1、Designation: D 5609 94 (Reapproved 2002)Standard Guide forDefining Boundary Conditions in Ground-Water FlowModeling1This standard is issued under the fixed designation D 5609; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the yea
2、r 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 guide covers the specification of appropriateboundary conditions that are an essential part of conceptualiz
3、-ing and modeling ground-water systems. This guide describestechniques that can be used in defining boundary conditionsand their appropriate application for modeling saturatedground-water flow model simulations.1.2 This guide is one of a series of standards on ground-water flow model applications. D
4、efining boundary conditionsis a step in the design and construction of a model that istreated generally in Guide D 5447.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-pr
5、iate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.4 This guide offers an organized collection of informationor a series of options and does not recommend a specificcourse of action. This document cannot replace education orexperience and shoul
6、d be used in conjunction with professionaljudgment. Not all aspects of this guide may be applicable in allcircumstances. This ASTM standard is not intended to repre-sent or replace the standard of care by which the adequacy ofa given professional service must be judged, nor should thisdocument be ap
7、plied without consideration of a projects manyunique aspects. The word “Standard” in the title of thisdocument means only that the document has been approvedthrough the ASTM consensus process.2. Referenced Documents2.1 ASTM Standards:D 653 Terminology Relating to Soil, Rock, and ContainedFluids2D 54
8、47 Guide for Application of a Ground-Water FlowModel to a Site-Specific Problem33. 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 boundarygeometrical configuration of the surfacee
9、nclosing the model domain.3.1.3 boundary conditiona mathematical expression ofthe state of the physical system that constrains the equations ofthe mathematical model.3.1.4 conceptual modela simplified representation of thehydrogeologic setting and the response of the flow system tostress.3.1.5 fluxt
10、he volume of fluid crossing a unit cross-sectional surface area per unit time.3.1.6 ground-water flow modelan application of a math-ematical model to the solution of a ground-water flow problem.3.1.7 hydraulic conductivity(field aquifer tests), the vol-ume of water at the existing kinematic viscosit
11、y that will movein a unit time under unit hydraulic gradient through a unit areameasured at right angles to the direction of flow.3.1.8 hydrologic conditiona set of ground-water inflowsor outflows, boundary conditions, and hydraulic properties thatcause potentiometric heads to adopt a distinct patte
12、rn.3.1.9 simulationone complete execution of the computerprogram, including input and output.3.1.10 transmissivitythe volume of water at the existingkinematic viscosity that will move in a unit time under a unithydraulic gradient through a unit width of the aquifer.3.1.11 unconfined aquiferan aquife
13、r that has a water table.3.1.12 For definitions of other terms used in this testmethod, see Terminology D 653.4. Significance and Use4.1 Accurate definition of boundary conditions is an essen-tial part of conceptualizing and modeling ground-water flowsystems. This guide describes the properties of t
14、he mostcommon boundary conditions encountered in ground-watersystems and discusses major aspects of their definition andapplication in ground-water models. It also discusses thesignificance and specification of boundary conditions for some1This guide is under the jurisdiction of ASTM Committee D18 o
15、n Soil and Rockand is the direct responsibility of Subcommittee D18.21 on Ground Water andVadose Zone Investigations.Current edition approved Sept. 15, 1994. Published October 1994.2Annual Book of ASTM Standards, Vol 04.08.3Annual Book of ASTM Standards, Vol 04.09.1Copyright ASTM International, 100
16、Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.field situations and some common errors in specifying bound-ary conditions in ground-water models.5. Types of Boundaries5.1 The flow of ground water is described in the generalcase by partial differential equations. Quan
17、titative modeling ofa ground-water system entails the solution of those equationssubject to site-specific boundary conditions.5.2 Types of Modeled Boundary ConditionsFlow modelboundary conditions can be classified as specified head orDirichlet, specified flux or Neumann, a combination of speci-fied
18、head and flux, or Cauchy, free surface boundary, andseepage-face. Each of these types of boundaries and some oftheir variations are discussed below.5.2.1 Specified Head, or Dirichlet, Boundary TypeAspecified head boundary is one in which the head can bespecified as a function of position and time ov
