1、Designation: D6029 17Standard Test Method (Analytical Procedure) forDetermining Hydraulic Properties of a Confined Aquifer anda Leaky Confining Bed with Negligible Storage by theHantush-Jacob Method1This standard is issued under the fixed designation D6029; the number immediately following the desig
2、nation 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 method covers an ana
3、lytical procedure fordetermining the transmissivity and storage coefficient of aconfined aquifer and the leakance value of an overlying orunderlying confining bed for the case where there is negligiblechange of water in storage in a confining bed. This test methodis used to analyze water-level or he
4、ad data collected from oneor more observation wells or piezometers during the pumpingof water from a control well at a constant rate. With appropriatechanges in sign, this test method also can be used to analyzethe effects of injecting water into a control well at a constantrate.1.2 This analytical
5、procedure is used in conjunction withTest Method D4050.1.3 LimitationsThe valid use of the Hantush-Jacobmethod is limited to the determination of hydraulic propertiesfor aquifers in hydrogeologic settings with reasonable corre-spondence to the assumptions of the Theis nonequilibriummethod (Test Meth
6、od D4106) with the exception that in thiscase the aquifer is overlain, or underlain, everywhere by aconfining bed having a uniform hydraulic conductivity andthickness, and in which the gain or loss of water in storage isassumed to be negligible, and that bed, in turn, is bounded onthe distal side by
7、 a zone in which the head remains constant.The hydraulic conductivity of the other bed confining theaquifer is so small that it is assumed to be impermeable (seeFig. 1).1.4 The values stated in SI units are to be regarded asstandard. The values given in parentheses are mathematicalconversions to inc
8、h-pound units, which are provided forinformation only and are not considered standard.1.4.1 The converted inch-pound units use the gravitationalsystem of units. In this system, the pound (lbf) represents a unitof force (weight), while the unit for mass is slugs. Theconverted slug unit is not given,
9、unless dynamic (F = ma)calculations are involved.1.5 All observed and calculated values shall conform to theguidelines for significant digits and round established inPractice D6026, unless superseded by this standard.1.5.1 The procedures used to specify how data are collected/recorded or calculated,
10、 in this standard are regarded as theindustry standard. 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 use
11、rs objectives; and it is common practice toincrease or reduce significant digits of reported date to becommensurate with these considerations. It is beyond the scopeof this standard to consider significant digits used in analysismethod for engineering design.1.6 This standard does not purport to add
12、ress 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 limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminol
13、ogy 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 Procedure) for Withdrawaland Injection Well Testing for Determining Hydra
14、ulicProperties of Aquifer Systems1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Jan. 1, 2017. Published January 2017. Originallyapproved in
15、1996. Last previous edition approved in 2010 as D602996(2010)1.DOI: 10.1520/D6029-17.2For 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
16、page onthe ASTM website.*A Summary 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
17、 on standardization established 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.1D4106 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and
18、 Storage Coefficient of Non-leaky Confined Aquifers by the Theis NonequilibriumMethodD6026 Practice for Using Significant Digits in GeotechnicalDataD6028 Test Method (Analytical Procedure) for DeterminingHydraulic Properties of a Confined Aquifer Taking intoConsideration Storage of Water in Leaky Co
19、nfining Bedsby Modified Hantush Method3. Terminology3.1 Definitions:3.1.1 For definitions of common terms used in this testmethod, see Terminology D653.3.2 Symbols and Dimensions:3.2.1 Khydraulic conductivity of the aquifer LT1.3.2.1.1 DiscussionThe use of the symbol K for the termhydraulic conducti
20、vity is the predominant usage in groundwa-ter literature by hydrogeologists, whereas the symbol k iscommonly used for this term in soil and rock mechanics andsoil science.3.2.2 Kvertical hydraulic conductivity of the confiningbed through which leakage can occur LT1.3.2.3 L(u,v)leakance function of u
