5.1 This practice is one of several available for determining vertical anisotropy ratio. Among other available methods are Weeks ((5); see Practice D5473/D5473M), that relies on distance-drawdown data, and Way and McKee (6), that utilizes time-drawdown data. An important restriction of the Weeks distance-drawdown method is that the observation wells need to have identical construction (screened intervals) and two or more of the observation wells need to be located at a distance from the pumped well beyond the effects of partial penetration. The procedure described in this practice general distance-drawdown method, in that it works in theory for most observation well configurations 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, 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 that in the pumped well and some screened at different elevations.

5.2.4 The aquifer is confined, homogeneous and areally extensive. The aquifer may be anisotropic, and, if so, the directions of maximum 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 Requirements—Application of this method is computationally intensive. The function, f_s, shown in (Eq 4) should be evaluated numerous times using arbitrary input parameters. It is not practical to use existing, somewhat limited, tables of values for f_s and, because this equation is rather formidable, it may not be easily tractable by hand. Because of this, it is assumed the practitioner using this will have available a computerized procedure for evaluating the function f_s. This can be accomplished using commercially available mathematical software including some spreadsheet applications, or by writing programs. (7)

Note 2: The quality of the result produced by this standard is dependent on the competence of the personnel performing it, and the suitability of the equipment and facilities used. Agencies that meet the criteria of Practice D3740 are generally considered capable of competent and objective testing/sampling/inspection/etc. Users of this standard are cautioned that compliance with Practice D3740 does not in itself assure reliable results. Reliable results depend on many factors; Practice D3740 provides a means of evaluating some of those factors.

Note 3: Most fractured (unconfined) aquifers, even noncarbonates, will have some form of convergent flow to master fissures or channels (Worthington et al., 2016). A relationship is known to occur in carbonates where potentiometric troughs correspond with sub-surface conduits or channels (Quinlan and Ewers, 1989).

Note 4: Commercially available software is available for the calculating, graphing, plotting, and analyses of this practice. The user should verify the correctness of the formulas, graphs, plots and analyses of the software.

1.1 This practice covers an analytical procedure for determining the transmissivity, storage coefficient, and ratio of vertical to horizontal hydraulic conductivity of a confined aquifer using observation well drawdown measurements from a constant-rate pumping test. This practice uses data from a minimum of four partially penetrating, recommended to be positioned observation 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 Limitations—The limitations of the technique for determination of the horizontal and vertical hydraulic conductivity of aquifers are primarily related to the correspondence between the field situation and the simplifying assumption of this practice.

1.4 Units—The values stated in inch-pound units are to be regarded as the standard. The SI units given in parentheses are mathematical conversions, which are provided for information purposes only and are not considered standard. The reporting of results in units other than inch-pound shall not be regarded as nonconformance with this standard.

1.5 All observed and calculated values shall conform to the guidelines for significant digits and rounding established in Practice D6026, unless superseded by this standard.

1.6 The procedures used to specify how data are collected/recorded or calculated in this standard are regarded as the industry standard. In addition, they are representative of the significant digits that generally should be retained. The procedures used do not consider material variation, purpose for obtaining the data, special purpose studies, or any considerations for the user’s 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 analysis method or engineering design.

1.7 This practice offers a set of instructions for performing one or more specific operations. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of the practice may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without the consideration of a project’s many unique aspects. The word “Standard” in the title of this document means only that the document has been approved through the ASTM consensus process.

1.8 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.9 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.