1、Designation: D 4106 96 (Reapproved 2002)Standard Test Method(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 the de
2、signation 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers an
3、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 with t
4、hefield 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 The values sta
5、ted in SI units are to be regarded asstandard.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 regul
6、atory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:D 653 Terminology Relating to Soil, Rock, and ContainedFluids2D 4043 Guide for Selection of Aquifer Test Method inDetermining of Hydraulic Properties by Well Techniques2D 4050 Test Method (Field Procedure) for Withdrawal andInj
7、ection Well Tests for Determining Hydraulic Propertiesof Aquifer Systems23. 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 mat
8、erial bounding one or more aquifers.3.1.3 control wellwell by 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.
9、3.1.6 head, staticthe height above a standard datum of thesurface 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 tim
10、e under a unit hydraulic gradient through a unitarea measured 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
11、volume of water released fromor taken into storage per unit 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 co
12、efficient is equal to the product of the specific storageand 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 unithydraul
13、ic gradient through a unit width of the aquifer.3.1.13 unconfined 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:Symbols and Dimensions:3.2.1 K LT1hydraulic conductivity.3.2.2 Kxyhydraulic conductivity in the h
14、orizontal 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.1This test method is under the jurisdiction of ASTM Committee D18 on Soil andRock and is the direct responsibility of
15、 Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Oct. 10, 1996. Published June 1997. Originallypublished as D 4106 91.2Annual Book of ASTM Standards, Vol 04.08.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-29
16、59, United States.3.2.7 T L2T1transmissivity.3.2.8 W(u) ndwell function of u.3.2.9 b Lthickness of aquifer.3.2.10 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
17、 injection welltest. The field procedure (see Test Method D 4050) 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
18、 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.
19、 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 SolutionThe solution given by Theis (1)3may beexpressed as follows:s 5Q4pT*u e2yydy (1)where:u 5r2S4Tt
20、(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 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 n
21、onleaky 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 ass
22、umptions 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
23、penetrating observation well should be located at adistance, r, beyond which vertical flow components are negli-gible, 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 storag
24、e 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
25、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 cont
26、rol 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
27、 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 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 a
28、pplied 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 ThicknessIn an unconfinedaquifer dewatering o
29、ccurs 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 the3The boldface numbers in parentheses refer to a list of references at the end ofthe text.FIG. 1 Cross Section Through a Discharging Well in a
30、 NonleakyConfined AquiferD 41062aquifer thickness as shown by Jacob (5). The drawdown, s,needs to 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 invali
31、date 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 a dis-tance, r, from the control well, where:r 5bKzKxy(8)After the time, t, as given in Eq 9 from
32、 Neuman (6).t 5 10 3 Syr2/T! (9)where:Sy= the specific yield. For fully penetrating observationwells, 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)
33、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 WellScreen the control wellin the aquifer to be tested and equip with a pump capable ofdischarging water from the well at a c
34、onstant 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 WellsC
35、onstruct 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 WellsLocate observationwells at various distances from the control well within the areaof influence of pumping.
36、 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 we
37、lls 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 D 4050) and analysis of the field data that isaddressed in this test method.7.2 The integral expr
38、ession 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 5Q4pTWu! (10)and:u 5r2S4Tt(11)8. Calculation8.1 The graphical procedure used to calculate test results isbased on the functiona
39、l 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 ofdraw
40、down, 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
41、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 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
42、1/u are integervalues.NOTE 1Alternatively, the type curve can be constructed by plotting W(u) against 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 app
43、ly 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. Report9.1 Prepare a report including the informatio
44、n described inthis section. The report of the analytical procedure will includeinformation from the report on test method selection (seeGuide D 4043) and the field testing procedure (see Test MethodD 4050).9.1.1 IntroductionThe introductory section is intended topresent the scope and purpose of the
45、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 b
46、oth, the method ofmeasurement of discharge and water levels, and the duration ofthe test and pumping rate. Discuss rationale for selecting theTheis nonequilibrium method.D 410639.1.2 Hydrogeologic SettingReview the informationavailable on the hydrogeology of the site; interpret anddescribe the hydro
47、geology 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 EquipmentReport the field installation and equip-ment for
48、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
49、,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 Testing ProceduresState the steps taken in conduct-ing pre-test, drawdown, and recovery phases of the test.Include the date, clock time, and time since pumping started orstopped for measurements of discharge rate, wat
