ASTM D5609-16

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: Published
• Publication Date: 29-Feb-2016
• 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(2015)e1 - Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling
• Effective Date: 01-Mar-2016
• Refers: ASTM D653-14 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2014
• Refers: ASTM D653-11 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Sep-2011
• Refers: ASTM D5447-04(2010) - Standard Guide for Application of a Groundwater Flow Model to a Site-Specific Problem
• Effective Date: 01-Aug-2010
• Refers: ASTM D653-09 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jan-2009
• Refers: ASTM D653-08a - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Dec-2008
• Refers: ASTM D653-08 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2008
• Refers: ASTM D653-07f - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 15-Dec-2007
• Refers: ASTM D653-07e - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2007
• Refers: ASTM D653-07d - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Aug-2007
• Refers: ASTM D653-07c - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jul-2007
• Refers: ASTM D653-07b - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-May-2007
• Refers: ASTM D653-06 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Nov-2006
• Refers: ASTM D653-05 - Standard Terminology Relating to Soil, Rock, and Contained Fluids
• Effective Date: 01-Jul-2005
• Refers: ASTM D5447-04 - Standard Guide for Application of a Ground-Water Flow Model to a Site-Specific Problem
• Effective Date: 01-Nov-2004

Overview

ASTM D5609-16, Standard Guide for Defining Boundary Conditions in Groundwater Flow Modeling, provides comprehensive guidance on specifying appropriate boundary conditions as part of conceptualizing and modeling groundwater systems. Recognizing that accurate boundary condition definition is fundamental to effective groundwater modeling, this standard outlines the most common types of boundary conditions, discusses their properties, and describes methods for their implementation in groundwater flow models. Proper application of this guide aids in enhancing the reliability and validity of modeling results, thereby supporting robust hydrogeological analysis for site-specific and regional projects.

Key Topics

• Types of Boundary Conditions: The standard categorizes boundary conditions commonly encountered in groundwater modeling, such as:
  • Specified Head (Dirichlet): Where the hydraulic head is set as a known value, constant or time-varying.
  • Specified Flux (Neumann): Where the groundwater flux across the model boundary is specified.
  • Head Dependent Flux (Cauchy): Boundaries where flux varies as a function of head, integrating both specified head and flux characteristics.
  • Free Surface Boundaries: Such as the water table, which may rise or fall in response to system changes.
  • Seepage-Face Boundaries: Where groundwater discharges to the land surface or atmosphere.
• Boundary Identification and Representation: Guidance is provided on identifying natural and model boundaries, including groundwater divides, water tables, and interactions with surface water bodies.
• Stress-Dependency: Emphasizes the need to assess if boundary conditions will change in response to imposed stresses (e.g., pumping, climatic shifts) and the importance of sensitivity analysis.
• Documentation: Calls for thorough reporting and justification of boundary condition selections, including a description of natural boundaries, processes, model representation, and sensitivity analyses.

Applications

ASTM D5609-16 is widely used in the design, construction, and verification of groundwater flow models. Its practical applications include:

• Environmental Site Assessment: Supporting the development of accurate groundwater models for contaminated site investigations.
• Water Resource Management: Assisting in delineating aquifer boundaries for sustainable extraction, recharge assessment, or regional water budgeting.
• Engineering Projects: Providing foundational methodology for groundwater flow modeling in construction, mining, and infrastructure projects where groundwater impacts need to be anticipated and controlled.
• Regulatory Compliance: Aiding consultants and regulators in ensuring that groundwater models used for permitting or impact assessment are based on sound scientific principles.
• Sensitivity Analysis: Facilitating evaluation of model robustness through sensitivity testing of boundary assumptions to anticipated or extreme system stresses.

Accurate boundary condition specification, as outlined in ASTM D5609-16, is vital for reliable prediction of groundwater flows, contaminant transport, and aquifer responses under both natural and stressed conditions.

Related Standards

• ASTM D5447: Guide for Application of a Groundwater Flow Model to a Site-Specific Problem - addresses broader aspects of groundwater modeling, including the integration of boundary condition definition as part of the modeling workflow.
• ASTM D653: Terminology Relating to Soil, Rock, and Contained Fluids - provides essential definitions of terms used in groundwater modeling and boundary condition specification.
• International Standards: This ASTM standard is aligned with the principles established by the World Trade Organization Technical Barriers to Trade (TBT) Committee, facilitating consistency with global best practices in groundwater modeling.

