1、Designation: D5609 94 (Reapproved 2015)1Standard 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, the year
2、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.1NOTEReapproved with editorial changes in September 2015.1. Scope*1.1 This guide covers the specification of appropriateboundar
3、y conditions that are to be considered part of concep-tualizing and modeling groundwater systems. This guide de-scribes techniques that can be used in defining boundaryconditions and their appropriate application for modelingsaturated groundwater flow model simulations.1.2 This guide is one of a ser
4、ies of standards on groundwa-ter flow model applications. Defining boundary conditions is astep in the design and construction of a model that is treatedgenerally in Guide D5447.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is therespons
5、ibility of the user of this standard to establish appro-priate 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. Thi
6、s document cannot replace education orexperience and should 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 professi
7、onal service must be judged, nor should thisdocument be applied 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:2D653 Te
8、rminology Relating to Soil, Rock, and ContainedFluidsD5447 Guide for Application of a Groundwater Flow Modelto a Site-Specific Problem3. Terminology3.1 For common definitions of terms in this standard, referto Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 aquifer, confine
9、dan aquifer bounded above and be-low by confining beds and in which the static head is above thetop of the aquifer.3.2.2 boundarygeometrical configuration of the surfaceenclosing the model domain.3.2.3 boundary conditiona mathematical expression ofthe state of the physical system that constrains the
10、 equations ofthe mathematical model.3.2.4 conceptual modela simplified representation of thehydrogeologic setting and the response of the flow system tostress.3.2.5 fluxthe volume of fluid crossing a unit cross-sectional surface area per unit time.3.2.6 groundwater flow modelan application of a math
11、-ematical model to the solution of a groundwater flow problem.3.2.7 hydraulic conductivity(field aquifer tests), the vol-ume of water at the existing kinematic viscosity that will movein a unit time under unit hydraulic gradient through a unit areameasured at right angles to the direction of flow.3.
12、2.8 hydrologic conditiona set of groundwater inflows oroutflows, boundary conditions, and hydraulic properties thatcause potentiometric heads to adopt a distinct pattern.1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.21
13、 on Groundwater andVadose Zone Investigations.Current edition approved Sept. 15, 2008. Published October 2015. Originallyapproved in 1994. Last previous edition approved in 2008 as D5609 94 (2008).DOI: 10.1520/D5609-94R15E01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcon
14、tact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West
15、Conshohocken, PA 19428-2959. United States13.2.9 simulationone complete execution of the computerprogram, including input and output.3.2.10 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 aq
16、uifer.3.2.11 unconfined aquiferan aquifer that has a water table.4. Significance and Use4.1 Accurate definition of boundary conditions is an impor-tant part of conceptualizing and modeling groundwater flowsystems. This guide describes the properties of the mostcommon boundary conditions encountered
17、in groundwatersystems and discusses major aspects of their definition andapplication in groundwater models. It also discusses thesignificance and specification of boundary conditions for somefield situations and some common errors in specifying bound-ary conditions in groundwater models.5. Types of
18、Boundaries5.1 The flow of groundwater is described in the general caseby partial differential equations. Quantitative modeling of agroundwater system entails the solution of those equationssubject to site-specific boundary conditions.5.2 Types of Modeled Boundary ConditionsFlow modelboundary conditi
19、ons 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-face. Each of these types of boundaries and some oftheir variations are discussed below.5.2.1 Specified Head, or Dirichlet, Boundary
20、 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 groundwater system. A boundary ofspecified head may be the general type of specified headboundary in which the head may vary with time or positionover t
21、he 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 boundary. These twotypes of specified head boundaries are discussed below.5.2.1.1 General Specified-Head BoundaryThe generaltype of specifi
22、ed-head boundary condition occurs whereverhead can be specified as a function of position and time over apart of the boundary surface of a groundwater system. Anexample of the simplest type might be an aquifer that isexposed along the bottom of a large stream whose stage isindependent of groundwater
23、 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 flow. Heads along the stream bed are specified accord-ing to circumstances external to the groundwater system andmaintain these specified
24、values throughout the problemsolution, regardless of changes within the groundwater system.5.2.1.2 Constant-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 wh
25、ich 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 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 f
