1、Designation: D 4105 96 (Reapproved 2002)Standard Test Method(Analytical Procedure) for Determining Transmissivity andStorage Coefficient of Nonleaky Confined Aquifers by theModified Theis Nonequilibrium Method1This standard is issued under the fixed designation D 4105; the number immediately followi
2、ng 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 reapproval.1. Scope1.1 This test method c
3、overs an analytical procedure fordetermining transmissivity and storage coefficient of a non-leaky confined aquifer under conditions of radial flow to a fullypenetrating well of constant flux. This test method is a shortcutprocedure used to apply the Theis nonequilibrium method. TheTheis method is d
4、escribed in Test Method D 4106.1.2 This test method is used in conjunction with the fieldprocedure given in Test Method D 4050.1.3 LimitationsThe limitations of this test method areprimarily related to the correspondence between the fieldsituation and the simplifying assumptions of this test method(
5、see 5.1). Furthermore, application is valid only for values of uless than 0.01 (u is defined in Eq 2, in 8.6).1.4 The values stated in SI units are to be regarded asstandard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibil
6、ity 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:D 653 Terminology Relating to Soil, Rock, and ContainedFluids2D 4043 Guide for Selection of Aquifer
7、-Test Method inDetermining Hydraulic Properties by Well Techniques2D 4050 Test Method (Field Procedure) for Withdrawal andInjection Well Tests for Determining Hydraulic Propertiesof Aquifer Systems2D 4106 Test Method (Analytical Procedure) for Determin-ing Transmissivity and Storage Coefficient of N
8、onleakyConfined Aquifers by the Theis Nonequilibrium Method23. Terminology3.1 Definitions:3.1.1 aquifer, confinedan aquifer bounded above andbelow by confining beds and in which the static head is abovethe top of the aquifer.3.1.2 aquifer, unconfinedan aquifer that has a water table.3.1.3 confining
9、beda hydrogeologic unit of less perme-able material bounding one or more aquifers.3.1.4 control wellwell by which the aquifer is stressed, forexample, by pumping, injection, or change of head.3.1.5 drawdownvertical distance the static head is low-ered due to the removal of water.3.1.6 hydraulic cond
10、uctivity(field aquifer tests), the vol-ume of water at the existing kinematic viscosity that will movein a unit time under unit hydraulic gradient through a unit areameasured at right angles to the direction of flow.3.1.7 observation wella well open to all or part of anaquifer.3.1.8 piezometeruse to
11、 measure static head at a point inthe subsurface.3.1.9 specific storagethe volume of water released fromor taken into storage per unit volume of the porous medium perunit change in head.3.1.10 storage coeffcientthe volume of water an aquiferreleases from or takes into storage per unit surface area o
12、f theaquifer per unit change in head. For a confined aquifer, it isequal to the product of specific storage and aquifer thickness.For an unconfined aquifer, the storage coefficient is approxi-mately equal to the specific yield.3.1.11 transmissivitythe volume of water at the existingkinematic viscosi
13、ty that will move in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.1.12 For definitions of other terms used in this testmethod, see Terminology D 653.3.2 Symbols:Symbols and Dimensions:3.2.1 K LT1hydraulic conductivity.3.2.2 Kxyhydraulic conductivity in the horizon
14、tal direc-tion.3.2.3 Kzhydraulic conductivity in the vertical direction.3.2.4 T L2T1transmissivity.3.2.5 S ndstorage coefficient.1This test method is under the jurisdiction of ASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone In
15、vestigations.Current edition approved Oct. 10, 1996. Published June 1997. Originallypublished as D 4105 91. Last previous edition D 4105 91.2Annual Book of ASTM Standards, Vol 04.08.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2
16、.6 Ss L1specific storage.3.2.7 s Ldrawdown.3.2.8 Q L3T1discharge.3.2.9 r Lradial distance from control well.3.2.10 t Ttime.3.2.11 b Lthickness of the aquifer.4. Summary of Test Method4.1 This test method describes an analytical procedure foranalyzing data collected during a withdrawal or injection w
17、elltest. The field procedure (see Test Method D 4050) involvespumping a control well at a constant rate and measuring thewater level response in one or more observation wells orpiezometers. The water-level response in the aquifer is afunction of the transmissivity and coefficient of storage of theaq
18、uifer. Alternatively, the test can be performed by injectingwater at a constant rate into the aquifer through the controlwell. Analysis of buildup of water level in response to injectionis similar to analysis of drawdown of water level in response towithdrawal in a confined aquifer. Drawdown of wate
