ASTM D5850-20

Standard Practice for (Analytical Procedure) Determining Transmissivity, Storage Coefficient, and Anisotropy Ratio from a Network of Partially Penetrating Wells

SIGNIFICANCE AND USE
5.1 This practice is one of several available for determining vertical anisotropy ratio. Among other available methods are Weeks ((5); see Practice D5473/D5473M), that relies on distance-drawdown data, and Way and McKee (6), that utilizes time-drawdown data. An important restriction of the Weeks distance-drawdown method is that the observation wells need to have identical construction (screened intervals) and two or more of the observation wells need to be located at a distance from the pumped well beyond the effects of partial penetration. The procedure described in this practice general distance-drawdown method, in that it works in theory for most observation well configurations incorporating three or more wells, provided some of the wells are within the zone where flow is affected by partial penetration.  
5.2 Assumptions:  
5.2.1 Control well discharges at a constant rate, Q.  
5.2.2 Control well is of infinitesimal diameter and partially penetrates the aquifer.  
5.2.3 Data are obtained from a number of partially penetrating observation wells, some screened at elevations similar to that in the pumped well and some screened at different elevations.  
5.2.4 The aquifer is confined, homogeneous and areally extensive. The aquifer may be anisotropic, and, if so, the directions of maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.  
5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.  
5.3 Calculation Requirements—Application of this method is computationally intensive. The function, fs, shown in (Eq 4) should be evaluated numerous times using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of values for fs and, because this equation is rather formidable, it may not be easily tractable by hand. Because of this, it is assumed the practitioner using this will have available a computerized procedure for evaluating the function fs. This can be accomplished u...
SCOPE
1.1 This practice covers an analytical procedure for determining the transmissivity, storage coefficient, and ratio of vertical to horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-rate pumping test. This practice uses data from a minimum of four partially penetrating, recommended to be positioned observation wells around a partially penetrating control well.  
1.2 The analytical procedure is used in conjunction with the field procedure in Test Method D4050.  
1.3 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this practice.  
1.4 Units—The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are mathematical conversions, which are provided for information purposes only and are not considered standard. The reporting of results in units other than inch-pound shall not be regarded as nonconformance with this standard.  
1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026, unless superseded by this standard.  
1.6 The procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objective; and it is common practice to increase or reduce the significant digits of reported data to be commensurate with these considerations. It is beyond the scope of this standard to consider significant digits used in analysis method or engineeri...

General Information

• Status: Published
• Publication Date: 31-May-2020
• ICS: 13.060.10 - Water of natural resources
• ICS: 73.100.30 - Equipment for drilling and mine excavation
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Replaces: ASTM D5850-18 - Standard Test Method for (Analytical Procedure) Determining Transmissivity, Storage Coefficient, and Anisotropy Ratio from a Network of Partially Penetrating Wells
• Effective Date: 01-Jun-2020
• 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 D5473/D5473M-15 - Standard Test Method for (Analytical Procedure for) Analyzing the Effects of Partial Penetration of Control Well and Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer
• Effective Date: 01-Nov-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

Overview

ASTM D5850-20 is a standard practice developed by ASTM International that specifies an analytical procedure for determining aquifer transmissivity, storage coefficient, and the vertical-to-horizontal hydraulic conductivity ratio using drawdown measurements from a network of partially penetrating wells during a constant-rate pumping test. This practice is widely used in hydrogeologic investigations focusing on confined aquifers, where understanding hydraulic properties and anisotropy is essential for groundwater resource management, site assessment, and remediation projects.

The method requires observation wells installed at various depths and distances from a partially penetrating control well. It relies on corrections for partial penetration effects and iterative data analysis to provide accurate estimates of aquifer properties, even in complex anisotropic conditions.

Key Topics

• Transmissivity: The ability of an aquifer to transmit water, measured using data from multiple observation wells during a controlled pumping test.
• Storage Coefficient: A dimensionless value representing how much water an aquifer releases or stores per unit change in hydraulic head.
• Hydraulic Conductivity Anisotropy: The ratio of vertical to horizontal hydraulic conductivity, important for understanding flow patterns in heterogeneous groundwater systems.
• Partial Penetration Effects: Adjustment of observed drawdown values to account for wells not fully penetrating the aquifer, using analytical corrections.
• Iterative Analysis: The method requires iterative calculations to refine corrections and improve estimates of aquifer transmissivity, storage coefficient, and anisotropy.
• Computational Requirements: Due to the complexity of the corrections and calculations, the standard assumes the use of spreadsheet applications or mathematical software for data analysis.
• Test Set-Up: Involves at least four observation wells, paired at two locations and at different screened elevations, strategically placed to maximize the quality of aquifer data.

Applications

ASTM D5850-20 is extensively used by hydrogeologists, engineering consultants, and environmental professionals who need to characterize groundwater flow, storage, and anisotropic behavior in confined aquifers. Key practical applications include:

• Groundwater Resource Assessment: Determining aquifer capacity and behavior for water supply planning and management.
• Site Investigation: Characterizing subsurface hydraulic properties before construction, remediation, or resource development.
• Contaminant Hydrogeology: Supporting design and monitoring of remediation systems in anisotropic aquifers where accurate flow modeling is crucial.
• Water Well Design: Informing well installation, spacing, and completion strategies based on transmissivity and hydraulic conductivity.
• Regulatory Compliance: Providing standardized data for permits, reports, and regulatory submissions in accordance with industry best practices.

The practice is particularly valuable when observation wells are of varied construction and when well screens are at different elevations-conditions common in many real-world hydrogeological investigations.

Related Standards

To ensure comprehensive groundwater testing and reporting, ASTM D5850-20 should be used in conjunction with other key ASTM standards, including:

• ASTM D4050: Standard Test Method for Field Procedure for Withdrawal and Injection Well Testing for Determining Hydraulic Properties of Aquifer Systems.
• ASTM D5473/D5473M: Analytical Procedure for Analyzing the Effects of Partial Penetration and Determining Horizontal and Vertical Hydraulic Conductivity.
• ASTM D653: Terminology Relating to Soil, Rock, and Contained Fluids.
• ASTM D3740: Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock.
• ASTM D6026: Practice for Using Significant Digits in Geotechnical Data.

By adhering to ASTM D5850-20 and its related practices, professionals ensure standardized, reliable aquifer testing and data analysis, supporting high-quality groundwater investigations and informed decision-making.

Keywords: transmissivity, storage coefficient, hydraulic conductivity, anisotropy, aquifer test, ASTM D5850-20, groundwater, observation wells, pumping test, drawdown, aquifer properties, groundwater assessment.

