1、Designation: D 4106 96 (Reapproved 2008)Standard 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 D 4106; the number immediately following th
2、e 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
3、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 is used in conjunction wit
4、h thefield procedure given in Test Method D 4050.1.3 LimitationsThe 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 This standa
5、rd 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 AST
6、M Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 4043 Guide for Selection of Aquifer Test Method inDetermining Hydraulic Properties by Well TechniquesD 4050 Test Method for (Field Procedure) for Withdrawaland Injection Well Tests for Determining Hydraulic Prop-erties of Aq
7、uifer Systems3. Terminology3.1 Definitions:3.1.1 aquifer, confinedan aquifer bounded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.1.2 confining beda hydrogeologic unit of less perme-able material bounding one or more aquifers.3.1.3 control wellwell b
8、y which the head and flow in theaquifer is changed, for example, by pumping, injection, orimposing a constant change of head.3.1.4 drawdownvertical distance the static head is low-ered due to the removal of water.3.1.5 headsee head, static.3.1.6 head, staticthe height above a standard datum of thesu
9、rface of a column of water (or other liquid) that can besupported by the static pressure at a given point.3.1.7 hydraulic conductivity (field aquifer tests)the vol-ume of water at the existing kinematic viscosity that will movein a unit time under a unit hydraulic gradient through a unitarea measure
10、d at right angles to the direction of flow.3.1.8 observation wella well open to all or part of anaquifer.3.1.9 piezometera device so constructed and sealed as tomeasure hydraulic head at a point in the subsurface.3.1.10 specific storagethe volume of water released fromor taken into storage per unit
11、volume of the porous medium perunit change in head.3.1.11 storage coeffcientthe volume of water an aquiferreleases from or takes into storage per unit surface area of theaquifer per unit change in head. For a confined aquifer, thestorage coefficient is equal to the product of the specific storageand
12、 aquifer thickness. For an unconfined aquifer, the storagecoefficient is approximately equal to the specific yield.3.1.12 transmissivitythe volume of water at the existingkinematic viscosity that will move in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.1.13 uncon
13、fined aquiferan aquifer that has a watertable.3.1.14 For definitions of other terms used in this testmethod, see Terminology D 653.3.2 Symbols and Dimensions:3.2.1 K LT1hydraulic conductivity.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsib
14、ility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations .Current edition approved Sept. 15, 2008. Published October 2008. Originallyapproved in 1991. Last previous edition approved in 2002 as D 4106 96 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, or
15、contact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2.2 Kxyhydraulic
16、 conductivity in the horizontal plane,radially from the control well.3.2.3 Kzhydraulic conductivity in the vertical direction.3.2.4 Q L3T1discharge.3.2.5 S ndstorage coefficient.3.2.6 SsL1specific storage.3.2.7 T L2T1transmissivity.3.2.8 W(u) ndwell function of u.3.2.9 b Lthickness of aquifer.3.2.10
17、 r Lradial distance from control well.3.2.11 s Ldrawdown.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 D 4050) involvespumping a control well at a constant ra
18、te 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 aq
19、uifer 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 fro
20、m the control well, orboth, and matching the drawdown response with a type curve.4.2 SolutionThe solution given by Theis (1)3may beexpressed as follows:s 5Q4pT*u e2yydy (1)where:u 5r2S4Tt(2)*u e2yydy 5 Wu!520.577216 2 logeu 1 u 2u22!21u33!32u44!41 .(3)5. Significance and Use5.1 Assumptions:5.1.1 Wel
21、l 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
22、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 p
23、enetrates 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 are negli-g
24、ible, where according to Reed (2):r 5 1.5bKzKxy(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,
25、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
26、 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 differenc
27、ebetween 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 whichthe
28、water 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 d
29、rawdown is3The 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 AquiferD 4106 96 (2008)2corrected for reduction in thickness of the aquifer, and theeffects of delayed gravity yield are small
30、.5.2.3.2 Reduction in Aquifer ThicknessIn an unconfinedaquifer dewatering occurs when the water levels decline in thevicinity of a pumping well. Corrections in drawdown need tobe made when the drawdown is a significant fraction of theaquifer thickness as shown by Jacob (5). The drawdown, s,needs to
31、be replaced by s8, the drawdown that would occur inan equivalent confined aquifer, where:s8 5 s 2 Ss22bD (7)5.2.3.3 Gravity Yield EffectsIn unconfined aquifers, de-layed gravity yield effects may invalidate measurements ofdrawdown during the early part of the test for application to theTheis method.
32、 Effects of delayed gravity yield are negligible inpartially penetrating observation wells at and beyond a dis-tance, r, from the control well, where:r 5bKzKxy(8)After the time, t, as given in Eq 9 from Neuman (6).t 5 10 3 Syr2/T! (9)where:Sy= the specific yield. For fully penetrating observationwel
33、ls, the effects of delayed yield are negligible at thedistance, r, in Eq 8 after one tenth of the time given inthe Eq 9.6. Apparatus6.1 Analysis of data from the field procedure (see TestMethod D 4050) by the method specified in this test methodrequires that the control well and observation wells me
34、et thespecifications in the following paragraphs.6.2 Construction of Control WellScreen 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
35、 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 WellsConstruct one ormore observation wells at a distance from the control well.Observation wells may be
36、 partially open or open throughoutthe thickness of the aquifer.6.4 Location of Observation WellsLocate 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 well
37、s 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 c
38、onsists of conducting the fieldprocedure for withdrawal or injection well tests (described inTest Method D 4050) 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 solvefo
39、r the two unknown parameters transmissivity and storagecoefficient where:s 5Q4pTWu! (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 o
40、n 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 observat
41、ion 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
42、 values of W (u), 1/u, s, and t atan arbitrary 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 1Alternatively, the type curve can be constructed by plotting W(u) agai
43、nst u, then plotting the data as s versus r2/t.8.1.5 Using the coordinates of the point, determine thetransmissivity and storage coefficient from Eq 12 and Eq 13:T 5QWu!4ps(12)S 5 4Tutr2(13)8.1.6 To apply the Theis nonequilibrium method to thinunconfined aquifers where the drawdown is a significantf
44、raction of the initial saturated thickness, apply a correction tothe drawdown in solving for transmissivity and coefficient ofstorage (see 5.2.3.2).9. Report9.1 Prepare a report including the information described inthis section. The report of the analytical procedure will includeinformation from th
45、e report on test method selection (seeGuide D 4043) and the field testing procedure (seeTest MethodD 4050).9.1.1 IntroductionThe introductory section is intended topresent the scope and purpose of the constant discharge methodfor determining transmissivity and storativity in a confinedD 4106 96 (200
46、8)3nonleaky 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 ofth
47、e test and pumping rate. Discuss rationale for selecting theTheis nonequilibrium method.9.1.2 Hydrogeologic SettingReview 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
48、 analyzing anaquifer test. Compare the hydrogeologic characteristics of thesite as it conforms and differs from the assumptions of this testmethod.9.1.3 EquipmentReport the field installation and equip-ment for the aquifer test, including the construction, diameter,depth of screened and gravel packe
49、d 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 and date and method of the last calibration, if applicable.9.1.5
