Groundwater Hydrology

Groundwater Hydrology Course No: C09-002

Credit: 9 PDH

Gilbert Gedeon, P.E.

Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 322-5800 F: (877) 322-4774 [email protected]

CECW-EH

Engineer Manual1110-2-1421

Department of the ArmyU.S. Army Corps of Engineers

Washington, DC 20314-1000

EM 1110-2-1421

28 February 1999

Engineering and Design

GROUNDWATER HYDROLOGY

Distribution Restriction StatementApproved for public release; distribution is

unlimited.

DEPARTMENT OF THE ARMY EM 1110-2-1421U.S. Army Corps of Engineers

CECW-EH Washington, DC 20314-1000

ManualNo. 1110-2-1421 28 February 1999

Engineering and DesignGROUNDWATER HYDROLOGY

1. Purpose. The purpose of this manual is to provide guidance to Corps of Engineers personnel who areresponsible for groundwater-related projects.

2. Applicability. This manual applies to all USACE Commands having responsibility for design of civilworks projects.

3. Distribution Statement. Approved for public release, distribution is unlimited.

FOR THE COMMANDER:

ALBERT J. GENETTI, JR.Major General, USAChief of Staff

i

DEPARTMENT OF THE ARMY EM 1110-2-1421U.S. Army Corps of EngineersWashington, DC 20314-1000

ManualNo. 1110-2-1421 28 February 1999

Engineering and DesignGROUNDWATER HYDROLOGY

Table of Contents

Subject Paragraph Page Subject Paragraph Page

Chapter 1 Estimating Capture Zones of Introduction Pumping Wells . . . . . . . . . . . . . . . . . 2-19 2-14Purpose . . . . . . . . . . . . . . . . . . . . . . . . 1-1 1-1Applicability . . . . . . . . . . . . . . . . . . . . 1-2 1-1References . . . . . . . . . . . . . . . . . . . . . . 1-3 1-1Distribution Statement . . . . . . . . . . . . . 1-4 1-1Focus . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5 1-1Approach . . . . . . . . . . . . . . . . . . . . . . 1-6 1-2Scope . . . . . . . . . . . . . . . . . . . . . . . . . 1-7 1-2Format . . . . . . . . . . . . . . . . . . . . . . . . 1-8 1-2

Chapter 2 Study . . . . . . . . . . . . . . . . . . . . . . . . 3-2 3-1Occurrence and Movement Project Management . . . . . . . . . . . . . . 3-3 3-7of Groundwater Personnel . . . . . . . . . . . . . . . . . . . . . . 3-4 3-8General . . . . . . . . . . . . . . . . . . . . . . . . 2-1 2-1Hydrologic Cycle . . . . . . . . . . . . . . . . . 2-2 2-1Subsurface Distribution . . . . . . . . . . . . 2-3 2-1Forces Acting on Groundwater . . . . . . 2-4 2-2Water Table . . . . . . . . . . . . . . . . . . . . . 2-5 2-3Potentiometric Surface . . . . . . . . . . . . . 2-6 2-3Aquifer Formations . . . . . . . . . . . . . . . 2-7 2-3Principal Types of Aquifer Wells . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2 4-1 Materials . . . . . . . . . . . . . . . . . . . . . 2-8 2-4Movement of Groundwater . . . . . . . . . 2-9 2-6Porosity and Specific Yield . . . . . . . . . 2-10 2-6Darcy’s Law and Hydraulic Pumping Tests . . . . . . . . . . . . . . . . . . . 4-6 4-7 Conductivity . . . . . . . . . . . . . . . . . . . 2-11 2-7Flow and Transmissivity . . . . . . . . . . . 2-12 2-8Homogeneity and Isotropy . . . . . . . . . . 2-13 2-9Flow in Stratified Media . . . . . . . . . . . 2-14 2-9Aquifer Storage . . . . . . . . . . . . . . . . . . 2-15 2-10General Flow Equations . . . . . . . . . . . 2-16 2-11Aquifer Diffusivity . . . . . . . . . . . . . . . 2-17 2-13Flow Lines and Flow Nets . . . . . . . . . . 2-18 2-13

Specialized Flow Conditions . . . . . . . . 2-20 2-17

Chapter 3Planning a GroundwaterInvestigation and ModelingStudyGeneral . . . . . . . . . . . . . . . . . . . . . . . . 3-1 3-1Steps Involved in a Hydrogeologic Site Investigation and Potential Modeling

Example of Site Characterization and Modeling Process . . . . . . . . . . . . 3-5 3-9Conclusion . . . . . . . . . . . . . . . . . . . . . 3-6 3-11

Chapter 4Field Investigative MethodsGeneral . . . . . . . . . . . . . . . . . . . . . . . . 4-1 4-1

Monitoring Wells . . . . . . . . . . . . . . . . 4-3 4-5Geologic Logging . . . . . . . . . . . . . . . . 4-4 4-5Measuring Water Levels . . . . . . . . . . . 4-5 4-5

Slug Tests . . . . . . . . . . . . . . . . . . . . . . 4-7 4-11Borehole Geophysics . . . . . . . . . . . . . . 4-8 4-11Surface Geophysics . . . . . . . . . . . . . . . 4-9 4-16Cone Penetrometer Testing . . . . . . . . . 4-10 4-21Isotope Hydrology . . . . . . . . . . . . . . . . 4-11 4-23Response of Groundwater Levels to Loading Events . . . . . . . . . . . . . . . 4-12 4-26Conclusion . . . . . . . . . . . . . . . . . . . . . 4-13 4-31

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ii

Subject Paragraph Page Subject Paragraph Page

Chapter 5 Estimating Baseflow Contribution Computer Modeling of from Storm Events to Streamflow . . . 6-8 6-8Groundwater Flow Estimating Aquifer Diffusivity from General . . . . . . . . . . . . . . . . . . . . . . . . 5-1 5-1Code Selection . . . . . . . . . . . . . . . . . . . 5-2 5-1Initial Model Development . . . . . . . . . 5-3 5-4Model Calibration and Sensitivity Numerical Modeling of Surface Water Analysis . . . . . . . . . . . . . . . . . . . . . . 5-4 5-7History Matching . . . . . . . . . . . . . . . . . 5-5 5-9Model Execution and Interpretation Appendix A of Results . . . . . . . . . . . . . . . . . . . . . 5-6 5-9Post Audit . . . . . . . . . . . . . . . . . . . . . . 5-7 5-10

Chapter 6 GlossaryInteraction Between SurfaceWater and Groundwater Appendix CGeneral . . . . . . . . . . . . . . . . . . . . . . . . 6-1 6-1System Components . . . . . . . . . . . . . . 6-2 6-1Infiltration . . . . . . . . . . . . . . . . . . . . . . 6-3 6-2Stream-Aquifer Interaction . . . . . . . . . 6-4 6-3Interaction Between Lakes and Appendix D Groundwater . . . . . . . . . . . . . . . . . . 6-5 6-3Analytical Methods . . . . . . . . . . . . . . . 6-6 6-4Estimating the Transient Effects Test Data of Flood Waves on Ground- water Flow . . . . . . . . . . . . . . . . . . . . 6-7 6-5

Streamflow Records . . . . . . . . . . . . . 6-9 6-9Estimating Effects of Pumping Wells on Stream Depletion . . . . . . . . . . . . . 6-10 6-10

and Groundwater Systems . . . . . . . . 6-11 6-13

References

Appendix B

Summary of the HydrogeologicFlow Model for Tooele ArmyDepot, Utah

General Analytical Solutionsfor Application to Pumping

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1-1

Chapter 1Introduction

1-1. Purpose

This Engineer Manual provides guidance to Corps ofEngineers (CE) personnel who are responsible forgroundwater-related projects. This manual was writtenwith special attention to groundwater-relatedapplications prevalent within the CE. Thus, sectionsaddressing site investigation procedures and theperformance of modeling studies are included.Additionally, a chapter focusing on the interactionbetween surface water and groundwater is included.

