ASTM D4104/D4104M-20

Standard Practice for (Analytical Procedures) Determining Transmissivity of Nonleaky Confined Aquifers by Overdamped Well Response to Instantaneous Change in Head (Slug Tests)

SIGNIFICANCE AND USE
5.1 Assumptions of Solution of Cooper et al (1):  
5.1.1 The head change in the control well is instantaneous at time t  = 0.  
5.1.2 Well is of finite diameter and fully penetrates the aquifer.  
5.1.3 Flow in the nonleaky aquifer is radial.
Note 2: The exact conservation equation of Richards (5)with the volumetric water content can be simplified to take the form used in the solution of (1)with the storage coefficient, which implies several assumptions including that of constant total stresses (6).  
5.2 Implications of Assumptions:  
5.2.1 The mathematical equations applied ignore inertial effects and assume the water level returns the static level in an approximate exponential manner. The geometric configuration of the well and aquifer are shown in Fig. 1.
FIG. 1 Cross Section Through a Well in Which a Slug of Water is Suddenly Injected  
5.2.2 Assumptions are applicable to artesian or confined conditions and fully penetrating wells. However, this practice is commonly applied to partially penetrating wells and in unconfined aquifers where it may provide estimates of hydraulic conductivity for the aquifer interval adjacent to the open interval of the well if the horizontal hydraulic conductivity is significantly greater than the vertical hydraulic conductivity.
Note 3: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information.  
5.2.3 As pointed out by Cooper et al (1) the determination of storage coefficient by this practice has questionable reliability because of the similar shape of the curves, whereas, the determination of transmissivity is not as sensitive to choosing the correct curve. However, the curve selected should not imply a storage coefficient unrealistically large or small.
Note 4: 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 us...
SCOPE
1.1 This practice covers the determination of transmissivity from the measurement of force-free (overdamped) response of a well-aquifer system to a sudden change of water level in a well. Force-free response of water level in a well to a sudden change in water level is characterized by recovery to initial water level in an approximate exponential manner with negligible inertial effects.  
1.2 The analytical procedure in this practice is used in conjunction with the field procedure in Test Method D4044/D4044M for collection of test data.  
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity. Although the assumptions of this practice prescribe a fully penetrating well (a well open through the full thickness of the aquifer), the slug test is commonly conducted using a partially penetrating well. Such a practice may be acceptable for application under conditions in which the aquifer is stratified and horizontal hydraulic conductivity is much greater than vertical hydraulic conductivity. In such a case the test would be considered to be representative of the average hydraulic conductivity of the portion of the aquifer adjacent to the open interval of the well.  
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 this practice to consider significant digits use...

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 D5912-20 - Standard Practice for (Analytical Procedure) Determining Hydraulic Conductivity of an Unconfined Aquifer by Overdamped Well Response to Instantaneous Change in Head (Slug)
• Effective Date: 01-Jun-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 D4043-17 - Standard Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques
• Effective Date: 01-Jan-2017
• Refers: ASTM D4044/D4044M-15 - Standard Test Method for (Field Procedure) for Instantaneous Change in Head (Slug) Tests for Determining Hydraulic Properties of Aquifers (Withdrawn 2024)
• Effective Date: 01-Sep-2015
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-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 D4043-96(2010)e1 - Standard Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques
• Effective Date: 01-Aug-2010
• 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

Overview

ASTM D4104/D4104M-20 provides standardized practices for determining the transmissivity of nonleaky, confined aquifers using slug tests that measure the overdamped well response to an instantaneous change in water level (head). Developed and maintained by ASTM International, this standard outlines the analytical procedures required to interpret field data collected during slug tests, aiding in the evaluation of aquifer hydraulic properties, which are vital for groundwater resource management and environmental site assessments.

This practice focuses on analyzing the recovery behavior of the water level in a well following a rapid, force-free head change, where the return to static water level occurs in an approximately exponential fashion with negligible inertial effects. The method's underlying assumptions and practical limitations are clearly defined, ensuring the reliability and repeatability of transmissivity estimations for confined aquifers.

Key Topics

• Scope and Applicability

  • Determination of transmissivity from overdamped (force-free) well-aquifer responses to slug tests.
  • Applicable to nonleaky, confined aquifers with control wells of finite diameter that fully penetrate the aquifer.
  • Commonly used for partially penetrating wells under certain hydrogeologic conditions.

