEq15for
aquifer bounded only by one leaky confining bed suggested
field conditions described by Cases 1, 2, or 3, respectively. Equations 8
and Equations 15 correspond to the condition that there are no further
that these assumptions are acceptably accurate wherever
changes in storage in the leaky confining beds bounded by constant head
K b
layersandleakageintothepumpedaquiferthoughthoseconfiningbedsby
.100 (18)
K' b' those times correspond entirely to water transmitted from the source
(constant head) layers. That situation is discussed in Practice D6029/
That form of relation between aquifer and confining bed
D6029M.Reed((4)p.28–29)notesthatthelate-timedataforCases1and
properties may also be a useful guide for the case of two leaky 3 will fall on the flat part of the W(u,r/B) type curves and a time-
drawdownplotmatchwouldbeindeterminate.Equation13correspondsto
confining bed
...

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: D6028 − 17 D6028/D6028M − 20
Standard Test Method (Analytical Procedure) 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
This standard is issued under the fixed designation D6028;D6028/D6028M; 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 taking into consideration the change in storage of water in overlying or underlying confining beds, or both. 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 modified Hantush method (1) is limited to the determination of hydraulic properties for
aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Test Method
D6029) with the exception that in this case the gain or loss of water in storage in the confining beds is taken into consideration
(see 5.1). All possible combinations of impermeable beds and source beds (for example, beds in which the head remains uniform)
are considered on the distal side of the leaky beds that confine the aquifer of interest (see Fig. 1).
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice
D6026.
1.4.1 The procedures used to specify how data are collected/recorded and calculated in the 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 data to be commensurate with these considerations.
It is beyond the scope of these test methods to consider significant digits used in analysis methods for engineering data.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
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
D4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of
Aquifer Systems
This test method practice is under the jurisdiction of 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 2010 as
ɛ1
D6028–96(2010)D6028 .–17. DOI: 10.1520/D6028-17.10.1520/D6028_D6028M-20.
The boldface numbers in parentheses refer to a list of references at the end of this test method.practice.
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
D6028/D6028M − 20
FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating Three
Different Cases of Boundary Conditions (from Reed (2) )
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
D6029 Practice for (Analytical Procedures) Determining Hydraulic Properties of a Confined Aquifer and a Leaky Confining Bed
with Negligible Storage by the Hantush-Jacob Method
3. Terminology
3.1 Definitions—For definitions of other terms used in this test method, see Terminology D653.
3.2 Symbols and Dimensions:
D6028/D6028M − 20
3.2.1 H (u,β)—well function for leaky systems where water storage in confining beds is important [nd].
−1
3.2.2 K—hydraulic conductivity of the aquifer [LT ].
3.2.2.1 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
3.2.3 K', K"—vertical hydraulic conductivities of the confining beds through which leakage can occur [LT ].
3 −1
3.2.4 Q—discharge [L T ].
3.2.5 S = bS —storage coefficient of the aquifer [nd].
s
3.2.6 S'5b'S' —storage coefficients of the confining beds [nd].
s
S"5b"S"
s
−1
3.2.7 S —specific storage of the aquifer [L ].
s
3.2.8 S' S" —specific storages of the confining beds.
s s
L
@ #
2 −1
3.2.9 T—transmissivity [L T ].
r s
3.2.10 u = @nd#.
4Tt
3.2.11 W(u,r/B)—well function for leaky aquifer systems with negligible storage changes in confining beds [ nd].
3.2.12 W(u)—well function for nonleaky aquifer systems [nd].
3.2.13 b—thickness of aquifer [ L].
3.2.14 b', b"—thicknesses of the confining beds through which leakage can occur [L].
3.2.15 r—radial distance from control well [L].
3.2.16 s—drawdown [L].
Tb'
3.2.17 B5 L .
Π@ #
K'
3.2.18 t—time since pumping or injection began [T].
r K'S' K"S"
3.2.19 β5 S 1D nd .
ΠΠ@ #
4b b'KS b"KS
s 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 coefficients and
storage coefficients of the confining beds. 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 water level in
response to withdrawal in a confined aquifer. The water-level response data are analyzed using a set of type curves.
