1、Designation: D 5269 96 (Reapproved 2002)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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers an analytical procedure fordetermining the transmissivi
3、ty 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 The values stated in SI units are to be regarded asstandard.1.5 Th
5、is 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 Documen
6、ts2.1 ASTM Standards:D 653 Terminology Relating to Soil, Rock and ContainedFluids2D 4043 Guide for Selection of Aquifer-Test Method inDetermining Hydraulic Properties by Well Techniques2D 4050 Test Method (Field Procedure) for Withdrawal andInjection Well Tests for Determining Hydraulic Propertiesof
7、 Aquifer Systems2D 4105 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers by the Modified Theis NonequilibriumMethod2D 4106 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConf
8、ined Aquifers by the Theis Nonequilibrium Method2D 4750 Test Method for Determining Subsurface LiquidLevels in a Borehole or Monitoring Well (ObservationWell)23. Terminology3.1 Definitions:3.1.1 aquifer, confinedan aquifer bounded above andbelow by confining beds and in which the static head is abov
9、ethe 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 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
10、 the removal of water.3.1.5 hydraulic conductivity (field aquifer 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
11、 part of anaquifer.3.1.7 piezometera device used to measure head 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
12、 water released fromor taken into storage per unit volume of the 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 prolo
13、nged.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 it isequal to the product of specific storage and aquifer thickness.For an unconfined aquifer, the storage coefficient i
14、s approxi-mately equal to the specific yield.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:Symbols and Dimensions:1This test method is under the jurisdiction of
15、 ASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Oct. 10, 1996. Published June 1997. Originallypublished as D 5269 92.2Annual Book of ASTM Standards, Vol 04.08.1Copyright ASTM Internatio
16、nal, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2.1 b Laquifer thickness.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, w
17、hereas the symbol k iscommonly used for this term in rock mechanics and soilscience.3.2.3 Krhydraulic conductivity in 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
18、 L3T1discharge.3.2.8 r Lradial distance from control well.3.2.9 rcLequivalent inside radius of control well.3.2.10 S 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.3.2.1
19、5 Ds8 Lchange in residual drawdown over one logcycle of t/t8.3.2.16 T L2T1transmissivity.3.2.17 t Ttime since pumping 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
20、 of Test Method4.1 This test method describes an analytical procedure fordetermining transmissivity using data collected 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 thic
21、kness of a confinedaquifer at a constant rate for a specified period. The water-levels in the control well, observation 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
22、method can be performed byinjecting water into the control well at a constant rate. Withsome modification, this test 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
23、time and discharge and determining theslope of a straight line fitted to the points.4.2 SolutionThe solution given by 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 radiu
24、s, r, the Theisequation reduces, as shown by Cooper and Jacob (2) and Jacob(3) to the following:s8 5Q4pTlnt/t8! (3)where: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 overo
25、ne 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 pumped 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 52.3DQ14pTSlog10t
26、1t8D12.3DQ24pTSlog10t2t8D(5)1 .2.3DQn4pTSlog10tnt8Dwhere:t1,t2, . tn= the elapsed times since either pump-ing was begun 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 52.3Qn4ps8log1
27、0ft, Q! (6)where:ft, Q! 5t1DQ1/Qnt2DQ2/Qnt3DQ3/Qn. tnDQn/Qnt8(7)and:T 52.3Qn4pDs8h(8)where:Ds8h= the residual drawdown 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 disch
28、arge can be generalized as a series of constant-discharge steps.5. Significance and Use5.1 Assumptions:5.1.1 The well discharges at a constant rate, Q, or at steps of3The boldface numbers given in parentheses refer to a list of references at theend of the text.D 52692constant rate Q1, Q2. Qn.5.1.2 W
29、ell is of infinitesimal diameter and is open throughthe full thickness of the aquifer.5.1.3 The nonleaky aquifer 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
30、 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, not open to theaquifer through the full thickness of the aquifer. If vertical flowcompo
31、nents are significant, the nearest partially penetratingobservation well should be located at a distance, r, 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 andpiezomete
32、rs.5.2.2 The Theis method assumes the control well is ofinfinitesimal diameter. The storage in the control 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 stora
33、geon drawdown.5.2.3 Application of Theis Recovery Method for UnconfinedAquifers:5.2.3.1 Although the assumptions 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 i
34、f the drawdown iscorrected for reduction in thickness of the aquifer and (B) theeffects of delayed gravity 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
35、this test method from the fieldprocedure given in Test Method D 4050 requires that thecontrol well and observation 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 wat
36、erfrom the well at a constant rate, or several steps at constantrate, for the duration of the test. Preferably, 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 obse
37、rvation wells(see 5.2.1).6.3 Construction of Observation Wells and PiezometersConstruct one or more observation 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 PiezometersW
38、ellsmay be located at any distance from the control well within thearea of influence of pumping. However, if 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 theaq
39、uifer is unconfined, constraints are imposed on the distanceto partially penetrating observation wells and 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 Metho
40、d D 4050) and analysis of the field data, which isaddressed in Section 8.8. Calculation and Interpretation 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
41、unconfined aquifers:u8 5r2Sy4Tt8(10)NOTE 1The limiting value for u of less than 0.01 may be excessivelyrestrictive 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
42、only the calculation of trans-missivity, T, not storage coefficient, S, or specific yield, Sy.Therefore, to 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
43、 data are available during the pumpingperiod, the storage may be computed using the procedures inTest Method 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
44、(6). After calculating T,substitute the appropriate values into Eq 9 or Eq 10 and solvefor u8. It is not adequate to simply note that the data describedFIG. 1 Cross Section Through a Discharging Well in a NonleakyAquiferD 52693a straight line on semi-log graph paper.8.2 Plot either residual drawdown
45、, s8, or water level, on thearithmetic axis of semilogarithmic graph paper versus eithert/t8 (for 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, usua
46、lly at smaller values of t/t8. Extend the straightline to intercept the t/t8 = 1 axis. At t/t8 = 1, 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. Substit
47、utethe values for Ds8 or Ds8hin Eq 4 or Eq 8 and solve fortransmissivity. Check that all values of t8 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 repo
48、rt of the analysis will include information fromthe field testing procedure.9.1.1 IntroductionThe introductory 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 an
49、d 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 SettingReview the informationavailable on the hydrogeology of the site. Include drillers logsand geologists description of drill cuttings. Interpret anddescribe the hydrogeology of the site as it pertains to