• Assumptions and Limitations

  • Head change in the control well is considered instantaneous at time zero.
  • Radial flow within the aquifer is assumed.
  • Negligible inertial effects, resulting in an exponential water level recovery curve.
  • Best suited for aquifers where horizontal hydraulic conductivity significantly exceeds vertical conductivity.
  • Less suitable for fractured rock or carbonate aquifers due to non-porous media assumptions.

• Analytical Procedures

  • Requires field data from slug tests, typically collected following ASTM D4044/D4044M.
  • Data analysis utilizes graphical solutions (type curves) to determine transmissivity, using plots that compare measured recovery with theoretical models.
  • Calculation of transmissivity is prioritized over storage coefficient due to greater reliability under the test's assumptions.

• Reporting and Quality

  • Reports must detail field setup, test procedures, hydrogeologic context, equipment specifications, and data analysis steps.
  • Emphasizes adherence to significant digits and rounding practices as described in ASTM D6026.
  • The accuracy of results depends on the competence of personnel and the suitability of equipment.

Applications

• Groundwater Resource Management

  • Used by hydrogeologists and engineers to estimate aquifer transmissivity, which informs sustainable groundwater withdrawal and supply planning.
  • Crucial for water well design, siting, and pumping tests.

• Environmental Site Assessment

  • Assists in evaluating groundwater flow characteristics to assess potential contaminant migration and risk.

• Remediation Design

  • Supports the selection and sizing of remediation technologies, including pump-and-treat systems and in situ treatments, that rely on knowledge of aquifer transmissivity.

• Regulatory Compliance

  • Provides documentation and data consistent with industry standards for regulatory submissions, permitting, and compliance monitoring in the water resources and environmental sectors.

Related Standards

• ASTM D653 - Terminology Relating to Soil, Rock, and Contained Fluids
• ASTM D4043 - Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques
• ASTM D4044/D4044M - Test Method for (Field Procedure) for Instantaneous Change in Head (Slug) Tests for Determining Hydraulic Properties of Aquifers
• ASTM D3740 - Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in Engineering Design and Construction
• ASTM D4750 - Test Method for Determining Subsurface Liquid Levels in a Borehole or Monitoring Well (Observation Well)
• ASTM D5912 - Practice for Determining Hydraulic Conductivity of an Unconfined Aquifer by Overdamped Well Response to Instantaneous Change in Head (Slug)
• ASTM D6026 - Practice for Using Significant Digits in Geotechnical Data

Summary

ASTM D4104/D4104M-20 is a vital standard for practitioners engaged in hydrogeologic investigations. By providing reliable practices for the analytical evaluation of slug test data, it ensures consistent and accurate estimation of aquifer transmissivity in various groundwater applications. Adhering to this standard supports effective resource management, environmental protection, and compliance with regulatory requirements.

