# ASTM D4106-15

Designation: D4106 − 15Standard Test Method for(Analytical Procedure) for Determining Transmissivity andStorage Coefficient of Nonleaky Confined Aquifers by theTheis Nonequilibrium Method1This standard is issued under the fixed designation D4106; 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. Scope*1.1 This test method covers an analytical procedure fordetermining the transmissivity and storage coefficient of anonleaky confined aquifer. It is used to analyze data onwater-level response collected during radial flow to or from awell of constant discharge or injection.1.2 This analytical procedure, along with others, is used inconjunction with the field procedure given in Test MethodD4050.1.3 Limitations—The limitations of this test method fordetermination of hydraulic properties of aquifers are primarilyrelated to the correspondence between the field situation andthe simplifying assumptions of this test method (see 5.1).1.4 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D6026.1.4.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as theindustry standard. In addition, they are representative of thesignificant digits that generally should be retained. The proce-dures used do not consider material variation, purpose forobtaining the data, special purpose studies, or any consider-ations for the user’s objectives; and it is common practice toincrease or reduce significant digits of reported data to becommensurate with these considerations. It is beyond the scopeof this standard to consider significant digits used in analyticalmethods for engineering design.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 SystemsD6026 Practice for Using Significant Digits in GeotechnicalData3. Terminology3.1 Definitions:3.1.1 For definitions of other terms used in this test method,see Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 observation well—a well open to all or part of anaquifer.3.2.2 unconfined aquifer—an aquifer that has a water table.3.3 Symbols and Dimensions:3.3.1 K [LT−1]—hydraulic conductivity.3.3.2 Kxy—hydraulic conductivity in the horizontal plane,radially from the control well.3.3.3 Kz—hydraulic conductivity in the vertical direction.3.3.4 Q [L3T−1]—discharge.3.3.5 S [nd]—storage coefficient.3.3.6 Ss[L−1]—specific storage.3.3.7 T [L2T−1]—transmissivity.3.3.8 W(u) [nd]—well function of u.1This 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 April 15, 2015. Published June 2015. Originallyapproved in 1991. Last previous edition approved in 2008 as D4106 – 96 (2008).DOI: 10.1520/D4106-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.3.9 b [L]—thickness of aquifer.3.3.10 r [L]—radial distance from control well.3.3.11 s [L]—drawdown.4. Summary of Test Method4.1 This test method describes an analytical procedure foranalyzing data collected during a withdrawal or injection welltest. The field procedure (see Test Method D4050) involvespumping a control well at a constant rate and measuring thewater level response in one or more observation wells orpiezometers. The water-level response in the aquifer is afunction of the transmissivity and storage coefficient of theaquifer. Alternatively, this test method can be performed byinjecting water at a constant rate into the aquifer through thecontrol well. Analysis of buildup of water level in response toinjection is similar to analysis of drawdown of water level inresponse to withdrawal in a confined aquifer. Drawdown ofwater level is analyzed by plotting drawdown against factorsincorporating either time or distance from the control well, orboth, and matching the drawdown response with a type curve.4.2 Solution—The solution given by Theis (1)3may beexpressed as follows:s 5Q4πT*u` e2yydy (1)where:u 5r2S4Tt(2)*u` e2yydy 5 W~u!520.577216 2 logeu1u 2u22!21u33!32u44!41…(3)5. Significance and Use5.1 Assumptions:5.1.1 Well discharges at a constant rate, Q.5.1.2 Well is of infinitesimal diameter and fully penetratesthe aquifer.5.1.3 The nonleaky aquifer is homogeneous, isotropic, andaerially extensive. A nonleaky aquifer receives insignificantcontribution of water from confining beds.5.1.4 Discharge from the well is derived exclusively fromstorage in the aquifer.5.1.5 The geometry of the assumed aquifer and well condi-tions are shown in Fig. 1.5.2 Implications of Assumptions:5.2.1 Implicit in the assumptions are the conditions of radialflow. Vertical flow components are induced by a control wellthat partially penetrates the aquifer, that is, the well is not opento the aquifer through its full thickness. If the control well doesnot fully penetrate the aquifer, the nearest piezometer orpartially penetrating observation well should be located at adistance, r, beyond which vertical flow components arenegligible, where according to Reed (2):r 5 1.5bŒKzKxy(4)This section applies to distance-drawdown calculations oftransmissivity and storage coefficient and time-drawdown cal-culations of storage coefficient. If possible, compute transmis-sivity from time-drawdown data from wells located within adistance, r, of the pumped well using data measured after theeffects of partial penetration have become constant. The time atwhich this occurs is given by Hantush (3) by:t 5 b2s/2T ~Kz/Kr! (5)Fully penetrating observation wells may be placed at lessthan distance r from the control well. Observation wells maybe on the same or on various radial lines from the control well.5.2.2 The Theis method assumes the control well is ofinfinitesimal diameter. Also, it assumes that the water level inthe control well is the same as in the aquifer contiguous to thewell. In practice these assumptions may cause a differencebetween the theoretical drawdown and field measurements ofdrawdown in the early part of the test and in and near thecontrol well. Control well storage is negligible after a time, t,given by the Eq 6 after Weeks (4).t 5 25 3r2cT(6)where:rc= the radius of the control well in the interval in which thewater level changes.5.2.3 Application of Theis Method to Unconfined Aquifers:5.2.3.1 Although the assumptions are applicable to artesianor confined conditions, the Theis solution may be applied tounconfined aquifers if drawdown is small compared with thesaturated thickness of the aquifer or if the drawdown iscorrected for reduction in thickness of the aquifer, and theeffects of delayed gravity yield are small.5.2.3.2 Reduction in Aquifer Thickness—In an unconfinedaquifer dewatering occurs when the water levels decline in