1.1 本规程涵盖了一种分析程序，用于确定承压含水层的透射率和蓄水系数，以及在限制层蓄水量变化可忽略的情况下，上覆或下覆限制层的渗漏值。本规程用于分析在以恒定速率从控制井抽水期间从一个或多个观察井或测压计收集的水位或水头数据。随着符号的适当变化，这种做法也可用于分析以恒定速率向控制井注水的效果。 1.2 该分析程序与试验方法一起使用 D4050 . 1.3 限制- Hantush-Jacob方法的有效使用仅限于确定水文地质环境中含水层的水力特性，并与泰斯非平衡方法（实践）的假设合理对应 D4106 )例外情况是，在这种情况下，含水层到处被具有均匀导水率和厚度的限制层覆盖或覆盖，其中假设蓄水的增量或损失可以忽略，而该限制层反过来在远端以水头保持恒定的区域为界。限制含水层的另一层的导水率很小，因此假设其不透水（见 图1 ). 图1 渗漏含水层中排水井的横截面（从Reed ( 1. ) 3. ). 封闭和不透水河床位置可以互换 1.4 单位- 以国际单位制或英寸-磅单位表示的数值应单独视为标准值。每个系统中规定的值可能不是精确的等效值； 因此，每个系统应相互独立使用。将两个系统的值合并可能会导致不符合标准。以国际单位制以外的单位报告结果不应视为不符合本标准。 1.5 所有观察值和计算值应符合实践中制定的有效数字和舍入准则 D6026 ，除非被本标准取代。 1.5.1 本标准中用于规定如何收集/记录或计算数据的程序被视为行业标准。此外，它们代表了通常应保留的有效数字。使用的程序不考虑材料变化、获取数据的目的、特殊目的研究或用户目标的任何考虑因素； 通常的做法是增加或减少报告日期的有效数字，以与这些考虑相称。考虑工程设计分析方法中使用的有效数字超出了本标准的范围。 1.6 本实践提供了一组用于执行一个或多个特定操作的说明。本文件不能取代教育或经验，应与专业判断一起使用。并非实践的所有方面都适用于所有情况。本ASTM标准不代表或取代必须根据其判断给定专业服务的充分性的谨慎标准，也不应在不考虑项目的许多独特方面的情况下应用本文件。 本文件标题中的“标准”一词仅表示该文件已通过ASTM共识程序获得批准。 1.7 本标准并非旨在解决与其使用相关的所有安全问题（如有）。本标准的用户有责任在使用前制定适当的安全、健康和环境实践，并确定监管限制的适用性。 1.8 本国际标准是根据世界贸易组织技术性贸易壁垒（TBT）委员会发布的《关于制定国际标准、指南和建议的原则的决定》中确立的国际公认标准化原则制定的。 ====意义和用途====== 5.1 假设: 5.1.1 控制井以恒定速率排放， Q . 5.1.2 控制井直径无限小，完全穿透含水层。 5.1.3 含水层是均质、各向同性的，区域广泛。 注2: 段塞和泵送试验隐含假设为多孔介质。断裂岩石和碳酸盐岩环境可能无法提供有意义的数据和信息。 5.1.4 含水层保持饱和（即水位不会下降到含水层顶部以下）。 5.1.5 含水层被具有均匀导水率和厚度的围隔层覆盖或覆盖。假设该限制层中的蓄水量没有变化，并且该层上的水力梯度随含水层水头的变化而瞬时变化。 该限制层在远端由均匀的头部源限制，头部不随时间变化。 5.1.6 另一个封闭层不透水。 5.1.7 渗漏到含水层是垂直的，与水位下降成比例，含水层中的水流是严格水平的。 5.1.8 含水层中的水流是二维的，在水平面呈径向。 5.2 井和含水层系统的几何形状如所示 图1 . 5.3 假设的含义: 5.3.1 段落 5.1.1 表明控制井的排放速率恒定。部分 8.1 试验方法 D4050 讨论了可接受的严格恒定速率的变化。流量变化的持续趋势可能导致对水的误解- 液位变化数据，除非考虑在内。 5.3.2 Hantush-Jacob解所考虑的泄漏约束层问题要求控制井的直径为无穷小且没有储层。阿卜杜勒·卡德尔和拉马杜尔盖亚 ( 5. ) 开发了大直径控制井中水位下降的解决方案图，该控制井以恒定速率从由渗漏封闭层限制的含水层中排水。 图2 ( 图3 阿卜杜勒·卡德尔和拉马杜尔盖亚 ( 5. ) )给出了一个图，显示了假设含水层蓄水系数，控制井中无量纲水位下降随无量纲时间的变化， S = 10 −3. ，以及泄漏参数， 注意，在早期无量纲时间，非渗漏含水层（BCE）和渗漏含水层（BCD）中的大直径井的曲线是一致的。 在后来的无量纲时间，渗漏含水层中大直径井的曲线与渗漏含水层中无限小直径井（ACD）的曲线合并。在水位下降变得明显恒定之前，它们聚合了大约一个对数周期的无量纲时间。对于值 r w /B 小于10 −3. ，持续下降( D )在无量纲水位降的较大值时会发生，并且在达到稳定水位降之前，会有一段更长的时间，在此期间，井筒储能效应可以忽略不计（ACD和BCD重合的时间）。对于值 大于10 −3. ，持续下降( D )将在较小的水位下降值下发生，并且将有较短的无量纲时间- 在达到稳定水位下降之前，蓄水影响可以忽略不计（ACD和BCD重合的时期）。阿卜杜勒·卡德尔和拉马杜尔盖亚 ( 5. ) 给出排放控制井中无量纲时间与无量纲降深的关系图，其值为 S = 10 −1. , 10 −2. , 10 −3. , 10 −4. ，和10 −5. 和 r w / B = 10 −2. , 10 −3. , 10 −4. , 10 −5. , 10 −6. ，和0。这些图可用于含水层测试前的分析，利用水力特性的估计值来估计控制井中的井筒蓄水效应可能会掩盖其他效应，并且水位下降不符合Hantush-Jacob解的时间段。 图2 控制井的时间降深变化 S = δ = 10 −3. （来自Abdul Khader和Ramadurgaiah）( 5. )) 图3 两含水层系统示意图 5.3.2.1 控制井筒蓄水的影响需要足够的时间来减少，以使观察井的水位下降符合Hantush-Jacob解，这一点尚不清楚。但是，当排放控制井中的水位下降不再由井筒储存影响决定时，所采用的时间可能应该是观测井数据所采用时间的最小估计值。 5.3.3 含水层在一侧的渗漏层和另一侧的非渗漏层的上方或下方形成边界的假设在现场不太可能完全满足。纽曼和威瑟斯彭( 6. ，第1285页）指出，由于Hantush-Jacob公式仅使用抽水（或补给）含水层的水位变化数据，因此无法用于区分渗漏层是否位于含水层的上方或下方（或两侧）。 汉图什 ( 7. ) 提出了一种改进方法，允许将含水层现场测试分析确定的参数解释为反映上覆和下伏承压层综合影响的复合参数。纽曼和威瑟斯彭 ( 6. ) 描述一种通过使用限制层水头变化来估计该层水力特性的方法。 5.3.4 Hantush-Jacob理论的发展要求渗漏到含水层与水位下降成比例，并且水位下降在含水层的垂直方向上不发生变化。这些要求有时通过说明封闭层中的水流基本上是垂直的，含水层中的水流基本上是水平的来描述。Hantush氏 ( 8. ) 对仅以一个渗漏围隔层为边界的含水层的分析表明，无论在何处，该近似值都是可以接受的准确度 5.3.5 Hantush-Jacob方法要求渗漏封闭层中的蓄水量没有变化。