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: D5850 − 20
Standard Practice for
(Analytical Procedure) Determining Transmissivity, Storage
Coefficient, and Anisotropy Ratio from a Network of
Partially Penetrating Wells
This standard is issued under the fixed designation D5850; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* commensuratewiththeseconsiderations.Itisbeyondthescope
of this standard to consider significant digits used in analysis
1.1 This practice covers an analytical procedure for deter-
method or engineering design.
mining the transmissivity, storage coefficient, and ratio of
vertical to horizontal hydraulic conductivity of a confined 1.7 This practice offers a set of instructions for performing
aquifer using observation well drawdown measurements from one or more specific operations.This document cannot replace
a constant-rate pumping test. This practice uses data from a educationorexperienceandshouldbeusedinconjunctionwith
minimum of four partially penetrating, recommended to be professional judgment. Not all aspects of the practice may be
positioned observation wells around a partially penetrating applicable in all circumstances. This ASTM standard is not
control well. intended to represent or replace the standard of care by which
the adequacy of a given professional service must be judged,
1.2 Theanalyticalprocedureisusedinconjunctionwiththe
nor should this document be applied without the consideration
field procedure in Test Method D4050.
ofaproject’smanyuniqueaspects.Theword“Standard”inthe
1.3 Limitations—The limitations of the technique for deter-
title of this document means only that the document has been
mination of the horizontal and vertical hydraulic conductivity
approved through the ASTM consensus process.
ofaquifersareprimarilyrelatedtothecorrespondencebetween
1.8 This standard does not purport to address all of the
the field situation and the simplifying assumption of this
safety concerns, if any, associated with its use. It is the
practice.
responsibility of the user of this standard to establish appro-
1.4 Units—The values stated in inch-pound units are to be
priate safety, health, and environmental practices and deter-
regarded as the standard.The SI units given in parentheses are
mine the applicability of regulatory limitations prior to use.
mathematical conversions, which are provided for information
1.9 This international standard was developed in accor-
purposes only and are not considered standard. The reporting
dance with internationally recognized principles on standard-
of results in units other than inch-pound shall not be regarded
ization established in the Decision on Principles for the
as nonconformance with this standard.
Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.5 All observed and calculated values shall conform to the
Barriers to Trade (TBT) Committee.
guidelines for significant digits and rounding established in
Practice D6026, unless superseded by this standard.
2. Referenced Documents
1.6 The procedures used to specify how data are collected/
2.1 ASTM Standards:
recorded or calculated in this standard are regarded as the
D653Terminology Relating to Soil, Rock, and Contained
industry standard. In addition, they are representative of the
Fluids
significant digits that generally should be retained. The proce-
D3740Practice for Minimum Requirements for Agencies
dures used do not consider material variation, purpose for
Engaged in Testing and/or Inspection of Soil and Rock as
obtaining the data, special purpose studies, or any consider-
Used in Engineering Design and Construction
ations for the user’s objective; and it is common practice to
D4050Test Method for (Field Procedure) for Withdrawal
increase or reduce the significant digits of reported data to be
and Injection Well Testing for Determining Hydraulic
Properties of Aquifer Systems
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. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved June 1, 2020. Published June 2020. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1995. Last previous edition approved in 2018 as D5850–18. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D5850-20. 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
D5850 − 20
D5473/D5473MPractice for (Analytical Procedures) Ana- 3.3.4 d—distance from top of aquifer to top of screened
lyzing the Effects of Partial Penetration of Control Well interval of control well [L].
and Determining the Horizontal and Vertical Hydraulic
3.3.5 d'—distance from top of aquifer to top of screened
Conductivity in a Nonleaky Confined Aquifer
interval of observation well [L].
D6026Practice for Using Significant Digits in Geotechnical
3.3.6 f —incremental dimensionless drawdown component
s
Data
resulting from partial penetration [ nd].
−1
3. Terminology
3.3.7 K—hydraulic conductivity [LT ].
3.3.7.1 Discussion—The use of symbol K for the term
3.1 Definitions:
hydraulic conductivity is the predominant usage in groundwa-
3.1.1 For definitions of common technical terms in this
ter literature by hydrogeologists, whereas the symbol k is
standard, see Terminology D653.
commonly used for this term in the rock and soil mechanics
3.2 The following definitions from Terminology D653 are
literature.
used in this standard and are presented for the convenience of
3.3.8 K —modified Bessel function of the second kind and
the user. o
zero order.
3.2.1 anisotropy—having different properties in different
directions.
3.3.9 K —hydraulic conductivity in the plane of the aquifer,
r
radially from the control well (horizontal hydraulic conductiv-
3.2.2 confined aquifer—in hydrogeology, an aquifer
−1
ity) [LT ].
bounded above and below by confining beds and in which the
static head is above the top of the aquifer.
3.3.10 K —hydraulicconductivitynormaltotheplaneofthe
z
−1
aquifer (vertical hydraulic conductivity) [LT ].
3.2.3 control well—in aquifer testing, well by which the
aquifer is stressed, for example, by pumping, injection, or
3.3.11 l—distancefromtopofaquifertobottomofscreened
change of head.
interval of control well [L].
3.2.4 drawdown [L]—in field aquifer tests, vertical distance
3.3.12 l'—distancefromtopofaquifertobottomofscreened
the free water elevation is lowered or the pressure head is
interval of observation well [L].
reduced due to the removal of free water. 3 −1
3.3.13 Q—discharge [L T ].
3.2.5 hydraulic conductivity—in field aquifer tests, the vol-
3.3.14 r—radial distance from control well [L].
umeofwaterattheexistingkinematicviscositythatwillmove
3.3.15 S—storage coefficient [nd].
in a unit time under a unit hydraulic gradient through a unit
3.3.16 s—drawdown observed in partially penetrating well
area measured at right angles to the direction of flow.
network [L].
3.2.6 monitoring well (observation well), n—in
3.3.17 s —drawdown observed in fully penetrating well
hydrogeology, a well installed, usually of small diameter, for
f
network [L].
measuring water levels, collecting water samples, or determin-
2 −1
ing other ground water characteristics.
3.3.18 T—transmissivity [L T ].
3.2.6.1 Discussion—The well may be cased or uncased, but
3.3.19 t—time since pumping began [T].
if cased the casing should have openings to allow flow of
3.3.20 u—(r S)/(4Tt)[nd ].
ground water into or out of the casing, such as a well screen.
3.3.21 W(u)—an exponential integral known in hydrology
3.2.7 storage coeffıcient—in aquifers, the volume of water
as the Theis well function of u[nd].
that an aquifer releases from or takes into storage per unit
surface area of the aquifer per unit change in head. For a
4. Summary of Practice
confined aquifer, the storage coefficient is equal to the product
ofthespecificstorageandaquiferthickness.Foranunconfined
4.1 This practice makes use of the deviations in drawdown
aquifer, the storage coefficient is approximately equal to the
near a partially penetrating control well from those that would
specific yield.
occur near a control well fully penetrating the aquifer. In
general, drawdown within the screened horizon of a partially
3.2.8 transmissivity—in aquifers,thevolumeofwateratthe
penetrating control well tends to be greater than that which
existingkinematicviscositythatwillmoveinaunittimeunder
would have been observed near a fully penetrating well,
a unit hydraulic gradient through a unit width of the aquifer.
whereasthedrawdownaboveorbelowthescreenedhorizonof
3.2.8.1 Discussion—It is equal to an integration of the
the partially penetrating control well tends to be less than the
hydraulicconductivitiesacrossthesaturatedpartoftheaquifer
corresponding fully penetrating case. Drawdown deviations
perpendicular to the flow paths.
due to partial penetration are amplified when the vertical
3.3 Symbols and Dimensions:
hydraulic conductivity is less than the horizontal hydraulic