Keywords: aquifer transmissivity, slug test, confined aquifer, groundwater, overdamped well response, ASTM D4104/D4104M, hydraulic conductivity, aquifer tests, transmissivity estimation, groundwater 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:D4104/D4104M −20
Standard Practice for
(Analytical Procedures) Determining Transmissivity of
Nonleaky Confined Aquifers by Overdamped Well Response
to Instantaneous Change in Head (Slug Tests)
This standard is issued under the fixed designation D4104/D4104M; 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* commensuratewiththeseconsiderations.Itisbeyondthescope
of this practice to consider significant digits used in analysis
1.1 This practice covers the determination of transmissivity
methods for engineering data.
from the measurement of force-free (overdamped) response of
a well-aquifer system to a sudden change of water level in a
1.5 Units—The values stated in either SI units or inch-
well. Force-free response of water level in a well to a sudden
pound units are to be regarded separately as standard. The
change in water level is characterized by recovery to initial
values stated in each system may not be exact equivalents;
water level in an approximate exponential manner with negli-
therefore,eachsystemshallbeusedindependentlyoftheother.
gible inertial effects.
Combining values from the two systems may result in noncon-
1.2 The analytical procedure in this practice is used in
formance with the standard. Reporting of results in units other
conjunction with the field procedure in Test Method D4044/
than SI shall not be regarded as nonconformance with this
D4044M for collection of test data.
standard.
1.3 Limitations—Slug tests are considered to provide an
1.6 This practice offers a set of instructions for performing
estimate of transmissivity. Although the assumptions of this
one or more specific operations.This document cannot replace
practiceprescribeafullypenetratingwell(awellopenthrough
educationorexperienceandshouldbeusedinconjunctionwith
the full thickness of the aquifer), the slug test is commonly
professional judgment. Not all aspects of the practice may be
conducted using a partially penetrating well. Such a practice
applicable in all circumstances. This ASTM standard is not
may be acceptable for application under conditions in which
intended to represent or replace the standard of care by which
theaquiferisstratifiedandhorizontalhydraulicconductivityis
the adequacy of a given professional service must be judged,
much greater than vertical hydraulic conductivity. In such a
nor should this document be applied without the consideration
case the test would be considered to be representative of the
ofaproject’smanyuniqueaspects.Theword“Standard”inthe
average hydraulic conductivity of the portion of the aquifer
title of this document means only that the document has been
adjacent to the open interval of the well.
approved through the ASTM consensus process.
1.4 All observed and calculated values shall conform to the
1.7 This standard does not purport to address all of the
guidelines for significant digits and rounding established in
Practice D6026. safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
1.4.1 Theproceduresusedtospecifyhowdataarecollected/
recorded and calculated in the standard are regarded as the priate safety, health, and environmental practices and deter-
industry standard. In addition, they are representative of the mine the applicability of regulatory limitations prior to use.
significant digits that generally should be retained. The proce-
1.8 This international standard was developed in accor-
dures used do not consider material variation, purpose for
dance with internationally recognized principles on standard-
obtaining the data, special purpose studies, or any consider-
ization established in the Decision on Principles for the
ations for the user’s objectives; and it is common practice to
Development of International Standards, Guides and Recom-
increase or reduce significant digits of reported data to be
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
This 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 June 1, 2020. Published June 2020. Originally
approved in 1991. Last previous edition approved in 2017 as D4104 – 17. DOI:
10.1520/D4104_D4104M-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
D4104/D4104M−20
2. Referenced Documents 3.3.5 S [nd]—storage coefficient.
3.3.6 Y [nd]—zeroorderBesselfunctionofthesecondkind.
2.1 ASTM Standards:
D653Terminology Relating to Soil, Rock, and Contained
3.3.7 Y [nd]—first order Bessel function of the second kind.
Fluids
3.3.8 r [L]—radius of control-well casing or open hole in
c
D3740Practice for Minimum Requirements for Agencies
interval where water level changes.
Engaged in Testing and/or Inspection of Soil and Rock as
3.3.9 r [L]—radius of control well screen or open hole
w
Used in Engineering Design and Construction
adjacent to water bearing unit.
D4043Guide for Selection of Aquifer Test Method in
Determining Hydraulic Properties by Well Techniques 3.3.10 u—variable of integration.
D4044/D4044MTest Method for (Field Procedure) for In-
3.3.11 H [L]—change in head in control well.