周 ( 9 ) 指出，如果“渗漏”封闭层较薄且相对可渗透且不可压缩，则Hantush和Jacob的解 ( 2. ) 将适用，而Hantush的解决方案 ( 7. ) ，这在实践中得到了描述 D6028/D6028M 考虑到在大多数情况下，如果一个封闭层很厚、渗透性低且可压缩性高，则在封闭层中的储存将适用。对于一个封闭含水层的层明显不透水，而另一个封闭层漏水，并在远端以水头恒定的层为边界的情况，它遵循Hantush ( 7. ) 当时间到了， t ，满足 含水层中的水位下降将由等式描述 哪里 注意，在Hantush的 ( 7. ) 解决方案，术语 出现，而不是给定的表达式 u 在里面 等式3 即 来自韩图什的暗示 ( 7. ) 在给出的时间标准之后 等式9 如果满足，含水层的表观蓄水系数将包括含水层蓄水系数和限制层蓄水系数的三分之一。如果约束层的储能系数远小于含水层的储能系数，则约束层中的储能影响将非常小或为零。为了说明Hantush时间准则的使用，假设约束层具有以下特征: b ′ = 3米， K ′ = 0.001米/天，以及 S ′ s = 3.6 × 10 −6. m −1. ，然后是Hantush-Jacob解 等式10 适用于任何地方 或 如果约束层的垂直导水率大一个数量级， K ′ = 0.01米/天，然后是Hantush Jacob ( 2. ) 解决方案适用于以下情况: t >23分钟。 5.3.5.1 应该注意的是，汉图什 ( 7. ) 分析假设井筒储存可忽略不计。 5.3.5.2 Moench公司 ( 10 ) 给出了数值结果，深入了解了不同参数值下控制井蓄水量和限制层蓄水量变化对含水层水位下降的影响。然而，Moench并没有提供一个明确的公式来说明这些影响何时减少到足以使后续的水位下降数据符合Hantush-Jacob解。 5.3.6 中所述假设 5.1.5 Neuman和Witherspoon认为，渗漏的封闭床另一侧由统一的水头源限制，其水位不随时间变化( 11 ，第810页）。他们考虑了由两个含水层组成的封闭系统，由一个封闭层隔开，如图所示 图3 . 他们的分析得出结论，在满足以下条件的时间内，含水层中的水位下降不会受到另一个未开采含水层特性的影响:

1.1 This practice covers an analytical procedure for determining the transmissivity and storage coefficient of a confined aquifer and the leakance value of an overlying or underlying confining bed for the case where there is negligible change of water in storage in a confining bed. This practice is used to analyze water-level or head data collected from one or more observation wells or piezometers during the pumping of water from a control well at a constant rate. With appropriate changes in sign, this practice also can be used to analyze the effects of injecting water into a control well at a constant rate. 1.2 This analytical procedure is used in conjunction with Test Method D4050 . 1.3 Limitations— The valid use of the Hantush-Jacob method is limited to the determination of hydraulic properties for aquifers in hydrogeologic settings with reasonable correspondence to the assumptions of the Theis nonequilibrium method (Practice D4106 ) with the exception that in this case the aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness, and in which the gain or loss of water in storage is assumed to be negligible, and that bed, in turn, is bounded on the distal side by a zone in which the head remains constant. The hydraulic conductivity of the other bed confining the aquifer is so small that it is assumed to be impermeable (see Fig. 1 ). FIG. 1 Cross Section Through a Discharging Well in a Leaky Aquifer (from Reed ( 1 ) 3 ). The Confining and Impermeable Bed Locations Can Be Interchanged 1.4 Units— The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in nonconformance with the standard. Reporting of results in units other than SI 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 round established in Practice D6026 , unless superseded by this standard. 1.5.1 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 objectives; and it is common practice to increase or reduce significant digits of reported date to be commensurate with these considerations. It is beyond the scope of this standard to consider significant digits used in analysis method for engineering design. 