19、er a part of theboundary surface of the ground-water system. A boundary ofspecified head may be the general type of specified headboundary in which the head may vary with time or positionover the surface of the boundary, or both, or the constant-headboundary in which the head is constant in time, bu
20、t head maydiffer in position, over the surface of the boundary. These twotypes of specified head boundaries are discussed below.5.2.1.1 General Specified-Head BoundaryThe generaltype of specified-head boundary condition occurs whereverhead can be specified as a function of position and time over apa
21、rt of the boundary surface of a ground-water system. Anexample of the simplest type might be an aquifer that isexposed along the bottom of a large stream whose stage isindependent of ground-water seepage. As one moves upstreamor downstream, the head changes in relation to the slope of thestream chan
22、nel and the head varies with time as a function ofstream flow. Heads along the stream bed are specified accord-ing to circumstances external to the ground-water system andmaintain these specified values throughout the problem solu-tion, regardless of changes within the ground-water system.5.2.1.2 Co
23、nstant-Head BoundaryA constant head bound-ary is boundary in which the aquifer system coincides with asurface of unchanging head through time. An example is anaquifer that is bordered by a lake in which the surface-waterstage is constant over all points of the boundary in time andposition or an aqui
24、fer that is bordered by a stream of constantflow that is unchanging in head with time but differs in headwith position.5.2.2 Specified Flux or Neumann Boundary TypeA speci-fied flux boundary is one for which the flux across theboundary surface can be specified as a function of position andtime. In t
25、he simplest type of specified-flux boundary, the fluxacross a given part of the boundary surface is considereduniform in space and constant with time. In a more generalcase, the flux might be constant with time but specified as afunction of position. In the most general case, flux is specifiedas a f
26、unction of time as well as position. In all cases ofspecified flux boundaries, the flux is specified according tocircumstances external to the ground-water flow system andthe specified flux values are maintained throughout the prob-lem solution regardless of changes within the ground-waterflow syste
27、m.5.2.2.1 No Flow or Streamline BoundaryThe no-flow orstreamline boundary is a special case of the specified fluxboundary. A streamline is a curve that is tangent to theflow-velocity vector at every point along its length; thus noflow crosses a streamline. An example of a no-flow boundaryis an imper
28、meable boundary. Natural earth materials are neverimpermeable. However, they may sometimes be regarded aseffectively impermeable for modeling purposes if the hydraulicconductivities of the adjacent materials differ by orders ofmagnitude. Ground-water divides are normal to streamlinesand are also no-
29、flow boundaries. However, the ground-waterdivide does not intrinsically correspond to physical or hydrau-lic properties of the aquifer. The position of a ground-waterdivide is a function of the response of the aquifer system tohydrologic conditions and may be subject to change withchanging condition
30、s. The use of ground-water divides as modelboundaries may produce invalid results.5.2.3 Head Dependent Flux, or Cauchy TypeIn somesituations, flux across a part of the boundary surface changes inresponse to changes in head within the aquifer adjacent to theboundary. In these situations, the flux is
31、a specified function ofthat head and varies during problem solution as the head varies.NOTE 1An example of this type of boundary is the upper surface ofan aquifer overlain by a confining bed that is in turn overlain by a bodyof surface water. In this example, as in most head-dependent boundarysituat
32、ions, a practical limit exists beyond which changes in head cease tocause a change in flux. In this example, the limit will be reached where thehead within the aquifer falls below the top of the aquifer so that the aquiferis no longer confined at that point, but is under an unconfined orwater-table
33、condition, while the confining bed above remains saturated.Under these conditions, the bottom of the confining bed becomes locallya seepage face. Thus as the head in the aquifer is drawn down further, thehydraulic gradient does not increase and the flux through the confining bedremains constant. In
34、this hypothetical case, the flux through the confiningbed increases linearly as the head in the aquifer declines until the headreaches the level of the base of the confining bed after which the fluxremains constant. Another example of a head dependent boundary with asimilar behavior is evapotranspir