stantaneous Change in Head (Slug) Tests for Determining
3.3.12 H [L]—initial head rise (or decline) in control well.
o
Hydraulic Properties of Aquifers
3.3.13 t—time.
D4750Test Method for Determining Subsurface Liquid
Levels in a Borehole or Monitoring Well (Observation 3.3.14 β—Tt/r .
c
2 2
Well) (Withdrawn 2010)
3.3.15 α—r S/r .
w c
D5912Practice for (Analytical Procedure) Determining Hy-
draulic Conductivity of an Unconfined Aquifer by Over- 4. Summary of Practice
damped Well Response to Instantaneous Change in Head
4.1 This practice describes the analytical procedure for
(Slug)
analyzing data collected during an instantaneous head (slug)
D6026Practice for Using Significant Digits in Geotechnical
test using an overdamped well. The field procedures in
Data
conducting a slug test are given in Test Method D4044/
D4044M. The analytical procedure consists of analyzing the
3. Terminology
recovery of water level in the well following the change in
3.1 Definitions:
water level induced in the well.
3.1.1 Fordefinitionsofcommontechnicaltermsusedinthis
4.2 Solution—The solution given by Cooper et al (1) is as
standard, refer to Terminology D653.
follows:
3.2 The following terms used in this standard are contained
`
2H
o
in Terminology D653 and provided here for the convenience of 2
H 5 exp 2βu /α J ur/r (1)
* @@ ~ ! @ ~ !
0 w
π
the user. 0
3.2.1 control well—wellbywhichtheaquiferisstressed,for
@uY u 2 2αY u # 2 Y ur/r
~ ! ~ ! ~ !
0 1 0 w
example, by pumping, injection, or change of head.
3.2.2 hydraulic conductivity—(field aquifer tests), the vol-
@uJ ~u! 2 2αJ ~u!## / ∆ ~u!#du
0 1
umeofwaterattheexistingkinematicviscositythatwillmove
where:
in a unit time under a unit hydraulic gradient through a unit
2 2
α 5 r S/r ,
area measured at right angles to the direction of flow.
w c
β 5 Tt/r ,
c
3.2.3 overdamped-well response—characterized by the wa-
ter level returning to the static level in an approximately
and:
exponential manner following a sudden change in water level.
2 2
∆~u! 5 @uJ ~u! 2 2αJ ~u!# 1@uY ~u! 2 2αY ~u!#
0 1 0 1
(See for comparison underdamped-well response.)
NOTE 1—See Practice D5912 and Hvorslev (2) Bouwer and Rice (3),
and Bouwer (4).
3.2.4 slug—avolumeofwaterorsolidobjectusedtoinduce
a sudden change of head in a well.
5. Significance and Use
3.2.5 head, static—theheightaboveastandarddatumofthe
5.1 Assumptions of Solution of Cooper et al (1):
surface of a column of water (or other liquid) that can be
5.1.1 Theheadchangeinthecontrolwellisinstantaneousat
supported by the static pressure at a given point.
time t =0.
3.3 Symbols:
5.1.2 Well is of finite diameter and fully penetrates the
3.3.1 J [nd]—zero-order Bessel function of the first kind.
aquifer.
3.3.2 J [nd]—first-order Bessel function of the first kind.
1 5.1.3 Flow in the nonleaky aquifer is radial.
−1
3.3.3 K[LT ]—hydraulic conductivity.
NOTE 2—The exact conservation equation of Richards (5)with the
2 −1
3.3.4 T [L T ]—transmissivity. volumetric water content can be simplified to take the form used in the
solution of (1)with the storage coefficient, which implies several assump-
tions including that of constant total stresses (6).
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 5.2 Implications of Assumptions:
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.
3 4
The last approved version of this historical standard is referenced on The boldface numbers in parentheses refer to a list of references at the end of
www.astm.org. the text.
D4104/D4104M−20
5.2.1 The mathematical equations applied ignore inertial 6.2 The integral expression in the solution given in (Eq 1)
effects and assume the water level returns the static level in an cannot be evaluated analytically. A graphical solution for
approximate exponential manner. The geometric configuration
determination of transmissivity and coefficient of storage can
of the well and aquifer are shown in Fig. 1.
be made using a set of type curves that can be drawn from the
5.2.2 Assumptions are applicable to artesian or confined
values in Table 1.
conditions and fully penetrating wells. However, this practice
NOTE 6—Commercially available software can be used to assist in the
is commonly applied to partially penetrating wells and in
calculations, plotting, and analyses for this practice. The user should
unconfined aquifers where it may provide estimates of hydrau-
verify the correctness of the formulas, calculations, plots, and data
lic conductivity for the aquifer interval adjacent to the open
analyses.
interval of the well if the horizontal hydraulic conductivity is
significantly greater than the vertical hydraulic conductivity.
NOTE 3—Slug and pumping tests implicitly assume a porous medium.
Fractured rock and carbonate settings may not provide meaningful data
TABLE 1 Values of H/H
o
and information.
From Cooper, Bredehoeft, and Papadopulos (1)
2 −1 −2 −3 −4 −5
5.2.3 AspointedoutbyCooperetal (1)thedeterminationof β = Tt/r α 10 10 10 10 10
c
storage coefficient by this practice has questionable reliability 1.00 0.9771 0.9920 0.9969 0.9985 0.9992
−3
10 2.15 0.9658 0.9876 0.9949 0.9974 0.9985
because of the similar shape of the curves, whereas, the
4.64 0.9490 0.98
...