thevicinity of a pumping well. Corrections in drawdown need to3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.FIG. 1 Cross Section Through a Discharging Well in a NonleakyConfined AquiferD4106 − 152be made when the drawdown is a significant fraction of theaquifer thickness as shown by Jacob (5). The drawdown, s,needs to be replaced by s , the drawdown that would occur inan equivalent confined aquifer, where:s 5 s 2Ss22bD(7)5.2.3.3 Gravity Yield Effects—In unconfined aquifers, de-layed gravity yield effects may invalidate measurements ofdrawdown during the early part of the test for application to theTheis method. Effects of delayed gravity yield are negligible inpartially penetrating observation wells at and beyond adistance, r, from the control well, where:r 5bŒKzKxy(8)After the time, t, as given in Eq 9 from Neuman (6).t 5 10 3 Sy~r2/T! (9)where:Sy= the specific yield. For fully penetrating observationwells, the effects of delayed yield are negligible at thedistance, r,inEq 8 after one tenth of the time given inthe Eq 9.NOTE 1—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 ensurereliable results. Reliable results depend on many factors; Practice D3740provides a means of evaluating some of those factors.6. Apparatus6.1 Analysis of data from the field procedure (see TestMethod D4050) by the method specified in this test methodrequires that the control well and observation wells meet thespecifications in the following paragraphs.6.2 Construction of Control Well—Screen the control wellin the aquifer to be tested and equip with a pump capable ofdischarging water from the well at a constant rate for theduration of the test. Preferably, screen the control well through-out the full thickness of the aquifer. If the control well partiallypenetrates the aquifer, take special precaution in the placementand design of observation wells (see 5.2.1).6.3 Construction of Observation Wells—Construct one ormore observation wells at a distance from the control well.Observation wells may be partially open or open throughoutthe thickness of the aquifer.6.4 Location of Observation Wells—Locate observationwells at various distances from the control well within the areaof influence of pumping. However, if vertical flow componentsare significant and if partially penetrating observation wells areused, locate them at a distance beyond the effect of verticalflow components (see 5.2.1). If the aquifer is unconfined,constraints are imposed on the distance to partially penetratingobservation wells and the validity of early time measurements(see 5.2.3).7. Procedure7.1 The overall procedure consists of conducting the fieldprocedure for withdrawal or injection well tests (described inTest Method D4050) and analysis of the field data that isaddressed in this test method.7.2 The integral expression in Eq 1 and Eq 2 can not beevaluated analytically. A graphical procedure is used to solvefor the two unknown parameters transmissivity and storagecoefficient where:s 5Q4πTW~u! (10)and:u 5r2S4Tt(11)8. Calculation8.1 The graphical procedure used to calculate test results isbased on the functional relations between W(u) and s andbetween u and t or t/r2.8.1.1 Plot values of W(u) versus 1/u on logarithmic-scalepaper (see Table 1). This plot is referred to as the type curveplot.8.1.2 On logarithmic tracing paper of the same scale andsize as the W(u) versus 1/u type curve, plot values ofdrawdown, s, on the vertical coordinate versus either time onthe horizontal coordinate if one observation well is used orversus t/r2on the horizontal coordinate if more than oneobservation well is used.8.1.3 Overlay the data plot on the type curve plot and, whilethe coordinate axes of the two plots are held parallel, shift theplot to align with the type curve (see Fig. 2).8.1.4 Select and record the values of W(u), 1/u, s, and t at anarbitrary point, referred to as the match point (see Fig. 2),anywhere on the overlapping part of the plots. For conveniencethe point may be selected where W(u) and 1/ u are integervalues.NOTE 2—Alternatively, the type curve can be constructed by plottingW(u) against u, then plotting the data as s versus r2/t.NOTE 3—Commercially available software is available from severalsources that can perform the calculation and plotting.8.1.5 Using the coordinates of the point, determine thetransmissivity and storage coefficient from Eq 12 and Eq 13:T 5QW~u!4πs(12)S 5 4Tutr2(13)8.1.6 To apply the Theis nonequilibrium method to thinunconfined aquifers where the drawdown is a significantfraction of the initial saturated thickness, apply a correction tothe drawdown in solving for transmissivity and coefficient ofstorage (see 5.2.3.2).9. Report/Record9.1 Prepare a report including the minimum informationdescribed in this section. The report of the analytical procedureD4106 − 153will include information from the report on test methodselection (see Guide D4043) and the field testing procedure(see Test Method D4050).9.1.1 Introduction—The introductory section is intended topresent the scope and purpose of the constant discharge methodfor determining transmissivity and storativity in a confinednonleaky aquifer under constant flux. Summarize the fieldhydrogeologic conditions and the field equipment and instru-mentation including the construction of the control well andobservation wells or piezometers, or both, the method ofmeasurement of discharge and water levels, and the duration ofthe test and pumping rate. Discuss rationale for selecting theTheis nonequilibrium method.9.1.2 Hydrogeologic Setting—Review the informationavailable on the hydrogeology of the site; interpret anddescribe the hydrogeology of the site as it pertains to theselection of this test method for conducting and analyzing anaquifer test. Compare the hydrogeologic characteristics of thesite as it conforms and differs from the assumptions of this testmethod.9.1.3 Equipment—Report the field installation and equip-ment for the aquifer test, including the construction, diameter,depth of screened and gravel packed intervals, and location ofcontrol well and pumping equipment, and the construction,diameter, depth, and screened interval of observation wells orpiezometers.9.1.4 Describe the methods of observing water levels,pumping rate, barometric changes, and other environmentalconditions pertinent to the test. Include a list of measuringdevices used during the test, the manufacturers name, modelnumber, and basic specifications for each major item, and thename a