35、ation from the water table, where the fluxfrom the water table is often modeled as decreasing linearly with depth towater and becomes zero where the water table reaches some specified“cutoff” depth.5.2.4 Free-Surface Boundary TypeA free-surface bound-ary is a moveable boundary where the head is equa
36、l to theelevation of the boundary. The most common free-surfaceboundary is the water table, which is the boundary surfacebetween the saturated flow field and the atmosphere (capillaryzone not considered). An important characteristic of thisboundary is that its position is not fixed; that is its posi
37、tion mayrise and fall with time. In some problems, for example, flowthrough an earth dam, the position of the free surface is notknown before but must be found as part of the problemsolution.5.2.4.1 Another example of a free surface boundary is thetransition between freshwater and underlying seawate
38、r in acoastal aquifer. If diffusion is neglected and the salty groundwater seaward of the interface is assumed to be static, thefreshwater-saltwater transition zone can be treated as a sharpinterface and can be taken as the bounding stream surface(no-flow) boundary of the fresh ground-water flow sys
39、tem.Under these conditions, the freshwater head at points on theD 56092interface varies only with the elevation and the freshwater headat any point on this idealized stream-surface boundary is thusa linear function of the elevation head of that point.5.2.5 Seepage-Face Boundary TypeA surface of seep
40、ageis a boundary between the saturated flow field and theatmosphere along which ground water discharges, either byevaporation or movement “downhill” along the land surface asa thin film in response to the force of gravity. The location ofthis type of boundary is generally fixed, but its length isdep
41、endent upon other system boundaries. A seepage surface isalways associated with a free surface boundary. Seepage facesare commonly neglected in models of large aquifer systemsbecause their effect is often insignificant at a regional scale ofproblem definition. However, in problems defined over asmal
42、ler area, which require more accurate system definition,they must be considered.6. Procedure6.1 The definition of boundary conditions of a model is apart of the application of a model to a site-specific problem (seeGuide D 5447). The steps in boundary definition may be statedas follows:6.1.1 Identif
43、ication of the physical boundaries of the flowsystem boundaries,6.1.2 Formulation of the mathematical representation of theboundaries,6.1.3 Examination and sensitivity testing of boundary con-ditions that change when the system is under stress, that is,stress-dependent boundaries, and6.1.4 Revision
44、and final formulation of the initial modelboundary representation.6.1.5 Further examination, testing, and refinement of themodel boundaries is a part of the verification and validationprocess of the application of each model and is discussed inGuide D 5447.6.2 Boundary IdentificationIdentify as accu
45、rately as pos-sible the physical boundaries of the flow system. The three-dimensional bounding surfaces of the flow system must bedefined even if the model is to be represented by a two-dimensional model. Even if the lateral boundaries are distantfrom the region of primary interest, it is important
46、to under-stand the location and hydraulic conditions on the boundariesof the flow system.6.2.1 Ground-Water DividesGround-water divides havebeen chosen as boundaries by some modelers because they canbe described as stream lines and can be considered as no flowboundaries. However, the locations of gr
47、ound-water dividesdepend upon hydrologic conditions in the sense that they canmove or disappear in response to stress on the system. Forthese reasons, ground-water divides are not physical bound-aries of the flow system.4Their representation as no-flowboundaries can sometimes be justified if the obj
48、ective of thesimulation is to gain an understanding of natural flow withoutapplied stress or if the changed conditions used for simulationcan be shown, for example, by sensitivity analysis, to have anegligible effect on the position of the boundary.6.2.2 Water TableThe water table is an important bo
49、und-ary in many ground-water flow systems and various ways oftreating the water table may be appropriate in different ground-water models. The position of the water table is not fixed andthe water table boundary may act as a source or sink of water.Some of these ways of treating the water table are discussedbelow.6.2.2.1 The position of the water table is not fixed, but itmay be appropriate to treat the water table as a constant-headboundary in a steady-state simulation where the flow distribu-tion in an unstressed model is simulated.6.2.2.2 The water table may be
