1、Designation: D4106 96 (Reapproved 2008)D4106 15Standard Test Method for(Analytical Procedure) for Determining Transmissivity andStorage Coefficient of Nonleaky Confined Aquifers by theTheis Nonequilibrium Method1This standard is issued under the fixed designation D4106; the number immediately follow
2、ing 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 m
3、ethod covers an analytical procedure for determining the transmissivity and storage coefficient of a nonleakyconfined aquifer. It is used to analyze data on water-level response collected during radial flow to or from a well of constantdischarge or injection.1.2 This analytical procedure procedure,
4、along with others, is used in conjunction with the field procedure given in Test MethodD4050.1.3 LimitationsThe limitations of this test method for determination of hydraulic properties of aquifers are primarily relatedto the correspondence between the field situation and the simplifying assumptions
5、 of this test method (see 5.1).1.4 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in PracticeD6026.1.4.1 The procedures used to specify how data are collected/recorded or calculated, in this standard are regarded as the industrystan
6、dard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do notconsider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the users objectives;and it is common practice to increase
7、 or reduce 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 analytical methods for engineering design.1.5 This standard does not purport to address all of the safety concerns, if any, assoc
8、iated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and Contained Fluids
9、D3740 Practice for Minimum Requirements for Agencies Engaged in Testing and/or Inspection of Soil and Rock as Used inEngineering Design and ConstructionD4043 Guide for Selection of Aquifer Test Method in Determining Hydraulic Properties by Well TechniquesD4050 Test Method for (Field Procedure) for W
10、ithdrawal and Injection Well Testing for Determining Hydraulic Properties ofAquifer SystemsD6026 Practice for Using Significant Digits in Geotechnical Data3. Terminology3.1 Definitions:3.1.1 For definitions of other terms used in this test method, see Terminology D653.3.2 Definitions:Definitions of
11、Terms Specific to This Standard:1 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 Sept. 15, 2008April 15, 2015. Published October 2008June 201
12、5. Originally approved in 1991. Last previous edition approved in 20022008 asD4106 96 (2008). (2002). DOI: 10.1520/D4106-96R08.10.1520/D4106-15.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvo
13、lume 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. Becauseit may not be technically possible to ade
14、quately 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 appears at the end of this standardCopyright ASTM
15、 International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.1 aquifer, confinedan aquifer bounded above and below by confining beds and in which the static head is above the topof the aquifer.3.1.2 confining beda hydrogeologic unit of less permeable materi
16、al bounding one or more aquifers.3.1.3 control wellwell by which the head and flow in the aquifer is changed, for example, by pumping, injection, or imposinga constant change of head.3.1.4 drawdownvertical distance the static head is lowered due to the removal of water.3.1.5 headsee head, static.3.1
17、.6 head, staticthe height above a standard datum of the surface of a column of water (or other liquid) that can be supportedby the static pressure at a given point.3.1.7 hydraulic conductivity (field aquifer tests)the volume of water at the existing kinematic viscosity that will move in a unittime u
18、nder a unit hydraulic gradient through a unit area measured at right angles to the direction of flow.3.2.1 observation wella well open to all or part of an aquifer.3.1.9 piezometera device so constructed and sealed as to measure hydraulic head at a point in the subsurface.3.1.10 specific storagethe
19、volume of water released from or taken into storage per unit volume of the porous medium per unitchange in head.3.1.11 storage coeffcientthe volume of water an aquifer releases from or takes into storage per unit surface area of the aquiferper unit change in head. For a confined aquifer, the storage