4.2 Solution—Hantush (1) gave solutions applicable to each of Cases 1, 2, and 3 shown in Fig. 1 for “relatively small” values
of time and for “relatively large” values of time. The solution applicable for each case for relatively small values of time can be
written as follows
Q
s 5 H ~u,β! (1)
4πT
where:
r S
u 5 (2)
4Tt
and
r K'S' K" S"
β5 1 (3)
S D
4b b'KS b"KS
s s
2y
` β=u
e
H u,β 5 erfc dy (4)
~ ! *
u y
=y y 2 u
~ !
D6028/D6028M − 20
2 `
y2
erfc ~x! 5 e2 dy (5)
*
u
= π
where y is the variable of integration.
4.2.1 The “relatively small” times when Eq 1 is applicable are when:
b'S' b"S"
t, and t, (6)
10K' 10K"
Equation 1 is applicable at early times for each of the cases shown in Fig. 1 even though the conditions on the distal sides of
the confining beds are quite different because for early times the solution in the aquifer is essentially independent of conditions
on the distal side of the confining beds. The effects of those distant boundary conditions are not felt in the aquifer for a while. Eq
1-5 are the basis for the type curve solution that is described by this test method.
4.2.2 For relatively large values of time the solutions given by Hantush (1) can be written as:
4.2.2.1 Case 1—Heads in zones on the distal side of the confining beds remain constant and are unaffected by discharge of the
pumped well. For times when
b'S' b"S"
t.5 and t.5 (7)
K' K"
are both satisfied, then
Q
s 5 W uδ , α (8)
~ !
4πT
where:
~S'1S"! K' K"
δ 5 11 and α5 rŒ 1 (9)
3S Tb' Tb"
Hantush (1) notes that if K", S', and S" are taken as zero in the flow systems shown in Fig. 1 as Case 1 or Case 3, the resulting
flow system is that of a confined aquifer overlying an impermeable bed and the aquifer being overlain by a confining bed in which
the storage is negligible. Hantush gives the solution for that special case as follows:
Q
s 5 W u,r/B (10)
~ !
4πT
where:
r K'
5 r
Œ
B Tb'
Note that W(u,r/B) is the well function for leaky systems with negligible storage in the confining beds given by Hantush and
Jacob (3) and described in Test Method (D6029). That function is defined as follows:
` dy
2 2
W ~u,r/B! 5* exp~2y 2 r /~4B y! ! (11)
u
y
4.2.2.2 Case 2—The materials in the zones on the distal sides of the confining beds are impermeable. For times when
b'S' b"S"
t.10 and t.10 (12)
K' K"
are both satisfied, then
Q
s 5 W u,δ (13)
~ !
4πT
where:
S'1S"
~ !
δ 5 11
S
and where the function W(u) is the well function for non-leaky aquifers that appears in the solution given by Theis (4) described
in Test Method D4106 for drawdowns in response to a well pumped at a constant rate from a non-leaky aquifer.
4.2.2.3 Case 3—The materials on the distal side of one confining bed are impermeable and the heads on the distal sides of the
other confining bed remain constant and are unaffected by discharge of the pumped well. For times when
5b'S' 10b"S"
t. and t. (14)
K' K"
D6028/D6028M − 20
are both satisfied, then
Q K' Q
s 5 WS uδ , rŒ D5 W ~uδ ,r/B! (15)
3 3
4πT Tb' 4πt
where:
δ 5 11 S " 1 S ' ⁄ 3 S (16)
~ !
and W(u,r/B) is defined in Case 1 (see Eq 11).
Hantush (1) did not develop expressions for the solutions to these cases for intermediate times (between“ small” and “large”
times). Reed ((2) p. 26) notes that Neuman and Witherspoon ((5), p. 250) developed a complete (that is, applicable for all times)
solution for Case 1 (source beds on the distal sides of both confining beds) but did not tabulate it.
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, or both, everywhere by confining beds individually having uniform hydraulic
conductivities, specific storages, and thicknesses. The confining beds are bounded on the distal sides by one of the cases shown
in Fig. 1.
5.1.6 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. Paragraph 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.
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.
