Designation: D5270 − 96 (Reapproved 2014)Standard Test Method forDetermining Transmissivity and Storage Coefficient ofBounded, Nonleaky, Confined Aquifers1This standard is issued under the fixed designation D5270; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers an analytical procedure fordetermining the transmissivity, storage coefficient, and possiblelocation of boundaries for a confined aquifer with a linearboundary. This test method is used to analyze water-level orhead data from one or more observation wells or piezometersduring the pumping of water from a control well at a constantrate. This test method also applies to flowing artesian wellsdischarging at a constant rate. With appropriate changes insign, this test method also can be used to analyze the effects ofinjecting water into a control well at a constant rate.1.2 The analytical procedure in this test method is used inconjunction with the field procedure in Test Method D4050.1.3 Limitations—The valid use of this test method is limitedto determination of transmissivities and storage coefficients foraquifers in hydrogeologic settings with reasonable correspon-dence to the assumptions of the Theis nonequilibrium method(see Test Method D4106) (see 5.1), except that the aquifer islimited in areal extent by a linear boundary that fully penetratesthe aquifer. The boundary is assumed to be either a constant-head boundary (equivalent to a stream or lake that hydrauli-cally fully penetrates the aquifer) or a no-flow (impermeable)boundary (equivalent to a contact with a significantly lesspermeable rock unit). The Theis nonequilibrium method isdescribed in Test Methods D4105 and D4106.1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD3740 Practice for Minimum Requirements for AgenciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD4043 Guide for Selection of Aquifer Test Method inDetermining Hydraulic Properties by Well TechniquesD4050 Test Method for (Field Procedure) for Withdrawaland Injection Well Testing for Determining HydraulicProperties of Aquifer SystemsD4105 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and Storage Coefficient of Non-leaky Confined Aquifers by the Modified Theis Nonequi-librium MethodD4106 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and Storage Coefficient of Non-leaky Confined Aquifers by the Theis NonequilibriumMethodD6026 Practice for Using Significant Digits in GeotechnicalData3. Terminology3.1 Definitions—For definitions of general technical termsused within this practice, refer to Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 constant-head boundary—the conceptual representa-tion of a natural feature such as a lake or river that effectivelyfully penetrates the aquifer and prevents water-level change inthe aquifer at that location.3.2.2 equipotential line—a line connecting points of equalhydraulic head. A set of such lines provides a contour map ofa potentiometric surface.3.2.3 image well—an imaginary well located opposite acontrol well such that a boundary is the perpendicular bisector1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Feb. 1, 2014. Published February 2014. Originallyapproved in 1992. Last previous edition approved in 2008 as D5270 – 96 (2008).DOI: 10.1520/D5270-96R14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1of a straight line connecting the control and image wells; usedto simulate the effect of a boundary on water-level changes.3.2.4 impermeable boundary—the conceptual representa-tion of a natural feature such as a fault or depositional contactthat places a boundary of significantly less-permeable materiallaterally adjacent to an aquifer.3.3 Symbols and Dimensions:3.3.1 Kl[nd]—constant of proportionality, ri⁄rr.3.3.2 Q [L3T−1]—discharge.3.3.3 r [L]—radial distance from control well.3.3.4 ri[L]—distance from observation well to image well.3.3.5 rr[L]—distance from observation well to control well.3.3.6 S [nd]—storage coefficient.3.3.7 s [L]—drawdown.3.3.8 si[L]—component of drawdown due to image well.3.3.9 so[L]—drawdown at an observation well.3.3.10 sr[L]—component of drawdown due to control well.3.3.11 T [L2T−1]—transmissivity.3.3.12 t [T]—time since pumping or injection began.3.3.13 to[T]—time at projection of zero drawdown.4. Summary of Test Method4.1 This test method prescribes two analytical proceduresfor analysis of a field test. This test method requires pumpingwater from, or injecting water into, a control well that is opento the entire thickness of a confined bounded aquifer at aconstant rate and measuring the