1、Designation: D 5270 96 (Reapproved 2008)Standard Test Method forDetermining Transmissivity and Storage Coefficient ofBounded, Nonleaky, Confined Aquifers1This standard is issued under the fixed designation D 5270; the number immediately following the designation indicates the year oforiginal adoptio
2、n 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 an analytical procedure fordetermining the transmis
3、sivity, storage coefficient, and possiblelocation of boundaries for a confined aquifer with a linearboundary. This test method is used to analyze water-level orhead data from one or more observation wells or piezometersduring the pumping of water from a control well at a constantrate. This test meth
4、od also applies to flowing artesian wellsdischarging at a constant rate. With appropriate changes insign, this test method also can be used to analyze the effects ofinjecting water into a control well at a constant rate.1.2 The analytical procedure in this test method is used inconjunction with the
5、field procedure in Test Method D 4050.1.3 LimitationsThe valid use of this test method is limitedto determination of transmissivities and storage coefficients foraquifers in hydrogeologic settings with reasonable correspon-dence to the assumptions of the Theis nonequilibrium method(see Test Method D
6、 4106) (see 5.1), except that the aquifer islimited in areal extent by a linear boundary that fully penetratesthe aquifer. The boundary is assumed to be either a constant-head boundary (equivalent to a stream or lake that hydrauli-cally fully penetrates the aquifer) or a no-flow (impermeable)boundar
7、y (equivalent to a contact with a significantly lesspermeable rock unit). The Theis nonequilibrium method isdescribed in Test Methods D 4105 and D 4106.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of thi
8、s 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, and ContainedFluidsD 4043 Guide for Selection of Aquifer Test Method inDetermi
9、ning 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) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aq
10、uifers 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 Method for Determining Subsurface LiquidLevels in a Borehole or Monitoring Wel
11、l (ObservationWell)3. Terminology3.1 Definitions:3.1.1 constant-head boundarythe conceptual representa-tion of a natural feature such as a lake or river that effectivelyfully penetrates the aquifer and prevents water-level change inthe aquifer at that location.3.1.2 equipotential linea line connecti
12、ng points of equalhydraulic head. A set of such lines provides a contour map ofa potentiometric surface.3.1.3 image wellan imaginary well located opposite acontrol well such that a boundary is the perpendicular bisectorof a straight line connecting the control and image wells; usedto simulate the ef
13、fect of a boundary on water-level changes.3.1.4 impermeable boundarythe conceptual representa-tion of a natural feature such as a fault or depositional contactthat places a boundary of significantly less-permeable materiallaterally adjacent to an aquifer.3.1.5 See Terminology D 653 for other terms.3
14、.2 Symbols and Dimensions:3.2.1 Klndconstant of proportionality, ri/rr.3.2.2 QL3T1discharge.3.2.3 r Lradial distance from control well.3.2.4 riLdistance from observation well to image well.3.2.5 rrLdistance from observation well to control well.1This test method is under the jurisdiction ofASTM Comm
15、ittee 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 D 5270 96 (2002).2For referenced AST
16、M 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 Harbor Drive, PO Box C700, West Conshoho
17、cken, PA 19428-2959, United States.3.2.6 S ndstorage coefficient.3.2.7 s Ldrawdown.3.2.8 siLcomponent of drawdown due to image well.3.2.9 soLdrawdown at an observation well.3.2.10 srLcomponent of drawdown due to control well.3.2.11 TL2T1transmissivity.3.2.12 t Ttime since pumping or injection began.