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: D4104 − 17 D4104/D4104M − 20
Standard Test Method Practice for
(Analytical Procedure) for Procedures) Determining
Transmissivity of Nonleaky Confined Aquifers by
Overdamped Well Response to Instantaneous Change in
Head (Slug Tests)
This standard is issued under the fixed designation D4104;D4104/D4104M; 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 the determination of transmissivity from the measurement of force-free (overdamped) response of
a well-aquifer system to a sudden change of water level in a well. Force-free response of water level in a well to a sudden change
in water level is characterized by recovery to initial water level in an approximate exponential manner with negligible inertial
effects.
1.2 The analytical procedure in this test method is used in conjunction with the field procedure in Test Method D4044 for
collection of test data.
1.3 Limitations—Slug tests are considered to provide an estimate of transmissivity. Although the assumptions of this test method
prescribe a fully penetrating well (a well open through the full thickness of the aquifer), the slug test method is commonly
conducted using a partially penetrating well. Such a practice may be acceptable for application under conditions in which the
aquifer is stratified and horizontal hydraulic conductivity is much greater than vertical hydraulic conductivity. In such a case the
test would be considered to be representative of the average hydraulic conductivity of the portion of the aquifer adjacent to the
open interval of the well.
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, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.7 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
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 Nov. 1, 2017June 1, 2020. Published November 2017June 2020. Originally approved in 1991. Last previous edition approved in 20102017 as
ɛ1
D4104 – 96 (2010)17. . DOI: 10.1520/D4104-17.10.1520/D4104_D4104M-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
D4104/D4104M − 20
D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used in
Engineering Design and Construction
D4043 Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well Techniques
D4044 Test Method for (Field Procedure) for Instantaneous Change in Head (Slug) Tests for Determining Hydraulic Properties
of Aquifers
D4750 Test Method for Determining Subsurface Liquid Levels in a Borehole or Monitoring Well (Observation Well)
(Withdrawn 2010)
D5912 Practice for (Analytical Procedure) Determining Hydraulic Conductivity of an Unconfined Aquifer by Overdamped Well
Response to Instantaneous Change in Head (Slug)
D6026 Practice for Using Significant Digits in Geotechnical Data
3. Terminology
3.1 Definitions:
3.1.1 For definitions of common technical terms used in this standard, refer to Terminology D653.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 aquifer, confined—an aquifer bounded above and below by confining beds and in which the static head is above the top
of the aquifer.
3.2.2 observation well—a well open to all or part of an aquifer.
3.2.3 transmissivity—the volume of water at the existing kinematic viscosity that will move in a unit time under a unit hydraulic
gradient through a unit width of the aquifer.
3.3 The following terms used in this standard are contained in Terminology D653 and provided here for the convenience of the
user.
3.3.1 confining bed—a hydrogeologic unit of less permeable material bounding one or more aquifers.
3.3.2 control well—well by which the aquifer is stressed, for example, by pumping, injection, or change of head.
3.3.3 hydraulic conductivity—(field aquifer tests), the volume of water at the existing kinematic viscosity that will move in a
unit time under a unit hydraulic gradient through a unit area measured at right angles to the direction of flow.
3.3.4 overdamped-well response—characterized by the water level returning to the static level in an approximately exponential
manner following a sudden change in water level. (See for comparison underdamped-well response.)