1-2. Applicability

This manual applies to all USACE Commands havingcivil works responsibilities. This manual providesinformation for application to common Corpsgroundwater-related studies, including:

a. Site characterization for contaminantremediation.

b. Computer modeling of groundwater flow.

c. Groundwater and surface water interactionstudies.

d. Reservoir operations.

e. Groundwater flow to adjacent locks and dams.

f. Remediation of reservoir leakage.

g. Infiltration of runoff to the subsurface.

h. Baseflow between aquifers and fixed bodiesincluding streams and reservoirs.

i. Effects of aquifer pumping on adjacent lakesand streams.

j. Well installation involved with seawaterinfiltration barriers.

k. Dewatering of an excavation for constructionpurposes.

l. General regional and local applications.

1-3. References

A variety of sources were used to compile theinformation presented herein. This includes publica-tions of professional societies, and guidance developedby the Corps of Engineers and other federal agencies.Appendix A contains a complete list of references.The following texts provide a general understanding ofgroundwater concepts and principles.

a. Driscoll, F. G. 1986. “Groundwater andWells,” 2nd ed., Johnson Wheelabrator Water Tech-nologies, Inc., St. Paul, MN.

b. Domenico, P. A., and Schwartz, F. W. 1990.“Physical and chemical hydrogeology,” John Wiley andSons, NY.

c. Fetter, C. W. 1994. “Applied hydrogeology,”3rd ed., Charles E. Merrily Pub., Columbus, OH.

d. Freeze, R. A., and Cherry, J. A. 1979.“Groundwater,” Prentice-Hall, Inc., Englewood Cliffs,NJ.

e. U.S. Department of the Interior. 1977.“Ground water manual - A water resources technicalpublication,” U.S. Department of the Interior, Bureauof Reclamation.

f. Heath, Ralph C. 1987. “Basic ground-waterhydrology,” U.S. Geological Survey Water-SupplyPaper 2220.

1-4. Distribution Statement

Approved for public release; distribution is unlimited.

1-5. Focus

This manual focuses on areas of particular concern toCorps projects. In the past 10 years, significanttechnical progress has been made in the field ofcomputer modeling of groundwater flow. These newmodeling technologies have had widespreadapplications within the Corps. This manual provides

EM 1110-2-142128 Feb 99

1-2

specific information regarding the performance of a a. Chapter 2. “Occurrence and Movement ofsite investigation and conducting a modeling study. Groundwater,” presents an overview of generalAdditionally, a significant portion of Corps concepts. For Corps-specific applications, a section onapplications are involved with surface water. The estimating the capture zones of pumping wells isinterrelationship of surface water and groundwater included.should be considered on all Corps surface water andapplicable groundwater projects. This manual b. Chapter 3. “Planning a Groundwater Investi-addresses analytical and numerical methods for gation and Modeling Study,” provides general guide-quantifying the water exchange between surface water lines for performing a site characterization, andand groundwater. integrating hydrogeologic information into a computer

1-6. Approach

This manual is intended for the use by Corps personnelin planning and designing groundwater-relatedprojects. In many field applications, it is not possibleto provide specific instructions and/or specificprocedures that are universally applicable to everysituation that may be encountered. Therefore, thismanual emphasizes the use of sound judgement and thedevelopment of a good understanding of basicgroundwater concepts rather than providing specificguidelines.

1-7. Scope

The manual provides a general overview of ground-water principles. Practical discussions are providedfor planning groundwater investigations and modelingof groundwater flow. Additionally, a section onsurface water and groundwater interaction is included.To enhance understanding of concepts, examples areprovided throughout the document.

1-8. Format

This manual initially presents an overview of theoccurrence and movement of groundwater. Proceduresfor planning and managing a site characterization andmodeling study are then presented. This is followed bychapters addressing the technical aspects of fieldinvestigative methods and computer modeling. A finalchapter discussing the interaction of groundwater andsurface water is then presented. Appendices areincluded that contain detailed references, definitions,and additional supporting information.

model. This includes: initial site reconnaissance, datainterpretation, acquisition of additional data, con-ceptual model formulation, and general steps in devel-oping a groundwater flow model. Additionally, projectmanagement guidelines are included.

c. Chapter 4. “Field Investigative Methods.”Adequate conceptualization of a hydrogeologic systemoften requires the acquisition of new field data. Thischapter provides an overview of different methods thatcan be employed to gain a better understanding ofsubsurface conditions. Key references are provided toallow for a more detailed understanding of conceptsand applications.

d. Chapter 5. “Computer Modeling of Ground-water Flow,” presents a technical overview of numeri-cal modeling of groundwater flow.

e. Many Corps projects are related to theinteraction of groundwater and surface water. Chap-ter 6, “Interaction Between Surface Water andGroundwater,” provides an overview of the distributionand movement of water in the subsurface. Practicalanalytical methods which quantify the interactionbetween surface water and groundwater are presented.Numerical models are often employed to quantify thewater exchange between the surface and subsurface.This chapter presents an overview of currenttechnology available for the simulation of interactionbetween surface water and groundwater. Keyreferences are provided to allow for a more detailedunderstanding of concepts and applications.

Snow

Infiltration

Precipitation

Water table

Lake

Spring

Surface

Transpiration

Evaporation

Condensation

Groundwater

RiverOcean

runoff

EM 1110-2-142128 Feb 99

2-1

Figure 2-1. Hydrologic cycle

Chapter 2Occurrence and Movement of Groundwater

2-1. General

The occurrence and movement of groundwater arerelated to physical forces acting in the subsurface andthe geologic environment in which they occur. Thischapter presents a general overview of basic conceptswhich explain and quantify these forces andenvironments as related to groundwater. For Corps-specific applications, a section on estimating capturezones of pumping wells is included. Additionally, adiscussion on saltwater intrusion is included. For amore detailed understanding of general groundwaterconcepts, the reader is referred to Fetter (1994).

2-2. Hydrologic Cycle

a. The Earth's hydrologic cycle consists of manyvaried and interacting processes involving all threephases of water. A schematic diagram of the flow ofwater from the atmosphere, to the surface andsubsurface, and eventually back to the atmosphere isshown in Figure 2-1.

b. Groundwater flow is but one part of this com-plex dynamic hydrologic cycle. Saturated formationsbelow the surface act as mediums for the transmissionof groundwater, and as reservoirs for the storage ofwater. Water infiltrates to these formations from thesurface and is transmitted slowly for varying distances

until it returns to the surface by action of natural flow,vegetation, or man (Todd 1964). Groundwater is thelargest source of available water within the UnitedStates, accounting for 97 percent of the available freshwater in the United States, and 23 percent of fresh-water usage (Solley and Pierce 1992).