3.3.1 A—K /K , anisotropy ratio [nd].
z r
conductivity. The effects of partial penetration diminish with
3.3.2 b—thickness of aquifer [L].
increasing distance from the pumped well, becoming negli-
1/2
3.3.3 C —drawdown correction factor, equal to the ratio of gible at a distance of about 1.5b/(K /K ) . This practice relies
f z r
the drawdown for a fully penetrating well network to the on obtaining drawdown measurements at a minimum of two
drawdown for a partially penetrating well network (W(u)/ locations within this distance of the pumped well and at each
(W(u) + f )). location obtaining data from observation wells completed to
s
D5850 − 20
two different depths. At each location, one observation well process is repeated until the calculated T and S values change
shouldbescreenedataboutthesameelevationasthescreenin only slightly from those obtained in the previous iteration.
the pumped well, while the other observation well should be 4.2.4 The correction factors are also a function of the
screened in sediments not screened by the pumped well. anisotropy ratio, A. For this reason, the calculations described
above should be performed for several different assumed
NOTE 1—Slug and pumping tests implicitly assume a porous medium.
anisotropy ratios. The assumed anisotropy value that leads to
Fractured rock and carbonate settings may not provide meaningful data
the best solution, that is, best straight line fit or best curve
and information.
3 match, is deemed to be the actual anisotropy ratio.
4.2 According to Theis (1), the drawdown around a fully
penetrating control well pumped at a constant rate and tapping
5. Significance and Use
a homogeneous, confined aquifer is as follows:
5.1 This practice is one of several available for determining
Q
s 5 W u (1) vertical anisotropy ratio. Among other available methods are
~ !
f
4πT
Weeks ((5); see Practice D5473/D5473M), that relies on
where: distance-drawdowndata,andWayandMcKee (6),thatutilizes
time-drawdown data. An important restriction of the Weeks
2x
` e
W u 5 dx (2)
~ ! *
distance-drawdown method is that the observation wells need
u x
to have identical construction (screened intervals) and two or
4.2.1 Drawdown near a partially penetrating control well
more of the observation wells need to be located at a distance
pumped at a constant rate and tapping a homogeneous,
fromthepumpedwellbeyondtheeffectsofpartialpenetration.
anisotropic, confined aquifer is presented by Hantush (2, 3, 4):
The procedure described in this practice general distance-
drawdown method, in that it works in theory for most obser-
Q
s 5 ~W~u!1f ! (3)
s vation well configurations incorporating three or more wells,
4πT
provided some of the wells are within the zone where flow is
According to Hantush (2, 3, 4), at late pumping times, when
affected by partial penetration.
t>b S/(2TA), f can be expressed as follows:
s
5.2 Assumptions:
`
4b 1 nπr=K /K 5.2.1 Control well discharges at a constant rate, Q.
z r
f 5 K S D (4)
S D
2 2
s ( o
π l 2 d l'2d' n b
~ !~ ! 5.2.2 Control well is of infinitesimal diameter and partially
n51
penetrates the aquifer.
nπi nπd nπl' nπd'
5.2.3 Dataareobtainedfromanumberofpartiallypenetrat-
sin 2 sin sin 2 sin
F S D S DGF S D S DG
b b b b
ing observation wells, some screened at elevations similar to
that in the pumped well and some screened at different
4.2.2 For a given observed drawdown, it is practicable to
elevations.
compute a correction factor, C, defined as the ratio of the
f
5.2.4 The aquifer is confined, homogeneous and areally
drawdown for a fully penetrating well to the drawdown for a
extensive. The aquifer may be anisotropic, and, if so, the
partially penetrating well:
directions of maximum and minimum hydraulic conductivity
W u
~ !
are horizontal and vertical, respectively.
C 5 (5)
f
W~u!1f
s
5.2.5 Discharge from the well is derived exclusively from
storage in the aquifer.
The observed drawdown for each observation well may be
corrected to the fully penetrating equivalent drawdown by
5.3 Calculation Requirements—Application of this method
multiplying by the correction factor:
is computationally intensive. The function, f , shown in (Eq 4)
s
should be evaluated numerous times using arbitrary input
s 5 C s (6)
f f
parameters. It is not practical to use existing, somewhat
The drawdown values corresponding to the fully penetrating
limited, tables of values for f and, because this equation is
s
casemaythenbeanalyzedbyconventionaldistance-drawdown
rather formidable, it may not be easily tractable by hand.
methods to compute transmissivity and storage coefficient.
Because of this, it is assumed the practitioner using this will
4.2.3 The correction factors are a function of both transmis-
have available a computerized procedure for evaluating the
sivity and storage coefficient, that are the parameters being
function f . This can be accomplished using commercially
s
sought. Because of this, the practice relies on an iterative
available mathematical software including some spreadsheet
procedureinwhichaninitialestimateof Tand Saremadefrom
applications, or by writing programs. (7)
which initial correction factors are computed. Using these
NOTE 2—The quality of the result produced by this standard is
correction factors, fully penetrating drawdown values are
dependent on the competence of the personnel performing it, and the
computed and analyzed using distance-drawdown methods to
suitability of the equipment and facilities used. Agencies that meet the
determine revised values for T and S. The revised T and S
criteria of Practice D3740 are generally considered capable of competent
values are used to compute revised correction factors, C. This
and objective testing/sampling/inspection/etc. Users of this standard are
f
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.
The boldface numbers given in parentheses refer to a list of references at the NOTE 3—Most fractured (unconfined) aquifers, even noncarbonates,
end of the text. will have some form of convergent flow to master fissures or channels
D5850 − 20
(Worthington et al., 2016).Arelationship is known to occur in carbonates
during the test. Check to see that hand measurements of
where potentiometric troughs correspond with sub-surface conduits or
drawdown agree well with electronically measured values.
channels (Quinlan and Ewers, 1989).
Finally, check the background water-level fluctuations ob-
NOTE 4—Commercially available software is available for the
served prior to or following the pumping test to see if
calculating, graphing, plotting, and analyses of this practice. The user
adjustmentsneedtobemadetotheobserveddrawdownvalues
should verify the correctness of the formulas, graphs, plots and analyses
of the software.
to account for background fluctuations. If appropriate, adjust
the observed drawdown values accordingly.
6. Apparatus
7.3 Analysis of the field data is described in Section 8.
6.1 Apparatus for withdrawal tests is given in Test Method
D4050. The apparatus described below are those components
8. Calculation and Interpretation of Results
of the apparatus that require special attributes for this specific
8.1 Initial Estimates of Transmissivity and Storage
test.
Coeffıcient—This practice requires that initial estimates of T
6.2 Construction of the Control Well—Screen the control
and S be obtained. These estimates can be made using a wide
wellthroughonlypartoftheverticalextentoftheaquifertobe
variety of procedures, including time-drawdown analysis, re-
tested.Theexactdistancesfromthetopoftheaquifertothetop
covery analysis, distance-drawdown analysis, estimation of T
and bottom of the pumped well screen interval should be
using specific capacity, grain-size analyses of formation
known.
samples, or results of laboratory permeability tests, and esti-
mation of storage coefficient based on geology, sediment type,
6.3 Construction and Placement of Observation Wells—The
and aquifer thickness.
procedure will work for arbitrary positioning of observation
wells and placement of their screens, as long as three or more
8.2 Select Data for Analysis—This test method requires a
observation wells are used and some of the observation wells
singledrawdownobservationforeachobservationwellusedin
fall inside the zone where flow is affected by partial
the test. The drawdowns used should correspond to the same
penetration, that is, the area where significant vertical flow
timesincepumpingbegan,usuallynearorattheendofthetest.
components exists. However, strategic selection of the number
Select a time, t, late enough in the test so that it satisfies the
and location of observation wells will increase the potential
relationship t > b S/(2TA).
quality of the data set and improve the reliability of the
8.3 Distance-Drawdown Analysis Methods—The selected
interpretation.
drawdown values will be corrected
...

