1、Designation: D6029 96 (Reapproved 2010)1Standard 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
2、following 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.1NOTEThe units statement
3、 in 1.4 was revised editorially in August 2010.1. Scope1.1 This test method covers an analytical 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
4、water in storage in a confining bed. This test methodis used to analyze water-level or head 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 analyzet
5、he effects of injecting water into a control well at a constantrate.1.2 This analytical 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 re
6、asonable corre-spondence to the assumptions of the Theis nonequilibriummethod (Test Method 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 st
7、orage isassumed to be negligible, and that bed, in turn, is bounded onthe distal side by 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
8、 regarded asstandard. The values given in parentheses are mathematicalconversions to inch-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
9、 force (weight), while the unit for mass is slugs. Theconverted slug unit is not given, unless dynamic (F = ma)calculations are involved.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 e
10、stablish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD4050 Test Method for (Field Procedure) for Withdrawaland Injection Well Te
11、sts for Determining Hydraulic Prop-erties of Aquifer SystemsD4106 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and Storage Coefficient of Non-leaky Confined Aquifers by the Theis NonequilibriumMethodD6028 Test Method (Analytical Procedure) for DeterminingHydraulic Propertie
12、s of a Confined Aquifer Taking intoConsideration Storage of Water in Leaky Confining Bedsby Modified Hantush Method3. Terminology3.1 Definitions:3.1.1 aquifer, confined, nan aquifer bounded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.1.2 aquifer, un
13、confined, nan aquifer is unconfinedwhere it has a water table.3.1.3 coeffcient of leakage, nsee leakance.3.1.4 confining bed, na hydrogeologic unit of less perme-able material bounding one or more aquifers.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the di
14、rect responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Aug. 1, 2010. Published September 2010. Originallyapproved in 1996. Last previous edition approved in 2004 as D602996(2004).DOI: 10.1520/D6029-96R10E01.2For referenced ASTM standards, vi
15、sit 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 Conshohocken, PA 19428-
16、2959, United States.3.1.5 control well, nwell by which the head and flow inthe aquifer is changed, for example, by pumping, injection, orchange of head.3.1.6 drawdown, nvertical distance the static head islowered due to the removal of water.3.1.7 head, nsee head, static.3.1.8 head, static, nthe heig
17、ht above a standard datum ofthe surface of a column of water (or other liquid) that can besupported by the static pressure at a given point.3.1.9 hydraulic conductivity, n(field aquifer test) the vol-ume of water at the existing kinematic viscosity that will movein a unit time under a unit hydraulic
18、 gradient through a unitarea measured at right angles to the direction of flow.3.1.10 leakance, nthe ratio of the vertical hydraulic con-ductivity of a confining bed to its thickness.3.1.11 observation well, na well open to all or part of anaquifer.3.1.12 piezometer, na device used to measure static
19、 headat a point in the subsurface.3.1.13 specific storage, nthe volume of water releasedfrom or taken into storage per unit volume of the porousmedium per unit change in head.3.1.14 storage coeffcient, nthe volume of water an aqui-fer releases from or takes into storage per unit surface area ofthe a
20、quifer per unit change in head.3.1.14.1 DiscussionFor a confined aquifer, the storagecoefficient is equal to the product of the specific storage andaquifer thickness. For an unconfined aquifer, the storagecoefficient is approximately equal to the specific yield.33.1.15 transmissivity, nthe volume of
21、 water at the prevail-ing kinematic viscosity that will move in a unit time under aunit hydraulic gradient through a unit width of the aquifer.3.1.16 For definitions of other terms used in this testmethod, see Terminology D653.3.2 Symbols:Symbols and Dimensions:3.2.1 Khydraulic conductivity of the a
22、quifer LT1.3.2.1.1 DiscussionThe use of the symbol K for the termhydraulic conductivity 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 K8vertical hydraulic conductivity of the
23、 confiningbed through which leakage can occur LT1.3.2.3 L(u,v)leakance function of u,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 S8s specific storage of the confining bed L1.3.2.8 Ttransmissivity L2T1.3.2.9 u 5r2S4T
24、tnd.3.2.10 W(u,r/B)well function for leaky aquifer systemswith negligible storage changes in confining beds nd.3.2.11 bthickness of aquifer L. b8thickness 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
