1、Designation: D 5473 93 (Reapproved 2006)Standard Test Method for(Analytical Procedure for) Analyzing the Effects of PartialPenetration of Control Well and Determining the Horizontaland Vertical Hydraulic Conductivity in a Nonleaky ConfinedAquifer1This standard is issued under the fixed designation D
2、 5473; the number 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 reap
3、proval.1. Scope1.1 This test method covers an analytical solution fordetermining the horizontal and vertical hydraulic conductivityof an aquifer by analysis of the response of water levels in theaquifer to the discharge from a well that partially penetrates theaquifer.1.2 LimitationsThe limitations
4、of the technique for deter-mination of the horizontal and vertical hydraulic conductivityof aquifers are primarily related to the correspondence betweenthe field situation and the simplifying assumption of this testmethod.1.3 The values stated in either inch-pound or SI units are tobe regarded separ
5、ately as the standard. The values given inparentheses are for information only.1.4 This standard does not purport to address all of thesafety problems, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and dete
6、rmine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 4050 Test Method (Field Procedure) for Withdrawal andInjection Well Tests for Determining Hydraulic Propertiesof Aquifer SystemsD
7、4105 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of NonleakyConfined Aquifers by the Modified Theis NonequilibriumMethod3. Terminology3.1 Definitions:3.1.1 aquifer, confinedan aquifer bounded above andbelow by confining beds and in which the static head
8、 is abovethe top of the aquifer.3.1.2 confining beda hydrogeologic unit of less perme-able material bounding one or more aquifers.3.1.3 control wellwell by which the head and flow in theaquifer is changed, for example, by pumping, injection, orimposing a constant change of head.3.1.4 drawdownvertica
9、l distance the static head is low-ered due to the removal of water.3.1.5 hydraulic conductivity(field aquifer tests), 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
10、flow.3.1.6 observation wella well open to all or part of anaquifer.3.1.7 piezometera device so constructed and sealed as tomeasure hydraulic head at a point in the subsurface.3.1.8 specific storagethe volume of water released fromor taken into storage per unit volume of the porous medium perunit cha
11、nge in head.3.1.9 storage coeffcientthe volume of water an aquiferreleases from or takes into storage per unit surface area of theaquifer per unit change in head.3.1.10 transmissivitythe volume of water at the existingkinematic viscosity that will move in a unit time under a unithydraulic gradient t
12、hrough a unit width of the aquifer.3.1.11 unconfined aquiferan aquifer that has a water table.3.1.12 For definitions of other terms used in this testmethod, see Terminology D 653.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subc
13、ommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Oct. 1, 2006. Published October 2006. Originallyapproved in 1993. Last previous edition approved in 2000 as D 547393(2000).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Custo
14、mer 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 19428-2959, United States.3.2 Symbols:Symbols and Dimensions:3
15、.2.1 a nd( Kz/Kr)1/2.3.2.2 b Lthickness of aquifer.3.2.3 d Ldistance from top of aquifer to top of screenedinterval of control well.3.2.4 d8 Ldistance from top of aquifer to top of screenedinterval of observation well.3.2.5 fsnddimensionless drawdown factor.3.2.6 K LT1hydraulic conductivity.3.2.7 Kr
16、LT1hydraulic conductivity in the plane of theaquifer, radially from the control well.3.2.8 KzLT1hydraulic conductivity normal to theplane of the aquifer.3.2.9 K0 modified Bessel function of the second kind andzero order.3.2.10 l Ldistance from top of aquifer to bottom ofscreened interval of control
17、well.3.2.11 l8 Ldistance from top of aquifer to bottom ofscreened interval of observation well.3.2.12 Q L3T1discharge.3.2.13 r Lradial distance from control well.3.2.14 rc distance from pumped well at which an ob-served drawdown deviation, ds, would occur in the equivalentisotropic aquifer.3.2.15 S
18、ndstorage coefficient.3.2.16 s Ldrawdown.3.2.17 SsL1specific storage.3.2.18 T L2T1transmissivity.3.2.19 u nd(r2S)/(4 Tt).3.2.20 W(u) ndan exponential integral known in hydrol-ogy as the well function of u.3.2.21 W(u, fs)partial-penetration control well function.3.2.22 ds Ldrawdown deviation due to p
19、artial penetra-tion from that given by equations for purely radial flow.3.2.23 z Ldistance from top of aquifer to bottom ofpiezometer.4. Summary of Test Method4.1 This test method uses the deviations in drawdown neara partially penetrating control well from those that would occurnear a control well