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: D5850 − 18 D5850 − 20
Standard Test Method for (Analytical Procedure) Practice for
(Analytical Procedure) Determining Transmissivity, Storage
Coefficient, and Anisotropy Ratio from a Network of
Partially Penetrating Wells
This standard is issued under the fixed designation D5850; 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, storage coefficient, and ratio of vertical
to horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-rate
pumping test. This test method uses data from a minimum of four partially penetrating, recommended to be positioned observation
wells around a partially penetrating control well.
1.2 The analytical procedure is used in conjunction with the field procedure in Test Method D4050.
1.3 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of
aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this test method.
1.4 Units—The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are
mathematical conversions, which are provided for information purposes only and are not considered standard.
1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice
D6026, unless superseded by this standard.
1.6 The procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industry
standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not
consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objective;
and it is common practice to increase or reduce the significant digits of reported data to be commensurate with these considerations.
It is beyond the scope of this standard to consider significant digits used in analysis method or engineering design.
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.
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
D5473/D5473M Test Method for (Analytical Procedure for) Analyzing the Effects of Partial Penetration of Control Well and
Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer
This test method practice is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater
and Vadose Zone Investigations.
Current edition approved Jan. 1, 2018June 1, 2020. Published February 2018June 2020. Originally approved in 1995. Last previous edition approved in 20122018 as
D5850 – 95 (2012).D5850 – 18. DOI: 10.1520/D5850-18.10.1520/D5850-20.
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
D5850 − 20
D6026 Practice for Using Significant Digits in Geotechnical Data
3. Terminology
3.1 Definitions:
3.1.1 For definitions of common technical terms in this standard, see Terminology D653.
3.2 The following definitions from Terminology D653 are used in this standard and are presented for the convenience of the
user.
3.2.1 anisotropy—having different properties in different directions.
3.2.2 confined aquifer—in hydrogeology, an aquifer bounded above and below by confining beds and in which the static head
is above the top of the aquifer.
3.2.3 control well—in aquifer testing, well by which the aquifer is stressed, for example, by pumping, injection, or change of
head.
3.2.4 drawdown [L]—in field aquifer tests, vertical distance the free water elevation is lowered or the pressure head is reduced
due to the removal of free water.
3.2.5 hydraulic conductivity—in 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.
3.2.6 monitoring well (observation well), n—in hydrogeology, a well installed, usually of small diameter, for measuring water
levels, collecting water samples, or determining other groundwater characteristics.
3.2.6.1 Discussion—
The well may be cased or uncased, but if cased the casing should have openings to allow flow of groundwater into or out of the
casing, such as a well screen.
3.2.7 storage coeffıcient—in aquifers, the volume of water that an aquifer releases from or takes into storage per unit surface
area of the aquifer per unit change in head. For a confined aquifer, the storage coefficient is equal to the product of the specific
storage and aquifer thickness. For an unconfined aquifer, the storage coefficient is approximately equal to the specific yield.
3.2.8 transmissivity—in aquifers, 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.
3.2.8.1 Discussion—
It is equal to an integration of the hydraulic conductivities across the saturated part of the aquifer perpendicular to the flow paths.
3.3 Symbols and Dimensions:
3.3.1 A—K /K , anisotropy ratio [nd].
z r
3.3.2 b—thickness of aquifer [L].
3.3.3 C —drawdown correction factor, equal to the ratio of the drawdown for a fully penetrating well network to the drawdown
f
for a partially penetrating well network (W(u)/(W(u) + f )).
s
3.3.4 d—distance from top of aquifer to top of screened interval of control well [L].
3.3.5 d'—distance from top of aquifer to top of screened interval of observation well [L].
3.3.6 f —incremental dimensionless drawdown component resulting from partial penetration [ nd].
s
−1
3.3.7 K—hydraulic conductivity [LT ].
3.3.7.1 Discussion—
The use of 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 the rock and soil mechanics literature.
3.3.8 K —modified Bessel function of the second kind and zero order.
o
3.3.9 K —hydraulic conductivity in the plane of the aquifer, radially from the control well (horizontal hydraulic conductivity)
r
−1
[LT ].
−1
3.3.10 K —hydraulic conductivity normal to the plane of the aquifer (vertical hydraulic conductivity) [LT ].
z
3.3.11 l—distance from top of aquifer to bottom of screened interval of control well [L].
3.3.12 l'—distance from top of aquifer to bottom of screened interval of observation well [L].
D5850 − 20
3 −1
3.3.13 Q—discharge [L T ].
3.3.14 r—radial distance from control well [L].
3.3.15 S—storage coefficient [nd].
3.3.16 s—drawdown observed in partially penetrating well network [L].
3.3.17 s —drawdown observed in fully penetrating well network [L].
f
2 −1
3.3.18 T—transmissivity [L T ].
3.3.19 t—time since pumping began [T].
3.3.20 u—(r S)/(4Tt) [nd ].
3.3.21 W(u)—an exponential integral known in hydrology as the Theis well function of u[nd].
4. Summary of Test Method
4.1 This test method makes use of the deviations in drawdown near a partially penetrating control well from those that would
occur near a control well fully penetrating the aquifer. In general, drawdown within the screened horizon of a partially penetrating
control well tends to be greater than that which would have been observed near a fully penetrating well, whereas the drawdown
above or below the screened horizon of the partially penetrating control well tends to be less than the corresponding fully
penetrating case. Drawdown deviations due to partial penetration are amplified when the vertical hydraulic conductivity is less than
the horizontal hydraulic conductivity. The effects of partial penetration diminish with increasing distance from the pumped well,
1/2
becoming negligible at a distance of about 1.5b/(K /K ) . This test method relies on obtaining drawdown measurements at a
z r
minimum of two locations within this distance of the pumped well and at each location obtaining data from observation wells
completed to two different depths. At each location, one observation well should be screened at about the same elevation as the
screen in the pumped well, while the other observation well should be screened in sediments not screened by the pumped well.
