1、Designation: D6028 17Standard Test Method (Analytical Procedure) forDetermining Hydraulic Properties of a Confined AquiferTaking into Consideration Storage of Water in LeakyConfining Beds by Modified Hantush Method1This standard is issued under the fixed designation D6028; the number immediately fol
2、lowing the designation 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 () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test meth
3、od covers an analytical procedure fordetermining the transmissivity and storage coefficient of aconfined aquifer taking into consideration the change in storageof water in overlying or underlying confining beds, or both.This test method is used to analyze water-level or head datacollected from one o
4、r more observation wells or piezometersduring the pumping of water from a control well at a constantrate.With appropriate changes in sign, this test method also canbe used to analyze the effects of injecting water into a controlwell at a constant rate.1.2 This analytical procedure is used in conjunc
5、tion withTest Method D4050.1.3 LimitationsThe valid use of the modified Hantushmethod (1)2is limited to the determination of hydraulicproperties for aquifers in hydrogeologic settings with reason-able correspondence to the assumptions of the Hantush-Jacobmethod (Test Method D6029) with the exception
6、 that in thiscase the gain or loss of water in storage in the confining bedsis taken into consideration (see 5.1). All possible combinationsof impermeable beds and source beds (for example, beds inwhich the head remains uniform) are considered on the distalside of the leaky beds that confine the aqu
7、ifer of interest (seeFig. 1).1.4 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D6026.1.4.1 The procedures used to specify how data are collected/recorded and calculated in the standard are regarded as theindustry standard
8、. In addition, they are representative of thesignificant digits that generally should be retained. The proce-dures used do not consider material variation, purpose forobtaining the data, special purpose studies, or any consider-ations for the users objectives; and it is common practice toincrease or
9、 reduce significant digits of reported data to becommensurate with these considerations. It is beyond the scopeof these test methods to consider significant digits used inanalysis methods for engineering data.1.5 The values stated in SI units are to be regarded asstandard. No other units of measurem
10、ent are included in thisstandard.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 establish appro-priate safety and health practices and determine the applica-bility of regulatory limitat
11、ions prior to use.2. Referenced Documents2.1 ASTM Standards:3D653 Terminology Relating to Soil, Rock, and ContainedFluidsD3740 Practice for Minimum Requirements for AgenciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD4050 Test Method for (Field
12、 Procedure) for Withdrawaland Injection Well Testing for Determining HydraulicProperties of Aquifer SystemsD4106 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and Storage Coefficient of Non-leaky Confined Aquifers by the Theis NonequilibriumMethodD6026 Practice for Using Sig
13、nificant Digits in GeotechnicalDataD6029 Test Method (Analytical Procedure) for DeterminingHydraulic Properties of a Confined Aquifer and a LeakyConfining Bed with Negligible Storage by the Hantush-Jacob Method1This test method is under the jurisdiction of Committee D18 on Soil and Rockand is the di
14、rect responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Jan. 1, 2017. Published January 2017. Originallyapproved in 1996. Last previous edition approved in 2010 as D602896(2010)1.DOI: 10.1520/D6028-17.2The boldface numbers in parentheses refer
15、 to a list of references at the end ofthis test method.3For referenced ASTM 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.*A Sum
16、mary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization establishe
17、d in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13. Terminology3.1 DefinitionsFor definitions of other terms used in thistest method, see Terminology D653.3.2
18、Symbols and Dimensions:3.2.1 H (u,)well function for leaky systems where waterstorage in confining beds is important nd.3.2.2 Khydraulic conductivity of the aquifer LT1.3.2.2.1 DiscussionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in groundwa-ter literature by
19、 hydrogeologists, whereas the symbol k iscommonly used for this term in soil and rock mechanics andsoil science.3.2.3 K, K“vertical hydraulic conductivities of the con-fining beds through which leakage can occur LT1.FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Wa