19、r level isanalyzed by plotting drawdown against factors incorporatingeither time or distance from the control well, or both, andmatching the drawdown response with a straight line.4.2 SolutionThe solution given by Theis (1)3can beexpressed as follows:s 5Q4pT*u e2yydy (1)where:u 5r2S4Tt(2)and:*u e2yy
20、dy 5 Wu! 520.577216 2 logeu (3)1 u 2u22!21u33!32u44!41 .4.3 The sum of the terms to the right of logeu in the seriesof Eq 3 is not significant when u becomes small.NOTE 1The errors for small values of u, from Kruseman andDeRidder (1) are as follows:Error less than, %: 1 2 5 10For u smaller than: 0.0
21、3 0.05 0.1 0.15The value of u decreases with increasing time, t, anddecreases as the radial distance, r, decreases. Therefore, forlarge values of t and reasonably small values of r, the terms tothe right of logeu in Eq 3 may be neglected as recognized byTheis (2) and Jacob (3). The Theis equation ca
22、n then be writtenas follows:s 5Q4pTF20.577216 2 lnSr2S4TtDG(4)from which it has been shown by Lohman (4) thatT 52.3Q4pDs/Dlog10t(5)and:T 522.3Q2pDs/Dlog10r(6)where:Ds/Dlog10t = the drawdown (measured or projected) overone log cycle of time, andDs/Dlog10r = the drawdown (measured or projected) overon
23、e log cycle of radial distance from thecontrol well.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 penetratesthe aquifer, that is, the well is open to the full thickness of theaquifer.5.1.3 The nonleaky aquifer is
24、homogeneous, isotropic, andareally extensive. A nonleaky aquifer receives insignificantcontribution of water from confining beds.5.1.4 Discharge from the well is derived exclusively fromstorage in the aquifer.5.1.5 The geometry of the assumed aquifer and well condi-tions are shown in Fig. 1.5.2 Impl
25、ications of Assumptions:5.2.1 Implicit in the assumptions are the conditions of radialflow. Vertical flow components are induced by a control wellthat partially penetrates the aquifer, that is, not open to theaquifer through its full thickness. If the control well does notfully penetrate the aquifer
26、, the nearest piezometer or partiallypenetrating observation well should be located at a distance, r,beyond which vertical flow components are negligible, whereaccording to Reed (5)r 51.5bKzKxy(7)This section applies to distance-drawdown calculations oftransmissivity and storage coefficient and time
27、-drawdown cal-culations of storage coefficient. If possible, compute transmis-sivity from time-drawdown data from wells located within adistance, r, of the pumped well using data measured after theeffects of partial penetration have become constant. The time atwhich this occurs is given by Hantush (
28、6) by:3The boldface numbers in parentheses refer to a list of references at the end ofthe text.FIG. 1 Cross Section Through a Discharging Well in a NonleakyConfined AquiferD 41052t 5 b2s/2T Kz/Kr! (8)Fully penetrating observation wells may be placed at lessthan distance r from the control well. Obse
29、rvation wells maybe on the same or on various radial lines from the control well.5.2.2 The Theis method assumes the control well is ofinfinitesimal diameter. Also, it assumes that the water level inthe control well is the same as in the aquifer contiguous to thewell. In practice these assumptions ma
30、y cause a differencebetween the theoretical drawdown and field measurements ofdrawdown in the early part of the test and in and near thecontrol well. Control well storage is negligible after a time, t,given by the following equation after weeks (7).t 525 rc2T(9)where:rc= the radius of the control we
31、ll in the interval thatincludes the water level changes.5.2.3 Application of Theis Nonequilibrium Method to Un-confined Aquifers:5.2.3.1 Although the assumptions are applicable to confinedconditions, the Theis solution may be applied to unconfinedaquifers if drawdown is small compared with the satur
32、atedthickness of the aquifer or if the drawdown is corrected forreduction in thickness of the aquifer and the effects of delayedgravity yield are small.5.2.3.2 Reduction in Aquifer ThicknessIn an unconfinedaquifer, dewatering occurs when the water levels decline in thevicinity of a pumping well. Cor
33、rections in drawdown need tobe made when the drawdown is a significant fraction of theaquifer thickness as shown by Jacob (8). The drawdown, s,needs to be replaced by s8, the drawdown that would occur inan equivalent confined aquifer, where:s8 5 s 2s22b(10)5.2.3.3 Gravity Yield EffectsIn unconfined
34、aquifers, de-layed gravity yield effects may invalidate measurements ofdrawdown during the early part of the test for application to theTheis method. Effects of delayed gravity yield are negligible inpartially penetrating observation wells at a distance, r, from thecontrol well, where:r 5bKzKxy(11)a
