1、Designation: D 6028 96 (Reapproved 2004)Standard 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 D 6028; the nu
2、mber immediately 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. Sco
3、pe1.1 This test method 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 data
4、collected from one or 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 procedur
5、e is used in conjunction withTest Method D 4050.1.3 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 D 60
6、29) with the exception 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
7、 that confine the aquifer of interest (seeFig. 1).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, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate s
8、afety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3D 653 Terminology Relating to Soil, Rocks, and ContainedFluidsD 4050 Test Method (Field Procedure) for Withdrawal andInjection Well Tests for Determining Hydr
9、aulic Propertiesof Aquifer SystemsD 4106 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers by the Theis Nonequilibrium MethodD 6029 Test Method (Analytical Procedure) for Determin-ing Hydraulic Properties of a Confined Aquifer and
10、 aLeaky Confining Bed with Negligible Storage by theHantush Jacob 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, unconfined, nan aquifer is unconfinedwhere it
11、 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.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
12、 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 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.1This test method
13、 is under the jurisdiction of Committee D18 on Soil and Rockand 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 previou edition approved in 1996 as D 602
14、896.2The boldface numbers in parentheses refer 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 D
15、ocument Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.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
16、 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 open to all or part of anaquifer.3.1.12 piezometer, na device used to
17、 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 water an aqui-fer releases from or takes into storage per unit surfa
18、ce area ofthe aquifer per unit change in head.FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water in the Confining Beds, Illustrating ThreeDifferent Cases of Boundary Conditions (from Reed (2) )D 6028 96 (2004)23.1.14.1 DiscussionFor a confined aquifer, the storag
19、ecoefficient is equal to the product of the specific storage andaquifer thickness. For an unconfined aquifer, the storagecoefficient is approximately equal to the specific yield.3.1.15 transmissivity, nthe volume of water at the prevail-ing kinematic viscosity that will move in a unit time under aun
20、it hydraulic gradient through a unit width of the aquifer.3.1.16 For definitions of other terms used in this testmethod, see Terminology D 653.3.2 Symbols:Symbols and Dimensions:3.2.1 H (u,b)well function for leaky systems where waterstorage in confining beds is important nd.3.2.2 Khydraulic conduct
21、ivity of the aquifer LT1.3.2.2.1 DiscussionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in ground-water literature by hydrogeologists, whereas the symbol k iscommonly used for this term in soil and rock mechanics andsoil science.3.2.3 K8,K9vertical hydraulic co
22、nductivities of the con-fining beds through which leakage can occur LT1.3.2.4 Qdischarge L3T1.3.2.5 S=bSsstorage coefficient of the aquifer nd.3.2.6 S8 =b8S8sstorage coefficients of the confiningbeds nd.S9 =b9S9s3.2.7 Ssspecific storage of the aquifer L1.3.2.8 S8sS9sspecific storages of the confinin
23、g beds.L13.2.9 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 b8,b9thicknesses of the confining beds throug
24、hwhich leakage can occur L.3.2.15 rradial distance from control well L.3.2.16 sdrawdown L.3.2.17 B 5Tb8K8L.3.2.18 ttime since pumping or injection began T.3.2.19 b5r4bSK8S8b8KSs1 DK9S9b9KSsnd.4. Summary of Test Method4.1 This test method involves pumping a control well that isfully screened through
25、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 coefficients and storage
26、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 withdrawalin a confined aquifer. Th
27、e 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 case for relatively small v
28、alues oftime can be written as followss 5Q4pTH u,b! (1)where:u 5r2S4Tt(2)andb5r4bSK8S8b8KSs1K9 S9b9KSsD(3)H u,b! 5*u e2yyerfcb=u=y y 2 u!dy (4)erfc x! 52= p*xe2y2dy (5)where y is the variable of integration.4.2.1 The “relatively small” times when Eq 1 is applicableare when:t ,b8S810K8and t ,b9S910K9
29、(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 confining beds.
30、 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 1Heads in zones on
31、 the distal side of theconfining beds remain constant and are unaffected by dischargeof the pumped well. For times whent . 5b8S8K8and t . 5b9S9K9(7)are both satisfied, thens 5Q4pTW ud1, a! (8)where:d15 1 1S8 1 S9!3Sand a5rK8Tb81K9Tb9(9)Hantush (1) notes that if K9, S8, and S9 are taken as zero inthe
32、 flow 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 5Q4pTW u,r/B! (10)D
33、6028 96 (2004)3where:rB5 rK8Tb8Note 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 (D 6029). Thatfunction is defined as follows:W u,r/B! 5*uexp 2y 2 r2/ 4B2y!dyy(11)4.2.2.2 Case 2The materi
34、als in the zones on the distalsides of the confining beds are impermeable. For times whent . 10b8S8K8and t . 10b9S9K9(12)are both satisfied, thens 5Q4pTW u,d2! (13)where:d25 1 1S8 1 S9!Sand where the function W ( u) is the well function fornon-leaky aquifers that appears in the solution given by The
35、is(4) described in Test Method D 4106 for drawdowns inresponse 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 unaffected
36、by discharge of the pumped well. For times whent .5b8S8K8and t .10b9S9K9(14)are both satisfied, thens 5Q4pTW S ud3, rK8Tb8D 5Q4ptW ud3,r/B! (15)where:d35 1 1 S9 1S8/3!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 inte
37、rmediate times (between“ small” and“large” 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 As
38、sumptions:5.1.1 The control well discharges 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
39、top of the aquifer).5.1.5 The aquifer is overlain 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 aqu
40、ifer 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. Paragraph 8.1 of Test MethodD 4050 discusses the
41、variation 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 themodified Hantush method requires that
42、the control well has aninfinitesimal diameter and has no storage. Moench (6) gener-alized the field situation 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 resul
43、ts in a Laplace transformsolution whose analytical inversion has not been developed andprobably would be 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
44、large well bore storagemay mask effects of leakage derived from storage changes inthe confining beds. The 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
45、well bore storage aremaximized, for a given well diameter, when aquifer transmis-sivity Kb and the storage 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 pa
46、ckers and repeat the pump testunder pressurized conditions. Because well bore storage C willthen be due to 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 metho
47、d assumes, for Cases 1and 3 (see Fig. 1), that the heads in source layers on the distalside of confining beds remain constant. Neuman and Wither-spoon (7) developed a solution for a case that could correspondto Hantushs Case 1 with K9 = O = S9 except that they do notrequire the head in the unpumped
48、aquifer to remain constant.For that case, they concluded that the drawdowns in thepumped aquifer would not be affected by the properties of theother, unpumped, aquifer when (Neuman and Witherspoon (7)p. 810) time satisfies:t#0.1S8b8K8(17)5.3.4 Implicit in the assumptions are the conditions that thef
49、low in the confining beds is essentially vertical and in theaquifer is essentially horizontal. Hantushs (8) analysis of anaquifer bounded only by one leaky confining bed suggestedthat these assumptions are acceptably accurate whereverD 6028 96 (2004)4KK8. 100bb8(18)That 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
