1、Designation: D5269 15Standard Test Method forDetermining Transmissivity of Nonleaky Confined Aquifersby the Theis Recovery Method1This standard is issued under the fixed designation D5269; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revi
2、sion, 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 of a confined aqui
3、fer. 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,along with several others, is used in conjunction with the fieldprocedure in Test M
4、ethod D4050. Guide D4043 providesinformation for determining hydraulic properties.1.3 LimitationsThe valid use of the Theis recoverymethod is limited to determination of transmissivities foraquifers in hydrogeologic settings reasonably corresponding tothe assumptions of the Theis theory (see 5.2).1.
5、4 UnitsThe values stated in either SI Units or inch-pound units are to be regarded separately as standard. Thevalues in each system may not be exact equivalents; thereforeeach system shall be used independently of the other. Combin-ing values from the two systems may result in non-conformance with t
6、he standard. Reporting of test results inunits other than SI shall not be regarded as nonconformancewith this test method.1.5 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D6026. All observed and calculated values shallco
7、nform to the guidelines for significant digits and roundingestablished in Practice D6026, unless otherwise superseded bythis standard.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use.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 esta
8、blish 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
9、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 Aquif
10、er 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
11、Confined Aquifers by the Theis NonequilibriumMethodD6026 Practice for Using Significant Digits in GeotechnicalData3. Terminology3.1 Definitions:3.1.1 For definitions of common Terminology terms usedwithin this guide refer to Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 o
12、bservation wella well open to all or part of anaquifer.3.3 Symbols and Dimensions:3.3.1 b Laquifer thickness.3.3.2 K LT1hydraulic conductivity.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Groundwater andVa
13、dose Zone Investigations.Current edition approved April 15, 2015. Published May 2015. Originallyapproved in 1992. Last previous edition approved in 2008 as D5269 96 (2008).DOI: 10.1520/D5269-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at s
14、erviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.3.2.1 DiscussionThe use of the symbol K for the ter
15、mhydraulic conductivity is the predominant usage in groundwa-ter literature by hydrogeologists, whereas the symbol k iscommonly used for this term in rock mechanics and soilscience.3.3.3 Krhydraulic conductivity in the plane of the aquifer,radially from the control well.3.3.4 Kzhydraulic conductivit
16、y in the vertical direction.3.3.5 lnnatural logarithm.3.3.6 log10logarithm to the base 10.3.3.7 Q L3T1discharge.3.3.8 r Lradial distance from control well.3.3.9 rcLequivalent inside radius of control well.3.3.10 S ndstorage coefficient.3.3.11 s Ldrawdown.3.3.12 scLdrawdown corrected for the effects
17、of reduc-tion in saturated thickness.3.3.13 Syndspecific yield.3.3.14 s Lresidual drawdown.3.3.15 s Lchange in residual drawdown over one logcycle of t/t.3.3.16 T L2T1transmissivity.3.3.17 t Ttime since pumping or injection began.3.3.18 t Ttime since pumping or injection stopped.3.3.19 udimensionles
18、s parameter, equal to r2S/4Tt.3.3.20 udimensionless parameter, equal to r2S/4Tt.4. Summary 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
19、Method D4050) 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, observation wells, or piezometers aremeasured after pumping is stopped and used to calculate thetransmi
20、ssivity 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 method can also be used to analyzethe residual drawdown following a step test. This test metho
21、dis 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. The solutioncalculations are shown in Section 8.5. Significance and Use5.1 This test method is useful for analyzing data on th
22、erecovery of water levels following pumping or injection ofwater to or from a control well at a constant rate. The analyticalprocedure given in this test method along with several others isused in conjunction with the field procedure in Test MethodD4050.5.2 Assumptions:5.2.1 The well discharges at a
23、 constant rate, Q, or at steps ofconstant rate Q1, Q2. Qn.5.2.2 Well is of infinitesimal diameter and is open throughthe full thickness of the aquifer.5.2.3 The nonleaky aquifer is homogeneous, isotropic, andextensive in area.5.2.4 Discharge from the well is derived exclusively fromstorage in the aq
24、uifer.5.2.5 The geometry of the assumed aquifer and well areshown in Fig. 1.5.3 Implications of Assumptions:5.3.1 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
25、 through the full thickness of the aquifer. If vertical flowcomponents are significant, the nearest partially penetratingobservation well should be located at a distance, r, beyondwhich vertical flow components are negligible. See 5.3.1 ofTest Method D4106 for assistance in determining the minimumdi
26、stance to partially penetrating observation wells and piezom-eters.5.3.2 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 5.3.2 of Test Method D4106 for assistan
