ASTM D5609-94(2015)e1

Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling

SIGNIFICANCE AND USE
4.1 Accurate definition of boundary conditions is an important 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 to be considered 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.

General Information

• Status: Historical
• Publication Date: 14-Sep-2008
• ICS: 07.060 - Geology. Meteorology. Hydrology
• ICS: 13.060.10 - Water of natural resources
• Technical Committee: D18 - Soil and Rock
• Drafting Committee: D18.21 - Groundwater and Vadose Zone Investigations

Relations

• Replaces: ASTM D5609-94(2008) - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 15-Sep-2008
• Replaced By: ASTM D5609-16 - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 01-Mar-2016
• Referred By: ASTM D6170-17 - Standard Guide for Selecting a Groundwater Modeling Code
• Effective Date: 15-Sep-2008
• Referred By: ASTM D5981/D5981M-18 - Standard Guide for Calibrating a Groundwater Flow Model Application
• Effective Date: 15-Sep-2008
• Referred By: ASTM D5447-17 - Standard Guide for Application of a Numerical Groundwater Flow Model to a Site-Specific Problem
• Effective Date: 15-Sep-2008
• Referred By: ASTM D6033-16 - Standard Guide for Describing the Functionality of a Groundwater Modeling Code
• Effective Date: 15-Sep-2008
• Referred By: ASTM D6000/D6000M-15e1 - Standard Guide for Presentation of Water-Level Information from Groundwater Sites (Withdrawn 2024)
• Effective Date: 15-Sep-2008
• Referred By: ASTM D5979-96(2019)e1 - Standard Guide for Conceptualization and Characterization of Groundwater Systems
• Effective Date: 15-Sep-2008