18、3.2.13 toTtime at projection of zero drawdown.4. Summary of Test Method4.1 This test method prescribes two analytical proceduresfor analysis of a field test. This test method requires pumpingwater from, or injecting water into, a control well that is opento the entire thickness of a confined bounded
19、 aquifer at aconstant rate and measuring the water-level response in one ormore observation wells or piezometers. The water-level re-sponse in the aquifer is a function of the transmissivity andstorage coefficient of the aquifer, and the location and nature ofthe aquifer boundary or boundaries. Draw
20、down or build up ofthe water level is analyzed as a departure from the type curvedefined by the Theis nonequilibrium method (see Test MethodD 4106) or from straight-line segments defined by the modifiedTheis nonequilibrium method (see Test Method D 4105).4.2 A constant-head boundary such as a lake o
21、r stream thatfully penetrates the aquifer prevents drawdown or build up ofhead at the boundary, as shown in Fig. 1. Likewise, animpermeable boundary provides increased drawdown or buildup of head, as shown in Fig. 2. These effects are simulated bytreating the aquifer as if it were infinite in extent
22、 andintroducing an imaginary well or “image well” on the oppositeside of the boundary a distance equal to the distance of thecontrol well from the boundary.Aline between the control welland the image well is perpendicular to the boundary. If theboundary is a constant-head boundary, the flux from the
23、 imagewell is opposite in sign from that of the control well; forexample, the image of a discharging control well is an injectionwell, whereas the image of an injecting well is a dischargingwell. If the boundary is an impermeable boundary, the fluxfrom the image well has the same sign as that from t
24、he controlwell. Therefore, the image of a discharging well across animpermeable boundary is a discharging well. Because theeffects are symmetrical, only discharging control wells will bedescribed in the remainder of this test method, but this testmethod is equally applicable, with the appropriate ch
25、ange insign, to control wells into which water is injected.4.3 SolutionThe solution given by Theis (1)3can beexpressed as follows:s 5Q4pT*u e2yydy (1)and:u 5r2S4Tt(2)where:*u e2yydy 5 Wu!520.577216 2 logeu 1 u 2u22!21u33!32u44!41 .(3)4.4 According to the principle of superposition, the draw-down at
26、any point in the aquifer is the sum of the drawdowndue to the real and image wells (1) and (2) :so5 sr6 si(4)Equation (4) can be rewritten as follows:so5Q4pTWur! 6 Wui!# 5Q4pT( Wu! (5)where:ur5rr2S4Tt, ui5ri2S4Tt(6)so that:ui5SrirrD2ur, ui5 Kl2ur(7)3The boldface numbers in parentheses refer to a lis
27、t of references at the end ofthis standard.NOTE 1Modified from Ferris and others (6) and Heath (7).FIG. 1 Diagram Showing Constant-Head BoundaryD 5270 96 (2008)2where:Kl5rirr(8)NOTE 1Klis a constant of proportionality between the radii, not to beconfused with hydraulic conductivity.5. Significance a
28、nd Use5.1 Assumptions:5.1.1 The well discharges at a constant rate.5.1.2 Well is of infinitesimal diameter and is open throughthe full thickness of the aquifer.5.1.3 The nonleaky confined aquifer is homogeneous, iso-tropic, and areally extensive except where limited by linearboundaries.5.1.4 Dischar
29、ge from the well is derived initially fromstorage in the aquifer; later, movement of water may beinduced from a constant-head boundary into the aquifer.5.1.5 The geometry of the assumed aquifer and well areshown in Fig. 1 or Fig. 2.5.1.6 Boundaries are vertical planes, infinite in length thatfully p
30、enetrate the aquifer. No water is yielded to the aquifer byimpermeable boundaries, whereas recharging boundaries are inperfect hydraulic connection with the aquifer.5.1.7 Observation wells represent the head in the aquifer;that is, the effects of wellbore storage in the observation wellsare negligib
31、le.5.2 Implications of Assumptions:5.2.1 Implicit in the assumptions are the conditions of afully-penetrating control well and observation wells of infini-tesimal diameter in a confined aquifer. Under certain condi-tions, aquifer tests can be successfully analyzed when thecontrol well is open to onl
32、y part of the aquifer or contains asignificant volume of water or when the test is conducted in anunconfined aquifer. These conditions are discussed in moredetail in Test Method D 4105.5.2.2 In cases in which this test method is used to locate anunknown boundary, a minimum of three observation wells
33、 isneeded. If only two observation wells are available, twopossible locations of the boundary are defined, and if only oneobservation well is used, a circle describing all possiblelocations of the image well is defined.5.2.3 The effects of a constant-head boundary are oftenindistinguishable from the
