1、Designation: D5850 95 (Reapproved 2012)D5850 18Standard Test Method for (Analytical Procedure)Determining Transmissivity, Storage Coefficient, andAnisotropy Ratio from a Network of Partially PenetratingWells1This standard is issued under the fixed designation D5850; the number immediately following
2、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.1. Scope Scope*1.1 This test metho
3、d covers an analytical procedure for determining the transmissivity, storage coefficient, and ratio of verticalto horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-ratepumping test. This test method uses data from a minimum of four p
4、artially penetrating, properly recommended to be positionedobservation wells around a partially penetrating control well.1.2 The analytical procedure is used in conjunction with the field procedure in Test Method D4050.1.3 LimitationsThe limitations of the technique for determination of the horizont
5、al and vertical hydraulic conductivity ofaquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this test method.1.4 UnitsThe values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are forinf
6、ormation only.mathematical conversions, which are provided for information purposes only and are not considered standard.1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in PracticeD6026, unless superseded by this standard.1.6 The
7、 procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industrystandard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do notconsider material variation, purpose for obtain
8、ing the data, special purpose studies, or any considerations for the users objective;and it is common practice to increase or reduce the significant digits of reported data to be commensurate with these considerations.It is beyond the scope of this standard to consider significant digits used in ana
9、lysis method or engineering design.1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine theapplic
10、ability of regulatory limitations prior to use.1.8 This international standard was developed in accordance with internationally recognized principles on standardizationestablished in the Decision on Principles for the Development of International Standards, Guides and Recommendations issuedby the Wo
11、rld Trade Organization Technical Barriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and Contained FluidsD3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used inEngineering
12、Design and ConstructionD4050 Test Method for (Field Procedure) for Withdrawal and Injection Well Testing for Determining Hydraulic Properties ofAquifer SystemsD5473D5473/D5473M Test Method for (Analytical Procedure for) Analyzing the Effects of Partial Penetration of Control Welland Determining the
13、Horizontal and Vertical Hydraulic Conductivity in a Nonleaky Confined Aquifer1 This test method is under the jurisdiction ofASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater andVadoseZone Investigations.Current edition approved May 1, 2012Jan.
14、 1, 2018. Published December 2012February 2018. Originally approved in 1995. Last previous edition approved in 20062012as D5850 95 (2006).(2012). DOI: 10.1520/D5850-95R12. 10.1520/D5850-18.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at service
15、astm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Bec
16、auseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.*A Summary of Changes section appe
17、ars at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1D6026 Practice for Using Significant Digits in Geotechnical Data3. Terminology3.1 Definitions:3.1.1 For definitions of common technical terms in this stand
18、ard, see Terminology D653.3.2 Definitions:The following definitions from Terminology D653 are used in this standard and are presented for theconvenience of the user.3.2.1 anisotropyhaving different properties in different directions.3.2.2 aquifer, confinedconfined aquiferin hydrogeology, an aquifer
19、bounded above and below by confining beds and inwhich the static head is above the top of the aquifer.3.1.2 confining beda hydrogeologic unit of less permeable material bounding one or more aquifers.3.2.3 control wellin aquifer testing, well by which the head and flow in the aquifer is changed,stres
20、sed, for example, bypumping, injection, or imposing a constant change of head.3.2.4 drawdowndrawdown Lin field aquifer tests, vertical distance the static head is loweredfree water elevation islowered or the pressure head is reduced due to the removal of free water.3.2.5 hydraulic conductivity(field
