Designation: D5609 − 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, the 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. Scope*1.1 This guide covers the specification of appropriateboundary 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 series 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 theresponsibility 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. This 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 professional service must be judged, nor should thisdocument be applied without consideration of a project’s 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 Terminology 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 confined aquifer—in hydrogeology, an aquiferbounded above and below by confining beds and in which thestatic head is above the top of the aquifer3.2.2 boundary—in hydrogeology, the geometrical configu-ration of the surface enclosing the model domain.3.2.3 boundary condition—in hydrogeology, a mathematicalexpression of the state of the physical system that constrainsthe equations of the mathematical model.3.2.4 flux—in hydrogeology, the volume of fluid crossing aunit cross-sectional surface area per unit time.3.2.5 groundwater flow model—in groundwater hydraulics,an application of a mathematical model to the solution of agroundwater flow problem.3.2.6 hydrologic condition—in groundwater hydraulics,aset of groundwater inflows or outflows, boundary conditions,and hydraulic properties that cause potentiometric heads toadopt a distinct pattern.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 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 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.1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved March 1, 2016. Published March 2016. Originallyapproved in 1994. Last previous edition approved in 2015 as D5609 – 94 (2015)ɛ1.DOI: 10.1520/D5609-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s 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 Conshohocken, PA 19428-2959. United States15.2 Types of Modeled Boundary Conditions—Flow 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-face. Each of these types of boundaries and some oftheir variations are discussed below.5.2.1 Specified Head, or Dirichlet, Boundary Type—Aspecified 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 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 boundary. These twotypes of specified head boundaries are discussed below.5.2.1.1 General Specified-Head Boundary—The 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 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 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 values throughout the problemsolution, regardless of changes within the groundwater system.5.2.1.2 Constant-Head Boundary—A 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 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 Type—A 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 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 ofspecified flux boundaries, the flux is specified according tocircumstances external to the groundwater flow system and thespecified flux values are maintained throughout the problemsolution regardless of changes within the groundwater flowsystem.5.2.2.1 No Flow or Streamline Boundary—The 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 impermeable 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. 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 the 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 Type—In 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 solution as the head varies.NOTE 1—An 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 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.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 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 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 Free-Surface Boundary Type—A free-surface bound-ary is a moveable boundary where the head is equal 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 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.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 sharpinterface 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 thusa linear function of the elevation head of that point.5.2.5 Seepage-Face Boundary Type—A 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 to the force of gravity. The location ofD5609 − 162this 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 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-specific 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 change 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 of each model and is discussed inGuide D5447.6.2 Boundary Identification—Identify 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 if 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 Divides—Groundwater 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 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 system.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 Table—The 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 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 represented as a free-surfaceboundary with recharge, in which case, the water table isneither a potential nor a stream surface.6.2.2.3 The water table may be represented as a free surfaceboundary with discharge in which discharge is by evapotrans-piration as a function