1、Designation: D 5270 96 (Reapproved 2002)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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers an analytical procedure fordetermining the transmi
3、ssivity, 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 met
4、hod 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
6、D 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)bounda
7、ry (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 The values stated in SI units are to be regarded asstandard.1.5 This standard does not purport to address all of thesafety concerns, if any, as
8、sociated 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:D 653 Terminology Relating to Soil, Rock, and ContainedF
9、luids2D 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 Aquifer Systems2D 4105 Test Method (Analytical Procedure) for Determin-ing
10、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 NonleakyConfined Aquifers by the Theis Nonequilibrium Method2D 4750 Test Method for Dete
11、rmining Subsurface LiquidLevels in a Borehole or Monitoring Well (ObservationWell)23. 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
12、aquifer at that location.3.1.2 equipotential linea line connecting 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 lin
13、e connecting the control and image wells; usedto simulate the effect 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 adja
14、cent to an aquifer.3.1.5 See Terminology D 653 for other terms.3.2 Symbols and Dimensions:3.2.1 Klndconstant of proportionality, ri/rr.3.2.2 Q L3T1discharge.3.2.3 r Lradial distance from control well.3.2.4 riLdistance from observation well to image well.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 February 1997. Originallypublished as D 5270 92. Last previous edition D 5270 92.2Annual Book of ASTM Standards,
16、 Vol 04.08.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2.5 rrLdistance from observation well to control well.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
17、an observation well.3.2.10 srLcomponent of drawdown due to control well.3.2.11 T L2T1transmissivity.3.2.12 t Ttime since pumping or injection began.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
18、test. This test method requires pumpingwater from, or injecting water into, a control well that is opento the entire thickness of a confined bounded aquifer at aconstant rate and measuring the water-level response in one ormore observation wells or piezometers. The water-level re-sponse in the aquif
19、er is a function of the transmissivity andstorage coefficient of the aquifer, and the location and nature ofthe aquifer boundary or boundaries. Drawdown 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 f
20、rom straight-line segments defined by the modifiedTheis nonequilibrium method (see Test Method D 4105).4.2 A constant-head boundary such as a lake or stream thatfully penetrates the aquifer prevents drawdown or build up ofhead at the boundary, as shown in Fig. 1. Likewise, animpermeable boundary pro
21、vides 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 andintroducing an imaginary well or “image well” on the oppositeside of the boundary a distance equal to the distance of thecontrol well from the bound
22、ary. A line between the control welland the image well is perpendicular to the boundary. If theboundary is a constant-head boundary, the flux from the imagewell is opposite in sign from that of the control well; forexample, the image of a discharging control well is an injectionwell, whereas the ima
23、ge 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 the controlwell. Therefore, the image of a discharging well across animpermeable boundary is a discharging well. Because theeffects are symmetrical, on
24、ly discharging control wells will bedescribed in the remainder of this test method, but this testmethod is equally applicable, with the appropriate change 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)
25、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 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:s
26、o5Q4pTWur! 6 Wui!# 5Q4pT( Wu! (5)where:ur5rr2S4Tt, ui5ri2S4Tt(6)so that:ui5SrirrD2ur, ui5 Kl2ur(7)3The boldface numbers given in parentheses refer to a list of references at theend of the text.NOTE 1Modified from Ferris and others (6) and Heath (7).FIG. 1 Diagram Showing Constant-Head BoundaryD 5270
27、2where:Kl5rirr(8)NOTE 1Klis a constant of proportionality between the radii, not to beconfused with hydraulic conductivity.5. Significance and 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.
28、5.1.3 The nonleaky confined aquifer is homogeneous, iso-tropic, and areally extensive except where limited by linearboundaries.5.1.4 Discharge 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 Th
29、e 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 penetrate the aquifer. No water is yielded to the aquifer byimpermeable boundaries, whereas recharging boundaries are inperfect hydraulic connection with the aqu
30、ifer.5.1.7 Observation wells represent the head in the aquifer;that is, the effects of wellbore storage in the observation wellsare negligible.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-tesim
31、al diameter in a confined aquifer. Under certain condi-tions, aquifer tests can be successfully analyzed when thecontrol well is open to only part of the aquifer or contains asignificant volume of water or when the test is conducted in anunconfined aquifer. These conditions are discussed in moredeta
32、il 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 isneeded. If only two observation wells are available, twopossible locations of the boundary are defined, and if only oneobservation well is used, a circle des
33、cribing all possiblelocations of the image well is defined.5.2.3 The effects of a constant-head boundary are oftenindistinguishable from the 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
34、 thetest. See Guide D 4043.6. Apparatus6.1 Analysis of the data from the field procedure (see TestMethod D 4050) by this test method requires that the controlwell and observation wells meet the requirements specified inthe following subsections.6.2 Construction of Control WellInstall the control wel
35、l inthe aquifer and equip with a pump capable of discharging waterfrom the well at a constant rate for the duration of the test.Preferably, the control well should be open throughout the fullthickness of the aquifer. If the control well partially penetratesthe aquifer, take special precautions in th
36、e placement or designof observation wells (see 5.2.1).6.3 Construction of Observation Wells and PiezometersConstruct one or more observation wells or piezometers atspecified distances from the control well.6.4 Location of Observation Wells and PiezometersWellsmay be located at any distance from the
37、control well within thearea of influence of pumping. However, if vertical flowcomponents are expected to be significant near the control welland if partially penetrating observation wells are to be used, theobservation wells should be located at a distance beyond theeffect of vertical flow component
38、s. If the aquifer is unconfined,constraints are imposed on the distance to partially penetratingobservation wells and on the validity of early 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 loc
39、ated along lines parallelto the suspected boundary, no farther from the boundary than the controlwell.7. Procedure7.1 The general procedure consists of conducting the fieldprocedure for withdrawal or injection wells tests (see TestNOTE 1Modified from Ferris and others (6) and Heath (7).FIG. 2 Diagra
40、m Showing Impermeable BoundaryD 52703Method D 4050) and analyzing the field data, as addressed inthis test method.7.2 Analysis of 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, anddetermin
41、ation of the location of the boundary.7.3 Two methods of analysis can be used to determine theaquifer properties and the nature and 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 Noneq
42、uilibrium MethodExpressions in Eq 5-8are used to generate a family of curves of 1/urversus ( W (u)for values of Klfor recharging and 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
43、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 coefficient, 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
44、.7.3.2 Modified Theis Nonequilibrium MethodThe sum ofthe terms to the right of logeu in Eq 3 is not significant whenu becomes small, 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
45、 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 value 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 lo
46、geuin Eq 3 may be neglected, as recognized by Theis (1). Themodified Theis equation can then be written as follows:s 5Q4pTS20.577216 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. Calculat
47、ion and Interpretation of Results8.1 Determine the aquifer properties and the nature anddistance to the image well by either the Theis nonequilibriummethod or the modified Theis method.8.1.1 Theis Nonequilibrium MethodThe graphical proce-dure for solution by the Theis nonequilibrium method is basedo
48、n 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 verticalcoordinate 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
49、as afamily of type curves. Plots of the family of type curves arecontained in (2) and (4).8.1.1.2 Plot values of the log of drawdown, s, on the verticalcoordinate versus the log of t/r2on the horizontal coordinate.Use a different symbol for data from each observation well.8.1.1.3 Overlay the data plot on the type curve plot and,while the coordinate axes are held parallel, shift the plot toNOTE 1From Stallman (2).FIG. 3 Family of Type Curves for the Solution of the Modified Theis FormulaD 52704align the data with the type