2-3. Subsurface Distribution

a. General. Groundwater occurs in the subsurfacein two broad zones: the unsaturated zone and thesaturated zone. The unsaturated zone, also known asthe vadose zone, consists of soil pores that are filled toa varying degree with air and water. The zone ofsaturation consists of water-filled pores that areassumed to be at hydrostatic pressure. For anunconfined aquifer, the zone of saturation is overlainby an unsaturated zone that extends from the watertable to the ground surface (Figure 2-2).

b. Unsaturated zone. The unsaturated zone (orvadose zone) serves as a vast reservoir which, whenrecharged, typically discharges water to the saturatedzone for a relatively long period after cessation ofsurface input. The unsaturated zone commonlyconsists of three sub-zones: the root zone, anintermediate zone, and the capillary fringe. The rootzone varies in thickness depending upon growingseason and type of vegetation. The water content inthe root zone is usually less than that of saturation,except when surface fluxes are of great enoughintensity to saturate the surface. This region is subjectto large fluctuations in moisture content due toevaporation, plant transpiration, and precipitation.Water below the root zone is either percolating nearvertically downward under the influence of gravity, oris suspended due to surface tension after gravitydrainage is completed. This intermediate zone does notexist where the capillary fringe or the water tableintercepts the root zone. The capillary fringe extendsfrom the water table up to the limit of capillary rise.Water molecules at the water surface are subject to anupward attraction due to surface tension of the air-water interface and the molecular attraction of theliquid and solid phases. The thickness of this zonedepends upon the pore size of the soil medium, varyingdirectly with decrease in pore size. Water content canrange from very low to saturated, with the

h ' z% pDg

%v 2

2g

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2-2

Figure 2-2. Subsurface distribution of water

lower part of the capillary fringe often being saturated. groundwater flows through interconnected voids inInfiltration and flow in the unsaturated zone are response to the difference in fluid pressure anddiscussed in Section 6-3. elevation. The driving force is measured in terms of

c. Saturated zone. In the zone of saturation, all head) is defined by Bernoulli's equation:communicating voids are filled with water underhydrostatic pressure. Water in the saturated zone isknown as groundwater or phreatic water.

2-4. Forces Acting on Groundwater

External forces which act on water in the subsurfaceinclude gravity, pressure from the atmosphere andoverlying water, and molecular attraction betweensolids and water. In the subsurface, water can occur inthe following: as water vapor which moves fromregions of higher pressure to lower pressure, ascondensed water which is absorbed by dry soilparticles, as water which is retained on particles underthe molecular force of adhesion, and as water which isnot subject to attractive forces towards the surface ofsolid particles and is under the influence ofgravitational forces. In the saturated zone,

hydraulic head. Hydraulic head (or potentiometric

(2-1)

where

h = hydraulic head

z = elevation above datum

p = fluid pressure with constant density D

g = acceleration due to gravity

v = fluid velocity

Pressure head (or fluid pressure) h is defined as:p

hp 'pDg

h ' z%hp

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2-3

Figure 2-3. Relationship between hydraulic head,pressure head, and elevation head within a well

(2-2)

By convention, pressure head is expressed in unitsabove atmospheric pressure. In the unsaturated zone,water is held in tension and pressure head is less thanatmospheric pressure (h < 0). Below the water table,p

in the saturated zone, pressure head is greater thanatmospheric pressure (h > 0). Because groundwaterp

velocities are usually very low, the velocity componentof hydraulic head can be neglected. Thus, hydraulichead can usually be expressed as:

(2-3)

Figure 2-3 depicts Equation 2-3 within a well.

2-5. Water Table

As illustrated by Figure 2-3, the height of watermeasured in wells is the sum of elevation head andpressure head, where the pressure head is equal to theheight of the water column above the screened intervalwithin the well. Freeze and Cherry (1979) define thewater table as located at the level at which waterstands within a shallow well which penetrates thesurficial deposits just deeply enough to encounterstanding water. Thus, the hydraulic head at the watertable is equal to the elevation head; and the pore water

pressure at the water table is equivalent to atmosphericpressure.

2-6. Potentiometric Surface

The water table is defined as the surface in agroundwater body at which the pressure isatmospheric, and is measured by the level at whichwater stands in wells that penetrate the water body justfar enough to hold standing water. The potentiometricsurface approximates the level to which water will risein a tightly cased well which can be screened at thewater table or at greater depth. In wells that penetrateto greater depths within the aquifer, the potentiometricsurface may be above or below the water tabledepending on whether an upward or downwardcomponent of flow exists. The potentiometric surfacecan vary with the depth of a well. In confined aquifers(Section 2-6), the potentiometric surface will riseabove the aquifer surface. The water table is thepotentiometric surface for an unconfined aquifer(Section 2-6). Where the head varies appreciably withdepth in an aquifer, a potentiometric surface ismeaningful only if it describes the static head along aparticular specified stratum in that aquifer. Theconcept of potentiometric surface is only rigorouslyvalid for defining horizontal flow directions fromhorizontal aquifers.

2-7. Aquifer Formations

a. General. An aquifer is a geologic unit that canstore and transmit water. Aquifers are generallycategorized into four basic formation types dependingon the geologic environment in which they occur:unconfined, confined, semi-confined, and perched.Figure 2-4 describes basic aquifer formations.

b. Unconfined aquifers. Unconfined aquiferscontain a phreatic surface (water table) as an upperboundary that fluctuates in response to recharge anddischarge (such as from a pumping well). Unconfinedaquifers are generally close to the land surface, withcontinuous layers of materials of high intrinsicpermeability (Section 2-11) extending from the landsurface to the base of the aquifer.

c. Confined aquifers. Confined, or artesian, aqui-fers are created when groundwater is trapped between

Confined Aquifer

Recharge

Unconfined Aquifer

Potentiometric Surface

Bedrock Confining Layer

Perched Aquifer

Low Permeability Lens

Screening

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Figure 2-4. Aquifer formations

two layers of low permeability known as aquitards. In occurs when water moving down through thea confined aquifer, the groundwater is under pressure unsaturated zone is intercepted by an impermeableand the water level in a well rises above the upper formation. Clay lenses in sedimentary deposits oftenboundary of the aquifer. Flowing artesian conditions have shallow perched water bodies overlying them.exist when the water level in a well rises above land Wells tapping perched aquifers generally yieldsurface. Recharge to confined aquifers is predomi- temporary or small quantities of water. nantly from areas where the confining bed is breached,either by erosional unconformity, fracturing, ordepositional absence.

d. Semi-confined aquifers. Semi-confined, orleaky, aquifers occur when water-bearing strata areconfined, either above or below, by a semipermeablelayer. When water is pumped from a leaky aquifer,water moves both horizontally within the aquifer andvertically through the semipermeable layer.

e. Perched aquifers. A perched aquifer is aspecial type of unconfined aquifer where agroundwater body is separated above the water tableby a layer of unsaturated material. A perched aquifer

2-8. Principal Types of Aquifer Materials

a. General. Earth materials which can have thepotential to transmit water can be classified into fourbroad groups: unconsolidated materials, poroussedimentary rock, porous volcanics, and fracturedrock. In unconsolidated material, water is transportedthrough the primary openings in the rock/soil matrix.Consolidation is the process where loose materialsbecome firm and coherent. Sandstone andconglomerate are common consolidated sedimentaryrocks formed by compaction and cementation.Carbonate rocks (such as limestone and dolomite) aresedimentary rocks which can be formed by chemical

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precipitation. Water is usually transported through common sequence in the southern United States.secondary openings in carbonate rocks enlarged by the Additionally, coral reefs, shells, and other calcite-richdissolution of rock by water. The movement of water deposits commonly occur in areas with temperatethrough volcanics and fractured rock is dependent upon climatic conditions.the interconnectedness and frequency of flowpathways. (4) Eolian deposits. Materials which are

b. Gravel and sand. Gravel and sand aquifers are The sorting action of the wind tends to producethe source of most water pumped in the United States. deposits that are uniform on a local scale, and in someGravels and sands originate from alluvial, lacustrine, cases quite uniform over large areas. Eolian depositsmarine, or eolian glacial deposition. consist of silt or sand. Eolian sands occur wherever

(1) Alluvial deposits. Alluvial deposits of peren- comparison with alluvial deposits, eolian sands arenial streams are usually fairly well sorted and therefore quite homogeneous and are as isotropic (Section 2-13)permeable. Ephemeral streams typically deposit sand as any deposits occurring in nature. Eolian deposits ofand gravel with much less sorting. Stream channels silt, called loess, are associated with the abnormallyare sensitive to changes in sediment load, gradient, and high wind velocities associated with glacial ice fronts.velocity. This can result in lateral distribution of Loess occurs in the shallow subsurface in large areasalluvial deposits over large areas. Areas with greater of the Midwest and Great Plains regions of Northstreambed slope typically contain coarser deposits. America. Alluvial fans occur in arid or semiarid regions where astream issues from a narrow canyon onto a plain or (5) Glacial deposits. Unlike water and wind,valley floor. Viewed from above, they have the shape glacial ice can entrain unconsolidated deposits of allof an open fan, the apex being at the valley mouth. sizes from sediments to boulders. Glacial till is non-These alluvial deposits are coarsest at the point where sorted, non-stratified sediment deposited beneath, fromthe stream exits the canyon mouth, and become finer within, or from the top of glacial ice. Glacial outwashwith increasing distance from the point of initial (or glaciofluvial) deposits consist of coarse-graineddeposition. sediments deposited by meltwater in front of a glacier.