35、fter the time, t, as given in the following equation fromNeuman (9):t 5 10Syr2T(12)where:Sy= the specific yield.For fully penetrating observation wells, the effects of de-layed yield are negligible at the distance, r, in Eq 11 after onetenth of the time given in the Eq 12.6. Apparatus6.1 Analysis of
36、 data from the field procedure (see TestMethod D 4050) by this test method requires that the controlwell and observation wells meet the requirements specified in6.2-6.4.6.2 Control WellScreen the control well in the aquifer andequip with a pump capable of discharging water from the wellat a constant
37、 rate for the duration of the test. Preferably, screenthe control well throughout the full thickness of the aquifer. Ifthe control well partially penetrates the aquifer, take specialprecaution in the placement or design of observation wells (see5.2.1).6.3 Construction of Observation WellsConstruct o
38、ne ormore observation wells or piezometers at a distance from thecontrol well. Observation wells may be partially open or fullyopen throughout the thickness of the aquifer.6.4 Location of Observation WellsLocate observationwells at various distances from the control well within the areaof influence
39、of pumping. However, if vertical flow componentsare significant and if partially penetrating observation wells areused, locate them at a distance beyond the effect of verticalflow components (see 5.2.1). If the aquifer is unconfined,constraints are imposed on the distance to partially penetratingobs
40、ervation wells and the validity of early time measurements(see 5.2.3).7. Procedure7.1 The overall procedure consists of conducting the fieldprocedure for withdrawal or injection well tests described inTest Method D 4050 and analysis of the field data as addressedin this test method.7.2 Use a graphic
41、al procedure to solve for transmissivityand coefficient of storage as described in 8.2.8. Calculation8.1 Plot drawdown, s, at a specified distance on the arith-metic scale and time, t, on the logarithmic scale.8.2 Plot drawdown, s, for several observation wells at aspecified time on the arithmetic s
42、cale and distance on thelogarithmic scale.8.3 For convenience in calculations, by choosing draw-down, D st, as that which occurs over one log cycle of time:D log10t 5 log10 St2t1D5 1 (13)and, similarly for convenience in calculations, by choosingthe drawdown, Dsr, as that which occurs over one log c
43、ycle ofdistance,D log10r 5 log10 Sr2r1D5 1 (14)8.4 Calculate transmissivity using the semilog plot of draw-down versus time by the following equation derived from Eq 5:t 5 2.3Q/2pDsr(15)or calculate transmissivity using the semilog plot of draw-down versus radial distance from control well by the fo
44、llowingequation derived from Eq 6:T 522.3Q2pDsr(16)8.5 Determine the coefficient of storage from these semilogD 41053plots of drawdown versus time or distance by a methodproposed by Jacob (2) where:s 52.3Q4pTlog10 S2.25Ttr2SD(17)Taking s = 0 at the zero-drawdown intercept of the straight-line semilo
45、g plot of time or distance versus drawdown,S 52.25Ttr2(18)where:either r or t = the value at the zero-drawdown intercept.8.6 To apply the modified Theis nonequilibrium method tothin unconfined aquifers, where the drawdown is a significantfraction of the initial saturated thickness, apply a correctio
46、n tothe drawdown in solving for T and S (see 5.2.3.2).8.7 This test method is applicable only for values of u 0.01, that is:u 5r2S4Tt, 0.01 (19)It is seen from Eq 13 that u decreases as time increases, otherthings being equal. Because S is in the numerator, the value ofu is much smaller for a confin
47、ed aquifer, whose storagecoefficient may range from only about 105to 103, than for anunconfined aquifer, whose specific yield may be from 0.1 to0.3. To compensate for this, t must be greater by several ordersof magnitude in testing an unconfined aquifer than testing aconfined aquifer.8.7.1 In a draw
48、down-time test (s versus log10t or log10t/r2),data points for any particular distance will begin to fall on astraight line only after the time is sufficiently long to satisfy theabove criteria. In a drawdown-distance test (s versus log10r),the well must be pumped long enough that the data for the mo
49、stdistant observation well satisfy the requirements; then only thedrawdowns at or after this value of t may be analyzed on asemilogarithmic plot for one particular value of t.NOTE 2The analyst may also find it useful to analyze the data usingthe Theis nonequilibrium procedure (see Test Method D 4106).9. Report9.1 Report the information described below. The report ofthe analytical procedure will include information from thereport on test method selection (see Guide D 4043) and thefield testing procedure (see Test Method D 405