1.6 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. 1.7 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. 1.8 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. ====== Significance And Use ====== 5.1 Assumptions: 5.1.1 The control well discharges at a constant rate, Q . 5.1.2 The control well is of infinitesimal diameter and fully penetrates the aquifer. 5.1.3 The aquifer is homogeneous, isotropic, and areally extensive. Note 2: Slug and pumping tests implicitly assume a porous medium. Fractured rock and carbonate settings may not provide meaningful data and information. 5.1.4 The aquifer remains saturated (that is, water level does not decline below the top of the aquifer). 5.1.5 The aquifer is overlain, or underlain, everywhere by a confining bed having a uniform hydraulic conductivity and thickness. It is assumed that there is no change of water storage in this confining bed and that the hydraulic gradient across this bed changes instantaneously with a change in head in the aquifer. This confining bed is bounded on the distal side by a uniform head source where the head does not change with time. 5.1.6 The other confining bed is impermeable. 5.1.7 Leakage into the aquifer is vertical and proportional to the drawdown, and flow in the aquifer is strictly horizontal. 5.1.8 Flow in the aquifer is two-dimensional and radial in the horizontal plane. 5.2 The geometry of the well and aquifer system is shown in Fig. 1 . 5.3 Implications of Assumptions: 5.3.1 Paragraph 5.1.1 indicates that the discharge from the control well is at a constant rate. Section 8.1 of Test Method D4050 discusses the variation from a strictly constant rate that is acceptable. A continuous trend in the change of the discharge rate could result in misinterpretation of the water-level change data unless taken into consideration. 5.3.2 The leaky confining bed problem considered by the Hantush-Jacob solution requires that the control well has an infinitesimal diameter and has no storage. Abdul Khader and Ramadurgaiah ( 5 ) developed graphs of a solution for the drawdowns in a large-diameter control well discharging at a constant rate from an aquifer confined by a leaky confining bed. Fig. 2 ( Fig. 3 of Abdul Khader and Ramadurgaiah ( 5 ) ) gives a graph showing variation of dimensionless drawdown with dimensionless time in the control well assuming the aquifer storage coefficient, S = 10 −3 , and the leakage parameter, Note that at early dimensionless times the curve for a large-diameter well in a non-leaky aquifer (BCE) and in a leaky aquifer (BCD) are coincident. At later dimensionless times, the curve for a large diameter well in a leaky aquifer coalesces with the curve for an infinitesimal diameter well (ACD) in a leaky aquifer. They coalesce about one logarithmic