1、Designation: D 5269 96 (Reapproved 2008)Standard Test Method forDetermining Transmissivity of Nonleaky Confined Aquifersby the Theis Recovery Method1This standard is issued under the fixed designation D 5269; the number immediately following the designation indicates the year oforiginal adoption or,
2、 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 transmissivit
3、y of a confined aquifer. This testmethod is used to analyze data from the recovery of waterlevels following pumping or injection of water to or from acontrol well at a constant rate.1.2 The analytical procedure given in this test method isused in conjunction with the field procedure in Test MethodD
4、4050.1.3 LimitationsThe valid use of the Theis recoverymethod is limited to determination of transmissivities foraquifers in hydrogeologic settings with reasonable correspon-dence to the assumptions of the Theis theory (see 5.1).1.4 This standard does not purport to address all of thesafety concerns
5、, 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:2D 653 Terminology Relating to Soil, Rock, a
6、nd 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 Aquifer SystemsD 4105 Test Method (Analytical Procedure) f
7、or Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers by the Modified Theis NonequilibriumMethodD 4106 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers by the Theis Nonequilibrium MethodD 4750 Test M
8、ethod for Determining Subsurface LiquidLevels in a Borehole or Monitoring Well (ObservationWell)3. 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
9、 of less perme-able material bounding one or more aquifers.3.1.3 control wella well by which the aquifer is stressed,for example, by pumping, injection, or change of head.3.1.4 drawdownvertical distance the static head is low-ered due to the removal of water.3.1.5 hydraulic conductivity (field aquif
10、er tests)the vol-ume of water at the existing kinematic viscosity that will movein a unit time under unit hydraulic gradient through a unit areameasured at right angles to the direction of flow.3.1.6 observation wella well open to all or part of anaquifer.3.1.7 piezometera device used to measure hea
11、d at a pointin the subsurface.3.1.8 residual drawdownThe difference between the pro-jected prepumping water-level trend and the water level in awell or piezometer after pumping or injection has stopped.3.1.9 specific storagethe volume of water released fromor taken into storage per unit volume of th
12、e porous medium perunit change in head.3.1.10 step-drawdown testa test in which a control well ispumped at constant rates in “steps” of increasing discharge.Each step is approximately equal in duration, although the laststep may be prolonged.3.1.11 storage coeffcientthe volume of water an aquiferrel
13、eases from or takes into storage per unit surface area of theaquifer per unit change in head. For a confined aquifer it isequal to the product of specific storage and aquifer thickness.For an unconfined aquifer, the storage coefficient is approxi-mately equal to the specific yield.1This test method
14、is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations .Current edition approved Sept. 15, 2008. Published October 2008. Originallyapproved in 1992. Last previous edition approved in 2002 as
15、 D 5269 96 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact 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 Har
16、bor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.12 transmissivitythe volume of water of the prevail-ing kinematic viscosity transmitted in a unit time through a unitwidth of the aquifer under a unit hydraulic gradient.3.2 Symbols and Dimensions:3.2.1 b Laquifer thickness.
17、3.2.2 K LT1hydraulic conductivity.3.2.2.1 DiscussionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in ground-water literature by hydrogeologists, whereas the symbol k iscommonly used for this term in rock mechanics and soilscience.3.2.3 Krhydraulic conductivity i
18、n the plane of the aquifer,radially from the control well.3.2.4 Kzhydraulic conductivity in the vertical direction.3.2.5 lnnatural logarithm.3.2.6 log10logarithm to the base 10.3.2.7 Q L3T1discharge.3.2.8 r Lradial distance from control well.3.2.9 rcLequivalent inside radius of control well.3.2.10 S
19、 ndstorage coefficient.3.2.11 s Ldrawdown.3.2.12 scLdrawdown corrected for the effects of reduc-tion in saturated thickness.3.2.13 Syndspecific yield.3.2.14 s8 Lresidual drawdown.3.2.15 Ds8 Lchange in residual drawdown over one logcycle of t/t8.3.2.16 T L2T1transmissivity.3.2.17 t Ttime since pumpin
