1、Designation: D5609 94 (Reapproved 2015)1D5609 16Standard Guide forDefining Boundary Conditions in Groundwater FlowModeling1This standard is issued under the fixed designation D5609; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, t
2、he 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 NOTEReapproved with editorial changes in September 2015.1. Scope*1.1 This guide covers the specification of appropria
3、te boundary conditions that are to be considered part of conceptualizing andmodeling groundwater systems. This guide describes techniques that can be used in defining boundary conditions and theirappropriate application for modeling saturated groundwater flow model simulations.1.2 This guide is one
4、of a series of standards on groundwater flow model applications. Defining boundary conditions is a stepin the design and construction of a model that is treated generally in Guide D5447.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is t
5、he responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.1.4 This guide offers an organized collection of information or a series of options and does not recommend a specific courseof acti
6、on. This document cannot replace education or experience and should be used in conjunction with professional judgment.Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replacethe standard of care by which the adequacy of a given
7、professional service must be judged, nor should this document be appliedwithout consideration of a projects many unique aspects. The word “Standard” in the title of this document means only that thedocument has been approved through the ASTM consensus process.2. Referenced Documents2.1 ASTM Standard
8、s:2D653 Terminology Relating to Soil, Rock, and Contained FluidsD5447 Guide for Application of a Groundwater Flow Model to a Site-Specific Problem3. Terminology3.1 For common definitions of terms in this standard, refer to Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 aqu
9、ifer, confinedconfined aquiferin hydrogeology, an aquifer bounded above and below by confining beds and inwhich the static head is above the top of the aquifer.aquifer3.2.2 boundaryin hydrogeology, the geometrical configuration of the surface enclosing the model domain.3.2.3 boundary conditionin hyd
10、rogeology, a mathematical expression of the state of the physical system that constrains theequations of the mathematical model.3.2.4 conceptual modela simplified representation of the hydrogeologic setting and the response of the flow system to stress.3.2.4 fluxin hydrogeology, the volume of fluid
11、crossing a unit cross-sectional surface area per unit time.3.2.5 groundwater flow modelin groundwater hydraulics, an application of a mathematical model to the solution of agroundwater flow problem.1 This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct respon
12、sibility of Subcommittee D18.21 on Groundwater and VadoseZone Investigations.Current edition approved Sept. 15, 2008March 1, 2016. Published October 2015March 2016. Originally approved in 1994. Last previous edition approved in 20082015as D5609 94 (2008).(2015)1. DOI: 10.1520/D5609-94R15E01.10.1520/
13、D5609-16.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.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 intende
14、d 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 adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current
15、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 International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.7 hydraulic conductivity(field
16、aquifer tests), the volume of water at the existing kinematic viscosity that will move in aunit time under unit hydraulic gradient through a unit area measured at right angles to the direction of flow.3.2.6 hydrologic conditionin groundwater hydraulics, a set of groundwater inflows or outflows, boun
17、dary conditions, andhydraulic properties that cause potentiometric heads to adopt a distinct pattern.3.2.9 simulationone complete execution of the computer program, including input and output.3.2.10 transmissivitythe volume of water at the existing kinematic viscosity that will move in a unit time u
18、nder a unithydraulic gradient through a unit width of the aquifer.3.2.11 unconfined aquiferan aquifer that has a water table.4. Significance and Use4.1 Accurate definition of boundary conditions is an important part of conceptualizing and modeling groundwater flow systems.This guide describes the pr
19、operties of the most common boundary conditions encountered in groundwater systems and discussesmajor aspects of their definition and application in groundwater models. It also discusses the significance and specification ofboundary conditions for some field situations and some common errors in spec
20、ifying boundary conditions in groundwater models.5. Types of Boundaries5.1 The flow of groundwater is described in the general case by partial differential equations. Quantitative modeling of agroundwater system entails the solution of those equations subject to site-specific boundary conditions.5.2
21、 Types of Modeled Boundary ConditionsFlow model boundary conditions can be classified as specified head or Dirichlet,specified flux or Neumann, a combination of specified head and flux, or Cauchy, free surface boundary, and seepage-face. Eachof these types of boundaries and some of their variations
22、are discussed below.5.2.1 Specified Head, or Dirichlet, Boundary TypeA specified head boundary is one in which the head can be specified as afunction of position and time over a part of the boundary surface of the groundwater system. A boundary of specified head maybe the general type of specified h
23、ead boundary in which the head may vary with time or position over the surface of the boundary,or both, or the constant-head boundary in which the head is constant in time, but head may differ in position, over the surface ofthe boundary. These two types of specified head boundaries are discussed be
24、low.5.2.1.1 General Specified-Head BoundaryThe general type of specified-head boundary condition occurs wherever head canbe specified as a function of position and time over a part of the boundary surface of a groundwater system. An example of thesimplest type might be an aquifer that is exposed alo
25、ng the bottom of a large stream whose stage is independent of groundwaterseepage.As one moves upstream or downstream, the head changes in relation to the slope of the stream channel and the head varieswith time as a function of stream flow. Heads along the stream bed are specified according to circu
26、mstances external to thegroundwater system and maintain these specified values throughout the problem solution, regardless of changes within thegroundwater system.5.2.1.2 Constant-Head BoundaryA constant head boundary is boundary in which the aquifer system coincides with a surfaceof unchanging head
27、 through time. An example is an aquifer that is bordered by a lake in which the surface-water stage is constantover all points of the boundary in time and position or an aquifer that is bordered by a stream of constant flow that is unchangingin head with time but differs in head with position.5.2.2
28、Specified Flux or Neumann Boundary TypeA specified flux boundary is one for which the flux across the boundarysurface can be specified as a function of position and time. In the simplest type of specified-flux boundary, the flux across a givenpart of the boundary surface is considered uniform in spa
29、ce and constant with time. In a more general case, the flux might beconstant with time but specified as a function of position. In the most general case, flux is specified as a function of time as wellas position. In all cases of specified flux boundaries, the flux is specified according to circumst
30、ances external to the groundwaterflow system and the specified flux values are maintained throughout the problem solution regardless of changes within thegroundwater flow system.5.2.2.1 No Flow or Streamline BoundaryThe no-flow or streamline boundary is a special case of the specified flux boundary.