4.2 According to Theis (1), the drawdown around a fully penetrating control well pumped at a constant rate and tapping a
homogeneous, confined aquifer is as follows:
Q
s 5 W u (1)
~ !
f
4πT
where:
2x
` e
W u 5 dx (2)
~ ! *
u x
4.2.1 Drawdown near a partially penetrating control well pumped at a constant rate and tapping a homogeneous, anisotropic,
confined aquifer is presented by Hantush (2, 3, 4):
Q
s 5 W u 1f (3)
~ ~ ! !
s
4πT
According to Hantush (2, 3, 4), at late pumping times, when t > b S/(2TA), f can be expressed as follows:
s
`
4b 1 nπr=K /K
z r
f 5 K S D (4)
2 S 2D
s ( o
π ~l 2 d! ~l'2d'! n b
n51
nπi nπd nπl' nπd'
sin 2 sin sin 2 sin
F S D S DG F S D S DG
b b b b
4.2.2 For a given observed drawdown, it is practicable to compute a correction factor, C , defined as the ratio of the drawdown
f
for a fully penetrating well to the drawdown for a partially penetrating well:
W~u!
C 5 (5)
f
W u 1f
~ !
s
The observed drawdown for each observation well may be corrected to the fully penetrating equivalent drawdown by
multiplying by the correction factor:
s 5 C s (6)
f f
The drawdown values corresponding to the fully penetrating case may then be analyzed by conventional distance-drawdown
methods to compute transmissivity and storage coefficient.
4.2.3 The correction factors are a function of both transmissivity and storage coefficient, that are the parameters being sought.
Because of this, the test method relies on an iterative procedure in which an initial estimate of T and S are made from which initial
The boldface numbers given in parentheses refer to a list of references at the end of the text.
D5850 − 20
correction factors are computed. Using these correction factors, fully penetrating drawdown values are computed and analyzed
using distance-drawdown methods to determine revised values for T and S. The revised T and S values are used to compute revised
correction factors, C . This process is repeated until the calculated T and S values change only slightly from those obtained in the
f
previous iteration.
4.2.4 The correction factors are also a function of the anisotropy ratio, A. For this reason, the calculations described above must
be performed for several different assumed anisotropy ratios. The assumed anisotropy value that leads to the best solution, that is,
best straight line fit or best curve match, is deemed to be the actual anisotropy ratio.
5. Significance and Use
5.1 This test method is one of several available for determining vertical anisotropy ratio. Among other available methods are
Weeks ((5); see Test Method D5473/D5473M), that relies on distance-drawdown data, and Way and McKee (6), that utilizes
time-drawdown data. An important restriction of the Weeks distance-drawdown method is that the observation wells need to have
identical construction (screened intervals) and two or more of the observation wells need to be located at a distance from the
pumped well beyond the effects of partial penetration. The procedure described in this test method general distance-drawdown
method, in that it works in theory for most observation well configurations incorporating three or more wells, provided some of
the wells are within the zone where flow is affected by partial penetration.
5.2 Assumptions:
5.2.1 Control well discharges at a constant rate, Q.
5.2.2 Control well is of infinitesimal diameter and partially penetrates the aquifer.
5.2.3 Data are obtained from a number of partially penetrating observation wells, some screened at elevations similar to that
in the pumped well and some screened at different elevations.
5.2.4 The aquifer is confined, homogeneous and areally extensive. The aquifer may be anisotropic, and, if so, the directions of
maximum and minimum hydraulic conductivity are horizontal and vertical, respectively.
5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.
5.3 Calculation Requirements—Application of this method is computationally intensive. The function, f , shown in (Eq 4) must
s
be evaluated numerous times using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of values
for f and, because this equation is rather formidable, it may not be easily tractable by hand. Because of this, it is assumed the
s
practitioner using this test method will have available a computerized procedure for evaluating the function f . This can be
s
accomplished using commercially available mathematical software including some spreadsheet applications, or by writing
programs. (7)
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.
NOTE 2—Most fractured (unconfined) aquifers, even noncarbonates, will have some form of convergent flow to master fissures or channels
(Worthington et al., 2016). A relationship is known to occur in carbonates where potentiometric troughs correspond with sub-surface conduits or channels
(Quinlan and Ewers, 1989).
6. Apparatus
6.1 Apparatus for withdrawal tests is given in Test Method D4050. The apparatus described below are those components of the
apparatus that require special attributes for this specific test.
6.2 Construction of the Control Well—Screen the control well through only part of the vertical extent of the aquifer to be tested.
The exact distances from the top of the aquifer to the top and bottom of the pumped well screen interval must be known.
6.3 Construction and Placement of Observation Wells—The procedure will work for arbitrary positioning of observation wells
and placement of their screens, as long as three or more observation wells are used and some of the observation wells fall inside
the zone where flow is affected by partial penetration, that is, the area where significant vertical flow components exists. However,
strategic selection of the number and location of observation wells will increase the potential quality of the data set and improve
the reliability of the interpretation.
6.3.1 It is recommended that results be obtained by using a minimum of four observation wells incorporating two pairs of
observation wells located at two different distances from the pumped well, both within the zone where flow is affected by partial
penetration. Each well pair should consist of a shallow well and a deep well, that span vertically the area in which vertical
anisotropy is sought. For each well pair, one observation well screen should be at the same elevation as the screen in the pumped
well, whereas the other observation well screen should be at a different elevation than the screen in the pumped well.
6.3.2 This test method relies on choosing several arbitrary anisotropy ratios, correcting the observed drawdowns for partial
penetration, and evaluating the results. If the observation wells are screened at the same elevation, the quality of the data trace
produced by correcting the observed drawdown measurements is not sensitive to the choice of anisotropy, making it difficult to
determine this parameter accurately. If, however, observation well screens are located both within the pumped zone (where
D5850 − 20
drawdown is greater than the fully penetrating case) and the unpumped zone (where drawdown is less than the fully penetrating