By adhering to ASTM D5609-16, users can ensure their groundwater flow models are constructed with scientifically defensible boundary conditions, enhancing their utility for environmental, engineering, and regulatory applications.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation:D5609 −16
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 to be considered part of concep-
3. Terminology
tualizing and modeling groundwater systems. This guide de-
3.1 For common definitions of terms in this standard, refer
scribes techniques that can be used in defining boundary
to Terminology D653.
conditions and their appropriate application for modeling
saturated groundwater flow model simulations.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 confined aquifer—in hydrogeology, an aquifer
1.2 This guide is one of a series of standards on groundwa-
bounded above and below by confining beds and in which the
ter flow model applications. Defining boundary conditions is a
static head is above the top of the aquifer
step in the design and construction of a model that is treated
generally in Guide D5447. 3.2.2 boundary—in hydrogeology, the geometrical configu-
ration of the surface enclosing the model domain.
1.3 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the 3.2.3 boundary condition—in hydrogeology,amathematical
responsibility of the user of this standard to establish appro- expression of the state of the physical system that constrains
priate safety and health practices and determine the applica- the equations of the mathematical model.
bility of regulatory limitations prior to use.
3.2.4 flux—in hydrogeology, the volume of fluid crossing a
1.4 This guide offers an organized collection of information
unit cross-sectional surface area per unit time.
or a series of options and does not recommend a specific
3.2.5 groundwater flow model—in groundwater hydraulics,
course of action. This document cannot replace education or
an application of a mathematical model to the solution of a
experience and should be used in conjunction with professional
groundwater flow problem.
judgment. Not all aspects of this guide may be applicable in all
3.2.6 hydrologic condition—in groundwater hydraulics,a
circumstances. This ASTM standard is not intended to repre-
set of groundwater inflows or outflows, boundary conditions,
sent or replace the standard of care by which the adequacy of
and hydraulic properties that cause potentiometric heads to
a given professional service must be judged, nor should this
adopt a distinct pattern.
document be applied without consideration of a project’s many
unique aspects. The word “Standard” in the title of this
4. Significance and Use
document means only that the document has been approved
4.1 Accurate definition of boundary conditions is an impor-
through the ASTM consensus process.
tant part of conceptualizing and modeling groundwater flow
2. Referenced Documents
systems. This guide describes the properties of the most
2.1 ASTM Standards: common boundary conditions encountered in groundwater
systems and discusses major aspects of their definition and
D653 Terminology Relating to Soil, Rock, and Contained
Fluids application in groundwater models. It also discusses the
significance and specification of boundary conditions for some
This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rock field situations and some common errors in specifying bound-
and is the direct responsibility of Subcommittee D18.21 on Groundwater and
ary conditions in groundwater models.
Vadose Zone Investigations.
Current edition approved March 1, 2016. Published March 2016. Originally
5. Types of Boundaries
ɛ1
approved in 1994. Last previous edition approved in 2015 as D5609 – 94 (2015) .
DOI: 10.1520/D5609-16.
5.1 Theflowofgroundwaterisdescribedinthegeneralcase
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
by partial differential equations. Quantitative modeling of a
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
groundwater system entails the solution of those equations
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. subject to site-specific boundary conditions.
*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
D5609−16
5.2 Types of Modeled Boundary Conditions—Flow model effectivelyimpermeableformodelingpurposesifthehydraulic
boundary conditions can be classified as specified head or conductivities of the adjacent materials differ by orders of
Dirichlet, specified flux or Neumann, a combination of speci- magnitude. Groundwater divides are normal to streamlines and
fied head and flux, or Cauchy, free surface boundary, and are also no-flow boundaries. However, the groundwater divide
seepage-face. Each of these types of boundaries and some of does not intrinsically correspond to physical or hydraulic
their variations are discussed below. properties of the aquifer. The position of a groundwater divide
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
types of specified head boundaries are discussed below.
NOTE 1—An example of this type of boundary is the upper surface of
5.2.1.1 General Specified-Head Boundary—The general 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
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
example of the simplest type might be an aquifer that is
is no longer confined at that point, but is under an unconfined or
exposed along the bottom of a large stream whose stage is water-table condition, while the confining bed above remains saturated.
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
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 groundwater system and 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
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
5.2.1.2 Constant-Head Boundary—A constant head bound-
water and becomes zero where the water table reaches some specified
“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-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—A speci- 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 given part of the boundary surface is considered solution.
uniform in space and constant with time. In a more general
5.2.4.1 Another example of a free surface boundary is the
case, the flux might be constant with time but specified as a
transition between freshwater and underlying seawater in a
function of position. In the most general case, flux is specified
coastal aquifer. If diffusion is neglected and the salty ground-
as a function of time as well as position. In all cases of
water seaward of the interface is assumed to be static, the
specified flux boundaries, the flux is specified according to
freshwater-saltwater transition zone can be treated as a sharp
circumstances external to the groundwater flow system and the
interface and can be taken as the boundi
...

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 2015) D5609 − 16
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*
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.
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 of Terms Specific to This Standard:
3.2.1 aquifer, confined—confined aquifer—in hydrogeology, an aquifer bounded above and below by confining beds and in
which the static head is above the top of the aquifer.aquifer
3.2.2 boundary—in hydrogeology, the geometrical configuration of the surface enclosing the model domain.
3.2.3 boundary condition—in hydrogeology, 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.
3.2.4 flux—in hydrogeology, the volume of fluid crossing a unit 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 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, 2008March 1, 2016. Published October 2015March 2016. Originally approved in 1994. Last previous edition approved in 20082015
ɛ1
as D5609 – 94 (2008).(2015) . DOI: 10.1520/D5609-94R15E01.10.1520/D5609-16.
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
D5609 − 16
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.
3.2.6 hydrologic condition—in groundwater hydraulics, 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.
4. 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.
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.
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
D5609 − 16
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 Fre
...