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation:D5609 −94(Reapproved 2015)
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.
ε NOTE—Reapproved with editorial changes in September 2015.
1. Scope* 2. Referenced Documents
2.1 ASTM Standards:
1.1 This guide covers the specification of appropriate
D653 Terminology Relating to Soil, Rock, and Contained
boundary conditions that are to be considered part of concep-
Fluids
tualizing and modeling groundwater systems. This guide de-
D5447 Guide forApplication of a Groundwater Flow Model
scribes techniques that can be used in defining boundary
to a Site-Specific Problem
conditions and their appropriate application for modeling
saturated groundwater flow model simulations.
3. Terminology
1.2 This guide is one of a series of standards on groundwa-
3.1 For common definitions of terms in this standard, refer
ter flow model applications. Defining boundary conditions is a
to Terminology D653.
step in the design and construction of a model that is treated
3.2 Definitions of Terms Specific to This Standard:
generally in Guide D5447.
3.2.1 aquifer, confined—an aquifer bounded above and be-
1.3 This standard does not purport to address all of the low by confining beds and in which the static head is above the
top of the aquifer.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
3.2.2 boundary—geometrical configuration of the surface
priate safety and health practices and determine the applica-
enclosing the model domain.
bility of regulatory limitations prior to use.
3.2.3 boundary condition—a mathematical expression of
1.4 This guide offers an organized collection of information
the state of the physical system that constrains the equations of
or a series of options and does not recommend a specific
the mathematical model.
course of action. This document cannot replace education or
3.2.4 conceptual model—a simplified representation of the
experience and should be used in conjunction with professional
hydrogeologic setting and the response of the flow system to
judgment. Not all aspects of this guide may be applicable in all
stress.
circumstances. This ASTM standard is not intended to repre-
3.2.5 flux—the volume of fluid crossing a unit cross-
sent or replace the standard of care by which the adequacy of
sectional surface area per unit time.
a given professional service must be judged, nor should this
3.2.6 groundwater flow model—an application of a math-
document be applied without consideration of a project’s many
ematical model to the solution of a groundwater flow problem.
unique aspects. The word “Standard” in the title of this
3.2.7 hydraulic conductivity—(field aquifer tests), the vol-
document means only that the document has been approved
ume of water at the existing kinematic viscosity that will move
through the ASTM consensus process.
in a unit time under unit hydraulic gradient through a unit area
measured at right angles to the direction of flow.
3.2.8 hydrologic condition—a set of groundwater inflows or
outflows, boundary conditions, and hydraulic properties that
cause potentiometric heads to adopt a distinct pattern.
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
Vadose Zone Investigations. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Sept. 15, 2008. Published October 2015. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1994. Last previous edition approved in 2008 as D5609 – 94 (2008). Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/D5609-94R15E01. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
D5609−94 (2015)
3.2.9 simulation—one complete execution of the computer position or an aquifer that is bordered by a stream of constant
program, including input and output. flow that is unchanging in head with time but differs in head
with position.
3.2.10 transmissivity—the volume of water at the existing
5.2.2 Specified Flux or Neumann Boundary Type—A speci-
kinematic viscosity that will move in a unit time under a unit
fied flux boundary is one for which the flux across the
hydraulic gradient through a unit width of the aquifer.
boundary surface can be specified as a function of position and
3.2.11 unconfined aquifer—anaquiferthathasawatertable.
time. In the simplest type of specified-flux boundary, the flux
across a given part of the boundary surface is considered
4. Significance and Use
uniform in space and constant with time. In a more general
4.1 Accurate definition of boundary conditions is an impor-
case, the flux might be constant with time but specified as a
tant part of conceptualizing and modeling groundwater flow
function of position. In the most general case, flux is specified
systems. This guide describes the properties of the most
as a function of time as well as position. In all cases of
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
part of the boundary surface of a groundwater system. An headwithintheaquiferfallsbelowthetopoftheaquifersothattheaquifer
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
similar behavior is evapotranspiration from the water table, where the flux
solution, 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-
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-surf
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation: D5609 − 94 (Reapproved 2008) D5609 − 94 (Reapproved 2015)
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.
ε NOTE—Reapproved with editorial changes in September 2015.
1. Scope Scope*
1.1 This guide covers the specification of appropriate boundary conditions that are an essential to be considered 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.
2. Referenced Documents
2.1 ASTM Standards:
D653 Terminology Relating to Soil, Rock, and Contained Fluids
D5447 Guide for Application of a Groundwater Flow Model to a Site-Specific Problem
3. Terminology
3.1 For common definitions of terms in this standard, refer to Terminology D653.
3.2 Definitions:Definitions of Terms Specific to This Standard:
3.2.1 aquifer, confined—an aquifer bounded above and below by confining beds and in which the static head is above the top
of the aquifer.
3.2.2 boundary—geometrical configuration of the surface enclosing the model domain.
3.2.3 boundary condition—a mathematical expression of the state of the physical system that constrains the equations of the
mathematical model.
3.2.4 conceptual model—a simplified representation of the hydrogeologic setting and the response of the flow system to stress.
3.2.5 flux—the volume of fluid crossing a unit cross-sectional surface area per unit time.
3.2.6 groundwater flow model—an application of a mathematical model to the solution of a groundwater flow problem.
This guide is under the jurisdiction of ASTM Committee D18 on Soil and Rock and is the direct responsibility of Subcommittee D18.21 on Groundwater and Vadose
Zone Investigations.
Current edition approved Sept. 15, 2008. Published October 2008October 2015. Originally approved in 1994. Last previous edition approved in 20022008 as D5609 – 94
(2008). (2002). DOI: 10.1520/D5609-94R08.10.1520/D5609-94R15E01.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
D5609 − 94 (2015)
3.2.7 hydraulic conductivity—(field aquifer tests), the volume of water at the existing kinematic viscosity that will move in a
unit time under unit hydraulic gradient through a unit area measured at right angles to the direction of flow.
3.2.8 hydrologic condition—a set of groundwater inflows or outflows, boundary conditions, and hydraulic properties that cause
potentiometric heads to adopt a distinct pattern.
3.2.9 simulation—one complete execution of the computer program, including input and output.
3.2.10 transmissivity—the volume of water at the existing kinematic viscosity that will move in a unit time under a unit
hydraulic gradient through a unit width of the aquifer.
3.2.11 unconfined aquifer—an aquifer that has a water table.
3.1.12 For definitions of other terms used in this test method, see Terminology D653.
4. Significance and Use
4.1 Accurate definition of boundary conditions is an essentialimportant 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.
5. Types of Boundaries
5.1 The flow of groundwater is described in the general case by partial differential equations. Quantitative modeling of a
groundwater system entails the solution of those equations subject to site-specific boundary conditions.
5.2 Types of Modeled Boundary Conditions—Flow model boundary conditions can be classified as specified head or Dirichlet,
specified flux or Neumann, a combination of specified head and flux, or Cauchy, free surface boundary, and seepage-face. Each