20、ter in the Confining Beds, Illustrating ThreeDifferent Cases of Boundary Conditions (from Reed (2)D6028 1723.2.4 Qdischarge L3T1.3.2.5 S=bSsstorage coefficient of the aquifer nd.3.2.6 S5bSsstorage coefficients of the confiningbeds nd.S“5b“S“s3.2.7 Ssspecific storage of the aquifer L1.3.2.8 SsS“sspec
21、ific storages of the confining beds.L21#3.2.9 Ttransmissivity L2T1.3.2.10 u=r2s4Ttnd#.3.2.11 W(u,r/B)well function for leaky aquifer systemswith negligible storage changes in confining beds nd.3.2.12 W(u)well function for nonleaky aquifer systemsnd.3.2.13 bthickness of aquifer L.3.2.14 b, b“thicknes
22、ses of the confining beds throughwhich leakage can occur L.3.2.15 rradial distance from control well L.3.2.16 sdrawdown L.3.2.17 B5TbKL# .3.2.18 ttime since pumping or injection began T.3.2.19 5r4bSKSbKSs1DK“S“b“KSsnd#.4. Summary of Test Method4.1 This test method involves pumping a control well tha
23、t isfully screened through the confined aquifer and measuring thewater-level response in one or more observation wells orpiezometers. The well is pumped at a constant rate. Thewater-level response in the aquifer is a function of thetransmissivity and storage coefficient of the aquifer and theleakanc
24、e coefficients and storage coefficients of the confiningbeds. Alternatively, the test method can be performed byinjecting water at a constant rate into the control well.Analysisof buildup of water level in response to injection is similar toanalysis of drawdown of water level in response to withdraw
25、alin a confined aquifer. The water-level response data areanalyzed using a set of type curves.4.2 SolutionHantush (1) gave solutions applicable to eachof Cases 1, 2, and 3 shown in Fig. 1 for “relatively small”values of time and for “relatively large” values of time. Thesolution applicable for each
26、case for relatively small values oftime can be written as followss 5Q4TH u,! (1)where:u 5r2S4Tt(2)and 5r4bSKSbKSs1K“ S“b“KSsD(3)H u,! 5 *u e2yyerfc=u=y y 2 u!dy (4)erfc x! 52= *ue2y2dy (5)where y is the variable of integration.4.2.1 The “relatively small” times when Eq 1 is applicableare when:t,bS10
27、Kand t,b“S“10K“(6)Equation 1 is applicable at early times for each of the casesshown in Fig. 1 even though the conditions on the distal sidesof the confining beds are quite different because for early timesthe solution in the aquifer is essentially independent ofconditions on the distal side of the
28、confining beds. The effectsof those distant boundary conditions are not felt in the aquiferfor a while. Eq 1-5 are the basis for the type curve solution thatis described by this test method.4.2.2 For relatively large values of time the solutions givenby Hantush (1) can be written as:4.2.2.1 Case 1He
29、ads in zones on the distal side of theconfining beds remain constant and are unaffected by dischargeof the pumped well. For times whent.5bSKand t.5b“S“K“(7)are both satisfied, thens 5Q4TW u1, ! (8)where:15 11S1S“!3Sand 5 r KTb1K“Tb“(9)Hantush (1) notes that if K“, S, and S“ are taken as zero inthe f
30、low systems shown in Fig. 1 as Case 1 or Case 3, theresulting flow system is that of a confined aquifer overlying animpermeable bed and the aquifer being overlain by a confiningbed in which the storage is negligible. Hantush gives thesolution for that special case as follows:s 5Q4TW u,r/B! (10)where
31、:rB5 r KTbNote that W(u,r/B) is the well function for leaky systemswith negligible storage in the confining beds given by Hantushand Jacob (3) and described in Test Method (D6029). Thatfunction is defined as follows:W u,r/B! 5 *uexp2y 2 r2/4B2y!dyy(11)4.2.2.2 Case 2The materials in the zones on the
32、distalsides of the confining beds are impermeable. For times whenD6028 173t.10bSKand t.10b“S“K“(12)are both satisfied, thens 5Q4TW u,2! (13)where:25 11S1S“!Sand where the function W(u) is the well function fornon-leaky aquifers that appears in the solution given by Theis(4) described in Test Method
33、D4106 for drawdowns in re-sponse to a well pumped at a constant rate from a non-leakyaquifer.4.2.2.3 Case 3The materials on the distal side of oneconfining bed are impermeable and the heads on the distal sidesof the other confining bed remain constant and are unaffectedby discharge of the pumped wel
34、l. For times whent.5bSKand t.10b“S“K“(14)are both satisfied, thens 5Q4TW S u3, r KTbD 5Q4tW u3,r/B! (15)where:35 11S “ 1 S 3!S (16)and W(u,r/B) is defined in Case 1 (see Eq 11).Hantush (1) did not develop expressions for the solutions tothese cases for intermediate times (between“ small” and“large”