case), the quality of the corrected data is sensitive to the choice of anisotropy ratio, making it easier to quantify this parameter.
7. Procedure
7.1 Pre-test preparations, pumping test guidelines, and post-test procedures associated with the pumping test itself are described
in Test Method D4050.
7.2 Verify the quality of the data set. Review the record of measured flow rates to make sure the rate was held constant during
the test. Check to see that hand measurements of drawdown agree well with electronically measured values. Finally, check the
background water-level fluctuations observed prior to or following the pumping test to see if adjustments need to be made to the
observed drawdown values to account for background fluctuations. If appropriate, adjust the observed drawdown values
accordingly.
7.3 Analysis of the field data is described in Section 8.
8. Calculation and Interpretation of Results
8.1 Initial Estimates of Transmissivity and Storage Coeffıcient—This test method requires that initial estimates of T and S be
obtained. These estimates can be made using a wide variety of procedures, including time-drawdown analysis, recovery analysis,
distance-drawdown analysis, estimation of T using specific capacity, grain-size analyses of formation samples, or results of
laboratory permeability tests, and estimation of storage coefficient based on geology, sediment type, and aquifer thickness.
8.2 Select Data for Analysis—This test method requires a single drawdown observation for each observation well used in the
test. The drawdowns used should correspond to the same time since pumping began, usually near or at the end of the test. Select
a time, t, late enough in the test so that it satisfies the relationship t > b S/(2TA).
8.3 Distance-Drawdown Analysis Methods—The selected drawdown values will be corrected for partial penetration and the
corrected drawdown will be analyzed using distance-drawdown methods. Use either a semilog procedure or a log-log procedure.
The semilog procedure requires that u be small. For distant observation wells, this condition may be violated and the semilog
method may be invalid. If u is not sufficiently small, the logarithmic approximation of the Theis well function, W(u), is not
accurate. Examples of errors for some u values are as follows:
u Error, %
0.01 0.25
0.03 1.01
0.05 2.00
0.10 5.35
The log-log method is more general, being valid for all values of u.
8.3.1 Semilog Method:
8.3.1.1 If this method is used, plot the corrected drawdown, s , on the linear scale versus distance, r, on the log scale. Construct
f
a straight line of best fit through the data points and record the slope of the line, Δs, and the zero drawdown intercept, R,
where:
Δs = change in drawdown over one log cycle, and
R = distance where line of best fit crosses 0 drawdown.
8.3.1.2 Using these input parameters, calculate transmissivity and storage coefficient as follows:
2.3026Q
T 5 (7)
2πΔs
2.25 Tt
S 5 (8)
R
8.3.2 Log-Log Method—If the log-log method is selected, plot corrected drawdown, s , on the vertical logarithmic axis versus
f
the reciprocal of the distance squared, 1/r , on the horizontal logarithmic axis. On a separate graph having the same scale as the
data plot, prepare a standard Theis type curve by plotting W(u) on the vertical axis versus 1/u on the horizontal axis (see Fig. 1).
Overlay the data plot on the type curve and, while keeping the coordinate axes of the two plots parallel, shift the data plot to align
with the type curve effecting a match position. Select and record the values of an arbitrary point, referred to as the match point,
anywhere on the overlapping part of the plots. Record the match-point coordinates—W(u), 1/u,s , 1/r . For convenience, the match
f
point may be selected where W(u) and 1/u are integer values. Using these match-point values, compute transmissivity and storage
coefficient as follows:
Q
T 5 W~u! (9)
4πs
4Ttu
S 5 (10)
r
D5850 − 20
FIG. 1 Theis Type Curve
8.4 Iterative Calculations—Use the following steps to estimate vertical anisotropy ratio and refine the values for transmissivity
and storage coefficient.
8.4.1 Select several arbitrary anisotropy ratios, spanning a range likely to include the actual anisotropy of the aquifer. Usually
four or five values will suffice.
8.4.2 For each assumed anisotropy value, use the estimated T and S values to calculate correction factors, C , and corrected
f
drawdowns, s , for each observation well. Use Eq 2, Eq 4, Eq 5, and Eq 6
f
8.4.3 Using the corrected drawdowns, prepare a distance-drawdown graph for each value of assumed anisotropy. Compare the
graphs to determine which one provides the best data trace. For semilog graphs, this is the plot that best describes a straight line.
For log-log graphs, it is the plot that best fits the Theis type curve. Record the corresponding anisotropy value as the best estimate
for A.
8.4.4 Using the selected distance-drawdown graph, calculate T and S as described in 8.3. The values obtained are considered
revised estimates of transmissivity and storage coefficient.
8.4.5 Select several new, arbitrary anisotropy values spanning a range that is narrower than the previous one and that includes
the previous estimate for A. Go back to 8.4.2 to repeat the iteration process. Each iteration will generate new values for correction
factors and corrected drawdowns, new distance-drawdown graphs and revised estimates for A, T, and S.
8.5 Example Calculation:
8.5.1 A test well screened in the bottom 10 ft (3.05 m) of a 50-ft (15.24 m) thick aquifer was pumped at a rate of 2 gpm (385
cubic feet per day [cfd]) for one day. The corresponding data parameters are as follows:
Q = 385 cfd (10.9 cmd)
b = 50 ft (15.24 m)
d = 40 ft (12.19 m)
l = 50 ft (15.24 m)
t = one day
8.5.2 Table 1 shows well geometry and drawdown data for four observation wells that were monitored during the pumping test.
Observation Wells 1 and 2 comprise a shallow/deep pair near the pumped well, whereas Observation Wells 3 and 4 comprise and
shallow/deep pair at a greater distance from the pumped well.
8.5.3 Using other methods (omitted here), an initial transmissivity estimate of 400 gpd/ft (53.48 ft /day) was made. The storage
coefficient was estimated at 0.0005. The vertical anisotropy ratio was estimated to range between 1 (isotropic) and 0.01 (severely
anisotropic).
TABLE 1 Well Geometry and Drawdown Information
d', Distance l', Distance
r, Distance
from Top of from Top of s, Drawdown
Observation from Pumped
Aquifer to Top Aquifer to after 1 Day,
Well Well, in ft
of Screen, in ft Bottom of in ft (m)
(m)
(m) Screen, in ft (m)
1 10 (3.05) 0 (0) 10 (3.05) 3.11 (0.95)
2 11 (3.35) 30 (9.14) 40 (12.19) 7.49 (2.28)
3 50 (15.24) 40 (12.19) 50 (15.24) 4.56 (1.39)
4 60 (18.29) 0 (0) 10 (3.05) 2.65 (0.81)
D5850 − 20
8.5.4 Use Eq 2, Eq 4, Eq 5, and Eq 6 to compute correction factors, C , and corrected drawdowns, s , for each observation well
f f
for several anisotropy ratio values. The results of these computer-generated calculations are shown in Table 2. Make a
distance-drawdown graph for each anisotropy value as shown in Fig. 2, (7).
8.5.5 Select the distance-drawdown graph that provides the best match with the Theis type curve and note the anisotropy ratio