of these types of boundaries and some of their variations are discussed below.
5.2.1 Specified Head, or Dirichlet, Boundary Type—A specified head boundary is one in which the head can be specified as a
function of position and time over a part of the boundary surface of the groundwater system. A boundary of specified head may
be the general type of specified head boundary in which the head may vary with time or position over the surface of the boundary,
or both, or the constant-head boundary in which the head is constant in time, but head may differ in position, over the surface of
the boundary. These two types of specified head boundaries are discussed below.
5.2.1.1 General Specified-Head Boundary—The general type of specified-head boundary condition occurs wherever head can
be specified as a function of position and time over a part of the boundary surface of a groundwater system. An example of the
simplest type might be an aquifer that is exposed along the bottom of a large stream whose stage is independent of groundwater
seepage. As one moves upstream or downstream, the head changes in relation to the slope of the stream channel and the head varies
with time as a function of stream flow. Heads along the stream bed are specified according to circumstances external to the
groundwater system and maintain these specified values throughout the problem solution, regardless of changes within the
groundwater system.
5.2.1.2 Constant-Head Boundary—A constant head boundary is boundary in which the aquifer system coincides with a surface
of unchanging head through time. An example is an aquifer that is bordered by a lake in which the surface-water stage is constant
over all points of the boundary in time and position or an aquifer that is bordered by a stream of constant flow that is unchanging
in head with time but differs in head with position.
5.2.2 Specified Flux or Neumann Boundary Type—A specified flux boundary is one for which the flux across the boundary
surface can be specified as a function of position and time. In the simplest type of specified-flux boundary, the flux across a given
part of the boundary surface is considered uniform in space and constant with time. In a more general case, the flux might be
constant with time but specified as a function of position. In the most general case, flux is specified as a function of time as well
as position. In all cases of specified flux boundaries, the flux is specified according to circumstances external to the groundwater
flow system and the specified flux values are maintained throughout the problem solution regardless of changes within the
groundwater flow system.
5.2.2.1 No Flow or Streamline Boundary—The no-flow or streamline boundary is a special case of the specified flux boundary.
A streamline is a curve that is tangent to the flow-velocity vector at every point along its length; thus no flow crosses a streamline.
An example of a no-flow boundary is an impermeable boundary. Natural earth materials are never impermeable. However, they
may sometimes be regarded as effectively impermeable for modeling purposes if the hydraulic conductivities of the adjacent
materials differ by orders of magnitude. Groundwater divides are normal to streamlines and are also no-flow boundaries. However,
the groundwater divide does not intrinsically correspond to physical or hydraulic properties of the aquifer. The position of a
groundwater divide is a function of the response of the aquifer system to hydrologic conditions and may be subject to change with
changing conditions. The use of groundwater divides as model boundaries may produce invalid results.
5.2.3 Head Dependent Flux, or Cauchy Type—In some situations, flux across a part of the boundary surface changes in response
to changes in head within the aquifer adjacent to the boundary. In these situations, the flux is a specified function of that head and
varies during problem solution as the head varies.
´1
D5609 − 94 (2015)
NOTE 1—An example of this type of boundary is the upper surface of an aquifer overlain by a confining bed that is in turn overlain by a body of surface
water. In this example, as in most head-dependent boundary situations, a practical limit exists beyond which changes in head cease to cause a change
in flux. In this example, the limit will be reached where the head within the aquifer falls below the top of the aquifer so that the aquifer is no longer
confined at that point, but is under an unconfined or water-table condition, while the confining bed above remains saturated. Under these conditions, the
bottom of the confining bed becomes locally a seepage face. Thus as the head in the aquifer is drawn down further, the hydraulic gradient does not increase
and the flux through the confining bed remains constant. In this hypothetical case, the flux through the confining bed increases linearly as the head in
the aquifer declines until the head reaches the level of the base of the confining bed after which the flux remains constant. Another example of a head
dependent boundary with a similar behavior is evapotranspiration from the water table, where the flux from the water table is often modeled as decreasing
linearly with depth to water and becomes zero where the water table reaches some specified “cutoff” depth.
5.2.4 Free-Surface Boundary Type—A free-surface boundary is a moveable boundary where the head is equal to the elevation
of the boundary. The most common free-surface boundary is the water table, which is the boundary surface between the saturated
flow field and the atmosphere (capillary zone not considered). An important characteristic of this boundary is that its position is
not fixed; that is its position may rise and fall with time. In some problems, for example, flow through an earth dam, the position
of the free surface is not known before but must be found as part of the problem solution.
5.2.4.1 Another example of a free surface boundary is the transition between freshwater and underlying seawater in a coastal
aquifer. If diffusion is neglected and the salty groundwater seaward of the interface is assumed to be static, the freshwater-saltwater
transition zone can be treated as a sharp interface 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 the interface varies only with the elevation and
the freshwater head at any point on this idealized stream-surface boundary is thus a linear function of the elevation head of that
point.
5.2.5 Seepage-Face Boundary Type—A surface of seepage is a boundary between the saturated flow field and the atmosphere
along which groundwater discharges, either by evaporation or movement “downhill” along the land surface as a thin film in
response to the force of gravity. The location of this type of boundary is generally fixed, but its length is dependent upon other
system boundaries. A seepage surface is always associated with a free surface boundary. Seepage faces are commonly neglected
in models of large aquifer systems because their effect is often insignificant at a regional scale of problem definition. However,
in problems defined over a smaller area, which require more accurate system definition, they must be considered.
6. Procedure
6.1 The definition of boundary conditions of a model is a part of the application of a model to a site-specific problem (see Guide
D5447). The steps in boundary definition may be stated as follows:
6.1.1 Identification of the physical boundaries of the flow system boundaries,
6.1.2 Formulation of the mathematical representation of the boundaries,
6.1.3 Examination andReview of sensitivity testing of boundary conditions that change when the system is under stress, that is,
stress-dependent boundaries, and
6.1.4 Revision and finalof the formulation of the initial model boundary representation.
6.1.5 Further examination,evaluation, testing, and refinement of the model boundaries is a part of the verification and validation
process of the application of each model and is discussed in Guide D5447.
6.2 Boundary Identification—Identify as accurately as possible the physical boundaries of the flow system. The three-
dimensional bounding surfaces of the flow system must be defined even if the model is to be represented by a two-dimensional
model. Even if the lateral boundaries are distant from the region of primary interest, it is important to understand the location and
hydraulic conditions on the boundaries of the flow system.
6.2.1 Groundwater Divides—Groundwater divides have been chosen as boundari
...