20、g or injection began.3.2.18 t8 Ttime since pumping or injection stopped.3.2.19 udimensionless parameter, equal to r2S/4Tt.3.2.20 u8dimensionless parameter, equal to r2S/4Tt8.4. Summary of Test Method4.1 This test method describes an analytical procedure fordetermining transmissivity using data colle
21、cted during therecovery phase of a withdrawal or injection well test. The fieldtest (see Test Method D 4050) requires pumping or injecting acontrol well that is open to the entire thickness of a confinedaquifer at a constant rate for a specified period. The water-levels in the control well, observat
22、ion wells, or piezometers aremeasured after pumping is stopped and used to calculate thetransmissivity of the aquifer using the procedures in this testmethod. Alternatively, this test method can be performed byinjecting water into the control well at a constant rate. Withsome modification, this test
23、 method can also be used to analyzethe residual drawdown following a step test. This test methodis used by plotting residual drawdown against either a functionof time or a function of time and discharge and determining theslope of a straight line fitted to the points.4.2 SolutionThe solution given b
24、y Theis (1)3can beexpressed as follows:s 5Q4pT*u e2yydy (1)and:u 5r2S4Tt(2)4.3 At a control well, observation well, or piezometer, forlarge values of time, t, and small values of radius, r, the Theisequation reduces, as shown by Cooper and Jacob (2) and Jacob(3) to the following:s8 5Q4pTlnt/t8! (3)w
25、here:t = the time after pumping began andt8 = the time after pumping ceases. From which it can beshown that:T 52.3Q4pDs8(4)where:Ds8 = the measured or projected residual drawdown overone log10cycle of t/t8.4.4 A similar analysis (see 4.3) may also be used for astep-drawdown test in which a well is p
26、umped at a constantrate for an initial period, and then the pumping rate is increasedthrough several new constant rates in a series of steps. Harrill(4) shows that:s8 52.3DQ14pTSlog10t1t8D12.3DQ24pTSlog10t2t8D(5)1 .2.3DQn4pTSlog10tnt8Dwhere:t1,t2, . tn= the elapsed times since either pump-ing was be
27、gun or the discharge ratewas increased,Q1,Q2, . Qn= the well discharge rates, andDQ1, DQ2. DQn= the incremental increases in discharge.Eq 5 can be rewritten as follows:T 52.3Qn4ps8log10ft, Q! (6)where:ft, Q! 5t1DQ1/Qnt2DQ2/Qnt3DQ3/Qn. tnDQn/Qnt8(7)and:T 52.3Qn4pDs8h(8)where:Ds8h= the residual drawdo
28、wn over one log cycle of theexpression f (t, Q)inEq6.Eq 8 can also be used to analyze the residual drawdownfollowing a test in which discharge varies significantly, so longas the discharge can be generalized as a series of constant-discharge steps.5. Significance and Use5.1 Assumptions:3The boldface
29、 numbers in parentheses refer to a list of references at the end ofthis standard.D 5269 96 (2008)25.1.1 The well discharges at a constant rate, Q, or at steps ofconstant rate Q1, Q2. Qn.5.1.2 Well is of infinitesimal diameter and is open throughthe full thickness of the aquifer.5.1.3 The nonleaky aq
30、uifer is homogeneous, isotropic, andareally extensive.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 areshown in Fig. 1.5.2 Implications of Assumptions:5.2.1 Implicit in the assumptions are the conditions of radialfl
31、ow. Vertical flow components are induced by a control wellthat partially penetrates the aquifer, that is, not open to theaquifer through the full thickness of the aquifer. If vertical flowcomponents are significant, the nearest partially penetratingobservation well should be located at a distance, r
32、, beyondwhich vertical flow components are negligible. See 5.2.1 ofTest Method D 4106 for assistance in determining the mini-mum distance to partially penetrating observation wells andpiezometers.5.2.2 The Theis method assumes the control well is ofinfinitesimal diameter. The storage in the control
33、well mayadversely affect drawdown measurements obtained in the earlypart of the test. See 5.2.2 of Test Method D 4106 for assistancein determining the duration of the effects of well-bore storageon drawdown.5.2.3 Application of Theis Recovery Method for UnconfinedAquifers:5.2.3.1 Although the assump
34、tions are applicable to artesianor confined conditions, the Theis solution may be applied tounconfined aquifers if (A) drawdown is small compared withthe saturated thickness of the aquifer or if the drawdown iscorrected for reduction in thickness of the aquifer and (B) theeffects of delayed gravity
35、yield are small. See 5.2.3 of TestMethod D 4106 for guidance in treating reduction in saturatedthickness and delayed gravity drainage in unconfined aquifers.6. Apparatus6.1 Analysis of data by this test method from the fieldprocedure given in Test Method D 4050 requires that thecontrol well and obse