20、fully penetrating the aquifer. These devia-tions occur when a well partially penetrating the aquifer ispumped because water levels are drawn down more near thelevel of the screen, and less at levels somewhat above or belowthe screened interval, than they would be if the pumped wellfully penetrated t
21、he aquifer. These effects are shown in Fig. 1by comparing drawdown and flow lines for fully penetratingand partially penetrating control wells in an isotropic aquifer.Drawdown deviations due to partial penetration are amplifiedwhen the vertical permeability is less than the horizontalpermeability, a
22、s often occurs in stratified sediments (1).3Hantush (2) has shown that at a distance, r, from the controlwell the drawdown deviation due to pumping a partiallypenetrating well at a constant rate is the same as that at adistance r (Kz/Kr)1/2if the aquifers were transformed into anequivalent isotropic
23、 aquifer.4.2 SolutionsSolutions are given by Hantush (2) for thedrawdown near a partially penetrating control well beingpumped at a constant rate and tapping a homogeneous,isotropic artesian aquifer:3The boldface numbers in parentheses refer to a list of references at the end ofthe text.NOTE 1Solid
24、lines are for a well screened in the bottom three tenths of the aquifer; dashed lines are for a well screened the full thickness.FIG. 1 Vertical Section Showing Drawdown Lines and Approximate Flow Paths Near a Pumped Well in an Ideal Artesian AquiferD 5473 93 (2006)2s 5Q4pTWu! 1 fs# (1)where:Wu! 5*u
25、 e2yydy (2)and fsis the dimensionless drawdown correction factor. Thefunction W (u)+fs in Eq 1 can be referred to as the partialpenetration well function.4.2.1 The dimensionless drawdown correction factor for apiezometer is given by:fs5 fSu,arb,lb,db,zbD(3)52bpl 2 d!(n 5 11nSsinnplb2 sinnpdbDcosnpzb
26、WSu,nparbDand the solution for the dimensionless drawdown correctionfactor for an observation well is given by:fs5 fSu,arb,lb,db,l8b,d8bD(4)52b2p2l 2 d!l8 2 d8!(n 5 11n2Ssinnplb2 sinnpdbDSsinnpl8b2 sinnpd8bDWSu,nparbDwhere:Wm, x! 5*uexpS 2y 2x24yDydy (5)The hydrogeologic conditions and symbols used
27、in connec-tion with piezometer and well geometries are shown in Fig. 2.4.2.2 For large values of time, that is, for t b2S/(2a2T)ort bS/(2Kz), the effects of partial penetration are constant intime, and W(u, (npar)/b) can be approximated by 2K0(npar)/b) (2). K0is the modified Bessel function of these
28、cond kind of order zero.4.2.3 Eq 1 can be writtens 5Q4pTWu! 1Q4pTfs(6)The first term in Eq 6 is the drawdown in an isotropichomogeneous confined aquifer under radial flow, as given byTheis (3). The second term is deviation from the Theisdrawdown caused by partial penetration of the control well.This
29、 term is designated as the drawdown deviation by Weeks(1) and is given by:ds 5Q4pTfs(7)4.2.4 The effects of partial penetration need to be consideredfor ar/b (80 *0.21)/8) (0.5 + 1.25) (221/80) * 0.2 = 24.0 * (0.5 + 0.69) = 18, or forvalues of r2/t 1.5. Because Krand Kzwill not be known, thisevaluat
30、ion cannot be made prior to the completion of the final step of theprocedure. Proceed through the following steps and recompute the radialdistance from the control well affected by vertical flow components. If thepiezometers are not beyond the affected distance, it may be possible toevaluate the dat
31、a by the second drawdown deviation method.8.2.1.4 Extend the straight line down to an r value some-what smaller than that for the closest piezometer, IJ in Fig. 6.8.2.1.5 Compute values of drawdown deviation, ds =(Q/4pT)fsfor assumed values of r within the distance from thecontrol well where the mea
32、sured drawdown departs from thestraight line. This line is shown by deviation from the straightline drawdown in piezometers A, B, and C,inFig. 6. Values offsare calculated from Eq 3 or interpolated from Table 1.8.2.1.6 Construct the curve representing the drawdownprofile that would occur in an equiv
33、alent isotropic aquifer byadding, algebraically, the ds term for each of the r values, to thedrawdown of the straight line plot, IJ. Connect the resultingpoints by a smooth curve (see Fig. 6).8.2.1.7 Draw a line parallel to the line IJ through a point ofmeasured drawdown (such as Piezometer B in Fig
34、. 6) and thecomputed drawdown profile for the equivalent isotropic aqui-fer.8.2.1.8 Determine the rcvalue for the intercept of thisparallel line with the computed drawdown profile for equiva-lent isotropic conditions. The distance rc= 20 m for theintercept of the parallel line through B with the dra