3.3.5 slug—a volume of water or solid object used to induce a sudden change of head in a well.
3.3.6 head, static—the height above a standard datum of the surface of a column of water (or other liquid) that can be supported
by the static pressure at a given point.
3.4 Symbols:
3.4.1 J [nd]—zero-order Bessel function of the first kind.
3.4.2 J [nd]—first-order Bessel function of the first kind.
−1
3.4.3 K[LT ]—hydraulic conductivity.
2 −1
3.4.4 T [L T ]—transmissivity.
3.4.5 S [nd]—storage coefficient.
3.4.6 Y [nd]—zero order Bessel function of the second kind.
3.4.7 Y [nd]—first order Bessel function of the second kind.
3.4.8 r [L]—radius of control-well casing or open hole in interval where water level changes.
c
3.4.9 r [L]—radius of control well screen or open hole adjacent to water bearing unit.
w
3.4.10 u—variable of integration.
3.4.11 H [L]—change in head in control well.
3.4.12 H [L]—initial head rise (or decline) in control well.
o
3.4.13 t—time.
3.4.14 β—Tt/r .
c
2 2
3.4.15 α—r S/r .
w c
The last approved version of this historical standard is referenced on www.astm.org.
D4104/D4104M − 20
4. Summary of Test Method
4.1 This test method describes the analytical procedure for analyzing data collected during an instantaneous head (slug) test
using an overdamped well. The field procedures in conducting a slug test are given in Test Method D4044. The analytical procedure
consists of analyzing the recovery of water level in the well following the change in water level induced in the well.
4.2 Solution—The solution given by Cooper et al (1) is as follows:
`
2H
o
H 5 @@exp ~2βu /α! @J ~ur/r ! (1)
*
0 w
π
@uY ~u! 2 2αY ~u!# 2 Y ~ur/r !
0 1 0 w
uJ u 2 2αJ u # / Δ u #du
@ ~ ! ~ !# ~ !
0 1
where:
2 2
α5 r S/r ,
w c
β5 Tt/r ,
c
and:
2 2
Δ~u! 5 @uJ ~u! 2 2αJ ~u!# 1@uY ~u! 2 2αY ~u!#
0 1 0 1
NOTE 1—See D5912 and Hvorslev (2) Bouwer and Rice (3), and Bouwer (4).
5. Significance and Use
5.1 Assumptions of Solution of Cooper et al (1):
5.1.1 The head change in the control well is instantaneous at time t = 0.
5.1.2 Well is of finite diameter and fully penetrates the aquifer.
5.1.3 Flow in the nonleaky aquifer is radial.
5.2 Implications of Assumptions:
5.2.1 The mathematical equations applied ignore inertial effects and assume the water level returns the static level in an
approximate exponential manner. The geometric configuration of the well and aquifer are shown in Fig. 1.
5.2.2 Assumptions are applicable to artesian or confined conditions and fully penetrating wells. However, this test method is
commonly applied to partially penetrating wells and in unconfined aquifers where it may provide estimates of hydraulic
conductivity for the aquifer interval adjacent to the open interval of the well if the horizontal hydraulic conductivity is significantly
greater than the vertical hydraulic conductivity.
FIG. 1 Cross Section Through a Well in Which a Slug of Water is Suddenly Injected
The boldface numbers in parentheses refer to a list of references at the end of the text.
D4104/D4104M − 20
5.2.3 As pointed out by Cooper et al (1) the determination of storage coefficient by this test method has questionable reliability
because of the similar shape of the curves, whereas, the determination of transmissivity is not as sensitive to choosing the correct
curve. However, the curve selected should not imply a storage coefficient unrealistically large or small.
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.
NOTE 3—Some published literature (5)have discussed the appropriateness of the slug test. These have not been universally accepted and the industry
continues to use this test method.
6. Procedure
6.1 The overall procedure consists of conducting the slug test field procedure (see Test Method D4044) and analysis of the field
data, that is addressed in this test method.
6.2 The integral expression in the solution given in (Eq 1) cannot be evaluated analytically. A graphical solution for
determination of transmissivity and coefficient of storage can be made using a set of type curves that can be drawn from the values
in Table 1.
7. Calculation