26、or 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 a given part of the boundary surface is considereduniform in space and constant with time. In a more generalcase, the flux might be constan
27、t 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 ofspecified flux boundaries, the flux is specified according tocircumstances external to the groundwater flow system and thespecified flux values are
28、 maintained throughout the problemsolution regardless of changes within the groundwater flowsystem.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 poin
29、t along its length; thus noflow crosses a streamline. An example of a no-flow boundaryis an impermeable boundary. Natural earth materials are neverimpermeable. However, they may sometimes be regarded aseffectively impermeable for modeling purposes if the hydraulicconductivities of the adjacent mater
30、ials differ by orders ofmagnitude. Groundwater divides are normal to streamlines andare also no-flow boundaries. However, the groundwater dividedoes not intrinsically correspond to physical or hydraulicproperties of the aquifer. The position of a groundwater divideis a function of the response of th
31、e aquifer system to hydrologicconditions and may be subject to change with changingconditions. The use of groundwater divides as model bound-aries 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
32、changes in head within the aquifer adjacent to theboundary. In these situations, the flux is 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
33、overlain by a bodyof surface water. In this example, as in most head-dependent boundarysituations, 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 t
34、hat the aquiferis no longer confined at that point, but is under an unconfined orwater-table 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, thehyd
35、raulic gradient does not increase and the flux through the confining bedremains constant. In 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 c
36、onstant. Another example of a head dependent boundary with asimilar behavior is evapotranspiration 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 Fre
37、e-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-surfaceD5609 94 (2015)12boundary is the water table, which is the boundary surfacebetween the saturated flow field and the atmosphere (capillaryzone no
38、t 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 example, flowthrough an earth dam, the position of the free surface is notknown before but must be found as part of the problemsolution
39、.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 salty ground-water seaward of the interface is assumed to be static, thefreshwater-saltwater transition zone can be treated as a shar
40、pinterface and can be taken as the bounding stream surface(no-flow) boundary of the fresh groundwater flow system.Under these conditions, the freshwater head at points on theinterface varies only with the elevation and the freshwater headat any point on this idealized stream-surface boundary is thus
41、a 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 and theatmosphere along which groundwater discharges, either byevaporation or movement “downhill” along the land surface asa thin film in response
42、to the force of gravity. The location ofthis type of boundary is generally fixed, but its length isdependent 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
43、 often insignificant at a regional scale ofproblem definition. However, in problems defined over asmaller 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-spec
44、ific problem (seeGuide D5447). The steps in boundary definition may be statedas follows:6.1.1 Identification of the physical boundaries of the flowsystem boundaries,6.1.2 Formulation of the mathematical representation of theboundaries,6.1.3 Review of sensitivity testing of boundary conditionsthat ch
45、ange when the system is under stress, that is, stress-dependent boundaries, and6.1.4 Revision of the formulation of the initial modelboundary representation.6.1.5 Further evaluation, testing, and refinement of themodel boundaries is a part of the verification and validationprocess of the application
46、 of each model and is discussed inGuide D5447.6.2 Boundary IdentificationIdentify as accurately 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 i
47、f the lateral boundaries are distantfrom the region of primary interest, it is important to under-stand the location and hydraulic conditions on the boundariesof the flow system.6.2.1 Groundwater DividesGroundwater divides havebeen chosen as boundaries by some modelers because they canbe described a
48、s stream lines and can be considered as no flowboundaries. However, the locations of groundwater dividesdepend upon hydrologic conditions in the sense that they canmove or disappear in response to stress on the system. Forthese reasons, groundwater divides are not physical boundariesof the flow syst
49、em.3Their representation as no-flow boundariescan sometimes be justified if the objective of the simulation isto gain an understanding of natural flow without applied stressor if the changed conditions used for simulation can be shown,for example, by sensitivity analysis, to have a negligible effecton the position of the boundary.6.2.2 Water TableThe water table is an important bound-ary in many groundwater 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