35、wdown in anequivalent isotropic aquifer.8.2.1.9 Compute the ratio of horizontal to vertical hydraulicconductivity from the formula:KrKz5SrrcD2(20)where r is the distance from pumped well to piezometerthrough which the line drawn in 8.1.2 was constructed. In Fig.6, for Piezometer B:r 5 42.4, rc5 30,
36、Kr/Kz5 2 (21)8.2.1.10 Repeat 8.2.1.7 through 8.2.1.9 for each piezometerin which the drawdown deviates from the drawdown in anequivalent isotropic aquifer.8.2.1.11 Find the storage coefficient from data obtained inpiezometers located beyond the effects of partial penetrationusing the following equat
37、ion from Test Method D 4105:S 52.25Ttr2(22)where r is the value at the zero drawdown intercept.8.2.2 Method 2This method is applicable where two ormore piezometers are within the radial distant affected bypartial penetration but where piezometers are not available orthe period of pumping is too shor
38、t to determine the position ofthe distance-drawdown curve for the region unaffected bypartial penetration.8.2.2.1 Determine values of transmissivity from each pi-ezometer by the modified Theis nonequilibrium method, asdescribed in Test Method D 4105, using the data obtainedduring the later part of t
39、he test.8.2.2.2 Prepare a semilogarithmic plot, plotting drawdown,s, values for the piezometers for a selected time on thearithmetic scale and distance, r, on the logarithmic scale. Drawany line of slope Ds = 2.3Q/2pT beneath the plotted draw-down values if ds is indicated to be negative (drawdown l
40、essthan for an equivalent isotropic aquifer) or above the draw-down value ifd s appears to be positive. An example of such aplot is shown in Fig. 7, showing drawdown in piezometers andthe straight line plot EF.8.2.2.3 Determine values of the drawdown deviation, ds, foreach piezometer by subtracting
41、the drawdown value for thestraight-line plot, EF, from the observed drawdown.8.2.2.4 Use the ds values to compute values of fsfrom theformula: fs=4pTds/Q, and prepare a semilogarithmic graphplotting fson the arithmetic axis and (r/b) on the logarithmicaxis. An example of such a plot is shown in Fig.
42、 8.8.2.2.5 Prepare a semilogarithmic-type curve by plottingvalues of fsfrom Eq 3 or Eq 4 or Table 1 on the arithmetic axisfor various values of rc/b plotted on the logarithmic axis. Anexample of such a plot is shown in Fig. 9.8.2.2.6 Match the data plot to the type curve, keeping thecoordinate axes
43、of the two plots parallel, and select anyconvenient point common to both plots (see Fig. 8 and Fig. 9).8.2.2.7 Determine for the selected match point, the coordi-nate value of r/b from the data plot and the value of rc/ b fromthe type-curve plot. Solve for Kr/Kzfrom the formula:KrKz5Sr/brc/bD2(23)8.
44、2.2.8 For the selected match point, subtract the data-plotvalue of fs(see Fig. 8) from the type-curve value of fs(Fig. 9)and correct the data-plot values of fs(see 8.2.2.4) by adding,algebraically, the amount to each fs.8.2.2.9 Replot data using corrected values of fsand repeat8.2.2.6 (Points, B1, C
45、1, and D1 in Fig. 8); recalculate Kr/Kz.8.2.2.10 If the calculated values of Kr/Kzdiffer by more than10 %, repeat 8.2.2.8 and 8.2.2.9.8.2.2.11 Correct straight-line plot in 8.2.2.2 (EF, in Fig. 7)by adding, algebraically, Q/4pT *(fs(type-curve) fs(data-curve). Corrected line is GH in Fig. 7.8.2.2.12
46、 Using the zero drawdown intercept of the redrawnstraight-line plot, determine the coefficient of storage from Eq22.NOTE 8The following is provided to complement the procedures forcalculation of hydraulic properties using Deviation Method 2. Plot ofdrawdown in Fig. 7 is indicated to be greater than
47、for an equivalentisotropic aquifer. Straight line EF of slope Ds = 2.3Q/2pT = (2.3 *10 000 m3d1)/(2 * p * 1500 m2d1) = 2.44 m/log cycle is drawn abovedrawdown values in Fig. 7.D 5473 93 (2006)8Drawdown deviation, ds, for each piezometer is the observed drawdownminus the drawdown value for the straig
48、ht-line plot, EF, as shown in theaccompanying table. The corresponding values of fs=4pTds/Q arecalculated and a semilogarithmic graph of fson the arithmetic scale versusr/b (r of A =30m,B =50m,C = 100 m, and D = 150 m; b = 100 m)on the logarithmic scale as shown in Fig. 8.ABCDds 2.70 1.47 0.68 0.37f
49、s5.08 2.76 1.28 0.70r/b 0.3 0.5 1.0 1.50A type curve is prepared plotting values of fsversus rc/b, shown in Fig. 9.The plot of PointsA, B, C, and D (see Fig. 8) are matched with the typecurve (see Fig. 9). Match point 1, Fig. 8 and Fig. 9, are selected, andvalues of fsand r/b from the data plot (see Fig. 8) are recorded and valuesof fsand rc/b from the type curve (see Fig. 9) are recorded. From the matchpoint, determine:Kr/Kz5 r/b!/rc/b!#25 0.31/0.125 9.6 (24