25、hole ifuncased L.3.2.14 sdrawdown L.3.2.15 v 5r2B5r2K8Tb8, vdefined by Eq 7 nd.3.2.16 B=Tb8K8 L#.3.2.17 ttime since pumping or injection began T.3.2.18 K0(x) zero-order modified Bessel function of thesecond kind nd.3The boldface numbers in parentheses refer to a list of references at the end ofthis
26、test method.FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1).4The Confining and Impermeable Bed LocationsCan Be InterchangedD6029 96 (2010)123.2.19 b5r4bK8S8SKSS4. Summary of Test Method4.1 This test method involves pumping a control well that isfully screened throug
27、h 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 theleakance coefficient of a confin
28、ing bed.The other confining bedis assumed to be impermeable. 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 withd
29、rawal in a confined aquifer. The water-level response data may be analyzed in two ways. The timevariation of the water-level response in any one well can beanalyzed using one set of type curves, or the water-levelresponses measured at the same time but in observation wellsat different distances from
30、 the control well can be analyzedusing another set of type curves.4.2 SolutionHantush and Jacob (2) give two mathemati-cally equivalent expressions for the solution which can bewritten as follows:s 5Q4pT*u 1zexpS2z 2r24B2zDdz (1)where z is the variable of integration ands 5Q4pTF2K0SrBD2*r24B2u 1zexp
31、S2z 2r24B2zDdzG(2)where:u 5r2S4Tt(3)B25Tb8K8(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 infinite series for Eq 1converges more
32、 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 5Q4pTWSu,rBD(5)where WSu,rBDwas called the well function for leakysystems. Hantush tabulated values of this function for apractical range of the param
33、eters u andrB.4.2.3 Cooper (4) opted to express the Hantush-Jacob solu-tion in the following form:s 5Q4pTLu, v! (6)where Coopers v = Hantushsr2Borv 5r2B5r2Tb8K8(7)4.2.4 Cooper prepared two families of type curves. One setof Coopers curves allow the head changes as a function oftime at a fixed distan
34、ce 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 is of infinitesimal diameter a
35、nd 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 bed having a uniform hydrauli
36、c 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 auniform head source where the head
37、 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 plane.5.2 The geometry of the wel
38、l 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.Acontinuous trend in the chang
39、e 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 storage. Abdul Khader andRamadur
40、gaiah (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 drawdownwith dimensionless ti
41、me in the control well assuming theaquifer storage coefficient, S =103, and the leakage param-eter,rwB=103. Note that at early dimensionless times thecurve for a large-diameter well in a non-leaky aquifer (BCE)and in a leaky aquifer (BCD) are coincident. At later dimen-sionless times, the curve for
42、a large diameter well in a leakyaquifer coalesces with the curve for an infinitesimal diameterwell (ACD) in a leaky aquifer. They coalesce about oneD6029 96 (2010)13logarithmic cycle of dimensionless time before the drawdownbecomes sensibly constant. For a value of rw/B smaller than103, the constant
43、 drawdown (D) would occur at a greatervalue of dimensionless drawdown and there would be a longerperiod during which well-bore storage effects are negligible(the period where ACD and BCD are coincident) before asteady drawdown is reached.For values ofrwBgreater than 103, the constant drawdown (D)wou
44、ld 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) before a steady drawdown is reached.Abdul Khader and Ramadurgaiah (5) present graphs of dimen-sionless time ve
45、rsus 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 aquifer test making use ofestimates of the hydraulic properties to estimate the time periodduring which well-bore s
46、torage effects in the control wellprobably will mask other effects and the drawdowns would notfit the Hantush-Jacob solution.5.3.2.1 The time required for the effects of control-well borestorage to diminish enough that drawdowns in observationwells should fit the Hantush-Jacob solution is less clear
47、. 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 observation well data.5.3.3 The assumption that the aquifer is bounded, above orbelow, by a leaky layer on one s
48、ide and a nonleaky layer on theother side is not likely to be entirely satisfied in the field.Neuman and Witherspoon (7, p. 1285) have pointed out thatbecause the Hantush-Jacob formulation uses water-levelchange data only from the aquifer being pumped (or recharged)it can not be used to distinguish
49、whether the leaking beds areabove or below (or from both sides) of the aquifer. Hantush (8)presents a refinement that allows the parameters determined bythe aquifer test analysis to be interpreted as composite param-eters that reflect the combined effects of overlying and under-lying confined beds. Neuman and Witherspoon (7) describe amethod to estimate the hydraulic properties of a confining layerby using the head changes in that layer.5.3.4 The Hantush-Jacob theore