5.3.2 The leaky confining bed problem considered by the modified Hantush method requires that the control well has an
infinitesimal diameter and has no storage. Moench (6) generalized the field situation addressed by the modified Hantush (1) method
to include the well bore storage in the pumped well. The mathematical approach that he used to obtain a solution for that more
general problem results in a Laplace transform solution whose analytical inversion has not been developed and probably would
be very complicated, if possible, to evaluate. Moench (6) used a numerical Laplace inversion algorithm to develop type curves for
selected situations. The situations considered by Moench indicate that large well bore storage may mask effects of leakage derived
from storage changes in the confining beds. The particular combinations of aquifer and confining bed properties and well radius
that result in such masking is not explicitly given. However, Moench ((6), p. 1125) states “Thus observable effects of well bore
storage are maximized, for a given well diameter, when aquifer transmissivity Kb and the storage coefficient S b are small.”
s
Moench (p. 1129) notes that “.one way to reduce or effectively eliminate the masking effect of well bore storage is to isolate the
aquifer of interest with hydraulic packers and repeat the pump test under pressurized conditions. Because well bore storage C will
then be due to fluid compressibility rather than changing water levels in the well”.“the dimensionless well bore storage parameter
may be reduced by 4 to 5 orders of magnitude.”
5.3.3 The modified Hantush method assumes, for Cases 1 and 3 (see Fig. 1), that the heads in source layers on the distal side
of confining beds remain constant. Neuman and Witherspoon (7) developed a solution for a case that could correspond to Hantush’s
Case 1 with K" = O = S" except that they do not require the head in the unpumped aquifer to remain constant. For that case, they
concluded that the drawdowns in the pumped aquifer would not be affected by the properties of the other, unpumped, aquifer when
(Neuman and Witherspoon (7) p. 810) time satisfies:
S'b'
t # 0.1 (17)
K'
5.3.4 Implicit in the assumptions are the conditions 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 these
assumptions are acceptably accurate wherever
K b
.100 (18)
K' b'
D6028/D6028M − 20
That form of relation between aquifer and confining bed properties may also be a useful guide for the case of two leaky confining
beds.
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 ((9) p. 350) indicates that the effects of a partially penetrating control well can be neglected for
K
r
r.1.5bΠ(19)
K
z
where K and K are the aquifer hydraulic conductivities in the horizontal and vertical directions, respectively. Although that
r z
relationship was developed for an aquifer confined by a leaky confining bed in which storage is neglected, it may be a useful
guideline for the cases where storage in the confining beds is important. If an observation well fully penetrates the aquifer, it’s
drawdown is not affected by a partially penetrating control well and it reacts as if the control well completely penetrated the aquifer
(Hantush (9) p. 351).
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 for “relatively small” values of time are analyzed using Eq 1-3. The graphical procedure used to calculate
test results is based on the functional relations between H(u,β) and s and between u and t/r .
NOTE 2—Because the H(u,β) type curve method is based on the assumption that the duration of the test is such that the boundary conditions on the
distal sides of the confining beds have not yet affected drawdowns in the pumped aquifer, only the relatively early-time drawdown data should be used
in fitting the H(u,β) curves. “Relatively late-time” drawdown data can be analyzed using Eq 8, Eq 13, or Eq 15 for field conditions described by Cases
1, 2, or 3, respectively. Equations 8 and Equations 15 correspond to the condition that there are no further changes in storage in the leaky confining beds
bounded by constant head layers and leakage into the pumped aquifer though those confining beds by those times correspond entirely to water transmitted
from the source (constant head) layers. That situation is discussed in Test Method D6029. Reed ((4) p. 28–29) notes that the late-time data for Cases 1
and 3 will fall on the flat part of the W(u,r/B) type curves and a time-drawdown plot match would be indeterminate. Equation 13 corresponds to non-leaky
confined aquifers, and that situation is discussed in Test Method D4106. Spane and Wurstner (10) discuss 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 aid in selecting
an aquifer interpretation model and in estimating the aquifer parameters. They discuss also an approach that transforms water-level recovery (that is, the
response of water levels when the pump is shut off) data plots to a form that can be analyzed with drawdown data in constructing derivative plots. To
apply the derivative methods requires that measurements be spaced closely enough that numerically developed time derivatives can be reasonably
approximated.
8.1.1 Plot values of H(u,β) versus 1/u for selected values of β on logarithmic-scale paper. This plot is referred to as the type
curve plot. Table 1 gives a tabulation of values of H(u,β) for selected values of u and β. Fig. 2 is a logarithmic plot of H(u,β) versus
1/u for selected values of β (from Kruseman and deRidder (11)). If a set of type curves are inaccessible, these data can be used
to develop type curves. A more extensive tabulation of H(u,β) is given in Hantush (12). Some readily available sources of these
type curves are Lohman (13) and Reed (2). Commercially available software is available to calculate and plot these values and
curves.