21、 in field aquifer test)tests, the volume of water at the existing kinematic viscosity that willmove in a unit time under a unit hydraulic gradient through a unit area measured at right angles to the direction of flow.3.2.6 observation wellmonitoring well (observation well), nin hydrogeology, a well
22、open to all or part of an aquifer.installed,usually of small diameter, for measuring water levels, collecting water samples, or determining other groundwater characteristics.3.2.6.1 DiscussionThe well may be cased or uncased, but if cased the casing should have openings to allow flow of groundwater
23、into or out of thecasing, such as a well screen.3.1.7 piezometera device so constructed and sealed as to measure hydraulic head at a point in the subsurface.3.2.7 storage coeffcientin aquifers, the volume of water that an aquifer releases from or takes into storage per unit surfacearea of the aquife
24、r per unit change in head. For a confined aquifer, the storage coefficient is equal to the product of the specificstorage and aquifer thickness. For an unconfined aquifer, the storage coefficient is approximately equal to the specific yield.3.2.8 transmissivityin aquifers, the volume of water at the
25、 existing kinematic viscosity that will move in a unit time under aunit hydraulic gradient through a unit width of the aquifer.3.2.8.1 DiscussionIt is equal to an integration of the hydraulic conductivities across the saturated part of the aquifer perpendicular to the flow paths.3.1.10 For definitio
26、ns of other terms used in this test method, see Terminology D653.3.3 Symbols and Dimensions:3.3.1 AKz/Kr, anisotropy ratio nd.3.3.2 bthickness of aquifer L.3.3.3 Cfdrawdown correction factor, equal to the ratio of the drawdown for a fully penetrating well network to the drawdownfor a partially penet
27、rating well network (W(u)/(W(u) + fs).3.3.4 ddistance from top of aquifer to top of screened interval of control well L.3.3.5 ddistance from top of aquifer to top of screened interval of observation well L.3.3.6 fsincremental dimensionless drawdown component resulting from partial penetration nd.3.3
28、.7 Khydraulic conductivity LT1.3.3.7.1 DiscussionThe use of symbol K for the term hydraulic conductivity is the predominant usage in groundwater literature by hydrogeologists,whereas the symbol k is commonly used for this term in the rock and soil mechanics literature.3.3.8 Komodified Bessel functio
29、n of the second kind and zero order.3.3.9 Krhydraulic conductivity in the plane of the aquifer, radially from the control well (horizontal hydraulic conductivity)LT1.D5850 1823.3.10 Kzhydraulic conductivity normal to the plane of the aquifer (vertical hydraulic conductivity) LT1.3.3.11 ldistance fro
30、m top of aquifer to bottom of screened interval of control well L.3.3.12 ldistance from top of aquifer to bottom of screened interval of observation well L.3.3.13 Qdischarge L3T1.3.3.14 rradial distance from control well L.3.3.15 Sstorage coefficient nd.3.3.16 sdrawdown observed in partially penetra
31、ting well network L.3.3.17 sfdrawdown observed in fully penetrating well network L.3.3.18 Ttransmissivity L2T1.3.3.19 ttime since pumping began T.3.3.20 u(r2S)/(4Tt) nd .3.3.21 W(u)an exponential integral known in hydrology as the Theis well function of und.4. Summary of Test Method4.1 This test met
32、hod makes use of the deviations in drawdown near a partially penetrating control well from those that wouldoccur near a control well fully penetrating the aquifer. In general, drawdown within the screened horizon of a partially penetratingcontrol well tends to be greater than that which would have b
33、een observed near a fully penetrating well, whereas the drawdownabove or below the screened horizon of the partially penetrating control well tends to be less than the corresponding fullypenetrating case. Drawdown deviations due to partial penetration are amplified when the vertical hydraulic conduc
34、tivity is less thanthe horizontal hydraulic conductivity. The effects of partial penetration diminish with increasing distance from the pumped well,becoming negligible at a distance of about 1.5b/(Kz/Kr)1/2. This test method relies on obtaining drawdown measurements at aminimum of two locations with
35、in this distance of the pumped well and at each location obtaining data from observation wellscompleted to two different depths. At each location, one observation well should be screened at about the same elevation as thescreen in the pumped well, while the other observation well should be screened