water-level response in one ormore observation wells or piezometers. The water-level re-sponse in the aquifer is a function of the transmissivity andstorage coefficient of the aquifer, and the location and nature ofthe aquifer boundary or boundaries. Drawdown or build up ofthe water level is analyzed as a departure from the type curvedefined by the Theis nonequilibrium method (see Test MethodD4106) or from straight-line segments defined by the modifiedTheis nonequilibrium method (see Test Method D4105).4.2 A constant-head boundary such as a lake or stream thatfully penetrates the aquifer prevents drawdown or build up ofhead at the boundary, as shown in Fig. 1. Likewise, animpermeable boundary provides increased drawdown or buildup of head, as shown in Fig. 2. These effects are simulated bytreating the aquifer as if it were infinite in extent andintroducing an imaginary well or “image well” on the oppositeside of the boundary a distance equal to the distance of thecontrol well from the boundary.Aline between the control welland the image well is perpendicular to the boundary. If theboundary is a constant-head boundary, the flux from the imagewell is opposite in sign from that of the control well; forexample, the image of a discharging control well is an injectionwell, whereas the image of an injecting well is a dischargingwell. If the boundary is an impermeable boundary, the fluxfrom the image well has the same sign as that from the controlwell. Therefore, the image of a discharging well across animpermeable boundary is a discharging well. Because theeffects are symmetrical, only discharging control wells will bedescribed in the remainder of this test method, but this testmethod is equally applicable, with the appropriate change insign, to control wells into which water is injected.4.3 Solution—The solution given by Theis (3)3can beexpressed as follows:s 5Q4πT*u` e2yydy (1)and:u 5r2S4Tt(2)where:*u` e2yydy 5 W~u! (3)520.577216 2 logeu1u 2u22!21u33!32u44!41…3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.NOTE 1—Modified from Ferris and others (1) and Heath (2).3FIG. 1 Diagram Showing Constant-Head BoundaryD5270 − 96 (2014)24.4 According to the principle of superposition, the draw-down at any point in the aquifer is the sum of the drawdowndue to the real and image wells (3) and (4):so5 sr6si(4)Equation (5) can be rewritten as follows:so5Q4π

[email protected]~ur!6W~ui!# 5Q4πT(W~u! (5)where:ur5rr2S4Tt, ui5ri2S4Tt(6)so that:ui5SrirrD2ur, ui5 Kl2ur(7)where:Kl5rirr(8)NOTE 1—Klis a constant of proportionality between the radii, not to beconfused with hydraulic conductivity.5. Significance and Use5.1 Assumptions:5.1.1 The well discharges at a constant rate.5.1.2 Well is of infinitesimal diameter and is open throughthe full thickness of the aquifer.5.1.3 The nonleaky confined aquifer is homogeneous,isotropic, and areally extensive except where limited by linearboundaries.5.1.4 Discharge from the well is derived initially fromstorage in the aquifer; later, movement of water may beinduced from a constant-head boundary into the aquifer.5.1.5 The geometry of the assumed aquifer and well areshown in Fig. 1 or Fig. 2.5.1.6 Boundaries are vertical planes, infinite in length thatfully penetrate the aquifer. No water is yielded to the aquifer byimpermeable boundaries, whereas recharging boundaries are inperfect hydraulic connection with the aquifer.5.1.7 Observation wells represent the head in the aquifer;that is, the effects of wellbore storage in the observation wellsare negligible.5.2 Implications of Assumptions:5.2.1 Implicit in the assumptions are the conditions of afully-penetrating control well and observation wells of infini-tesimal diameter in a confined aquifer. Under certainconditions, aquifer tests can be successfully analyzed when thecontrol well is open to only part of the aquifer or contains asignificant volume of water or when the test is conducted in anunconfined aquifer. These conditions are discussed in moredetail in Test Method D4105.5.2.2 In cases in which this test method is used to locate anunknown boundary, a minimum of three observation wells isneeded. If only two observation wells are available, twopossible locations of the boundary are defined, and if only oneobservation well is used, a circle describing all possiblelocations of the image well is defined.5.2.3 The effects of a constant-head boundary are oftenindistinguishable from the effects of a leaky, confined aquifer.Therefore, care must be taken to ensure that a correct concep-tual model of the system has been