8.1.2 On logarithmic tracing paper of the same scale and size as the H(u,β) versus 1/u type curves, plot values of drawdown,
s, for each observation well on the vertical coordinate versus time divided by distance between the control well and the observation
well squared, t/r , on the horizontal coordinate. This plot is referred to as the data plot.
8.1.3 Overlay the data plot on the type curve plot and, keeping the coordinate axes of the two plots parallel, shift the plot to
the position where the data for each observation well falls either between one pair of the β curves, or along one of them. It is
preferable for two or more observation wells to be at different distances from the control well. Recall the definition of β (see Eq
3). The advantages of having two or more observation wells is that the distance values, r, for the observation wells should fall on
curves having proportional β values. For example, if data are available from three observation wells at 100, 200, and 800 ft from
the control well, the data plots for the three wells should match curves having corresponding β values having the ratios 1:2:8.
Weeks (14) notes that for values of β ranging from zero (this is the Theis curve which corresponds to a non-leaky case) to about
D6028/D6028M − 20
TABLE 1 Values of H(u,β) for Selected Values ofu and β (from Reed ).
NOTE 1—From Hantush . Numbers in parentheses are powers of 10 by which the other numbers are multiplied (for example 963(−4) = 0.0963)
β
u
0.03 0.1 0.2 1 3 10 30 100
−9
1 × 10 12.3088 11.1051 10.0066 8.8030 7.7051 6.5033 5.4101 4.2221
2 11.9622 10.7585 9.6602 8.4566 7.3590 6.1579 5.0666 3.8839
3 11.7593 10.5558 9.4575 8.2540 7.1565 5.9561 4.8661 3.6874
5 11.5038 10.3003 9.2021 7.9987 6.9016 5.7020 4.6142 3.4413
7 11.3354 10.1321 9.0339 7.8306 6.7337 5.5348 4.4487 3.2804
−8
1 × 10 11.1569 9.9538 8.8556 7.6525 6.5558 5.3578 4.2737 3.1110
2 10.8100 9.6071 8.5091 7.3063 6.2104 5.0145 3.9352 2.7858
3 10.6070 9.4044 8.3065 7.1039 6.0085 4.8141 3.7383 2.5985
5 10.3511 9.1489 8.0512 6.8490 5.7544 4.5623 3.4919 2.3662
7 10.1825 8.9806 7.8830 6.6811 5.5872 4.3969 3.3307 2.2159
−7
1 × 10 10.0037 8.8021 7.7048 6.5032 5.4101 4.2221 3.1609 2.0591
2 9.6560 8.4554 7.3585 6.1578 5.0666 3.8839 2.8348 1.7633
3 9.4524 8.2525 7.1560 5.9559 4.8661 3.6874 2.6469 1.5966
5 9.1955 7.9968 6.9009 5.7018 4.6141 3.4413 2.4137 1.3944
7 9.0261 7.8283 6.7329 5.5346 4.4486 3.2804 2.2627 1.2666
−6
1 × 10 8.8463 7.6497 6.5549 5.3575 4.2736 3.1110 2.1051 1.1361
2 8.4960 7.3024 6.2091 5.0141 3.9350 2.7857 1.8074 0.8995
3 8.2904 7.0991 6.0069 4.8136 3.7382 2.5984 1.6395 0.7725
5 8.0304 6.8427 5.7523 4.5617 3.4917 2.3661 1.4354 0.6256
7 7.8584 6.6737 5.5847 4.3962 3.3304 2.2158 1.3061 0.5375
−5
1 × 10 7.6754 6.4944 5.4071 4.2212 3.1606 2.0590 1.1741 0.4519
2 7.3170 6.1453 5.0624 3.8827 2.8344 1.7632 0.9339 0.3091
3 7.1051 5.9406 4.8610 3.6858 2.6464 1.5965 0.8046 0.2402
5 6.8353 5.6821 4.6075 3.4394 2.4131 1.3943 0.6546 0.1635
7 6.6553 5.5113 4.4408 3.2781 2.2619 1.2664 0.5643 0.1300
−4
1 × 10 6.4623 5.3297 4.2643 3.1082 2.1042 1.1359 0.4763 963(−4)
2 6.0787 4.9747 3.9220 2.7819 1.8062 0.8992 0.3287 494(−4)
3 5.8479 4.7655 3.7222 2.5937 1.6380 0.7721 0.2570 315(−4)
5 5.5488 4.4996 3.4711 2.3601 1.4335 0.6252 0.1818 166(−4)
7 5.3458 4.3228 3.3062 2.2087 1.3039 0.5370 0.1412 103(−4)
−3
1 × 10 5.1247 4.1337 3.1317 2.0506 1.1715 0.4513 0.1055 390(−5)
2 4.6753 3.7598 2.7938 1.7516 0.9305 0.3084 551(−4) 169(−5)