20、 coefficient is equal to the product of the specific storage and aquiferthickness. For an unconfined aquifer, the storage coefficient is approximately equal to the specific yield.3.1.12 transmissivitythe volume of water at the existing kinematic viscosity that will move in a unit time under a unithy
21、draulic gradient through a unit width of the aquifer.3.2.2 unconfined aquiferan aquifer that has a water table.3.1.14 For definitions of other terms used in this test method, see Terminology D653.3.3 Symbols and Dimensions:3.3.1 K LT1hydraulic conductivity.3.3.2 Kxyhydraulic conductivity in the hori
22、zontal plane, radially from the control well.3.3.3 Kzhydraulic conductivity in the vertical direction.3.3.4 Q L3T1discharge.3.3.5 S ndstorage coefficient.3.3.6 SsL1specific storage.3.3.7 T L2T1transmissivity.3.3.8 W(u) ndwell function of u.3.3.9 b Lthickness of aquifer.3.3.10 r Lradial distance from
23、 control well.3.3.11 s Ldrawdown.4. Summary of Test Method4.1 This test method describes an analytical procedure for analyzing data collected during a withdrawal or injection well test.The field procedure (see Test Method D4050) involves pumping a control well at a constant rate and measuring the wa
24、ter levelresponse in one or more observation wells or piezometers.The water-level response in the aquifer is a function of the transmissivityand storage coefficient of the aquifer. Alternatively, this test method can be performed by injecting water at a constant rate intothe aquifer through the cont
25、rol well. Analysis of buildup of water level in response to injection is similar to analysis of drawdownof water level in response to withdrawal in a confined aquifer. Drawdown of water level is analyzed by plotting drawdown againstfactors incorporating either time or distance from the control well,
26、 or both, and matching the drawdown response with a type curve.4.2 SolutionThe solution given by Theis (1)3 may be expressed as follows:s 5 Q4piT *u e2yy dy (1)where:u 5r2S4Tt (2)3 The boldface numbers in parentheses refer to a list of references at the end of this standard.D4106 152*u e2yy dy5Wu!52
27、0.5772162loge u1u 2 u22!21u 33!32u44!41 (3)5. Significance and Use5.1 Assumptions:5.1.1 Well discharges at a constant rate, Q.5.1.2 Well is of infinitesimal diameter and fully penetrates the aquifer.5.1.3 The nonleaky aquifer is homogeneous, isotropic, and aerially extensive. A nonleaky aquifer rece
28、ives insignificantcontribution of water from confining beds.5.1.4 Discharge from the well is derived exclusively from storage in the aquifer.5.1.5 The geometry of the assumed aquifer and well conditions are shown in Fig. 1.5.2 Implications of Assumptions : Assumptions:5.2.1 Implicit in the assumptio
29、ns are the conditions of radial flow. Vertical flow components are induced by a control well thatpartially penetrates the aquifer, that is, the well is not open to the aquifer through its full thickness. If the control well does notfully penetrate the aquifer, the nearest piezometer or partially pen
30、etrating observation well should be located at a distance, r,beyond which vertical flow components are negligible, where according to Reed (2):r 51.5 bKzKxy(4)This section applies to distance-drawdown calculations of transmissivity and storage coefficient and time-drawdown calculationsof storage coe
31、fficient. If possible, compute transmissivity from time-drawdown data from wells located within a distance, r, of thepumped well using data measured after the effects of partial penetration have become constant. The time at which this occurs isgiven by Hantush (3) by:t 5b2s/2T Kz/Kr! (5)Fully penetr
32、ating observation wells may be placed at less than distance r from the control well. Observation wells may be onthe same or on various radial lines from the control well.5.2.2 The Theis method assumes the control well is of infinitesimal diameter.Also, it assumes that the water level in the controlw
33、ell is the same as in the aquifer contiguous to the well. In practice these assumptions may cause a difference between thetheoretical drawdown and field measurements of drawdown in the early part of the test and in and near the control well. Controlwell storage is negligible after a time, t, given b
34、y the Eq 6 after Weeks (4).t 5253r2cT (6)where:rc = the radius of the control well in the interval in which the water level changes.5.2.3 Application of Theis Method to Unconfined Aquifers:5.2.3.1 Although the assumptions are applicable to artesian or confined conditions, the Theis solution may be a