The sorting and homogeneity of glaciofluvial deposits(2) Lacustrine deposits. The central and lower

portions of alluvium-filled valleys may consist of fine-grained lacustrine (or lakebed) deposits. When astream flows into a lake, the current is abruptly c. Sandstone and conglomerate. Sandstone andchecked. The coarser sediment settles rapidly to the conglomerates are the consolidated equivalents of sandbottom, while finer materials are transported further and gravel. Consolidation results from compaction andinto the body of relatively still water. Thus, the central cementation. The highest yielding sandstone aquifersareas of valleys which have received lacustrine occur where partial consolidation takes place. Thesedeposits often consist of finer-grained, yield water from the pores between grains, althoughlower-permeability materials. Lacustrine deposits secondary openings such as fractures and joints canusually consist of fine-grained materials that are not also serve as channels of flow.normally considered aquifers.

(3) Marine deposits. Marine deposits originate from calcium, magnesium, or iron, are widespreadfrom sediment transported to the ocean by rivers and throughout the United States. Limestone and dolomite,erosion of the ocean floor. As a sea moves inland, which originate from calcium-rich deposits, are thedeposits at a point in the ocean bottom near the shore most common carbonate rocks. Carbonates arebecome gradually finer due to uniform wave energy. typically brittle and susceptible to fracturing.Conversely, as the sea regresses, deposition progresses Fractures and joints in limestone yield water in small togradually from finer to coarser deposits. This is a moderate amounts. However, because water acts as a

transported by the wind are known as eolian deposits.

surface sediments are available for transport. In

depend upon environmental conditions and distancefrom the glacial front.

d. Carbonate rocks. Carbonate rocks, formed

n 'Vv

VT

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2-6

weak acid to carbonates, dissolution of rock by waterenlarges openings. The limestones that yield thehighest amount of water are those in which a sizableportion of the original rock has been dissolved orremoved. These areas are commonly referred to askarst. Thus, large amounts of flow can potentially betransmitted in carbonate rocks.

e. Volcanics. Basalt is an important aquifermaterial in parts of the western United States, mostnotably central Idaho, where enormous flows of lavahave spread out over large areas in successive sheets ofvarying thickness. The ability of basalt formations totransmit water is dependent on the presence offractures, cracks, and tubes or caverns, and can besignificant. Near the surface, rapid cooling producesjointing. Fracturing below the surface occurs as thecrust cools, causing differential flow velocities withdepth. Other volcanic rocks, including rhyolite andother more siliceous rocks, do not usually yield waterin quantities comparable to those secured from basalt.Another major source of groundwater in some parts ofthe western United States is found in sedimentary“interbed” materials which occur between basalt flows.This interbedded material is generally alluvial orcolluvial in nature, consisting of sands, gravels, andresiduum (particularly granite). When the interbeddedmaterials tend to be finer-grained, the interbed acts as aconfining layer.

f. Fractured rock. Crystalline and metamorphicrocks, including granite, basic igneous rocks, gneiss,schist, quartzite, and slate are relatively impermeable.Water in these areas is supplied as a result of jointingand fracturing. The yield of water from fractured rockis dependent upon the frequency and interconnected-ness of flow pathways.

2-9. Movement of Groundwater

Groundwater moves through the sub-surface fromareas of greater hydraulic head to areas of lowerhydraulic head (Equation 2-3). The rate ofgroundwater movement depends upon the slope of thehydraulic head (hydraulic gradient), and intrinsicaquifer and fluid properties.

2-10. Porosity and Specific Yield

a. Porosity. Porosity n is defined as the ratio ofvoid space to the total volume of media:

(2-4)

where

V = volume of void space [L ]v3

V = total volume (volume of solids plus volumeT

of voids) [L ]3

In unconsolidated materials, porosity is principallygoverned by three properties of the media: grainpacking, grain shape, and grain size distribution. Theeffect of packing may be observed in two-dimensionalmodels comprised of spherical, uniform-sized balls.Arranging the balls in a cubic configuration (each balltouching four other balls) yields a porosity of 0.476whereas rhombohedral packing of the balls (each balltouching eight other balls) results in a porosity of0.260. Porosity is not a function of grain size, butrather grain size distribution. Spherical modelscomprised of different sized balls will always yield alower porosity than the uniform model arranged in asimilar packing arrangement. Primary porosity in amaterial is due to the properties of the soil or rockmatrix, while secondary porosity is developed in thematerial after its emplacement through such processesas solution and fracturing. Representative porosityranges for sedimentary materials are given inTable 2-1.

Table 2-1Porosity Ranges for Sedimentary Materials

Material Porosity

Clay .45 - .55

Silt .40 - .50

Medium to coarse mixed sand .35 - .40

Uniform sand .30 - .40

Fine to medium mixed sand .30 - .35

Gravel .30 - .40

Gravel and sand .20 - .35

0

5

10

15

20

25

30

35

40

45

50

Cla

y an

d si

lt

Fin

e sa

nd

Med

ium

san

d

Coa

rse

sand

Fin

e gr

avel

Med

ium

gra

vel

Coa

rse

grav

el

Soil Classification

Per

cen

t

Total Porosity

Specific Yield

Specific Retention

Q ' &KA dhdl

EM 1110-2-142128 Feb 99

2-7

Figure 2-5. Typical relationship between specific yield, specific retention, and total porosity for different soil types

b. Effective porosity. Effective porosity n is thee

porosity available for fluid flow. The effectiveporosity of a unit of media is equal to the ratio of thevolume of interconnected pores that are large enough tocontain water molecules to the total volume of the rockor soil.

c. Specific yield. Specific yield S is the ratio ofy

the water that will drain from a saturated rock owing tothe force of gravity to the total volume of the media.Specific retention Sr is defined as the ratio of thevolume of water that a unit of media can retain againstthe attraction of gravity to the total volume of themedia. The porosity of a rock is equal to the sum ofthe specific yield and specific retention of the media.For most practical applications in sands and gravels,the value of effective porosity can be consideredequivalent to specific yield. In clays, there is a muchgreater surface area and corresponding adhesion ofwater molecules. Figure 2-5 illustrates a typicalrelationship of specific yield and specific retention tototal porosity for different soil types.