created prior to analyzing thetest. See Guide D4043.5.3 Practice D3740 provides evaluation factors for theactivities in this standard.NOTE 2—The quality of the result produced by this standard isdependent on the competence of the personnel performing it, and thesuitability of the equipment and facilities used. Agencies that meet thecriteria of Practice D3740 are generally considered capable of competentand objective testing/sampling/inspection/etc. Users of this standard arecautioned that compliance with Practice D3740 does not in itself assurereliable results. Reliable results depend on many factors; Practice D3740provides a means of evaluating some of those factors.6. Apparatus6.1 Analysis of the data from the field procedure (see TestMethod D4050) by this test method requires that the controlwell and observation wells meet the requirements specified inthe following subsections.NOTE 1—Modified from Ferris and others (1) and Heath (2).FIG. 2 Diagram Showing Impermeable BoundaryD5270 − 96 (2014)36.2 Construction of Control Well—Install the control well inthe aquifer and equip with a pump capable of discharging waterfrom the well at a constant rate for the duration of the test.Preferably, the control well should be open throughout the fullthickness of the aquifer. If the control well partially penetratesthe aquifer, take special precautions in the placement or designof observation wells (see 5.2.1).6.3 Construction of Observation Wells and Piezometers—Construct one or more observation wells or piezometers atspecified distances from the control well.6.4 Location of Observation Wells and Piezometers —Wellsmay be located at any distance from the control well within thearea of influence of pumping. However, if vertical flowcomponents are expected to be significant near the control welland if partially penetrating observation wells are to be used, theobservation wells should be located at a distance beyond theeffect of vertical flow components. If the aquifer is unconfined,constraints are imposed on the distance to partially penetratingobservation wells and on the validity of early time measure-ments (see Test Method D4106).NOTE 3—To ensure that the effects of the boundary may be observedduring the tests, some of the wells should be located along lines parallelto the suspected boundary, no farther from the boundary than the controlwell.7. Procedure7.1 The general procedure consists of conducting the fieldprocedure for withdrawal or injection wells tests (see TestMethod D4050) and analyzing the field data, as addressed inthis test method. Record information in accordance withPractice D6026.7.2 Analysis of the field data consists of two steps: deter-mination of the properties of the aquifer and the nature anddistance to the image well from each observation well, anddetermination of the location of the boundary.7.3 Two methods of analysis can be used to determine theaquifer properties and the nature and distance to the imagewell. One method is based on the Theis nonequilibriummethod; the other method is based on the modified Theisnonequilibrium method.7.3.1 Theis Nonequilibrium Method—Expressions in Eq 5-8are used to generate a family of curves of 1/urversus ∑ W( u)for values of Klfor recharging and discharging image wells asshown in Fig. 3 (4). Table 1 gives values of W(u) versus 1/u.This table may be used to create a table of ∑W(u) versus 1/u foreach value of Klby picking values for W(ur) and W(ui), andcomputing the ∑ W(u) for the each value of 1/u.7.3.1.1 Transmissivity, storage coefficient, and the possiblelocation of one or more boundaries are calculated fromparameters determined from the match point and a curveselected from a family of type curves.7.3.2 Modified Theis Nonequilibrium Method—The sum ofthe terms to the right of logeu in Eq 3 is not significant whenu becomes small, that is, equal to or less than 0.01.NOTE 4—The limiting value for u of less than 0.01 may be excessivelyrestrictive in some applications. The errors for small values of u, fromKruseman and DeRidder (7) are as follows:Error less than, %: 1 2 5 10For u smaller than: 0.03 0.05 0.1 0.157.3.2.1 The value of u decreases as time, t, increases anddecreases as radial distance, r, decreases. Therefore, for largevalues of t and small values of r, the terms to the right of logNOTE 1—From Stallman (4).FIG. 3 Family of Type Curves for the Solution of the Modified Theis FormulaD5270 − 96 (2014)4eu in Eq 3 may be neglected, as recognized by Theis (3). The modified Theis equation canthen be written as follows:s 5Q4πTS20