3 4.3993 3.5363 2.5969 1.5825 0.8006 0.2394 355(−4) 713(−6)
5 4.0369 3.2483 2.3499 1.3767 0.6498 0.1677 190(−4) 205(−6)
7 3.7893 3.0542 2.1877 1.2460 0.5589 0.1292 120)−4) 821(−7)
−2
1 × 10 3.5195 2.8443 2.0164 1.1122 0.4702 955(−4) 695(−5) 274(−7)
2 2.9759 2.4227 1.6853 0.8677 0.3214 487(−4) 205(−5) 226(−8)
3 2.6487 2.1680 1.4932 0.7353 0.2491 308)−4) 888(−6)
5 2.2312 1.8401 1.2535 0.5812 0.1733 160)−4) 261(−6)
7 1.9558 1.6213 1.0979 0.4880 0.1325 982(−5) 106(−6)
−1
1 × 10 1.6667 1.3893 0.9358 0.3970 966(−4) 552(−5) 365(−7)
2 1.1278 0.9497 0.6352 0.2452 468(−4) 149(−5) 307(−8)
3 0.8389 0.7103 0.4740 0.1729 281(−4) 592(−6)
5 0.5207 0.4436 0.29556 0.1006 130(−4) 151(−6)
7 0.3485 0.2980 0.1985 646(−4) 714(−5) 534(−7)
1 × 1 0.2050 0.1758 0.1172 365(−4) 337(−5) 151(−7)
2 458(−4) 395(−4) 264(−4) 760(−5) 487(−6)
3 122(−4) 106(−4) 707(−5) 196(−5) 102(−6)
5 108(−5) 934(−6) 624(−6) 167(−6) 672(−8)
7 109(−6) 941(−7) 629(−7) 165(−7)
1 × 10 391(−8) 339(−8) 227(−8)
0.7, there is virtually no difference in the shape of the curves on the H(u,β) versus 1/u plot. Weeks states that if β falls within this
range for a given observation well it is impossible to determine unique values of transmissivity and storativity for the aquifer and
β using only that well. The use of a composite plot involving more than one observation well at different distances, r, may permit
a unique fit to be obtained.
NOTE 3—Moench (6) notes that it is desirable to also obtain data on water-level changes in the pumped well because it can “.be helpful in determining
the presence or absence of leakage when compared with observation well data.” However, data from the pumped well are affected by variations in the
pumping rate, effects of well-bore storage, and the “skin” (a zone around the well hydraulically different from the native materials because of disturbance
and alteration caused by well drilling and construction).
8.1.4 Select and record the values of H(u,β), 1/u,s, and t/r at an arbitrary point, referred to as the match point, anywhere on
the overlapping part of the type curve plot and the data plot. For convenience, the match point may be selected where H(u,β) and
1/u are integer values. Record the value of β for each observation well’s data.
D6028/D6028M − 20
FIG. 2 Family of Curves of H(u,β) versus 1/u for Selected Values of β (from Kruseman and deRidder (11))
8.1.5 Using the selected values, determine the transmissivity and storage coefficient from Eq 1 and Eq 2:
Q
T 5 H~u,β! (20)
4πs
t
S 5 4Tu (21)
r
Equation 3 indicates that if the aquifer of interest is overlain and underlain by leaky confining beds, the value of β characterizes
a composite of the properties of the individual confining beds.
8.1.6 Reed ((2) p. 26–27) notes that for certain special situations, the β values may be used to characterize individual confining
bed properties. For example, suppose that the hydrogeologic information for an area suggests that the value of K"S" for the
underlying confining bed is negligible. This would occur if the bed is effectively impermeable and incompressible. For that
situation Eq 3 reduces to:
r K'S'
β5 Œ (22)
4b b'KS
S
which can be manipulated to give that
2 2
16β b KS
S
K'S'5 b' (23)
r
Recalling that T = bK and S = bS this can be rewritten as
s
16β TS
K'S'5 b' (24)
r
Note that b' and r are measured and T,S, and β are estimated from the test analysis so that a value for K'S' can be calculated.