7.1 Prepare a semilogarithmic plot of a set of type curves of values of F(β, α) = H/H , on the arithmetic scale, as a function of
o
β, on the logarithmic scale from the values of the functions in Table 1.
7.2 Prepare a semilogarithmic plot of the same scale as that of the type-curve. Plot the water level data in the control well,
expressed as a fraction, H/H , on the arithmetic scale, versus time, t, on the logarithmic scale.
o
NOTE 4—If the water level rise is very rapid with a small disparity between the calculated and measured change in water level, then time = 0 can be
used as the instant the change was initiated and H can be the calculated rise. If there is a significant time lag between initiation of the head change and
o
the peak rise or decline is significantly less than the calculated change use t = 0 as the time of maximum observed change and take H as the maximum
o
observed change.
7.3 Overlay the data plot on the set of type curve plots and, with the arithmetic axes coincident, shift the data plot to match one
curve or an interpolated curve of the type curve set. A match point for beta, t, and alpha picked from the two graphs.
7.4 Using the coordinates of the match line, determine the transmissivity and storage coefficient from the following equations:
T 5 βr /t
c
and:
2 2
S 5 αr /r
c w
8. Data Sheets/Forms/Report
8.1 Record as a minimum the following general information (data).
8.2 Prepare a report including the information described in this section. The report of the analytical procedure will include
information from the report on test method selection (see Guide D4043) and the field testing procedure (see Test Method D4044).
8.2.1 Introduction—The introductory section is intended to present the scope and purpose of the slug test method for
determining transmissivity and storage coefficient. Summarize the field hydrogeologic conditions and the field equipment and
instrumentation including the construction of the control well, and the method of measurement and of effecting a change in head.
Discuss the rationale for selecting the method used (see Guide D4043).
8.2.2 Hydrogeologic Setting—Review information available on the hydrogeology of the site; interpret and describe the
hydrogeology of the site as it pertains to the method selected for conducting and analyzing an aquifer test. Compare hydrogeologic
characteristics of the site as it conforms and differs from assumptions made in the solution to the aquifer test method.
8.2.3 Equipment—Report the field installation and equipment for the aquifer test. Include in the report, well construction
information, diameter, depth, and open interval to the aquifer, and location of control well.
8.2.3.1 Report the techniques used 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 manufacturers name, model number,
and basic specifications for each major item, and the name and date of the last calibration, if applicable.
8.2.4 Testing Procedures—Report the steps taken in conducting the pretest and test phases. Include the frequency of head
measurements made in the control well, and other environmental data recorded before and during the testing procedure.
8.2.5 Presentation and Interpretation of Test Results:
8.2.5.1 Data—Present tables of data collected during the test.
8.2.5.2 Data Plots—Present data plots used in analysis of the data. Show overlays of data plots and type curve with match points
and corresponding values of parameters at match points.
8.2.5.3 Show calculation of transmissivity and storage coefficient in accordance with Practice D6026.
D4104/D4104M − 20
TABLE 1 Values of H/H
o
From Cooper, Bredehoeft, and Papadopulos (1)
2 −1 −2 −3 −4 −5
β = Tt/r α 10 10 10 10 10
c
1.00 0.9771 0.9920 0.9969 0.9985 0.9992
−3
10 2.15 0.9658 0.9876 0.9949 0.9974 0.9985
4.64 0.9490 0.9807 0.9914 0.9954 0.9970
1.00 0.9238 0.9693 0.9853 0.9915 0.9942
−2
10 2.15 0.8860 0.9505 0.9744 0.9841 0.9883
4.64 0.8293 0.9187 0.9545 0.9701 0.9781
1.00 0.7460 0.8655 0.9183 0.9434 0.9572
−2
10 2.15 0.8860 0.9505 0.9744 0.9841 0.9883
4.64 0.8293 0.9187 0.9545 0.9701 0.9781
1.00 0.7460 0.8655 0.9183 0.9434 0.9572
−1
