1、Designation: D 6029 96 (Reapproved 2004)Standard 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 D 6029; 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test
3、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 water in storage in a confining bed. This test methodis used to analy
4、ze 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 analyzethe effects of injecting water into a control well at a constantrate.1
5、.2 This analytical procedure is used in conjunction withTest Method D 4050.1.3 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 nonequilibr
6、iummethod (Test Method D 4106) 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
7、 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 regarded asstandard.1.5 This standard does not purport to address
8、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:2D 653 Terminology
9、Relating to Soil, Rocks, and ContainedFluidsD 4050 Test Method (Field Procedure) for Withdrawal andInjection Well Tests for Determining Hydraulic Propertiesof Aquifer SystemsD 4106 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers
10、 by the Theis Nonequilibrium MethodD 6028 Test Method (Analytical Procedure) for Determin-ing Hydraulic Properties of a ConfinedAquiferTaking IntoConsideration Storage of Water in Leaky Confining Bedsby the Modified Hantush Method3. Terminology3.1 Definitions:3.1.1 aquifer, confined, nan aquifer bou
11、nded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.1.2 aquifer, unconfined, 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
12、one or more aquifers.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.1This test method is under t
13、he jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Nov. 1, 2004. Published December 2004. Originallyapproved in 1996. Last previous edition approved in 1996 as D 602996.2F
14、or 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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C7
15、00, West Conshohocken, PA 19428-2959, United States.3.1.8 head, static, nthe height 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
16、 existing kinematic viscosity that will movein a unit time under a unit hydraulic 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 ope
17、n to all or part of anaquifer.3.1.12 piezometer, na device used to measure static 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 wa
18、ter an aqui-fer releases from or takes into storage per unit surface area ofthe aquifer 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
19、 approximately equal to the specific yield.33.1.15 transmissivity, nthe volume of 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 Terminolo
20、gy D 653.3.2 Symbols: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 conductivity is the predominant usage in groundwa-ter literature by hydrogeologists, whereas the symbol k iscommonly used for this term in soil
21、 and rock mechanics andsoil science.3.2.2 K8vertical hydraulic conductivity of the 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
22、specific storage of the confining bed L1.3.2.8 Ttransmissivity L2T1.3.2.9 u 5r2S4Ttnd.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 rr
23、adial 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 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.3.2
24、.19 b5r4bK8S8SKSS4. Summary of Test Method4.1 This test method involves pumping a control well that isfully screened through the confined aquifer and measuring thewater-level response in one or more observation wells or3The boldface numbers in parentheses refer to a list of references at the end oft
25、his test method.FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed (1).4The Confining and Impermeable Bed LocationsCan Be InterchangedD 6029 96 (2004)2piezometers. The well is pumped at a constant rate. Thewater-level response in the aquifer is a function of thetransmissiv
26、ity and storage coefficient of the aquifer and theleakance coefficient of a confining 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 toi
27、njection is similar to analysis of drawdown of the water levelin response to withdrawal 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-levelrespo
28、nses measured at the same time but in observation wellsat different distances from 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 2r2
29、4B2zDdz (1)where z is the variable of integration ands 5Q4pTF2K0SrBD2*r24B2u 1zexpS2z 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 s
30、eriesthat can be numerically evaluated. The infinite 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 5Q4pTWSu,rBD(5)where WSu,rBDwas called the well function for leakysy
31、stems. Hantush tabulated values of this function 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 5Q4pTLu, v! (6)where Coopers v = Hantushsr2Borv 5r2B5r2Tb8K8(7)4.2.4 Cooper prepared two families of type curves. One
32、setof Coopers curves allow the head changes as a function 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 disc
33、harges at 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
34、 is overlain, or underlain, everywhere by aconfining 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
35、confining bed is bounded on the distal side by auniform 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 aquife
36、r is two-dimensional and radial inthe horizontal 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. Section 8.1 of Test MethodD 4050 discusses the varia
37、tion from a strictly constant rate thatis acceptable.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 co
38、ntrol well has aninfinitesimal diameter and has no storage. 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 Ramadurgaia
39、h (5)gives a graph showing variation of dimensionless drawdownwith dimensionless time 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
40、a leaky aquifer (BCD) are coincident. At later dimen-sionless times, the curve for a large diameter well in a leakyaquifer coalesces with the curve for an infinitesimal diameterwell (ACD) in a leaky aquifer. They coalesce about onelogarithmic cycle of dimensionless time before the drawdownbecomes se
41、nsibly constant. For a value of rw/B smaller than103, the constant 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 reac
42、hed.D 6029 96 (2004)3For 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) before a steady drawdown is
43、 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 aquifer test making use ofestima
44、tes 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 required for the effects of control-well borestorage to diminish enough tha
45、t 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 observation well data.5.3.3 T
46、he 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 (7, p. 1285) have pointed out thatbecause the Hantush-Jacob formulation uses water-levelchange data
47、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 (8)presents a refinement that allows the parameters determined bythe aquifer test analysis to be interpreted as composite param-e
48、ters 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 theoretical development requiresthat the leakage int
49、o the aquifer is proportional to the draw-down, and that the drawdown does not vary in the vertical inthe aquifer. These requirements are sometimes described bystating that the flow in the confining beds is essentially verticaland in the aquifer is essentially horizontal. Hantushs (9)analysis of an aquifer bounded only by one leaky confining bedsuggested that this approximation is acceptably accurate wher-everKK8. 100bb8(8)5.3.5 The Hantush-Jacob method requires that ther