2-11. Darcy’s Law and Hydraulic Conductivity

a. Darcy's Law. Henry Darcy, a Frenchhydraulic engineer, observed that the rate of laminarflow of a fluid (of constant density and temperature)between two points in a porous medium is proportionalto the hydraulic gradient (dh/dl) between the two points(Darcy 1856). The equation describing the rate of flowthrough a porous medium is known as Darcy’s Lawand is given as:

(2-5)

where

Q = volumetric flow rate [L T ]3 -1

K = hydraulic conductivity [LT ]-1

A = cross-sectional area of flow [L ]2

K'kDg

µ

v 'QA

' &K dhdl

Vx 'Q

neA' &

Kdhne dl

EM 1110-2-142128 Feb 99

2-8

h = hydraulic head [L]

l = distance between two points [L]

The negative sign on the right-hand side of Equa-tion 2-5 (Darcy's Law) is used by convention toindicate a downward trending flow gradient.

b. Hydraulic conductivity. The hydraulicconductivity of a given medium is a function of theproperties of the medium and the properties of thefluid. Using empirically derived proportionalityrelationships and dimensional analysis, the hydraulicconductivity of a given medium transmitting a givenfluid is given as:

(2-6)

where

k = intrinsic permeability of porous medium [L ]2

D = fluid density [ML ]-3

µ = dynamic viscosity of fluid [ML T ]-1 -1

g = acceleration of gravity [LT ]-2

The intrinsic permeability of a medium is a function ofthe shape and diameter of the pore spaces. Severalempirical relationships describing intrinsic perme-ability have been presented. Fair and Hatch (1933)used a packing factor, shape factor, and the geometricmean of the grain size to estimate intrinsic perme-ability. Krumbein (1943) uses the square of theaverage grain diameter to approximate the intrinsicpermeability of a porous medium. Values of fluiddensity and dynamic viscosity are dependent uponwater temperature. Fluid density is additionallydependent upon total dissolved solids (TDS). Rangesof intrinsic permeability and hydraulic conductivityvalues for unconsolidated sediments are presented inTable 2-2.

c. Specific discharge. The volumetric flowvelocity v can be determined by dividing the volumetricflow rate by the cross-sectional area of flow as:

Table 2-2Ranges of Intrinsic Permeability and Hydraulic Conductivity forUnconsolidated Sediments

Material Intrinsic Permeability Hydraulic Conductivity(cm ) (cm/s)2

Clay 10 - 10 10 - 10-6 -3 -9 -6

Silt, sandy silts, 10 - 10 10 - 10clayey sands, till

-3 -1 -6 -4

Silty sands, fine 10 - 1 10 - 10sands

-2 -5 -3

Well-sorted sands, 1 - 10 10 - 10glacial outwash

2 -3 -1

Well-sorted gravels 10 - 10 10 - 13 -2

(2-7)

The velocity given by Equation 2-7 is termed thespecific discharge, or Darcy flux. The specificdischarge is actually an apparent velocity, representingthe velocity at which water would move through anaquifer if the aquifer were an open conduit. The cross-sectional area is not entirely available for flow due tothe presence of the porous matrix.

d. Pore water velocity. The average linearvelocity of water in a porous medium is derived bydividing specific discharge by effective porosity (n ) toe

account for the actual open space available for theflow. The resulting velocity is termed the pore watervelocity, or the seepage velocity. The pore watervelocity V represents the average rate at which thex

water moves between two points and is given by

(2-8)

2-12. Flow and Transmissivity

Transmissivity T is a measure of the amount of waterthat can be transmitted horizontally through a unitwidth by the fully saturated thickness of an aquiferunder a hydraulic gradient equal to 1. Transmissivityis equal to the hydraulic conductivity multiplied by thesaturated thickness of the aquifer and is given by:

Kz1Kz2

Kx1Kx2

Kz1Kz2

Kx1Kx2

Kz1Kz2

Kx1Kx2

Kz1Kz2

Kx1Kx2

Homogeneous

Isotropic

Kz1 = Kz2

Kx1 = Kx2

Kx = Kz

Homogeneous

Anisotropic

Kz1 = Kz2

Kx1 = Kx2

Kx … Kz

Heterogeneous

Isotropic

Kz1 … Kz2

Kx1 … Kx2

Kx = Kz

Heterogeneous

Anisotropic

Kz1 … Kz2

Kx1 … Kx2

Kx … Kz

T ' Kb

Qx ' Kx Ax

)hT

x

EM 1110-2-142128 Feb 99

2-9

Figure 2-6. Homogeneity and isotropy

(2-9)

where

K = hydraulic conductivity [LT ]-1

b = saturated thickness of the aquifer [L]

Since transmissivity depends on hydraulic conductivityand saturated thickness, its value will differ at differentlocations within aquifers comprised of heterogeneousmaterial, bounded by sloping confining beds, or underunconfined conditions where the saturated thicknesswill vary with the water table.

2-13. Homogeneity and Isotropy

a. Definition. If hydraulic conductivity isconsistent throughout a formation, regardless ofposition, the formation is homogeneous. If hydraulicconductivity within a formation is dependent onlocation, the formation is heterogeneous. Whenhydraulic conductivity is independent of the directionof measurement at a point within a formation, theformation is isotropic at that point. If the hydraulicconductivity varies with the direction of measurementat a point within a formation, the formation isanisotropic at that point. Figure 2-6 is a graphicalrepresentation of homogeneity and isotropy.

b. Geologic controls. Geologic material is veryrarely homogeneous in all directions. A more probablecondition is that the properties, such as hydraulicconductivity, are approximately constant in onedirection. This condition results because: a) of effectsof the shape of soil particles, and b) different materialsincorporate the alluvium at different locations. Asgeologic strata are formed, individual particles usuallyrest with their flat sides down in a process calledimbrication. Consequently, flow is generally lessrestricted in the horizontal direction than the verticaland K is greater than K for most situations. Layeredx z

heterogeneity occurs when stratum of homogeneous,isotropic materials are overlain upon each other.Layered conditions commonly occur in alluvial,lacustrine, and marine deposits. At a large scale, thereis a relationship between anisotropy and layeredheterogeneity. In the field it is not uncommon

for sites with layered heterogeneity to have large scaleanisotropy values of 100:1 or greater. Discontinuousheterogeneity results from geologic structures such asbedrock outcrop contacts, clay lenses, and buriedoxbow stream cutoffs. Trending heterogeneitycommonly occurs in sedimentary formations of deltaic,alluvial, and glacial origin.

2-14. Flow in Stratified Media

a. General. Flow through stratified media can bedescribed through the definition of a hydraulicallyequivalent conductivity (or effective hydraulicconductivity). Expressions for horizontal and verticalequivalent conductivities can be generalized fromexpressions developed for flow through porous mediacomprised of three parallel homogeneous, isotropicstrata (Figure 2-7).

b. Horizontal flow. Horizontal flow through themedia is given by Darcy’s Law,

(2-10)

Kx 'j Ki bi

L

Qz ' Kz Az

)hT

L

Kz 'L

j bi

Ki

Ss ' Dwg ("%n$)

EM 1110-2-142128 Feb 99

2-10

Figure 2-7. Stratified media

where

)h = total hydraulic head drop across flowT

distance x

For the case of i, the strata method gives the expressionfor the horizontal equivalent hydraulic conductivityas:

(2-11)

c. Vertical flow. Similarly, vertical flow is givenby Darcy’s Law as:

(2-12)

For the case of i, the strata method gives the expressionfor the vertical equivalent hydraulic conductivity as:

(2-13)

2-15. Aquifer Storage

a. Storage coefficient. The storage coefficient,or storativity S is the volume of water that a permeableunit will absorb or expel from storage per unit surfacearea per unit change in head. At the water table, wateris released from storage by gravity drainage. Belowthe water table, water is released from storage due tothe release of hydrostatic pressure within the porespaces which accompanies the withdrawal of waterfrom the aquifer. The total load above an aquifer issupported by a combination of the solids skeleton ofthe aquifer and by the hydraulic pressure exerted bythe water in the aquifer. Withdrawal of water from theaquifer results in a decline in the pore water pressureand subsequently more of the load must be supportedby the solids skeleton. As a result, the rock particlesare distorted and the skeleton is compressed, leading toa reduction in effective porosity. Additionally, thedecreased water pressure causes the pore water toexpand. Compression of the skeleton and expansion ofthe pore water both cause water to be expelled from theaquifer.