34、 effects of a leaky, confined aquifer.Therefore, care must be taken to ensure that a correct concep-tual model of the system has been created prior to analyzing thetest. See Guide D 4043.6. Apparatus6.1 Analysis of the data from the field procedure (see TestMethod D 4050) by this test method require
35、s that the controlwell and observation wells meet the requirements specified inthe 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 for the duration of the test.Preferably,
36、the control well should be open throughout the fullthickness of the aquifer. If the control well partially penetratesthe aquifer, take special precautions in the placement or designof observation wells (see 5.2.1).6.3 Construction of Observation Wells and PiezometersConstruct one or more observation
37、 wells or piezometers atspecified distances from the control well.6.4 Location of Observation Wells and PiezometersWellsmay be located at any distance from the control well within thearea of influence of pumping. However, if vertical flowcomponents are expected to be significant near the control wel
38、land if partially penetrating observation wells are to be used, theobservation wells should be located at a distance beyond theeffect of vertical flow components. If the aquifer is unconfined,constraints are imposed on the distance to partially penetratingobservation wells and on the validity of ear
39、ly time measure-ments (see Test Method D 4106).NOTE 2To ensure that the effects of the boundary may be observedduring the tests, some of the wells should be located along lines parallelto the suspected boundary, no farther from the boundary than the controlwell.NOTE 1Modified from Ferris and others
40、(6) and Heath (7).FIG. 2 Diagram Showing Impermeable BoundaryD 5270 96 (2008)37. Procedure7.1 The general procedure consists of conducting the fieldprocedure for withdrawal or injection wells tests (see TestMethod D 4050) and analyzing the field data, as addressed inthis test method.7.2 Analysis of
41、the field data consists of two steps: deter-mination of the properties of the aquifer and the nature anddistance to the image well from each observation well, anddetermination of the location of the boundary.7.3 Two methods of analysis can be used to determine theaquifer properties and the nature an
42、d distance to the imagewell. One method is based on the Theis nonequilibriummethod; the other method is based on the modified Theisnonequilibrium method.7.3.1 Theis Nonequilibrium MethodExpressions in Eq 5-8are used to generate a family of curves of 1/urversus ( W (u)for values of Klfor recharging a
43、nd discharging image wells asshown in Fig. 3 (2). Table 1 gives values of W (u) versus 1/u.This table may be used to create a table of (W ( u) versus 1/ufor each value of Klby picking values for W (ur) and W (ui),and computing the ( W (u) for the each value of 1/u.7.3.1.1 Transmissivity, storage coe
44、fficient, and the possiblelocation of one or more boundaries are calculated fromparameters determined from the match point and a curveselected from a family of type curves.7.3.2 Modified Theis Nonequilibrium MethodThe sum ofthe terms to the right of logeu in Eq 3 is not significant whenu becomes sma
45、ll, that is, equal to or less than 0.01.NOTE 3The limiting value for u of less than 0.01 may be excessivelyrestrictive in some applications. The errors for small values of u, fromKruseman and DeRidder (3) are as follows:Error less than, %: 1 2 5 10For u smaller than: 0.03 0.05 0.1 0.157.3.2.1 The va
46、lue of u decreases as time, t, increases anddecreases as radial distance, r, decreases. Therefore, for largevalues of t and small values of r, the terms to the right of logeuin Eq 3 may be neglected, as recognized by Theis (1). Themodified Theis equation can then be written as follows:s 5Q4pTS20.577
47、216 2 logeSr2S4TtDD (9)from which it has been shown by Lohman (4) that:T 52.3Q4pDs(10)where:Ds = the drawdown (measured or projected) over one logcycle of time.8. Calculation and Interpretation of Results8.1 Determine the aquifer properties and the nature anddistance to the image well by either the
48、Theis nonequilibriummethod or the modified Theis method.8.1.1 Theis Nonequilibrium MethodThe graphical proce-dure for solution by the Theis nonequilibrium method is basedon the relationship between (W (u) and s, and between 1/u andt/r2.8.1.1.1 Plot the log of values of (W (u) on the verticalcoordina
49、te and 1/u on the horizontal coordinate. Plot a familyof curves for several values of Kl, for both recharging anddischarging images. This plot (see Fig. 3) is referred to as afamily of type curves. Plots of the family of type curves arecontained in (2) and (4).NOTE 1From Stallman (2).FIG. 3 Family of Type Curves for the Solution of the Modified Theis FormulaD 5270 96 (2008)48.1.1.2 Plot values of the log of drawdown, s, on the verticalcoordinate versus the log of t/r2on the horizontal coordinate.Use a different sy
