1、Designation: D6028 96 (Reapproved 2010)1Standard 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 num
2、ber 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 () indicates an editorial change since the last revision or reapproval.1NOTEThe
3、 units statement 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 taking into consideration the change in storageof water in overlying or underlying confining beds,
4、 or both.This test method is used to analyze water-level or head datacollected 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 wat
5、er into a controlwell at a constant rate.1.2 This analytical procedure is used in conjunction 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 correspond
6、ence to the assumptions of the Hantush-Jacobmethod (Test Method D6029) 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
7、remains uniform) are considered on the distalside of the leaky beds that confine the aquifer of interest (seeFig. 1).1.4 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.5 This standard does not purport to address all of thesaf
8、ety 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:3D653 Terminology Relating to So
9、il, Rock, and ContainedFluidsD4050 Test Method for (Field Procedure) for Withdrawaland Injection Well Tests 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 t
10、he Theis NonequilibriumMethodD6029 Test Method (Analytical Procedure) for DeterminingHydraulic Properties of a Confined Aquifer and a LeakyConfining Bed with Negligible Storage by the Hantush-Jacob Method3. Terminology3.1 Definitions:3.1.1 aquifer, confined, nan aquifer bounded above andbelow by con
11、fining 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 one or more aquifers.3.1.5
12、 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 height above a standard datum
13、 ofthe surface of a column of water (or other liquid) that can besupported by the static pressure at a given point.1This test method 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.Curren
14、t edition approved Aug. 1, 2010. Published September 2010. Originallyapproved in 1996. Last previou edition approved in 2004 as D602896(2004). DOI:10.1520/D6028-96R10E01.2The boldface numbers in parentheses refer to a list of references at the end ofthis test method.3For referenced ASTM standards, v
15、isit 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.3.1.9 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 gradient through a unitarea measured at right angles to the direction of flow.3.1.10 leakance, nthe ratio of the verti
17、cal 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 headat a point in the subsurface.3.1.13 specific storage, nthe volume of water releasedfrom or taken into storage per
18、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 aquifer per unit change in head.FIG. 1 Cross Sections Through Discharging Wells in Leaky Aquifers with Storage of Water
19、in the Confining Beds, Illustrating ThreeDifferent Cases of Boundary Conditions (from Reed (2) )D6028 96 (2010)123.1.14.1 DiscussionFor a confined aquifer, the storagecoefficient is equal to the product of the specific storage andaquifer thickness. For an unconfined aquifer, the storagecoefficient i
20、s 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 aunit hydraulic gradient through a unit width of the aquifer.3.1.16 For definitions of other terms used in this testmethod, see Terminolo
21、gy D653.3.2 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 conductivity of the aquifer LT1.3.2.2.1 DiscussionThe use of the symbol K for the termhydraulic conductivity is the predominant usage in groun
22、d-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 conductivities of the con-fining beds through which leakage can occur LT1.3.2.4 Qdischarge L3T1.3.2.5 S=bSsstorage coefficient of the aqu
23、ifer 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 confining 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 cha
24、nges 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 throughwhich 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 o
25、r 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 the confined aquifer and measuring thewater-level response in one or more observation wells orpiezometers. The well is pumped at a cons
26、tant rate. Thewater-level response in the aquifer is a function of thetransmissivity and storage coefficient of the aquifer and theleakance coefficients and storage coefficients of the confiningbeds. Alternatively, the test method can be performed byinjecting water at a constant rate into the contro
27、l 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. The water-level response data areanalyzed using a set of type curves.4.2 SolutionHantush (1) gave solutions applicable to eachof Cases 1,
28、 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 values 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
29、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(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 co
30、nfining beds are quite different because for early timesthe solution in the aquifer is essentially independent ofconditions on the distal side of the 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 soluti
31、on 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 the distal side of theconfining beds remain constant and are unaffected by dischargeof the pumped well. For times whent . 5b8S8K8and t
32、 . 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 flow systems shown in Fig. 1 as Case 1 or Case 3, theresulting flow system is that of a confined aquifer overlying animpermeable bed a
33、nd 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)D6028 96 (2010)13where:rB5 rK8Tb8Note that W (u,r/B) is the well function for leaky systemswith negligible storage in the confining beds
34、given by Hantushand Jacob (3) and described in Test Method (D6029). Thatfunction is defined as follows:W u,r/B! 5*uexp 2y 2 r2/ 4B2y!dyy(11)4.2.2.2 Case 2The materials in the zones on the distalsides of the confining beds are impermeable. For times whent . 10b8S8K8and t . 10b9S9K9(12)are both satisf
35、ied, 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 Theis(4) described in Test Method D4106 for drawdowns in re-sponse to a well pumped at a constant rate from a non-leakyaquifer.4.2.2.3 Case
36、 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 well. For times whent .5b8S8K8and t .10b9S9K9(14)are both satisfied, thens 5Q4pTW S ud3, rK8Tb8D 5Q4ptW ud3,
37、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 intermediate times (between“ small” and“large” times). Reed (2) p. 26) notes that Neuman andWitherspoon ( (5), p. 250) developed a complete
38、 (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 at a constant rate, Q.5.1.2 The control well is of infinitesimal diameter and fullypenetrat
39、es 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, or both, every-where by confining beds individually having uniform hydr
40、aulicconductivities, 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 horizontal plane.5.2 The geometry of the well and aquifer system is shown inFig. 1.5.3 Implica
41、tions 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 acceptable.Acontinuous trend in the change of the dischargerate could result in misinterp
42、retation of the water-level changedata unless taken into consideration.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 situation addressed by the modified
43、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 very complicated, if possible,
44、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 particular combinations of aqu
45、ifer 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 storage coefficient Ssb are small.” M
46、oench (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 to fluid compressibility rather
47、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 beds remain constant. Neuman an
48、d 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 aquifer to remain constant.For that case, they concluded that the drawdowns in thepumped aquifer would not be affected by the properties
49、 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 theflow 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 whereverD6028 96 (2010)14KK8. 100bb8(18)That form of relation between aquif