36、in sediments not screened by the pumped well.4.2 According to Theis (1),3 the drawdown around a fully penetrating control well pumped at a constant rate and tapping ahomogeneous, confined aquifer is as follows:sf 5 Q4piT Wu! (1)where:Wu!5*u e2xx dx (2)4.2.1 Drawdown near a partially penetrating cont
37、rol well pumped at a constant rate and tapping a homogeneous, anisotropic,confined aquifer is presented by Hantush (2, 3, 4):s 5 Q4piT Wu!1fs! (3)According to Hantush (2, 3, 4), at late pumping times, when t b2S/(2TA), fs can be expressed as follows:fs 5 4b2pi 2l 2d! l2d!(n51 S 1n 2DKo Snpir=Kz/Krb
38、D (4)F sin Snpiib D 2 sin Snpidb DG F sin Snpilb D 2 sin Snpidb DG4.2.2 For a given observed drawdown, it is possiblepracticable to compute a correction factor, Cf, defined as the ratio of thedrawdown for a fully penetrating well to the drawdown for a partially penetrating well:Cf 5 Wu!Wu!1fs(5)The
39、observed drawdown for each observation well may be corrected to the fully penetrating equivalent drawdown bymultiplying by the correction factor:sf 5Cfs (6)3 The boldface numbers given in parentheses refer to a list of references at the end of the text.D5850 183The drawdown values corresponding to t
40、he fully penetrating case may then be analyzed by conventional distance-drawdownmethods to compute transmissivity and storage coefficient.4.2.3 The correction factors are a function of both transmissivity and storage coefficient, that are the parameters being sought.Because of this, the test method
41、relies on an iterative procedure in which an initial estimate of T and S are made from which initialcorrection factors are computed. Using these correction factors, fully penetrating drawdown values are computed and analyzedusing distance-drawdown methods to determine revised values for T and S. The
42、 revised T and S values are used to compute revisedcorrection factors, Cf. This process is repeated until the calculated T and S values change only slightly from those obtained in theprevious iteration.4.2.4 The correction factors are also a function of the anisotropy ratio, A. For this reason, all
43、of the calculations described abovemust be performed for several different assumed anisotropy ratios. The assumed anisotropy value that leads to the best solution,that is, best straight line fit or best curve match, is deemed to be the actual anisotropy ratio.5. Significance and Use5.1 This test met
44、hod is one of several available for determining vertical anisotropy ratio. Among other available methods areWeeks (5); see Test Method D5473D5473/D5473M), that relies on distance-drawdown data, and Way and McKee (6), that utilizestime-drawdown data. An important restriction of the Weeks distance-dra
45、wdown method is that the observation wells must need tohave identical construction (screened intervals) and two or more of the observation wells must need to be located at a distance fromthe pumped well beyond the effects of partial penetration. The procedure described in this test method general di
46、stance-drawdownmethod, in that it works in theory for anymost observation well configurationconfigurations incorporating three or more wells,provided some of the wells are within the zone where flow is affected by partial penetration.5.2 Assumptions:5.2.1 Control well discharges at a constant rate,
47、Q.5.2.2 Control well is of infinitesimal diameter and partially penetrates the aquifer.5.2.3 Data are obtained from a number of partially penetrating observation wells, some screened at elevations similar to thatin the pumped well and some screened at different elevations.5.2.4 The aquifer is confin
48、ed, homogeneous and areally extensive. The aquifer may be anisotropic, and, if so, the directions ofmaximum and minimum hydraulic conductivity are horizontal and vertical, respectively.5.2.5 Discharge from the well is derived exclusively from storage in the aquifer.5.3 Calculation RequirementsApplic
49、ation of this method is computationally intensive. The function, fs, shown in (Eq 4) mustbe evaluated numerous times using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of valuesfor fs and, because this equation is rather formidable, it ismay not readily be easily tractable by hand. Because of this, it is assumedthe practitioner using this test method will have available a computerized procedure for evaluating the function fs. This