b. Specific storage. The specific storage S is thes

amount of water per unit volume of a saturatedformation that is stored or expelled from storage owingto compression and expansion of the mineral skeletonand the pore water per unit change in hydraulic head.The specific storage (1/L) is given by:

(2-14)

where

D = density of water [ML T ]w-3 -2

g = acceleration of gravity [LT ]-2

" = compressibility of the aquifer skeleton[1/(ML T ]-1 -2

n = porosity

$ = compressibility of water [1/(ML T ]-1 -2

S ' bSs

S ' Sy % hSs

Vw ' SA)h

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2-11

Figure 2-8. Elemental control volume

From field data, Helm (1975) estimated the specific e. Volumetric drainage. The volume of waterstorage of sands and gravels as 1×10 ft and clays drained from an aquifer due to a lowering of the-6 -1

and silts as 3.5×10 ft . hydraulic head can be computed from:-6 -1

c. Storage coefficient of a confined aquifer.Within a confined aquifer the full thickness of theaquifer remains saturated when water is released orstored. Therefore, all water is released due to thecompaction of the skeleton and expansion of the porewater and the storage coefficient (dimensionless) isgiven as:

(2-15)

where [L ]

b = thickness of the aquifer [L] )h = average decline in hydraulic head [L]

Values of storage coefficient in confined aquifers aregenerally less than 0.005 (Todd 1980). Valuesbetween 0.005 and 0.10 generally indicate a leakyconfined aquifer.

d. Storage coefficient of an unconfined aquifer.Within an unconfined aquifer the level of saturationvaries as water is added to or removed from theaquifer. As the water table falls, water is released bygravity drainage plus compaction of the skeleton andexpansion of the pore water. The volume of waterreleased by gravity drainage is given by the specificyield of the aquifer. The storage coefficient of anunconfined aquifer is therefore given by the sum of thespecific yield and the volume of water released due tothe specific storage as:

(2-16)

The value of specific storage is typically very small,generally less than 1 x 10 ft . As the value of-4 -1

specific yield is usually several orders of magnitudegreater than specific storage, the storage coefficient ofan unconfined aquifer approximates its specific yield.The storage coefficient of unconfined aquifers typicallyranges from 0.10 to 0.30. Estimates of specific yieldfor various deposits can be found in Johnson (1967).

(2-17)

where

V = volume of water drained from aquifer [L ]w3

S = storage coefficient (dimensionless)

A = surface area overlying the drained aquifer2

2-16. General Flow Equations

a. Confined aquifer. The governing flowequation for confined aquifers is developed fromapplication of the law of mass conservation (continuityprinciple) to the elemental volume shown in Figure 2-8.Continuity is given by:

Rate of mass accumulation = Rate of mass inflow - Rate of mass outflow (2-18)

SsMhM t

'MMx

KxMhMx

%MMy

KyMhMy

%MMz

KzMhMz

SsMhM t

%W'MMx

KxMhMx

%MMy

KyMhMy

%MMz

KzMhMz

SsMhM t

' KxMMx

MhMx

% KyMMy

MhMy

% KzMMz

MhMz

SsMhM t

' K MMx

MhMx

%MMy

MhMy

%MMz

MhMz

SsMhM t

' K M2 h

Mx 2%

M2 h

My 2%

M2 h

Mz 2

M2 h

Mx 2%

M2 h

My 2%

M2 h

Mz 2'

STMhM t

M2 h

Mx 2%

M2 h

My 2%

M2 h

Mz 2' 0

MMx

KxhMhMx

%MMy

KyhMhMy

%MMz

KzhMhMz

'SyMhM t

MMx

h MhMx

%MMy

h MhMy

%MMz

h MhMz

'Sy

KMhM t

EM 1110-2-142128 Feb 99

2-12

Integrating the conservation of mass (under constant Using the definitions for storage coefficient, (S = bS ),density) with Darcy’s Law, the general flow equation and transmissivity, (T = Kb), where b is the aquiferin three dimensions for a heterogeneous anisotropic thickness, Equation 2-22 becomes:material is derived:

(2-19)

Equation 2-19 is the general flow equation in threedimensions for a heterogeneous anisotropic material.Discharge (from a pumping well, etc.) or recharge to orfrom the control volume is represented as volumetricflux per unit volume (L /T/L = 1/T):3 3

(2-20)

where

W = volumetric flux per unit volume [1/T]

Assuming that the material is homogeneous, i.e. K doesnot vary with position, Equation 2-19 can be writtenas:

(2-21)

If the material is both homogeneous and isotropic, i.e.K = K = K , then Equation 2-21 becomes:x y z

or, combining partial derivatives:

(2-22)

s

(2-23)

If the flow is steady-state, the hydraulic head does notvary with time and Equation 2-23 becomes:

(2-24)

Equation 2-24 is known as the Laplace equation.

b. Unconfined aquifer. In an unconfined aquifer,the saturated thickness of the aquifer changes with timeas the hydraulic head changes. Therefore, the abilityof the aquifer to transmit water (the transmissivity) isnot constant:

(2-25)

where

S = specific yield [dimensionless]y

For a homogeneous, isotropic aquifer, the generalequation governing unconfined flow is known as theBoussinesq equation and is given by:

(2-26)

If the change in the elevation of the water table is smallin comparison to the saturated thickness of the aquifer,the variable thickness h can be replaced with anaverage thickness b that is assumed to be constant overthe aquifer. Equation 2-26 can then be linearized tothe form:

M2 h

Mx 2%

M2 h

My 2%

M2 h

Mz 2'

Sy

KbMhM t

TS

(M2 h

Mx 2%

M2 h

My 2%

M2 h

Mz 2) '

MhM t

q1 ' K)z )h)x

q1 ' K)h ' K)hT

Nd

qT ' q1 % q2

qT ' Nf q1

EM 1110-2-142128 Feb 99

2-13

(2-27)

2-17. Aquifer Diffusivity

Aquifer diffusivity is a term commonly used in surfacewater/groundwater interaction and is defined as theratio of transmissivity to storage coefficient (T/S).Equation 2-27 can be written as:

(2-28)

where

S = storage coefficient [dimensionless]

Equation 2-28 demonstrates the direct relationshipbetween the promulgation of a groundwater flood wave(and pressure wave) and aquifer diffusivity. Equation2-28 is applicable to homogeneous, isotropic aquifersunder either confined or unconfined (where the changein aquifer thickness is insignificant) conditions.

2-18. Flow Lines and Flow Nets

a. Definition. Two-dimensional, steady flowwhich can be described by the Laplace equation(Equation 2-24) can be solved by a graphicalconstruction of a flow net. A flow net is a network ofcurves called streamlines and equipotential lines. Astreamline is an imaginary line that traces the path thata particle of groundwater would follow as it flowsthrough an aquifer. In an isotropic aquifer, streamlinesare perpendicular to equipotential lines. If there isanisotropy in the plane of flow, then the streamlineswill cross the equipotential lines at an angle dictated bythe degree of anisotropy. An equipotential linerepresents locations of equal potentiometric head(Section 2-6). A flow net is a family of equipotentiallines with sufficient orthogonal flow lines drawn sothat a pattern of square figures (or elements) results.While different elements may be different in size, thechange in flow and change in hydraulic head is thesame for all elements. Except in cases of the mostsimple geometry, the figures will not truly be squares.

b. Boundary conditions.

(1) All boundary conditions of the flow domainmust be known prior to the construction of the flownet. Three types of boundary conditions are possible:a no-flow boundary, a constant-head boundary, and awater-table boundary. Along a no-flow boundarystreamlines will run parallel, and equipotential lineswill intersect the boundary at right angles. A constant-head boundary (such as large lake) represents anequipotential line and streamlines will intersect at aright angle while adjacent equipotential lines will runparallel to the boundary.

