ASTM D5609-94(2008)
(Guide)Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
SIGNIFICANCE AND USE
Accurate definition of boundary conditions is an essential part of conceptualizing and modeling groundwater flow systems. This guide describes the properties of the most common boundary conditions encountered in groundwater systems and discusses major aspects of their definition and application in groundwater models. It also discusses the significance and specification of boundary conditions for some field situations and some common errors in specifying boundary conditions in groundwater models.
SCOPE
1.1 This guide covers the specification of appropriate boundary conditions that are an essential part of conceptualizing and modeling groundwater systems. This guide describes techniques that can be used in defining boundary conditions and their appropriate application for modeling saturated groundwater flow model simulations.
1.2 This guide is one of a series of standards on groundwater flow model applications. Defining boundary conditions is a step in the design and construction of a model that is treated generally in Guide D5447.
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:D5609 −94(Reapproved 2008)
Standard Guide for
Defining Boundary Conditions in Groundwater Flow
Modeling
This standard is issued under the fixed designation D5609; 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 (´) indicates an editorial change since the last revision or reapproval.
1. Scope D5447 Guide forApplication of a Groundwater Flow Model
to a Site-Specific Problem
1.1 This guide covers the specification of appropriate
boundary conditions that are an essential part of conceptualiz-
3. Terminology
ing and modeling groundwater systems. This guide describes
3.1 Definitions:
techniques that can be used in defining boundary conditions
3.1.1 aquifer, confined—an aquifer bounded above and be-
and their appropriate application for modeling saturated
low by confining beds and in which the static head is above the
groundwater flow model simulations.
top of the aquifer.
1.2 This guide is one of a series of standards on groundwa-
3.1.2 boundary—geometrical configuration of the surface
ter flow model applications. Defining boundary conditions is a
enclosing the model domain.
step in the design and construction of a model that is treated
3.1.3 boundary condition—a mathematical expression of
generally in Guide D5447.
the state of the physical system that constrains the equations of
1.3 This standard does not purport to address all of the
the mathematical model.
safety concerns, if any, associated with its use. It is the
3.1.4 conceptual model—a simplified representation of the
responsibility of the user of this standard to establish appro-
hydrogeologic setting and the response of the flow system to
priate safety and health practices and determine the applica-
stress.
bility of regulatory limitations prior to use.
1.4 This guide offers an organized collection of information 3.1.5 flux—the volume of fluid crossing a unit cross-
or a series of options and does not recommend a specific
sectional surface area per unit time.
course of action. This document cannot replace education or
3.1.6 groundwater flow model—an application of a math-
experience and should be used in conjunction with professional
ematical model to the solution of a groundwater flow problem.
judgment. Not all aspects of this guide may be applicable in all
3.1.7 hydraulic conductivity—(field aquifer tests), the vol-
circumstances. This ASTM standard is not intended to repre-
ume of water at the existing kinematic viscosity that will move
sent or replace the standard of care by which the adequacy of
in a unit time under unit hydraulic gradient through a unit area
a given professional service must be judged, nor should this
measured at right angles to the direction of flow.
document be applied without consideration of a project’s many
3.1.8 hydrologic condition—a set of groundwater inflows or
unique aspects. The word “Standard” in the title of this
outflows, boundary conditions, and hydraulic properties that
document means only that the document has been approved
cause potentiometric heads to adopt a distinct pattern.
through the ASTM consensus process.
3.1.9 simulation—one complete execution of the computer
2. Referenced Documents
program, including input and output.
2.1 ASTM Standards:
3.1.10 transmissivity—the volume of water at the existing
D653 Terminology Relating to Soil, Rock, and Contained
kinematic viscosity that will move in a unit time under a unit
Fluids
hydraulic gradient through a unit width of the aquifer.
3.1.11 unconfined aquifer—anaquiferthathasawatertable.
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock
and is the direct responsibility of Subcommittee D18.21 on Groundwater and
3.1.12 For definitions of other terms used in this test
Vadose Zone Investigations.
method, see Terminology D653.