value. From Fig. 2, the best match is achieved with the graph corresponding to an anisotropy ratio value of 0.2.
8.5.6 Using this graph and Eq 9 and Eq 10, calculate revised estimates for T and S based upon matching the Theis type curve,
as shown in Fig. 3.
385·2
T 5 (11)
4π1.73
2 2
535.42 ft ~3.29 m !/day
4·35.42·1·0.000388
S 5 (12)
50.00055
8.5.7 Using the revised T and S values, repeat 8.5.4 through 8.5.6. The range of anisotropy ratios for which computations are
made is narrowed based upon information gained from the previous step. This results in correction factors and corrected
drawdowns as shown in Table 3 and the distance-drawdown graphs shown in Fig. 4. The distance-drawdown graph providing the
best fit to the Theis type curve corresponds to an anisotropy ratio of 0.17 and is shown with the type curve in Fig. 5. Using the
match-point values shown, T and S are calculated as follows:
385·2
T 5 (13)
4π1.87
2 2
532.77 ft 3.04 m /day
~ !
4·32.77·1·0.000496
S 5 (14)
50.00065
8.5.8 Using the revised T and S values, repeat 8.5.4 – 8.5.6 above. The range of anisotropy ratios for which computations are
made is narrowed based upon information gained from the previous step. This results in correction factors and corrected
drawdowns as shown in Table 4 and the distance-drawdown graphs shown in Fig. 6. The distance-drawdown graph providing the
best fit to the Theis type curve corresponds to an anisotropy ratio of 0.18 and is shown with the type curve in Fig. 7. Using the
match-point values shown, T and S are calculated as follows:
385·2
T 5 (15)
4π1.91
2 2
532.08 ft ~2.98 m !/day
TABLE 2 Correction Factors and Corrected Drawdown Calculated
2 2
Assuming a Tof 53.48 ft (4.97 m )/day and anSof 0.0005
s , Corrected
f
Observation C , A, Anisotropy
f
Drawdown,
Well Correction Factor Ratio
in ft (m)
1 1.327 4.13 (1.26) .
2 0.884 6.62 (2.02) .
3 0.977 4.46 (1.36) 1
4 1.012 2.68 (0.82) .
1 1.805 5.62 (1.71) .
2 0.856 6.41 (1.95) .
3 0.827 3.77 (1.15) 0.2
4 1.148 3.04 (0.93) .
1 2.676 8.32 (2.54) .
2 0.891 6.67 (2.03) .
3 0.606 2.76 (0.84) 0.05
4 1.568 4.16 (1.27) .
1 6.158 19.15 (5.84) .
2 1.006 7.53 (2.30) .
3 0.397 1.81 (0.55) 0.01
4 3.487 9.24 (2.82) .
D5850 − 20
2 2
FIG. 2 Graphs of Corrected Drawdown in ft Versus Reciprocal of Distance Squared in ft (m ) for Anisotropy Ratios of 1, 0.2, 0.05, and
2 2
0.01, a Tof 53.48 ft (4.97 m )/day, and anSof 0.0005
4·32.08·1·0.000545
S 5 (16)
50.0007
8.5.9 The iteration is complete because the change in transmissivity between the last two steps was negligible (about 2 %). Thus,
2 2
the calculated aquifer coefficients are as follows: T = 32.08 ft (2.98 m )/day, S = 0.0007, and A = 0.18.
9. Report: Test Data Sheet(s)/Form(s)
9.1 The methodology used to specify how data are recorded on the test data sheet(s)/form(s), as given below is covered below.
9.2 Report including the following information:
9.2.1 Introduction—The introductory section is intended to present the scope and purpose of the method for determining the
transmissivity, storage coefficient, and ratio of horizontal to vertical hydraulic conductivity in a nonleaky confined aquifer. Briefly
summarize the field hydrogeologic conditions and the field equipment and instrumentation, including the construction of the
control well and observation wells, the method of measurement of discharge and water levels, and the duration of the test and
pumping rate.
9.2.2 Conceptual Model—Review the information available on the hydrogeology of the site; interpret and describe the
hydrogeology of the site as it pertains to the selection of this method 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 aquifer test method.
D5850 − 20
FIG. 3 Analysis of Drawdown Data Corrected for Partial Penetra-
tion Assuming an Anisotropy of 0.20, Estimated Tof 53.48 ft
2 2
(4.97 m )/day, andSof 0.0005 Yields a RevisedTof 35.42 ft (3.29
m )/day andSof 0.00055
TABLE 3 Correction Factors and Corrected Drawdown Calculated
2 2
Assuming a Tof 35.42 ft (3.29 m )/day and anS of 0.00055
s , Corrected
f
Observation C , A, Anisotropy
f
Drawdown,
Well Correction Factor Ratio
in ft (m)
1 1.745 5.43 (1.66) .
2 0.847 6.34 (1.93) .
3 0.864 3.94 (1.20) 0.29
4 1.108 2.94 (0.90) .
1 1.848 5.75 (1.75) .
2 0.846 6.34 (1.93) .
3 0.831 3.79 (1.16) 0.23
4 1.145 3.03 (0.92) .
1 2.002 6.23 (1.90) .
2 0.848 6.35 (1.94) .
3 0.784 3.57 (1.09) 0.17
4 1.206 3.20 (0.98) .
1 2.277 7.08 (2.16) .
2 0.855 6.41 (1.95) .
3 0.711 3.24 (0.99) 0.11
4 1.327 3.52 (1.07) .
9.2.3 Equipment—Report the field installation and equipment for the aquifer test, including the construction, diameter, depth of
screened and filter-packed intervals, and location of control well and pumping equipment, and the construction, diameter, depth,
and screened interval of observation wells.
9.2.4 Instrumentation—Describe 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 the name and date and method of the last calibration, if
applicable.
9.2.5 Testing Procedures—List the steps taken in conducting pre-test, 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
testing procedure.
9.2.6 Presentation and Interpretation of Test Results:
9.2.6.1 Data—Present tables of data collected during the test. Show methods of adjusting water levels for background
water-level and barometric changes and calculation of drawdown and residual drawdown.
9.2.6.2 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.
D5850 − 20
2 2
FIG. 4 Graphs of Corrected Drawdown in Feet Versus Reciprocal of Distance Squared in ft (m ) for Anisotropy Ratios of 0.29, 0.23,
2 2
0.17, and 0.11, a Tof 35.42 ft (3.29 m )/day, and anSof 0.00055
9.2.7 Evaluate qualitatively the overall accuracy of the test, the corrections and adjustments made to the original water-level
measurements, the adequacy and accuracy of instrumentation, accuracy of observations of stress and response, and the
conformance of the hydrogeologic conditions and the performance of the test to the model assumptions.
10. Precision and Bias
10.1 Precision—Test data on precision is not presented due to the nature of the material (groundwater) tested by this test
method. It is either not feasible or too costly at this time to have ten or more laboratories participated in a round-robin testing
program. It is not practicable to specify the precision of this test method because the response of aquifer systems during aquifer
tests is dependent upon ambient system stresses.
10.2 Bias—There is no accepted reference value for this test method, therefore bias cannot be determined. No statement can be
made about bias because no true reference values exist.
11. Keywords
11.1 anisotropy; aquifers; aquifer tests; control wells; groundwater; hydraulic conductivity; observation well; storage
coefficient; transmissivity
D5850 − 20
FIG. 5 Analysis of Drawdown Data Corrected for Partial Penetra-
tion Assuming an Anisotropy of 0.17, Estimated Tof 35.42 ft
2 2
(3.29 m )/day, andSof 0.00055 Yields a RevisedTof 32.77 ft (3.04
m )/day andSof 0.00065
TABLE 4 Correction Factors and Corrected Drawdown Calculated
2 2
Assuming a Tof 32.77 ft (3.04 m )/day and anSof 0.00065
s , Corrected
f
Observation C , A, Anisotropy
f
Drawdown,
Well Correction Factor Ratio
in ft (m)
1 1.981 6.16 (1.88) .
2 0.842 6.31 (1.92) .
3 0.800 3.65 (1.11) 0.2