36、rvation wells meet the requirementsspecified in the following subsections.6.2 Construction of Control WellInstall the control well inthe aquifer and equip with a pump capable of discharging waterfrom the well at a constant rate, or several steps at constantrate, for the duration of the test. Prefera
37、bly, the control wellshould be open throughout the full thickness of the aquifer. Ifthe control well partially penetrates the aquifer, take specialprecautions in the placement or design of observation wells(see 5.2.1).6.3 Construction of Observation Wells and PiezometersConstruct one or more observa
38、tion wells or piezometers at adistance from the control well. Observation wells may be openthrough all or part of the thickness of the aquifer.6.4 Location of Observation Wells and PiezometersWellsmay be located at any distance from the control well within thearea of influence of pumping. However, i
39、f vertical flowcomponents are significant and if piezometers or partiallypenetrating observation wells are used, locate them at adistance beyond the effect of vertical flow components. If theaquifer is unconfined, constraints are imposed on the distanceto partially penetrating observation wells and
40、the validity ofearly time measurements (see 5.2.1).7. Procedure7.1 The overall procedure consists of conducting the fieldprocedure for withdrawal or injection well tests (described inTest Method D 4050) and analysis of the field data, which isaddressed in Section 8.8. Calculation and Interpretation
41、of Results8.1 The Theis recovery method gives satisfactory resultswhen properly used. However, the method is valid only forsmall values of u, that is:for confined aquifers:u8 5r2S4Tt8(9)or for unconfined aquifers:u8 5r2Sy4Tt8(10)NOTE 1The limiting value for u of less than 0.01 may be excessivelyrest
42、rictive in some applications. The errors for small values of u, fromKruseman and De Ridder (5) are:Error less than, % 1 2 5 10For u smaller than 0.03 0.05 0.1 0.158.1.1 This test method allows only the calculation of trans-missivity, T, not storage coefficient, S, or specific yield, Sy.Therefore, to
43、 determine whether the assumption in Eq 9 or Eq10 has been violated it is necessary to estimate a value forstorage coefficient for confined aquifers or specific yield forunconfined aquifers. If data are available during the pumpingperiod, the storage may be computed using the procedures inTest Metho
44、d D 4105. Storage coefficients can be estimated asabout 3 3 105b, where b is aquifer thickness in meters.Whereas the specific yield of unconfined aquifers averagesabout 0.2 according to Lohman (6). After calculating T,FIG. 1 Cross Section Through a Discharging Well in a NonleakyAquiferD 5269 96 (200
45、8)3substitute the appropriate values into Eq 9 or Eq 10 and solvefor u8. It is not adequate to simply note that the data describeda straight line on semi-log graph paper.8.2 Plot either residual drawdown, s8, or water level, on thearithmetic axis of semilogarithmic graph paper versus eithert/t8 (for
46、 recovery from a constant-discharge test) (see Fig. 2)orf(t, Q) (for recovery from a step-drawdown test) (see Fig. 3)onthe logarithmic axis. Fit a straight line to the linear part of thedata plot, usually at smaller values of t/t8. Extend the straightline to intercept the t/t8 = 1 axis.At t/t8 = 1,
47、residual drawdownshould be approximately equal to zero, or if water levels wereplotted, the intercept should be equal to the prepumping waterlevels corrected for prepumping water-level trends. Substitutethe values for Ds8 or Ds8hin Eq 4 or Eq 8 and solve fortransmissivity. Check that all values of t
48、8 for the points used indefining the straight line meet the criterion that u8 0.01 (Eq9 and Eq 10), as described in 8.1.9. Report9.1 Prepare a report including the information describedbelow. The report of the analysis will include information fromthe field testing procedure.9.1.1 IntroductionThe in
49、troductory section is intended topresent the scope and purpose of the Theis recovery method fordetermining transmissivity in a confined nonleaky aquifer.Summarize the field hydrogeologic conditions and the fieldequipment and instrumentation including the construction ofthe control well and observation wells and piezometers, themethod of measurement of discharge and water levels, and theduration of the test and pumping rates. Discuss rationale forselecting the Theis recovery method.9.1.2 Hydrogeologic Sett