27、cein determining the duration of the effects of well-bore storageon drawdown.5.3.3 Application of Theis Recovery Method for UnconfinedAquifers:5.3.3.1 Although the assumptions are applicable to artesianor confined conditions, the Theis solution may be applied tounconfined aquifers if (A) drawdown is
28、 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 yield are small. See 5.3.3 of TestFIG. 1 Cross Section Through a Discharging Well in a NonleakyAquiferD5269 152Method D4106 for gu
29、idance in treating reduction in saturatedthickness and delayed gravity drainage in unconfined aquifers.NOTE 1The 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 t
30、hecriteria of Practice D3740 are generally considered capable of competentand objective testing/sampling/inspection. 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 me
31、ans of evaluating some of those factors.6. Apparatus6.1 Analysis of data by this test method from the fieldprocedure given in Test Method D4050 requires that thecontrol well and observation wells meet the requirementsspecified in the following subsections.6.2 Construction of Control WellInstall the
32、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. Preferably, the control wellshould be open throughout the full thickness of the aquifer. Ifthe control well partially penetra
33、tes the aquifer, take specialprecautions in the placement or design of observation wells(see 5.3.1).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
34、thickness of the aquifer.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 significant and if piezometers or partiallypenetrating observation wells are used, loca
35、te 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 the validity ofearly time measurements (see 5.3.1).7. Procedure7.1 The overall procedure process consists of conducti
36、ngthe field procedure for withdrawal or injection well tests(described in Test Method D4050) and then the analysis of thefield data, which is addressed by this test method in Section 8.8. Calculation and Interpretation of Results8.1 SolutionThe solution given by Theis (1)3can beexpressed as follows:
37、s 5Q4T*u e2yyy (1)and:u 5r2S4Tt(2)8.2 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:s5Q4Tlnt t! (3)where:t = the time after pumping began andt =
38、the time after pumping ceases. From which it can beshown that:T 52.3Q4s(4)where:s = the measured or projected residual drawdown over onelog10cycle of t/t.8.3 A similar analysis (see 8.2) may also be used for astep-drawdown test in which a well is pumped at a constantrate for an initial period, and t
39、hen the pumping rate is increasedthrough several new constant rates in a series of steps. Harrill(4) shows that:s52.3Q14TSlog10t1t D12.3Q24TSlog10t2t D1.2.3Qn4TSlog10tnt Dwhere:t1,t2,tn= the elapsed times since either pumpingwas begun or the discharge rate wasincreased,Q1,Q2,Qn= the well discharge r
40、ates, andQ1, Q2, Qn= the incremental increases in discharge.Eq 5 can be rewritten as follows:T 52.3Qn4slog10ft, Q! (5)where:ft, Q! 5t1Q1/Qnt2Q2/Qnt3Q3/Qn tnQn/Qnt(6)and:T 52.3Qn4sh(7)where:sh= the residual drawdown over one log cycle of theexpression f(t, Q)inEq 6.Eq 8 can also be used to analyze th
41、e residual drawdownfollowing a test in which discharge varies significantly, so longas the discharge can be generalized as a series of constant-discharge steps.8.4 The Theis recovery method gives satisfactory resultswhen properly used. However, the method is valid only forsmall values of u, that is:
42、for confined aquifers:u 5r2S4Tt(8)or for unconfined aquifers:3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D5269 153u 5r2Sy4Tt(9)NOTE 2The limiting value for u of less than 0.01 may be excessivelyrestrictive in some applications. The errors for small v
43、alues of u, fromKruseman and De Ridder (5) are:Error less than, % 1 2 5 10For u smaller than 0.03 0.05 0.1 0.158.4.1 This test method allows only the calculation oftransmissivity, T, not storage coefficient, S, or specific yield, Sy.Therefore, to determine whether the assumption in Eq 9 or Eq10 has
44、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 Method D4105. Storage coefficients can be estimated asabout
45、 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,substitute the appropriate values into Eq 9 or Eq 10 and solvefor u. It is not adequate to simply note that the data describeda straight li
46、ne on semi-log graph paper.8.5 Plot either residual drawdown, s, or water level, on thearithmetic axis of semilogarithmic graph paper versus either t/t(for recovery from a constant-discharge test) (see Fig. 2)orf(t,Q) (for recovery from a step-drawdown test) (see Fig. 3)onthelogarithmic axis. Fit a
47、straight line to the linear part of the dataplot, usually at smaller values of t/t. Extend the straight line tointercept the t/t = 1 axis. At t/t = 1, residual drawdown shouldbe approximately equal to zero, or if water levels were plotted,the intercept should be equal to the prepumping water levelsc
48、orrected for prepumping water-level trends. Substitute thevalues for sorshin Eq 3 or Eq 8 and solve fortransmissivity. Check that values of t for the points used indefining the straight line meet the criterion that u 0.01 (Eq 9and Eq 10), as described in 8.4.9. Report: Test Data Sheet(s)/Forms9.1 Pr
49、epare a report including as a minimum the informa-tion described below. The report of the analysis will includeinformation from the 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 and the fieldequipment and instrumentation including the construction ofthe co