cycle of dimensionless time before the drawdown becomes sensibly constant. For a value of r w /B smaller than 10 −3 , the constant drawdown ( D ) would occur at a greater value of dimensionless drawdown and there would be a longer period during which well-bore storage effects are negligible (the period where ACD and BCD are coincident) before a steady drawdown is reached. For values of greater than 10 −3 , the constant drawdown ( D ) would occur at a smaller value of drawdown and there would be a shorter period of dimensionless time during which well-storage effects are negligible (the period where ACD and BCD are coincident) before a steady drawdown is reached. Abdul Khader and Ramadurgaiah ( 5 ) present graphs of dimensionless time versus dimensionless drawdown in a discharging control well for values of S = 10 −1 , 10 −2 , 10 −3 , 10 −4 , and 10 −5 and r w / B = 10 −2 , 10 −3 , 10 −4 , 10 −5 , 10 −6 , and 0. These graphs can be used in an analysis prior to the aquifer test making use of estimates of the hydraulic properties to estimate the time period during which well-bore storage effects in the control well probably will mask other effects and the drawdowns would not fit the Hantush-Jacob solution. FIG. 2 Time—Drawdown Variation in the Control Well for S = δ = 10 −3 (from Abdul Khader and Ramadurgaiah ( 5 )) FIG. 3 Schematic Diagram of Two-Aquifer System 5.3.2.1 The time needed for the effects of control-well bore storage to diminish enough that drawdowns in observation wells should fit the Hantush-Jacob solution is less clear. But the time adopted for when drawdowns in the discharging control well are no longer dominated by well-bore storage affects probably should be the minimum estimate of the time to adopt for observation well data. 5.3.3 The assumption that the aquifer is bounded, above or below, by a leaky layer on one side and a nonleaky layer on the other side is not likely to be entirely satisfied in the field. Neuman and Witherspoon ( 6 , p. 1285) have pointed out that because the Hantush-Jacob formulation uses water-level change data only from the aquifer being pumped (or recharged) it can not be used to distinguish whether the leaking beds are above or below (or from both sides) of the aquifer. Hantush ( 7 ) presents a refinement that allows the parameters determined by the aquifer field test analysis to be interpreted as composite parameters that reflect the combined effects of overlying and underlying confined beds. Neuman and Witherspoon ( 6 ) describe a method to estimate the hydraulic properties of a confining layer by using the head changes in that layer. 