(2) A flow net is presented in Figure 2-9 for thetwo-dimensional, steady-state flow in a homogeneous,isotropic aquifer between two reservoirs with differenthydraulic heads.

c. Analysis of results. The completed flow netcan be used to determine the quantity of water flowingthrough the domain. For the system shown in Fig-ure 2-9, the flow per unit thickness in one element is:

(2-29)

But )x = )z, so Equation 2-29 becomes:

(2-30)

where

N = the number of equipotential dropsd

The total flow per unit thickness is equal to the sum ofthe flow through each flow tube:

(2-31)

Since the flow through each flow tube is equal, q = q1 2

and:

(2-32)

qT ' K)hT

Nf

Nd

EM 1110-2-142128 Feb 99

2-14

Figure 2-9. Basic flow net

where This section presents analytical methods for estimating

N = the number of flow tubes in a domain conditions. Steady-state conditions are approximatedf

Substituting Equation 2-30 into Equation 2-32 gives: change in water levels (with time) in the well and its

(2-33)

Thus, the flow per unit thickness, as well as total flow,through this simplified system can be derived as afunction of hydraulic gradient (K), the drop inhydraulic head (ªh ), and the number of equipotentialt

drops (N ) and flow tubes (N ) in the domain.d f

2-19. Estimating Capture Zones of PumpingWells

a. General. A capture zone consists of theupgradient and downgradient areas that will drain intoa pumping well. If the water table (or potentiometricsurface) is flat, the capture zone is circular. However,in most cases the water table (or potentiometricsurface) is sloping. Calculating capture zones of wellsaids in the design of pump-and-treat groundwaterremediation systems, and well-head protection zones.Figure 2-10 illustrates a typical capture zone.

the capture zones of pumping wells under steady-state

after the well has been pumping for some time, and the

zone of influence are judged insignificant. Assump-tions included in the methods presented are as follows:

(1) The aquifer is homogeneous, isotropic, andinfinite in horizontal extent.

(2) Uniform flow (steady-state) conditions prevail.

(3) A confined aquifer has uniform transmissivityand no leakage.

(4) An unconfined aquifer has a horizontal lowerconfining layer with no leakage and no recharge fromprecipitation.

(5) Vertical gradients are negligible.

(6) The well is screened through the full saturatedthickness of the aquifer and pumps at a constant rate.

b. Confined steady-state flow. Assume the wellin Figure 2-10 is located at the origin (0,0) of the x,y

x '& y

tan(2BKbiy/Q)

x '& y

tan[BK(h 21&h 2

2 )y/QL]

EM 1110-2-142128 Feb 99

2-15

Figure 2-10. Capture zone of a pumping well in plan view. The well is located at the origin (0,0) of the x,y plane

plane. The equation to describe the edge of the capture The maximum width of the capture zone as thezone (groundwater divide) for a confined aquifer when distance (x) upgradient from the pumping wellsteady-state conditions have been reached is (Grubb approaches infinity is given by (Todd 1980):1993):

(2-34)

where

Q = pumping rate [L /T]3

K = hydraulic conductivity [L/T]

b = aquifer thickness [L]

i = hydraulic gradient of the flow field in theabsence of the pumping well (dh/dx) andtan (*) is in radians.

The distance from the pumping well downstream to thestagnation point that marks the end of the capture zoneis given by:

x = -Q/(2BKbi) (2-35)0

y = Q/Kbi (2-36)c

c. Unconfined steady-state flow. Assume thewell in Figure 2-10 is located at the origin (0,0) of thex,y plane. The equation to describe the edge of thecapture zone (groundwater divide) for an unconfinedaquifer when steady-state conditions have been reachedis (Grubb 1993):

(2-37)

where



h = upgradient head above lower boundary of1

aquifer prior to pumping

N

GW Flow Direction

2,000 m

400 mMunicipal WellQ = 19,250 m3/day

Toxic Spill

x '& y

tan(2BKbiy/Q)

EM 1110-2-142128 Feb 99

2-16

Figure 2-11. Location of toxic spill relative to pumpingwell

h = downgradient head above lower boundary of2

aquifer prior to pumping

L = distance between h and h and tan (*) is in1 2

radians.

The distance from the pumping well downstream to thestagnation point that marks the end of the capture zoneis given by:

x = -QL/(BK(h - h )) (2-38)0 1 22 2

The maximum width of the capture zone as thedistance (x) upgradient from the pumping wellapproaches infinity is given by:

y = 2(QL)/(K(h - h )) (2-39)c 1 22 2

d. Example problem.

(1) Background. City planners are concernedabout the potential contaminants from a toxic spill tocontaminate the municipal water supply. Themunicipal well (which pumps at 19,250 m /day) is3

screened in a confined aquifer located 30 m to 80 mbelow the surface. Aquifer materials consist of coarsesands with a hydraulic conductivity of about 80 m/day.The well has been pumping for several years andconditions approach steady state. Groundwater flow inthe aquifer trends toward the north. The potentiometricsurface of the aquifer (measured before pumpingcommenced) drops approximately 1 m for every 200m. The location of the well relative to the toxic spill isillustrated by Figure 2-11. Estimate the spatial extentof the capture zone of the pumping well.

(2) Solution. We are given:

the aquifer is confinedK = 80 m/dayb = 50 mi = 1/200 = 0.005

Q = 19,250 m /day3

• Find maximum extent of capture zone:

y = Q/Kbi = 19250/(80)(50)(0.005) = 960 mc

or ± 480 m from the x axis.

• Find location of stagnation point:

x = - y /2B = -960/2B = - 150 m0 c

• Delineate boundary of the capture zone:

= - y/tan(0.0065y)

±y x 1 -150100 -130200 -50300 120400 670450 2,045480 24,000

EM 1110-2-142128 Feb 99

2-17

(3) Analysis of results. The capture zone at a turbulent where Darcy’s law rarely applies. Solutiondistance x = 2,000 m from the pumping well extends channels leading to high permeability are favored in450 m from the horizontal (x) axis. Therefore, initial areas where topographic, bedding, or jointing featurescalculations indicate that a portion of the contaminant promote flow localization which focuses the solventplume will contaminate the municipal water supply action of circulating groundwater, or well-connectedunless mitigative measures are taken. Further pathways exist between recharge and discharge zones,investigation is warranted. favoring higher groundwater velocities (Smith and

2-20. Specialized Flow Conditions

a. General. Darcy's Law (Section 2-11) is anempirical relationship which is only valid under theassumption of constant density and laminar flow.These assumptions are not always met in nature. Flowconditions in which Darcy's Law is not necessarilyapplicable are cited below.

(1) Fractured flow. Fractured-rock aquifers occurin environments in which the flow of water is primarilythrough fractures, joints, faults, or bedding planeswhich have not been significantly enlarged bydissolution. Fracturing adds secondary porosity to asoil medium that already has some original porosity.The original porosity consists of pores that are roughlysimilar in length and width. These pores interconnect toform a tortuous water network for groundwater flow.Fractured porosity is significantly different. Thefractures consist of pathways that are much greater inlength than width. These pathways provide conduits forgroundwater flow that are much less tortuous than theoriginal porosity. At a local scale, fractured rock canbe extremely heterogeneous. Effective permeability ofcrystalline rock typically decreases by two or threeorders of magnitude in the first thousand feet belowground surface, as the number of fractures decrease orclose under increased lithostatic load (Smith andWheatcraft 1992).

(2) Karst aquifers. Karst aquifers occur inenvironments where all or most of the flow of water isthrough joints, faults, bedding planes, pores, cavities,conduits, and caves, any or all of which have beensignificantly enlarged by dissolution. Effectiveporosity in karst environments is mostly tertiary, wheresecondary porosity is modified by dissolution throughpores, bedding planes, fractures, conduits, and caves.Karst aquifers are generally highly anisotropic andheterogeneous. Flow in karst aquifers is often fast and

Wheatcraft 1992).