21、,v nd; equal to W(u,r/B).3.2.4 Qdischarge L3T1.3.2.5 S=bSSstorage coefficient nd.3.2.6 Ssspecific storage of the aquifer L1.3.2.7 Ssspecific storage of the confining bed L1.3.2.8 Ttransmissivity L2T1.3.2.9 u5r2S4Ttnd#.3.2.10 W(u,r/B)well function for leaky aquifer systemswith negligible storage chan
22、ges in confining beds nd.3.2.11 bthickness of aquifer L. bthickness of theconfining bed through which leakage can occur L.3.2.12 rradial distance from control well L.3.2.13 rcradius of the control well casing, or hole ifuncased L.3.2.14 sdrawdown L.3.2.15 v5r2B5r2KTb,vdefined by Eq 7 nd.3.2.16 TbK L
23、#.3.2.17 ttime since pumping or injection began T.3.2.18 K0(x)zero-order modified Bessel function of thesecond kind nd.3.2.19 5r4bKSSKSS4. Summary of Test Method4.1 This test method involves pumping a control well that isfully screened through the confined aquifer and measuring thewater-level respon
24、se 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 theleakance coefficient of a confining bed.The other confining bedis assumed to be impermeabl
25、e. Alternatively, the test methodcan be performed by injecting water at a constant rate into thecontrol well. Analysis of buildup of water level in response toinjection is similar to analysis of drawdown of the water levelin response to withdrawal in a confined aquifer. The water-level response data
26、 may be analyzed in two ways. The timeFIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1)3). The Confining and Impermeable Bed LocationsCan Be InterchangedD6029 172variation of the water-level response in any one well can beanalyzed using one set of type curves, or the
27、water-levelresponses measured at the same time but in observation wellsat different distances from the control well can be analyzedusing another set of type curves.NOTE 1The quality of the result produced by this standard isdependent on the competence of the personnel performing it, and thesuitabili
28、ty 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. Rel
29、iable results depend on many factors; Practice D3740provides a means of evaluating some of those factors.4.2 SolutionHantush and Jacob (2)3give two mathemati-cally equivalent expressions for the solution which can bewritten as follows:s 5Q4T*u1zexpS2z 2r24B2zDdz (1)where z is the variable of integra
30、tion ands 5Q4TF2K0SrBD2 *r24B2u1zexpS2z 2r24B2zDdzG(2)where:u 5r2S4Tt(3)B25TbK(4)4.2.1 Because a closed-form expression of the integrals thatappear in Eq 1 or Eq 2 are not known, Hantush and Jacobdeveloped equivalent expressions that involve infinite seriesthat can be numerically evaluated. The infi
31、nite series for Eq 1converges more rapidly for early times and the infinite seriesfor Eq 2 converges more rapidly for late times.4.2.2 Hantush (3) expressed Eq 1 and Eq 2 as follows:s 5Q4TWSu,rBD(5)where WSu,rBDwas called the well function for leakysystems. Hantush tabulated values of this function
32、for apractical range of the parameters u andrB.4.2.3 Cooper (4) opted to express the Hantush-Jacob solu-tion in the following form:s 5Q4TLu, v! (6)where Coopers v = Hantushsr2Borv 5r2B5r2TbK(7)4.2.4 Cooper prepared two families of type curves. One setof Coopers curves allow the head changes as a fun
33、ction oftime at a fixed distance to be analyzed for the aquiferparameters, and the other set of curves allow the head changesat different distances at some fixed time to be analyzed.5. Significance and Use5.1 Assumptions:5.1.1 The control well discharges at a constant rate, Q.5.1.2 The control well
34、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 overlain, or underlain, everywhere by aconfining
35、 bed having a uniform hydraulic conductivity andthickness. It is assumed that there is no change of water storagein this confining bed and that the hydraulic gradient across thisbed changes instantaneously with a change in head in theaquifer. This confining bed is bounded on the distal side by aunif
36、orm head source where the head does not change withtime.5.1.6 The other confining bed is impermeable.5.1.7 Leakage into the aquifer is vertical and proportional tothe drawdown, and flow in the aquifer is strictly horizontal.5.1.8 Flow in the aquifer is two-dimensional and radial inthe horizontal pla
37、ne.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. Section 8.1 of Test MethodD4050 discusses the variation from a strictly constant rate thatis acceptable.