5.3.4 The Hantush-Jacob theoretical development requires that the leakage into the aquifer is proportional to the drawdown, and that the drawdown does not vary in the vertical in the aquifer. These requirements are sometimes described by stating that the flow in the confining beds is essentially vertical and in the aquifer is essentially horizontal. Hantush's ( 8 ) analysis of an aquifer bounded only by one leaky confining bed suggested that this approximation is acceptably accurate wherever 5.3.5 The Hantush-Jacob method requires that there is no change in water storage in the leaky confining bed. Weeks ( 9 ) states that if the “leaky” confining bed is thin and relatively permeable and incompressible, the solution of Hantush and Jacob ( 2 ) will apply, whereas the solution of Hantush ( 7 ) , which is described in Practice D6028/D6028M , that considers storage in confining beds will apply in most cases if one confining bed is thick, of low permeability, and highly compressible. For the case where one layer confining the aquifer is sensibly impermeable, and the other confining bed is leaky and bounded on the distal side by a layer in which the head is constant it follows from Hantush ( 7 ) that when time, t , satisfies the drawdowns in the aquifer will be described by the equation where Note that in Hantush's ( 7 ) solution, the term appears instead of the expression given for u in Eq 3 , namely The implication being from Hantush ( 7 ) that after the time criterion given by Eq 9 is satisfied, the apparent storage coefficient of the aquifer will include the aquifer storage coefficient and one third of the storage coefficient for the confining bed. If the storage coefficient of the confining bed is very much less than that of the aquifer, then the effect of storage in the confining bed will be very small or sensibly nil. To illustrate the use of Hantush's time criterion, suppose a confining bed is characterized by b ′ = 3 m, K ′ = 0.001 m/day, and S ′ s = 3.6 × 10 −6 m −1 , then the Hantush-Jacob solution Eq 10 would apply everywhere when or If the vertical hydraulic conductivity of the confining bed was an order of magnitude larger, K ′ = 0.01 m/day, then the Hantush-Jacob ( 2 ) solution would apply when t > 23 min. 5.3.5.1 It should be noted that the Hantush ( 7 ) analysis assumes that well bore storage is negligible. 5.3.5.2 Moench ( 10 ) presents numerical results that give insight into the effects of control well storage and changes in storage in the confining bed on drawdowns in the aquifer for various parameter values. However, Moench does not offer an explicit formula for when those effects diminish enough for subsequent drawdown data to fit the Hantush-Jacob solution. 5.3.6 The assumption stated in 5.1.5 , that the leaky confining bed is bounded on the other side by a uniform head source, the level of which does not change with time, was considered by Neuman and Witherspoon ( 11 , p. 810). They considered a confined system of two aquifers separated by a confining bed as shown schematically in Fig. 3 . Their analysis concluded that the drawdowns in an aquifer in response to discharging from a well in that aquifer would not be affected by the properties of the other, unpumped, aquifer for times that satisfy