10 2.15 0.6289 0.7782 0.8538 0.8935 0.9167
4.64 0.4782 0.6436 0.7436 0.8031 0.8410
1.00 0.3117 0.4598 0.5729 0.6520 0.7080
−1
10 2.15 0.6289 0.7782 0.8538 0.8935 0.9167
4.64 0.4782 0.6436 0.7436 0.8031 0.8410
1.00 0.3117 0.4598 0.5729 0.6520 0.7080
10 2.15 0.1665 0.2597 0.3543 0.4364 0.5038
4.64 0.07415 0.1086 0.1554 0.2082 0.2620
7.00 0.04625 0.06204 0.08519 0.1161 0.1521
1.00 0.03065 0.03780 0.04821 0.06355 0.08378
1.40 0.02092 0.02414 0.02844 0.03492 0.04426
10 2.15 0.01297 0.01414 0.01545 0.01723 0.01999
3.00 0.009070 0.009615 0.01016 0.01083 0.01169
4.64 0.005711 0.004919 0.006111 0.006319 0.006554
7.00 0.003722 0.003809 0.003884 0.003962 0.004046
1.00 0.002577 0.002618 0.002653 0.002688 0.002725
10 2.15 0.001179 0.001187 0.001194 0.001201 0.001208
From Papadopulos, Bredehoeft, and Cooper (6)
From Papadopulos, Bredehoeft, and Cooper (8)
2 −6 −7 −8 −9 −10
β = Tt/r α 10 10 10 10 10
c
1 0.9994 0.9996 0.9996 0.9997 0.9997
2 0.9989 0.9992 0.9993 0.9994 0.9995
1 0.9994 0.9996 0.9996 0.9997 0.9997
2 0.9989 0.9992 0.9993 0.9994 0.9995
−3
10 4 0.9980 0.9985 0.9987 0.9989 0.9991
6 0.9972 0.9978 0.9982 0.9984 0.9986
8 0.9964 0.9971 0.9976 0.9980 0.9982
1 0.9956 0.9965 0.9971 0.9975 0.9978
2 0.9919 0.9934 0.9944 0.9952 0.9958
−2
10 4 0.9848 0.9875 0.9894 0.9908 0.9919
6 0.9782 0.9819 0.9846 0.9866 0.9881
8 0.9718 0.9765 0.9799 0.9824 0.9844
1 0.9655 0.9712 0.9753 0.9784 0.9807
2 0.9361 0.9459 0.9532 0.9587 0.9631
−1
10 4 0.8828 0.8995 0.9122 0.9220 0.9298
6 0.8345 0.8569 0.8741 0.8875 0.8984
8 0.7901 0.8173 0.8383 0.8550 0.8686
1 0.7489 0.7801 0.8045 0.8240 0.8401
2 0.5800 0.6235 0.6591 0.6889 0.7139
3 0.4554 0.5033 0.5442 0.5792 0.6096
4 0.3613 0.4093 0.4517 0.4891 0.5222
10 5 0.2893 0.3351 0.3768 0.4146 0.4487
6 0.2337 0.2759 0.3157 0.3525 0.3865
7 0.1903 0.2285 0.2655 0.3007 0.3337
8 0.1562 0.1903 0.2243 0.2573 0.2888
9 0.1292 0.1594 0.1902 0.2208 0.2505
1 0.1078 0.1343 0.1620 0.1900 0.2178
2 0.02720 0.03343 0.04129 0.05071 0.06149
3 0.01286 0.01448 0.01667 0.01956 0.02320
10 4 0.008337 0.008898 0.009637 0.01062 0.01190
5 0.006209 0.006470 0.006789 0.007192 0.007709
6 0.004961 0.005111 0.005283 0.005487 0.005735
8 0.003547 0.003617 0.003691 0.003773 0.003863
1 0.002763 0.002803 0.002845 0.002890 0.002938
10 2 0.001313 0.001322 0.001330 0.001339 0.001348
8.2.5.4 Evaluate the overall quality of the test on the basis of the adequacy of instrumentation and observations of stress and
response and the conformance of the hydrogeologic conditions and the performance of the test to the assumptions (see 5.1).
D4104/D4104M − 20
9. Precision and Bias
9.1 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.
9.2 Bias—There is not accepted reference value for this test method, therefore, bias cannot be determined.
10. Keywords
10.1 aquifers; aquifer tests; control wells; groundwater; hydraulic conductivity; storage coefficient storativity; transmissivity
REFERENCES
(1) Cooper, H. H., Jr., Bredehoeft, J. D., and Papadopulos, I. S., “Response of a Finite-Diameter Well to an Instantaneous Charge of Water,” Water
Resources Research, Vol 3, No. 1, 1967, pp. 263–269.
(2) Hvorslev, M. J., “Time Lag and Soil Permeability in Ground-Water Observations,” Waterways Experiment Station, Corps of Engineers, U.S. Army,
Bulletin No. 36, 1951, p. 50.
(3) Bouwer, H., and Rice, R. C., “A Slug Test for Determining Hydraulic Conductivity of Unconfined Aquifers with Completely or Partially Penetrating
Wells,” Water Resources Research, Vol 12, No. 3, 1976, pp. 423–423.
(4) Bouwer, H., “The Bouwer-Rice Slug Test—An Update,” Ground Water, Vol 27, No. 3, 1989, pp. 304–309.
(5) Chapuis, R., “Overdamped Slug Tests in Aquifers: The three diagnostic graphs for user-independent interpretation,” Geotechnical Testing Journal,
Vol 38, No. 4, pp 474-489.
(6) Papadopulos, I. S., Bredehoeft, J. D., and Cooper, H. H., Jr.,“ On the Analysis of Slug Test Data,” Water Resources Research, Vol 9, No. 4, 1973,
pp. 1087–1089.
SUMMARY OF CHANGES
ɛ1
Committee D81 has identified the location of selected changes to this standard since the last issue (96(2010) )
that may impact the use of this standard.
...