1、Designation: D5473/D5473M 15Standard 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 D5473/D5473M;
2、 the number immediately following the designation indicates theyear of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of lastreapproval. A superscript epsilon () indicates an editorial change since the last revision or reapproval.
3、1. Scope*1.1 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. This standard uses data derived from
4、 Test MethodD4050.1.2 LimitationsThe limitations 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 UnitsThe values stated in
5、 either inch-pound or SIunits are to be regarded separately as the standard. The valuesgiven in parentheses are for information only.1.4 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D6026.1.4.1 The procedures used to spe
6、cify how data are collected/recorded or calculated, in this standard are regarded as theindustry standard. In addition, they are representative of thesignificant digits that generally should be retained. The proce-dures used do not consider material variation, purpose forobtaining the data, special
7、purpose studies, or any consider-ations for the users objectives; and it is common practice toincrease or reduce significant digits of reported data to becommensurate with these considerations. It is beyond the scopeof this standard to consider significant digits used in analyticalmethods for engine
8、ering design1.5 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 determine the applica-bility of regulatory limitations prior to use.2.
9、Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD3740 Practice for Minimum Requirements for AgenciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD4050 Test Method for (Field Procedure) for Withd
10、rawaland Injection Well Testing for Determining HydraulicProperties of Aquifer SystemsD4105 Test Method for (Analytical Procedure) for Deter-mining Transmissivity and Storage Coefficient of Non-leaky Confined Aquifers by the Modified Theis Nonequi-librium MethodD6026 Practice for Using Significant D
11、igits in GeotechnicalData3. Terminology3.1 Definitions:3.1.1 For common definitions of terms in this standard, referto Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 observation wella well open to all or part of anaquifer.3.2.2 unconfined aquiferan aquifer that has a water
12、 table.3.3 Symbols and Dimensions:3.3.1 a nd(Kz/Kr)1/2.3.3.2 b Lthickness of aquifer.3.3.3 d Ldistance from top of aquifer to top of screenedinterval of control well.1This test method is under the jurisdiction ofASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.
13、21 on Groundwater andVadose Zone Investigations.Current edition approved Nov. 1, 2015. Published December 2015. Originallyapproved in 1993. Last previous edition approved in 2006 as D547393(2006),which was withdrawn July 2015 and reinstated in November 2015. DOI: 10.1520/D5473_D5473M15.2For referenc
14、ed 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.*A Summary of Changes section appears at the end of this standardCopyright
15、 ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.3.4 d Ldistance from top of aquifer to top of screenedinterval of observation well.3.3.5 fsnddimensionless drawdown factor.3.3.6 KLT1hydraulic conductivity.3.3.7 KrLT1hydraulic conductivity in
16、the plane of theaquifer, radially from the control well.3.3.8 KzLT1hydraulic conductivity normal to the planeof the aquifer.3.3.9 K0modified Bessel function of the second kind andzero order.3.3.10 l Ldistance from top of aquifer to bottom ofscreened interval of control well.3.3.11 l Ldistance from t
17、op of aquifer to bottom ofscreened interval of observation well.3.3.12 Q L3T1discharge.3.3.13 r Lradial distance from control well.3.3.14 rcdistance from pumped well at which an observeddrawdown deviation, s, would occur in the equivalent isotro-pic aquifer.3.3.15 S ndstorage coefficient.3.3.16 s Ld
18、rawdown.3.3.17 SsL1specific storage.3.3.18 T L2T1transmissivity.3.3.19 u nd(r2S)/(4 Tt).3.3.20 W(u) ndan exponential integral known in hydrol-ogy as the well function of u.3.3.21 W(u, fs)partial-penetration control well function.3.3.22 s Ldrawdown deviation due to partial penetra-tion from that give
19、n by equations for purely radial flow.3.3.23 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 fully penetrating the aquifer. The
20、se 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 the aquifer. These effects are show
21、n 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, as often occurs in stratified sedim
22、ents (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 aquifer.4.2 SolutionsSolutions are