31、Astreamline is a curve that is tangent to the flow-velocity vector at every point along its length; thus no flow crosses a streamline.An example of a no-flow boundary is an impermeable boundary. Natural earth materials are never impermeable. However, theymay sometimes be regarded as effectively impe
32、rmeable for modeling purposes if the hydraulic conductivities of the adjacentmaterials differ by orders of magnitude. Groundwater divides are normal to streamlines and are also no-flow boundaries. However,the groundwater divide does not intrinsically correspond to physical or hydraulic properties of
33、 the aquifer. The position of agroundwater divide is a function of the response of the aquifer system to hydrologic conditions and may be subject to change withchanging conditions. The use of groundwater divides as model boundaries may produce invalid results.5.2.3 Head Dependent Flux, or Cauchy Typ
34、eIn some situations, flux across a part of the boundary surface changes in responseto changes in head within the aquifer adjacent to the boundary. In these situations, the flux is a specified function of that head andvaries during problem solution as the head varies.NOTE 1An example of this type of
35、boundary is the upper surface of an aquifer overlain by a confining bed that is in turn overlain by a body of surfacewater. In this example, as in most head-dependent boundary situations, a practical limit exists beyond which changes in head cease to cause a changeD5609 162in flux. In this example,
36、the limit will be reached where the head within the aquifer falls below the top of the aquifer so that the aquifer is no longerconfined at that point, but is under an unconfined or water-table condition, while the confining bed above remains saturated. Under these conditions, thebottom of the confin
37、ing bed becomes locally a seepage face.Thus as the head in the aquifer is drawn down further, the hydraulic gradient does not increaseand the flux through the confining bed remains constant. In this hypothetical case, the flux through the confining bed increases linearly as the head inthe aquifer de
38、clines until the head reaches the level of the base of the confining bed after which the flux remains constant. Another example of a headdependent boundary with a similar behavior is evapotranspiration from the water table, where the flux from the water table is often modeled as decreasinglinearly w
39、ith depth to water and becomes zero where the water table reaches some specified “cutoff” depth.5.2.4 Free-Surface Boundary TypeA free-surface boundary is a moveable boundary where the head is equal to the elevationof the boundary. The most common free-surface boundary is the water table, which is t
40、he boundary surface between the saturatedflow field and the atmosphere (capillary zone not considered). An important characteristic of this boundary is that its position isnot fixed; that is its position may rise and fall with time. In some problems, for example, flow through an earth dam, the posit
41、ionof the free surface is not known before but must be found as part of the problem solution.5.2.4.1 Another example of a free surface boundary is the transition between freshwater and underlying seawater in a coastalaquifer. If diffusion is neglected and the salty groundwater seaward of the interfa
42、ce is assumed to be static, the freshwater-saltwatertransition zone can be treated as a sharp interface and can be taken as the bounding stream surface (no-flow) boundary of the freshgroundwater flow system. Under these conditions, the freshwater head at points on the interface varies only with the
43、elevation andthe freshwater head at any point on this idealized stream-surface boundary is thus a linear function of the elevation head of thatpoint.5.2.5 Seepage-Face Boundary TypeA surface of seepage is a boundary between the saturated flow field and the atmospherealong which groundwater discharge
44、s, either by evaporation or movement “downhill” along the land surface as a thin film inresponse to the force of gravity. The location of this type of boundary is generally fixed, but its length is dependent upon othersystem boundaries. A seepage surface is always associated with a free surface boun
45、dary. Seepage faces are commonly neglectedin models of large aquifer systems because their effect is often insignificant at a regional scale of problem definition. However,in problems defined over a smaller area, which require more accurate system definition, they must be considered.6. Procedure6.1
46、The definition of boundary conditions of a model is a part of the application of a model to a site-specific problem (see GuideD5447). The steps in boundary definition may be stated as follows:6.1.1 Identification of the physical boundaries of the flow system boundaries,6.1.2 Formulation of the mathe
47、matical representation of the boundaries,6.1.3 Review of sensitivity testing of boundary conditions that change when the system is under stress, that is, stress-dependentboundaries, and6.1.4 Revision of the formulation of the initial model boundary representation.6.1.5 Further evaluation, testing, a
48、nd refinement of the model boundaries is a part of the verification and validation process ofthe application of each model and is discussed in Guide D5447.6.2 Boundary IdentificationIdentify as accurately as possible the physical boundaries of the flow system. The three-dimensional bounding surfaces
49、 of the flow system must be defined even if the model is to be represented by a two-dimensionalmodel. Even if the lateral boundaries are distant from the region of primary interest, it is important to understand the location andhydraulic conditions on the boundaries of the flow system.6.2.1 Groundwater DividesGroundwater divides have been chosen as boundaries by some modelers because they can bedescribed as stream lines and can be considered as no flow boundaries. However, the locations of groundwater divides depend uponhydrologic conditions in the sen