Reed (2) notes that if one expects K"S" = K'S' then Eq 3 can be manipulated to give that:
16β b'b"
K'S'5 TS (25)
r
b'1b"12= b'b"
NOTE 4—Fig. 3 shows an application of the type-curve method using the modified Hantush method taken from Stallman and Weeks (15). An example
of a match of multiple observation-well data to the Hantush (1) type curves is shown in Fig. 3. This test, performed on a well near Houston, Texas, is
an area where significant subsidence has been induced by groundwater withdrawal, and thus almost undoubtedly should fit the Hantush (1) curves. Note
that differences in positions of the data curves are in the right direction to indicate the effects of confining-bed storage, but their departures from the Theis
curve are too small to be totally convincing. Nonetheless, selection of the best-matching β curve values, the appropriate r values for the observation wells,
and an estimate of S' results in a hydraulic conductivity of the confining layer comparable to that used in modeling the Houston aquifer (Jorgensen (16)).
s
The lack of clear definition of the effects of confining-bed leakage in the data response curves suggests that an observation piezometer in the confining
layer would have been desirable in order to apply the Neuman-Witherspoon (17) ratio method.
D6028/D6028M − 20
FIG. 3 Graph Showing Match of Drawdown Data for Three Observation Wells Showing Three Selected β Curves (from Stallman and
Weeks (15))
9. Report
9.1 Record as a minimum the following general information (data).
9.1.1 Introduction—The introductory section presents the scope and purpose of the modified Hantush 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 modified Hantush formulation which assumes that the gain or loss of water
from storage in the confining bed(s) is significant.
9.1.2 Hydrogeologic Setting—Review the information available on the hydrogeology of the site. Include the driller’s logs and
geologists’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.
D6028/D6028M − 20
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 Calculation—Show calculations of transmissivity, storage coefficient, and any parameters characterizing the leaky
confining beds. Show calculation of transmissivity and storage coefficient in accordance with Practice D6026.
9.1.7 Evaluate qualitatively the overall accuracy of the test 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 the 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.
10.2 Bias—There is not 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) Hantush, M. S., “Modification of the Theory of Leaky Aquifers,” Journal of Geophysical Research, Vol 65, No. 11, 1960, pp. 3713–3725.
(2) 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.
(3) 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.
(4) Theis, C. V., “The Relation Between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Ground-Water
Storage,” American Geophysical Union Transactions, Vol 16, Part 2, 1935, pp. 519–524.
(5) Neuman, S. P., and Witherspoon, P.A., “Transient Flow of Ground Water to Wells in Multiple-aquifer Systems,” “Sea-Water Intrusion: Aquitards in
the Coastal Ground Water Basin of Oxnard Plain, Ventura County,” California Department of Water Resources Bulletin 63-4, 1971, pp. 159–359.
(6) Moench, A. F., “Transient Flow to a Large-Diameter Well in an Aquifer With Storative Semiconfining Layers,” Water Resources Research, Vol 21,
No. 8, 1985, pp. 1121–1131.
(7) 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.
(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) Hantush, M. S., “Hydraulics of Wells,” Chow, Ven Te, ed., Advances in Hydroscience, Vol 1, New York, Academic Press, 1964, pp. 281–432.
(10) 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.
(11) Kruseman, G. P., and deRidder, N. A., “Analysis and Evaluation of Pumping Test Data,” Publication 47, International Institute for Land Reclamation
and Improvement, Wageningen, The Netherlands, 1990 (Second edition, completely revised).
2y
`
e β=u
*
(12) Hantush, M. S., “Tables of the function H ~u,β!5 erfc dy,” New Mexico Institute of Mining and Technology Professional
F G
u y
=y y2u
~ !
Paper 103, 1961.
(13) Lohman, S. W., “Ground-Water Hydraulics,” U.S. Geological Survey Professional Paper 708, 1972.
(14) Weeks, E. P., “Aquifer Tests—The State of the Art in Hydrology,” Proceedings of the Invitational Well-Testing Symposium, Berkeley, California,
Oct. 19–21, 1977, LBL7027, Lawrence Berkeley Laboratory, pp. 14–26.
