ASTM D5609-94(2002)
(Guide)Standard Guide for Defining Boundary Conditions in Ground-Water Flow Modeling
Standard Guide for Defining Boundary Conditions in Ground-Water Flow Modeling
SIGNIFICANCE AND USE
Accurate definition of boundary conditions is an essential part of conceptualizing and modeling ground-water flow systems. This guide describes the properties of the most common boundary conditions encountered in ground-water systems and discusses major aspects of their definition and application in ground-water models. It also discusses the significance and specification of boundary conditions for some field situations and some common errors in specifying boundary conditions in ground-water models.
SCOPE
1.1 This guide covers the specification of appropriate boundary conditions that are an essential part of conceptualizing and modeling ground-water systems. This guide describes techniques that can be used in defining boundary conditions and their appropriate application for modeling saturated ground-water flow model simulations.
1.2 This guide is one of a series of standards on ground-water flow model applications. Defining boundary conditions is a step in the design and construction of a model that is treated generally in Guide D 5447.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
1.4 This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. 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 replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word "Standard" in the title of this document means only that the document has been approved through the ASTM consensus process.
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Designation: D 5609 – 94 (Reapproved 2002)
Standard Guide for
Defining Boundary Conditions in Ground-Water Flow
Modeling
This standard is issued under the fixed designation D 5609; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 3. Terminology
1.1 This guide covers the specification of appropriate 3.1 Definitions:
boundary conditions that are an essential part of conceptualiz- 3.1.1 aquifer, confined—an aquifer bounded above and
ing and modeling ground-water systems. This guide describes below by confining beds and in which the static head is above
techniques that can be used in defining boundary conditions the top of the aquifer.
and their appropriate application for modeling saturated 3.1.2 boundary—geometrical configuration of the surface
ground-water flow model simulations. enclosing the model domain.
1.2 This guide is one of a series of standards on ground- 3.1.3 boundary condition—a mathematical expression of
water flow model applications. Defining boundary conditions the state of the physical system that constrains the equations of
is a step in the design and construction of a model that is the mathematical model.
treated generally in Guide D 5447. 3.1.4 conceptual model—a simplified representation of the
1.3 This standard does not purport to address all of the hydrogeologic setting and the response of the flow system to
safety concerns, if any, associated with its use. It is the stress.
responsibility of the user of this standard to establish appro- 3.1.5 flux—the volume of fluid crossing a unit cross-
priate safety and health practices and determine the applica- sectional surface area per unit time.
bility of regulatory limitations prior to use. 3.1.6 ground-water flow model—an application of a math-
1.4 This guide offers an organized collection of information ematicalmodeltothesolutionofaground-waterflowproblem.
or a series of options and does not recommend a specific 3.1.7 hydraulic conductivity—(field aquifer tests), the vol-
course of action. This document cannot replace education or ume of water at the existing kinematic viscosity that will move
experience and should be used in conjunction with professional in a unit time under unit hydraulic gradient through a unit area
judgment. Not all aspects of this guide may be applicable in all measured at right angles to the direction of flow.
circumstances. This ASTM standard is not intended to repre- 3.1.8 hydrologic condition—a set of ground-water inflows
sent or replace the standard of care by which the adequacy of or outflows, boundary conditions, and hydraulic properties that
a given professional service must be judged, nor should this cause potentiometric heads to adopt a distinct pattern.
document be applied without consideration of a project’s many 3.1.9 simulation—one complete execution of the computer
unique aspects. The word “Standard” in the title of this program, including input and output.
document means only that the document has been approved 3.1.10 transmissivity—the volume of water at the existing
through the ASTM consensus process. kinematic viscosity that will move in a unit time under a unit
hydraulic gradient through a unit width of the aquifer.
2. Referenced Documents
3.1.11 unconfined aquifer—anaquiferthathasawatertable.
2.1 ASTM Standards: 3.1.12 For definitions of other terms used in this test
D 653 Terminology Relating to Soil, Rock, and Contained
method, see Terminology D 653.
Fluids
4. Significance and Use
D 5447 Guide for Application of a Ground-Water Flow
Model to a Site-Specific Problem 4.1 Accurate definition of boundary conditions is an essen-
tial part of conceptualizing and modeling ground-water flow
systems. This guide describes the properties of the most
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
common boundary conditions encountered in ground-water
and is the direct responsibility of Subcommittee D18.21 on Ground Water and
systems and discusses major aspects of their definition and
Vadose Zone Investigations.