38、Acontinuous trend in the change of the dischargerate could result in misinterpretation of the water-level changedata unless taken into consideration.5.3.2 The leaky confining bed problem considered by theHantush-Jacob solution requires that the control well has aninfinitesimal diameter and has no st
39、orage. Abdul Khader andRamadurgaiah (5) developed graphs of a solution for thedrawdowns in a large-diameter control well discharging at aconstant rate from an aquifer confined by a leaky confiningbed. Fig. 2 (Fig. 3 of Abdul Khader and Ramadurgaiah (5)gives a graph showing variation of dimensionless
40、 drawdownwith dimensionless time in the control well assuming theaquifer storage coefficient, S =103, and the leakage parameter,rwBNote that at early dimensionless times the curve for alarge-diameter well in a non-leaky aquifer (BCE) and in aleaky aquifer (BCD) are coincident. At later dimensionless
41、times, the curve for a large diameter well in a leaky aquifercoalesces with the curve for an infinitesimal diameter well(ACD) in a leaky aquifer. They coalesce about one logarithmiccycle of dimensionless time before the drawdown becomessensibly constant. For a value of rw/B smaller than 103, thecons
42、tant drawdown (D) would occur at a greater value ofdimensionless drawdown and there would be a longer period3The boldface numbers in parentheses refer to a list of references at the end ofthis test method.D6029 173during which well-bore storage effects are negligible (theperiod where ACD and BCD are
43、 coincident) before a steadydrawdown is reached.For values ofrwBgreater than 103, the constant drawdown (D)would occur at a smaller value of drawdown and there wouldbe a shorter period of dimensionless time during whichwell-storage effects are negligible (the period where ACD andBCD are coincident)
44、before a steady drawdown is reached.Abdul Khader and Ramadurgaiah (5)present graphs of dimen-sionless time versus dimensionless drawdown in a dischargingcontrol well for values of S =101,102,103,104, and 105andrwB =102,103,104,105,106, and 0. These graphs canbe used in an analysis prior to the aquif
45、er test making use ofestimates of the hydraulic properties to estimate the time periodduring which well-bore storage effects in the control wellprobably will mask other effects and the drawdowns would notfit the Hantush-Jacob solution.5.3.2.1 The time needed for the effects of control-well borestora
46、ge to diminish enough that drawdowns in observationwells should fit the Hantush-Jacob solution is less clear. But thetime adopted for when drawdowns in the discharging controlwell are no longer dominated by well-bore storage affectsprobably should be the minimum estimate of the time to adoptfor obse
47、rvation well data.5.3.3 The assumption that the aquifer is bounded, above orbelow, by a leaky layer on one side and a nonleaky layer on theother side is not likely to be entirely satisfied in the field.Neuman and Witherspoon (6, p. 1285) have pointed out thatbecause the Hantush-Jacob formulation use
48、s water-levelchange data only from the aquifer being pumped (or recharged)it can not be used to distinguish whether the leaking beds areabove or below (or from both sides) of the aquifer. Hantush (7)presents a refinement that allows the parameters determined bythe aquifer test analysis to be interpr
49、eted as composite param-eters that reflect the combined effects of overlying and under-lying confined beds. Neuman and Witherspoon (6) describe amethod to estimate the hydraulic properties of a confining layerby using the head changes in that layer.5.3.4 The Hantush-Jacob theoretical development requiresthat the leakage into the aquifer is proportional to thedrawdown, and that the drawdown does not vary in the verticalin the aquifer. These requirements are sometimes described