35、pplied tounconfined aquifers if drawdown is small compared with the saturated thickness of the aquifer or if the drawdown is corrected forreduction in thickness of the aquifer, and the effects of delayed gravity yield are small.FIG. 1 Cross Section Through a Discharging Well in a Nonleaky Confined A
36、quiferD4106 1535.2.3.2 Reduction in Aquifer ThicknessIn an unconfined aquifer dewatering occurs when the water levels decline in thevicinity of a pumping well. Corrections in drawdown need to be made when the drawdown is a significant fraction of the aquiferthickness as shown by Jacob (5). The drawd
37、own, s, needs to be replaced by s, the drawdown that would occur in an equivalentconfined aquifer, where:s5s 2Ss22bD (7)5.2.3.3 Gravity Yield EffectsIn unconfined aquifers, delayed gravity yield effects may invalidate measurements of drawdownduring the early part of the test for application to the T
38、heis method. Effects of delayed gravity yield are negligible in partiallypenetrating observation wells at and beyond a distance, r, from the control well, where:r 5 bKzKxy(8)After the time, t, as given in Eq 9 from Neuman (6).t 5103Syr2/T! (9)where:Sy = the specific yield. For fully penetrating obse
39、rvation wells, the effects of delayed yield are negligible at the distance, r, inEq 8 after one tenth of the time given in the Eq 9.NOTE 1The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of theequipment and facilit
40、ies used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objectivetesting/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself ensure reliable results.Reliable results depend on many
41、factors; Practice D3740 provides a means of evaluating some of those factors.6. Apparatus6.1 Analysis of data from the field procedure (see Test Method D4050) by the method specified in this test method requires thatthe control well and observation wells meet the specifications in the following para
42、graphs.6.2 Construction of Control WellScreen the control well in the aquifer to be tested and equip with a pump capable ofdischarging water from the well at a constant rate for the duration of the test. Preferably, screen the control well throughout thefull thickness of the aquifer. If the control
43、well partially penetrates the aquifer, take special precaution in the placement and designof observation wells (see 5.2.1).6.3 Construction of Observation WellsConstruct one or more observation wells at a distance from the control well.Observation wells may be partially open or open throughout the t
44、hickness of the aquifer.6.4 Location of Observation WellsLocate observation wells at various distances from the control well within the area ofinfluence of pumping. However, if vertical flow components are significant and if partially penetrating observation wells are used,locate them at a distance
45、beyond the effect of vertical flow components (see 5.2.1). If the aquifer is unconfined, constraints areimposed on the distance to partially penetrating observation wells and the validity of early time measurements (see 5.2.3).7. Procedure7.1 The overall procedure consists of conducting the field pr
46、ocedure for withdrawal or injection well tests (described in TestMethod D4050) and analysis of the field data that is addressed in this test method.7.2 The integral expression in Eq 1 and Eq 2 can not be evaluated analytically. A graphical procedure is used to solve for thetwo unknown parameters tra
47、nsmissivity and storage coefficient where:s 5 Q4piT Wu! (10)and:u 5r2S4Tt (11)8. Calculation8.1 The graphical procedure used to calculate test results is based on the functional relations between W(u) and s and betweenu and t or t/r2.8.1.1 Plot values of W(u) versus 1/u on logarithmic-scale paper (s
48、ee Table 1). This plot is referred to as the type curve plot.8.1.2 On logarithmic tracing paper of the same scale and size as the W(u) versus 1/u type curve, plot values of drawdown, s,on the vertical coordinate versus either time on the horizontal coordinate if one observation well is used or versu
49、s t/r2 on thehorizontal coordinate if more than one observation well is used.D4106 1548.1.3 Overlay the data plot on the type curve plot and, while the coordinate axes of the two plots are held parallel, shift the plotto align with the type curve (see Fig. 2).8.1.4 Select and record the values of W(u), 1/u, s, and t at an arbitrary point, referred to as the match point (see Fig. 2), anywhereon the overlapping part of the plots. For convenience the point may be selected where W(u) and 1/ u are integer values.NOT