35、times). Reed (2) p. 26) notes that Neuman andWitherspoon (5), p. 250) developed a complete (that is,applicable for all times) solution for Case 1 (source beds on thedistal sides of both confining beds) but did not tabulate it.5. Significance and Use5.1 Assumptions:5.1.1 The control well discharges a
36、t a constant rate, Q.5.1.2 The control well is of infinitesimal diameter and fullypenetrates the aquifer.5.1.3 The aquifer is homogeneous, isotropic, and areallyextensive.5.1.4 The aquifer remains saturated (that is, water level doesnot decline below the top of the aquifer).5.1.5 The aquifer is over
37、lain or underlain, or both, every-where by confining beds individually having uniform hydraulicconductivities, specific storages, and thicknesses. The confin-ing beds are bounded on the distal sides by one of the casesshown in Fig. 1.5.1.6 Flow in the aquifer is two-dimensional and radial inthe hori
38、zontal plane.5.2 The geometry of the well and aquifer system is shown inFig. 1.5.3 Implications of Assumptions:5.3.1 Paragraph 5.1.1 indicates that the discharge from thecontrol well is at a constant rate. Paragraph 8.1 of Test MethodD4050 discusses the variation from a strictly constant rate thatis
39、 acceptable.Acontinuous trend in the change of the dischargerate could result in misinterpretation of the water-level changedata unless taken into consideration.NOTE 1The quality of the result produced by this standard isdependent on the competence of the personnel performing it, and thesuitability
40、of the equipment and facilities used. Agencies that meet thecriteria of Practice D3740 are generally considered capable of competentand objective testing/sampling/inspection/etc. Users of this standard arecautioned that compliance with Practice D3740 does not in itself assurereliable results. Reliab
41、le results depend on many factors; Practice D3740provides a means of evaluating some of those factors.5.3.2 The leaky confining bed problem considered by themodified Hantush method requires that the control well has aninfinitesimal diameter and has no storage. Moench (6) gener-alized the field situa
42、tion addressed by the modified Hantush (1)method to include the well bore storage in the pumped well.The mathematical approach that he used to obtain a solution forthat more general problem results in a Laplace transformsolution whose analytical inversion has not been developed andprobably would be
43、very complicated, if possible, to evaluate.Moench (6) used a numerical Laplace inversion algorithm todevelop type curves for selected situations. The situationsconsidered by Moench indicate that large well bore storagemay mask effects of leakage derived from storage changes inthe confining beds. The
44、 particular combinations of aquifer andconfining bed properties and well radius that result in suchmasking is not explicitly given. However, Moench (6),p.1125) states “Thus observable effects of well bore storage aremaximized, for a given well diameter, when aquifer transmis-sivity Kb and the storag
45、e coefficient Ssb are small.” Moench (p.1129) notes that “.one way to reduce or effectively eliminatethe masking effect of well bore storage is to isolate the aquiferof interest with hydraulic packers and repeat the pump testunder pressurized conditions. Because well bore storage C willthen be due t
46、o fluid compressibility rather than changing waterlevels in the well”.“the dimensionless well bore storageparameter may be reduced by 4 to 5 orders of magnitude.”5.3.3 The modified Hantush method assumes, for Cases 1and 3 (see Fig. 1), that the heads in source layers on the distalside of confining b
47、eds remain constant. Neuman and Wither-spoon (7) developed a solution for a case that could correspondto Hantushs Case 1 with K“ = O = S“ except that they do notrequire the head in the unpumped aquifer to remain constant.For that case, they concluded that the drawdowns in thepumped aquifer would not
48、 be affected by the properties of theother, unpumped, aquifer when (Neuman and Witherspoon (7)p. 810) time satisfies:t #0.1SbK(17)5.3.4 Implicit in the assumptions are the conditions that theflow in the confining beds is essentially vertical and in theaquifer is essentially horizontal. Hantushs (8)
49、analysis of anaquifer bounded only by one leaky confining bed suggestedthat these assumptions are acceptably accurate whereverKK.100bb(18)D6028 174That form of relation between aquifer and confining bedproperties may also be a useful guide for the case of two leakyconfining beds.6. Apparatus6.1 Analysis of data from the field procedure (see TestMethod D4050) by this test method requires that the controlwell and observati
