1、Designation: D 5609 94 (Reapproved 2008)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 () 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. De
4、fining 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-pri
5、ate 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 should
6、 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 app
7、lied 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:2D 653 Terminology Relating to Soil, Rock, and ContainedFluidsD 544
8、7 Guide for Application of a Ground-Water FlowModel to a Site-Specific Problem3. 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 surfaceenc
9、losing 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 fluxthe
10、 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 viscosity
11、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 pattern
12、.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 aquifer
13、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 the
14、 mostcommon boundary conditions encountered in ground-watersystems and discusses major aspects of their definition andapplication in ground-water models. It also discusses the1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D
15、18.21 on Ground Water andVadose Zone Investigations .Current edition approved Sept. 15, 2008. Published October 2008. Originallyapproved in 1994. Last previous edition approved in 2002 as D 5609 94 (2002).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer S
16、ervice at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.significance and specification of boundar
17、y conditions for somefield 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. Quantitative modeling ofa ground-water system entails the solut
18、ion 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 head and flux, or Cauchy, free surface boundary, andseepage
19、-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 over a part of theboundary surface of the ground-water system
20、. 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, but head maydiffer in position, over the surface of the bound
21、ary. 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 apart of the boundary surface of a ground-water system. Anexam
22、ple 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 channel and the head varies with time as a function ofstream fl
23、ow. 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 Constant-Head BoundaryA constant head bound-ary is boundary i
24、n 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 aquifer that is bordered by a stream of constantflow that is un
25、changing 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 the simplest type of specified-flux boundary, the fluxacross
26、 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 function of time as well as position. In all cases ofspecifi
27、ed 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 system.5.2.2.1 No Flow or Streamline BoundaryThe no-flow orstrea
28、mline 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 impermeable boundary. Natural earth materials are neverimpermeab
29、le. 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-flow boundaries. However, the ground-waterdivide does not i
30、ntrinsically 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 conditions. The use of ground-water divides as modelboundaries may p
31、roduce 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 a specified function ofthat head and varies during problem
32、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 boundarysituations, a practical limit exists beyond which changes in head
33、 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 condition, while the confining bed above remains saturated.
34、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 this hypothetical case, the flux through the confiningbed i
35、ncreases 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 evapotranspiration from the water table, where the fluxfrom the water ta
36、ble 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 equal to theelevation of the boundary. The most common free-sur
37、faceboundary 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 position mayrise and fall with time. In some problems, for exam
38、ple, 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 seawater in acoastal aquifer. If diffusion is neglected and the sa
39、lty groundwater seaward of the interface is assumed to be static, thefreshwater-saltwater transition zone can be treated as a sharpD 5609 94 (2008)2interface and can be taken as the bounding stream surface(no-flow) boundary of the fresh ground-water flow system.Under these conditions, the freshwater
40、 head at points on theinterface 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 seepageis a boundary between the saturated flow field
41、 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 isdependent upon other system boundaries. A seepage su
42、rface 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 asmaller area, which require more accurate system defi
43、nition,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 Identification of the physical boundaries of the flowsys
44、tem 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 and final formulation of the initial modelboundar
45、y 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 accurately as pos-sible the physical boundaries of th
46、e 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 to under-stand the location and hydraulic conditi
47、ons 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 ground-water dividesdepend upon hydrologic conditio
48、ns 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.3Their representation as no-flowboundaries can sometimes be justified if the objective of thesimulation is to gain an understandi
49、ng 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 bound-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 discussedbelo