23、 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 lines are for a well screened in th
24、e 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 AquiferD5473/D5473M 152s 5Q4TWu!1fs# (1)where:Wu! 5 *ue2yydy (2)and fsis the dimensionless d
25、rawdown correction factor. Thefunction W(u)+fsinEq 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)52bl 2 d!(n511nSsinnlb2 sinndbDcosnzbWSu,narbDand the solution for the dimensionless
26、drawdown correctionfactor for an observation well is given by:fs5 fSu,arb,lb,db,lb,dbD(4)52b22l 2 d!l2d!(n511n2 Ssinnlb2 sinndbDSsinnlb2 sinndbDWSu,narbDwhere:Wm, x! 5 *u expS2y 2x24yDydy (5)The hydrogeologic conditions and symbols used in connec-tion with piezometer and well geometries are shown in
27、 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, (nar)/b) can be approximated by2K0(nar)/b) (2). K0is the modified Bessel function of thesecond kind of order zero.4.2.3 Eq 1 can be writtens 5Q4TWu!1Q4Tfs(6
28、)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 term is designated as the drawdown deviation by Weeks(1) and is give
29、n by:s 5Q4Tfs(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 for values of r2/t 1.5. Because Krand Kzwill not be known, thisevaluation cannot be made prior to the completion of the final step of thepro
30、cedure. 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 data by the second drawdown deviation method.8.2.1.4 Extend the straight
31、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, s =(Q/4T)fsfor assumed values of r within the distance from thecontrol well where the measured drawdown departs from thestraight line. This line is shown by devi
32、ation 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 equivalent isotropic aquifer byadding, algebraically, the s term for each of
33、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. 6) and thecomputed drawdown profile for the equivalent isotropic aqui-f
34、er.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 drawdown in anequivalent isotropic aquifer.8.2.1.9 Compute the ratio of hori
35、zontal 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, Kr/Kz5 2 (21)8.2.1.10 Repeat 8.2.1.7 through 8.2.1.9 for each piezometeri
36、n 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 equation from Test Method D4105:FIG. 6 Drawdown Plot in an Anisotropic Aquifer
37、 With Computed Drawdown in an Equivalent Isotropic AquiferD5473/D5473M 1513S 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 no
38、t available orthe period of pumping is too short 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 D4105, usi
39、ng the data obtainedduring the later part of the 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 s = 2.3Q/2T beneath the plotted draw-down values i
40、f s is indicated to be negative (drawdown lessthan for an equivalent isotropic aquifer) or above the draw-down value if 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 deviati
41、on, s, foreach piezometer by subtracting the drawdown value for thestraight-line plot, EF, from the observed drawdown.8.2.2.4 Use the s values to compute values of fsfrom theformula: fs=4Ts/Q, and prepare a semilogarithmic graphplotting fson the arithmetic axis and (r/b) on the logarithmicaxis. An e
42、xample of such a plot is shown in Fig. 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 t
43、ype curve, keeping thecoordinate axes 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/Kz
44、from the formula:KrKz5Sr/brc/bD2(23)8.2.2.8 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
45、 of fsand repeat8.2.2.6 (Points, B1, C1, 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/4T *(fs(type-curve) fs(data-curve). Co
46、rrected line is GH in Fig. 7.8.2.2.12 Using the zero drawdown intercept of the redrawnstraight-line plot, determine the coefficient of storage from Eq22.NOTE 10The following is provided to complement the procedures forcalculation of hydraulic properties using Deviation Method 2. Plot ofdrawdown in F
47、ig. 7 is indicated to be greater than for an equivalentisotropic aquifer. Straight line EF of slope s = 2.3Q/2T = (2.3 *10 000 m3d1)/(2 * * 1500 m2d1) = 2.44 m/log cycle is drawn abovedrawdown values in Fig. 7.Drawdown deviation, s, for each piezometer is the observed draw-down minus the drawdown va
48、lue for the straight-line plot, EF, as shownin the accompanying table. The corresponding values of fs=4Ts/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.FIG. 7 Data
49、 Plots of Drawdown in Piezometer Near a Control Well and Straight-line PlotsD5473/D5473M 1514ABCDs 2.70 1.47 0.68 0.37fs5.08 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 inFig. 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.