4 1.185 3.14 (0.96) .
1 2.042 6.35 (1.94) .
2 0.843 6.31 (1.92) .
3 0.783 3.57 (1.09) 0.18
4 1.209 3.20 (0.98) .
1 2.114 6.58 (2.01) .
2 0.844 6.32 (1.93) .
3 0.763 3.48 (1.06) 0.16
4 1.239 3.28 (1.00) .
1 2.204 6.85 (2.09) .
2 0.846 6.34 (1.93) .
3 0.740 3.37 (1.03) 0.14
4 1.277 3.38 (1.03) .
D5850 − 20
2 2
FIG. 6 Graphs of Corrected Drawdown in Feet Versus Reciprocal of Distance Squared in ft (m ) for Anisotropy Ratios of 0.2, 0.18,
2 2
0.16, and 0.14, a Tof 32.77 ft (3.04 m )/day, and anSof 0.00065
D5850 − 20
2 2
FIG. 7 Analysis of Drawdown Data Corrected for Partial Penetration Assuming an Anisotropy of 0.18, Estimated Tof 32.77 ft (3.04 m )/
2 2
day, andSof 0.00065 Yields a RevisedTof 32.08 ft (2.98 m )/day andSof 0.0007
REFERENCES
(1) Theis, C. V., “The Relation Between the Lowering of the Piezometric Surface and the Rate and Duration of Discharge of a Well Using Groundwater
Storage,” Trans. Am. Geophys. Union, Vol 16, 1935, pp. 519–524.
(2) Hantush, M. S., “Drawdown Around a Partially Penetrating Well,” Am. Soc. Civil Eng. Proc., 87, HY4, 1961, pp. 83–93.
(3) Hantush, M. S., “Aquifer Tests on Partially Penetrating Wells,” Am. Soc. Civil Eng. Proc., 87, HY5, 1961, pp. 171–195.
(4) Hantush, M. S., “Hydraulics of Wells,” in Advances in Hydroscience, Vol 1, Edited by Ven Te Chow, Academic Press, New York, 1964, pp. 281–432.
(5) Weeks, E. P., “Field Methods for Determining Vertical Permeability and Aquifer Anisotropy,” U.S. Geological Survey, Professional Paper 501-D,
1964, pp. D193–D198.
(6) Way, S. C. and McKee, C. R., “In-Situ Determination of Three-Dimensional Aquifer Permeabilities,” Ground Water, Vol 20, No. 5, 1982, pp.
594–603.
(7) Schafer, David C, “Determining the Vertical Anisotropy Ratio Using a Graphical, Iterative Procedure Based on the Hantush Equation,” Groundwater,
Volume 36, Issue 2, March 1998.
SUMMARY OF CHANGES
In accordance with Committee D18 policy, this section identifies the location of changes to this document
since the last edition (1995(2012)) that may impact the use of this standard. (January 1, 2018)
(1) Section 1: Added caveat on D6026; updated section on units.
(2) Section 3: Removed definitions that are contained in D653; Added section to include D653 definitions for the convenience of
users.
(3) Section 2: Included references to D3740 and D6026.
(4) Section 4: Included D18 Note on D3740.
(5) Subsection 5.3: Removed reference to specific computer program languages.
(6) Section 9: Updated format on Reports Section; added D6026 statement.
(7) Section 10: Updated the Precision and Bias statement to current D18 statement.
(8) References: Added reference 7.
(9) Removed or reworded jargon and superlatives throughout.
D5850 − 20
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1. Scope*
1.1 This practice covers an analytical procedure for determining the transmissivity, storage coefficient, and ratio of vertical to
horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-rate
pumping test. This practice uses data from a minimum of four partially penetrating, recommended to be positioned observation
wells around a partially penetrating control well.
1.2 The analytical procedure is used in conjunction with the field procedure in Test Method D4050.
1.3 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of
aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this practice.
1.4 Units—The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are
mathematical conversions, which are provided for information purposes only and are not considered standard. The reporting of
results in units other than inch-pound shall not be regarded as nonconformance with this standard.
1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice
D6026, unless superseded by this standard.
1.6 The procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industry
standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not
consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s objective;
and it is common practice to increase or reduce the significant digits of reported data to be commensurate with these considerations.
It is beyond the scope of this standard to consider significant digits used in analysis method or engineering design.
1.7 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.
1.8 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.
1.9 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
D5473/D5473M Practice for (Analytical Procedures) Analyzing the Effects of Partial Penetration of Control Well and
Determining the Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer
D6026 Practice for Using Significant Digits in Geotechnical Data
D5850 − 20
3. Terminology
3.1 Definitions:
3.1.1 For definitions of common technical terms in this standard, see Terminology D653.
3.2 The following definitions from Terminology D653 are used in this standard and are presented for the convenience of the
user.
3.2.1 anisotropy—having different properties in different directions.
3.2.2 confined aquifer—in hydrogeology, an aquifer bounded above and below by confining beds and in which the static head
is above the top of the aquifer.
3.2.3 control well—in aquifer testing, well by which the aquifer is stressed, for example, by pumping, injection, or change of
head.
3.2.4 drawdown [L]—in field aquifer tests, vertical distance the free water elevation is lowered or the pressure head is reduced
due to the removal of free water.
3.2.5 hydraulic conductivity—in 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.
3.2.6 monitoring well (observation well), n—in hydrogeology, a well installed, usually of small diameter, for measuring water
levels, collecting water samples, or determining other ground water characteristics.
3.2.6.1 Discussion—
The well may be cased or uncased, but if cased the casing should have openings to allow flow of ground water into or out of the
casing, such as a well screen.
3.2.7 storage coeffıcient—in aquifers, the volume of water that an aquifer releases from or takes into storage per unit surface
area of the aquifer per unit change in head. For a confined aquifer, the storage coefficient is equal to the product of the specific
storage and aquifer thickness. For an unconfined aquifer, the storage coefficient is approximately equal to the specific yield.
3.2.8 transmissivity—in aquifers, 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.
3.2.8.1 Discussion—
It is equal to an integration of the hydraulic conductivities across the saturated part of the aquifer perpendicular to the flow paths.
3.3 Symbols and Dimensions:
3.3.1 A—K /K , anisotropy ratio [nd].
z r
3.3.2 b—thickness of aquifer [L].
3.3.3 C —drawdown correction factor, equal to the ratio of the drawdown for a fully penetrating well network to the drawdown
f
for a partially penetrating well network (W(u)/(W(u) + f )).
s
3.3.4 d—distance from top of aquifer to top of screened interval of control well [L].
3.3.5 d'—distance from top of aquifer to top of screened interval of observation well [L].
3.3.6 f —incremental dimensionless drawdown component resulting from partial penetration [ nd].
s
−1
3.3.7 K—hydraulic conductivity [LT ].
3.3.7.1 Discussion—
The use of symbol K for the term hydraulic conductivity is t
...