(15) Stallman, R. W., and Weeks, E. P., Section 2.H. Aquifer tests, in Chapter 2-GROUND WATER, National Handbook of Recommended Methods for
Water-Data Acquisition, 1980, pp. 2-115 to 2-149.
(16) Jorgensen, D. G., “Analog-Model Studies of Ground-Water Hydrology in the Houston District, Texas,” Texas Water-Development Board Report 190,
1975 .
(17) 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.
D6028/D6028M − 20
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) Updated to add references and wording for D3740 and D6026.
(2) Removed Terminology that was not used in text or was in D653.
(3) Added updated wording to Precision and Bias section.
(4) Removed wording for dated technology and removed citation.
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1. Scope*
1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer
taking into consideration the change in storage of water in overlying or underlying confining beds, or both. 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 modified Hantush method (1) is limited to the determination of hydraulic properties for
aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Hantush-Jacob method (Practice
D6029/D6029M) with the exception that in this case the gain or loss of water in storage in the confining beds is taken into
consideration (see 5.1). All possible combinations of impermeable beds and source beds (for example, beds in which the head
remains uniform) are considered on the distal side of the leaky beds that confine the aquifer of interest (see Fig. 1).
1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice
D6026.
1.4.1 The procedures used to specify how data are collected/recorded and calculated in the 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 data to be commensurate with these considerations.
It is beyond the scope of these test methods to consider significant digits used in analysis methods for engineering data.
1.5 The values stated in 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 for the two
systems may result in nonconformance with the standard. Reporting of results in units other than SI shall not be regarded as
nonconformance with this standard.
1.6 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace
education or experience and should be used in conjunction with professional judgment. Not all aspects of the practice may be
applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the
adequacy of a given professional service must be judged, nor should this document be applied without the consideration of a
project’s many unique aspects. The word “Standard” in the title of this document means only that the document has been approved
through the ASTM consensus process.
1.7 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, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
D6028/D6028M − 20
1.8 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.
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
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
D6029/D6029M Practice for (Analytical Procedures) Determining Hydraulic Properties of a Confined Aquifer and a Leaky
Confining Bed with Negligible Storage by the Hantush-Jacob Method
3. Terminology
3.1 Definitions—For definitions of common technical terms used in this standard, refer to Terminology D653.
3.2 Symbols and Dimensions:
3.2.1 H (u,β)—well function for leaky systems where water storage in confining beds is important [nd].
−1
3.2.2 K—hydraulic conductivity of the aquifer [LT ].
3.2.2.1 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
3.2.3 K', K"—vertical hydraulic conductivities of the confining beds through which leakage can occur [LT ].
3 −1
3.2.4 Q—discharge [L T ].
3.2.5 S = bS —storage coefficient of the aquifer [nd].
s
3.2.6 S'5b'S' —storage coefficients of the confining beds [nd].
s
S"5b"S"
s
−1
3.2.7 S —specific storage of the aquifer [L ].
s
3.2.8 S' S" —specific storages of the confining beds.
s s
L
@ #
2 −1
3.2.9 T—transmissivity [L T ].
r s
3.2.10 u = nd .
@ #
4Tt
3.2.11 W(u,r/B)—well function for leaky aquifer systems with negligible storage changes in confining beds [ nd].
3.2.12 W(u)—well function for nonleaky aquifer systems [nd].
3.2.13 b—thickness of aquifer [ L].
3.2.14 b', b"—thicknesses of the confining beds through which leakage can occur [L].
3.2.15 r—radial distance from control well [L].
3.2.16 s—drawdown [L].
Tb'
3.2.17 B5Π@L# .
K'
3.2.18 t—time since pumping or injection began [T].
r K'S' K"S"
3.2.19 β5 SŒ 1D @nd#.
Œ
4b b'KS b"KS
s s
4. Summary of Practice
4.1 This practice 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
D6028/D6028M − 20
response in the aquifer is a function of the transmissivity and storage coefficient of the aquifer and the leakance coefficients and
storage coefficients of the confining beds. Alternatively, the practice 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 water level in
response to withdrawal in a confined aquifer. The water-level response data are analyzed using a set of type curves.
4.2 Solution—Hantush (1) gave solutions applicable to each of Ca
...