Current edition approved Sept. 15, 1994. Published October 1994.
application in ground-water models. It also discusses the
Annual Book of ASTM Standards, Vol 04.08.
significance and specification of boundary conditions for some
Annual Book of ASTM Standards, Vol 04.09.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5609
field situations and some common errors in specifying bound- 5.2.2.1 No Flow or Streamline Boundary—The no-flow or
ary conditions in ground-water models. streamline boundary is a special case of the specified flux
boundary. A streamline is a curve that is tangent to the
5. Types of Boundaries
flow-velocity vector at every point along its length; thus no
5.1 The flow of ground water is described in the general
flow crosses a streamline. An example of a no-flow boundary
case by partial differential equations. Quantitative modeling of
is an impermeable boundary. Natural earth materials are never
a ground-water system entails the solution of those equations
impermeable. However, they may sometimes be regarded as
subject to site-specific boundary conditions.
effectively impermeable for modeling purposes if the hydraulic
5.2 Types of Modeled Boundary Conditions—Flow model
conductivities of the adjacent materials differ by orders of
boundary conditions can be classified as specified head or
magnitude. Ground-water divides are normal to streamlines
Dirichlet, specified flux or Neumann, a combination of speci-
and are also no-flow boundaries. However, the ground-water
fied head and flux, or Cauchy, free surface boundary, and
divide does not intrinsically correspond to physical or hydrau-
seepage-face. Each of these types of boundaries and some of
lic properties of the aquifer. The position of a ground-water
their variations are discussed below.
divide is a function of the response of the aquifer system to
5.2.1 Specified Head, or Dirichlet, Boundary Type—A
hydrologic conditions and may be subject to change with
specified head boundary is one in which the head can be
changingconditions.Theuseofground-waterdividesasmodel
specified as a function of position and time over a part of the
boundaries may produce invalid results.
boundary surface of the ground-water system. A boundary of
5.2.3 Head Dependent Flux, or Cauchy Type—In some
specified head may be the general type of specified head
situations,fluxacrossapartoftheboundarysurfacechangesin
boundary in which the head may vary with time or position
response to changes in head within the aquifer adjacent to the
over the surface of the boundary, or both, or the constant-head
boundary. In these situations, the flux is a specified function of
boundary in which the head is constant in time, but head may
thatheadandvariesduringproblemsolutionastheheadvaries.
differ in position, over the surface of the boundary. These two
NOTE 1—An example of this type of boundary is the upper surface of
types of specified head boundaries are discussed below.
an aquifer overlain by a confining bed that is in turn overlain by a body
5.2.1.1 General Specified-Head Boundary—The general
of surface water. In this example, as in most head-dependent boundary
type of specified-head boundary condition occurs wherever
situations, a practical limit exists beyond which changes in head cease to
head can be specified as a function of position and time over a
causeachangeinflux.Inthisexample,thelimitwillbereachedwherethe
part of the boundary surface of a ground-water system. An
headwithintheaquiferfallsbelowthetopoftheaquifersothattheaquifer
example of the simplest type might be an aquifer that is is no longer confined at that point, but is under an unconfined or
water-table condition, while the confining bed above remains saturated.
exposed along the bottom of a large stream whose stage is
Under these conditions, the bottom of the confining bed becomes locally
independent of ground-water seepage.As one moves upstream
a seepage face. Thus as the head in the aquifer is drawn down further, the
or downstream, the head changes in relation to the slope of the
hydraulicgradientdoesnotincreaseandthefluxthroughtheconfiningbed
stream channel and the head varies with time as a function of
remains constant. In this hypothetical case, the flux through the confining
stream flow. Heads along the stream bed are specified accord-
bed increases linearly as the head in the aquifer declines until the head
ing to circumstances external to the ground-water system and
reaches the level of the base of the confining bed after which the flux
maintain these specified values throughout the problem solu- remains constant. Another example of a head dependent boundary with a
similar behavior is evapotranspiration from the water table, where the flux
tion, regardless of changes within the ground-water system.
from the water table is often modeled as decreasing linearly with depth to
5.2.1.2 Constant-Head Boundary—A constant head bound-
water and becomes zero where the water table reaches some specified
ary is boundary in which the aquifer system coincides with a
“cutoff” depth.
surface of unchanging head through time. An example is an
5.2.4 Free-Surface Boundary Type—A free-surface bound-
aquifer that is bordered by a lake in which the surface-water
ary is a moveable boundary where the head is equal to the
stage is constant over all points of the boundary in time and
elevation of the boundary. The most common free-surface
position or an aquifer that is bordered by a stream of constant
boundary is the water table, which is the boundary surface
flow that is unchanging in head with time but differs in head
between the saturated flow field and the atmosphere (capillary
with position.
zone not considered). An important characteristic of this
5.2.2 Specified Flux or Neumann Boundary Type—Aspeci-
boundaryisthatitspositionisnotfixed;thatisitspositionmay
fied flux boundary is one for which the flux across the
rise and fall with time. In some problems, for example, flow
boundary surface can be specified as a function of position and
through an earth dam, the position of the free surface is not
time. In the simplest type of specified-flux boundary, the flux
known before but must be found as part of the problem
across a
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