Current edition approved Sept. 15, 2008. Published October 2008. Originally
approved in 1994. Last previous edition approved in 2002 as D5609 – 94 (2002).
4. Significance and Use
DOI: 10.1520/D5609-94R08.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
4.1 Accurate definition of boundary conditions is an essen-
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
tial part of conceptualizing and modeling groundwater flow
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. systems. This guide describes the properties of the most
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D5609−94 (2008)
common boundary conditions encountered in groundwater specified flux boundaries, the flux is specified according to
systems and discusses major aspects of their definition and circumstances external to the groundwater flow system and the
application in groundwater models. It also discusses the specified flux values are maintained throughout the problem
significance and specification of boundary conditions for some solution regardless of changes within the groundwater flow
field situations and some common errors in specifying bound- system.
ary conditions in groundwater models. 5.2.2.1 No Flow or Streamline Boundary—The no-flow or
streamline boundary is a special case of the specified flux
5. Types of Boundaries boundary. A streamline is a curve that is tangent to the
flow-velocity vector at every point along its length; thus no
5.1 Theflowofgroundwaterisdescribedinthegeneralcase
flow crosses a streamline. An example of a no-flow boundary
by partial differential equations. Quantitative modeling of a
is an impermeable boundary. Natural earth materials are never
groundwater system entails the solution of those equations
impermeable. However, they may sometimes be regarded as
subject to site-specific boundary conditions.
effectivelyimpermeableformodelingpurposesifthehydraulic
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. Groundwater divides are normal to streamlines and
Dirichlet, specified flux or Neumann, a combination of speci-
are also no-flow boundaries. However, the groundwater divide
fied head and flux, or Cauchy, free surface boundary, and
does not intrinsically correspond to physical or hydraulic
seepage-face. Each of these types of boundaries and some of
properties of the aquifer. The position of a groundwater divide
their variations are discussed below.
isafunctionoftheresponseoftheaquifersystemtohydrologic
5.2.1 Specified Head, or Dirichlet, Boundary Type—A
conditions and may be subject to change with changing
specified head boundary is one in which the head can be
conditions. The use of groundwater divides as model bound-
specified as a function of position and time over a part of the
aries may produce invalid results.
boundary surface of the groundwater 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
headwithintheaquiferfallsbelowthetopoftheaquifersothattheaquifer
part of the boundary surface of a groundwater system. An
is no longer confined at that point, but is under an unconfined or
example of the simplest type might be an aquifer that is
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 groundwater 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
remains constant. In this hypothetical case, the flux through the confining
stream channel and the head varies with time as a function of
bed increases linearly as the head in the aquifer declines until the head
stream flow. Heads along the stream bed are specified accord-
reaches the level of the base of the confining bed after which the flux
ing to circumstances external to the groundwater system and
remains constant. Another example of a head dependent boundary with a
maintain these specified values throughout the problem solu-
similar behavior is evapotranspiration from the water table, where the flux
tion, regardless of changes within the groundwater system. from the water table is often modeled as decreasing linearly with depth to
water and becomes zero where the water table reaches some specified
5.2.1.2 Constant-Head Boundary—A constant head bound-
“cutoff” depth.
ary is boundary in which the aquifer system coincides with a
surface of unchanging head through time. An example is an 5.2.4 Free-Surface Boundary Type—A free-surface bound-
ary is a moveable boundary where the head is equal to the
aquifer that is bordered by a lake in which the surface-water
stage is constant over all points of the boundary in time and elevation of the boundary. The most common free-surface
boundary is the water table, which is the boundary surface
position or an aquifer that is bordered by a stream of constant
flow that is unchanging in head with time but differs in head between the saturated flow field and the atmosphere (capillary
zone not considered). An important characteristic of this
with position.
5.2.2 Specified Flux or Neumann Boundary Type—A speci- boundaryisthatitspositionisnotfixed;thatisitspositionmay
rise and fall with time. In some problems, for ex
...
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