(3) Permafrost. Temperatures significantly below0E C are required to produce permafrost. The depthand location of frozen water within the soil dependsupon many factors such as fluid pressure, salt contentof the pore water, the grain size distribution of the soil,soil mineralogy, and the soil structure. The presence offrozen or partially frozen groundwater has atremendous effect upon flow. As water freezes, itexpands to fill pore spaces. Soil that normally conveyswater easily becomes an aquitard or aquiclude whenfrozen. The flow of water in permafrost regions isanalogous to fractured flow environments where flowis confined to conduits in which complete freezing hasnot taken place.

(4) Variable-density flow. Unlike aquifers con-taining constant-density water, where flow is controlledonly by the hydraulic head gradient and the hydraulicconductivity, variable-density flow is also affected bychange in the spatial location within the aquifer. Waterdensity is commonly affected by temperature, or totaldissolved solids. As water temperature increases, itsdensity decreases. A temperature gradient across anarea influences the measurements of hydraulic headand the corresponding hydraulic gradient. Intrinsichydraulic conductivity is also a function of watertemperature (Equation 2-6). Thus, it is important toassess effects of fluid density on hydraulic gradient andhydraulic gradient in all site investigations.

(5) Saltwater intrusion. Due to differentconcentrations of dissolved solids, the density of thesaline water is greater than the density of fresh water.In aquifers hydraulically connected to the ocean, asignificant density difference occurs which candiscourage mixing of waters and result in an interfacebetween salt water and sea water. The depth of thisinterface can be estimated by the Ghyben-Herzbergrelationship (Figure 2-12, Equation 2-40).

zs 'Df

Ds&Df

zw

zs ' 40zw

EM 1110-2-142128 Feb 99

2-18

Figure 2-12. Saltwater-freshwater interface in an unconfined coastal aquifer

(2-40)

where

z = depth of interface below sea levels

z = elevation of water table above sea levelw

D = saltwater densitys

D = freshwater densityw

For the common values of D = 1.0 and D = 1.25,w s

(2-41)

The Ghyben-Herzberg relationship assumeshydrostatic conditions in a homogeneous, unconfinedaquifer. Additionally, it assumes a sharp interfacebetween fresh water and salt water. In reality, theretends to be a mixing of salt water and fresh water in azone of diffusion around the interface. If the aquifer issubject to hydraulic head fluctuations caused by tides,the zone of mixed water will be enlarged.

EM 1110-2-142128 Feb 99

3-1

Chapter 3Planning a Groundwater Investigation andModeling Study

3-1. General

a. This chapter will present basic guidelines forperforming a site characterization study, integratinghydrogeologic information into a conceptual model,performing simple analytical procedures, andformulating a computer model of groundwater flow.Specific attention is given to site reconnaissance, initialdata interpretation, data acquisition, the formulation ofconceptual and numerical/computer models, andguidelines for project management and personnelrequirements. Additional information on performingan investigation study can be found in EC 1110-2-287(1995), and U.S. Geological Survey (1977). Chapter 4presents an overview of field investigation methods.Chapter 5 presents an overview on the technicalaspects of computer modeling of groundwater flow.

b. In order to properly plan a hydrogeologic siteinvestigation, the purpose of the investigation, thegeneral geologic and hydrologic characteristics of thesite, and the management constraints under which theinvestigation is to take place (financial and timerestraints, availability of necessary equipment,availability of expertise) should be well understood byall involved in the project. Subsurface investigationsare a dynamic and inexact science. The ability of thedata acquired to provide an increasingly accuraterepresentation of the hydrogeologic system increaseswith time, money, and the expertise of the specialistsinvolved. Thus, the success of a groundwaterinvestigation relies not only on the technical expertiseof the specialists involved, but also on the effectivenessand efficiency of project management.

c. Examples of groundwater investigations relatedto Corps projects include the following:

(1) Contaminant remediation.

(2) Well production.

(3) Infiltration of runoff to the subsurface.

(4) Baseflow between aquifers and fixed bodiesincluding streams and reservoirs.

(5) Effects of aquifer pumping on adjacent lakesand streams.

(6) Well installation involved with seawaterinfiltration barriers.

(7) Estimating grouting requirements.

(8) Dewatering of an excavation for constructionpurposes.

(9) Groundwater and surface water interrelatedprojects.

d. Groundwater investigations are based on thecreation of an accurate conceptual model. Aconceptual model is a simplified description of thegroundwater system to be studied. The conceptualmodel can serve as a basis for formulating a numericalmodel. Due to recent advances in computertechnology, the use of numerical models has beenincreasingly commonplace for predicting site reactionsto defined stresses. A simplified flowchart thatsummarizes the general steps involved in ahydrogeologic site characterization and potentialmodeling study is presented as Figure 3-1.

3-2. Steps Involved in a Hydrogeologic SiteInvestigation and Potential Modeling Study

Hydrogeologic investigations generally are complexand require expertise from a number of different fields.Developing a plan that coordinates all the aspects of aninvestigation is vital to the success of the project.Study results can be derived from simplified analyticalmethods (as presented in Chapters 2 and 6) or a morecomplex numerical model which requires the use ofcomputers (as presented in Chapter 5). Accuracy ofthe final product relies on efficient use of time, money,and personnel. The plan generally consists of adetailed outline of the objectives, scope, level of detail,procedures, available equipment, existing and potentialproblems, necessary data, well-thought-out schedule oftasks, and the resources available. Specific deliver-ables and milestones are defined. All personnel should

Initial interpretationof geological andhydrogeological

environment(Literature Search)

Acquisitionof additional

data fromfield

measurements

Use of simulationresults in a groundwatermanagement

problem

Adequate?

Yes

No

Completion

Conceptualmodel

development

Numericalmodel

formulation

Identification of sensitive parameters

anddata gaps

Define Study Objectives

Simplified analysis

adequate?

Yes

No

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Figure 3-1. General flow diagram for characterizing a groundwater flow system for a management decision-makingprocess

be well-informed of the importance of each job in time. It benefits the project manager, the technicalrelation to others. assistance team, and the customer to take the time at

the beginning of the study to define study objectivesa. Determining study objectives.

(1) Objectives defined. Objectives for a ground-water site investigation and analysis consist of a seriesof statements defining, as specifically as possible, theintended use and nature of the results being sought.The objectives define what answers are being sought. (a) The overall purpose of this study is to deter-Defining sound and clear objectives early in the study mine if reservoir inflows will significantly decrease asis not as easy as it sounds. In some cases, simple a result of upstream pumping at proposed irrigationanalytical hand calculations will sufficiently address and water supply wells. Groundwater modeling isstudy objectives. In other cases, a more in-depth desired to determine the maximum changes in waternumerical analysis using computers will be required. levels resulting from proposed pumping of up toWhen customers do not understand the capabilities and 1,000 m /min from three wells located 200 m north oflimitations of analytical procedures and groundwater the stream. The wells are located 2,000 m, 5,000 m,models, and the study managers do not fully and 7,000 m upstream of the reservoir inflow. Theunderstand the needs of the customer, the work may analysis should be performed for both the averagebegin with only a general idea of their objectives. This seasonal high and seasonal low conditions. Performmay lead to unmet expectations and waste of work the analysis using both a best-estimate approach and a

and also to define performance criteria.

(2) Desired specificity. Part of the studyobjectives statement should contain specific anddescriptive constraints on what is expected (see below).

3

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worst-case approach that considers the uncertainty in (4) Performance criteria. Performance criteriathe range of expected values of aquifer hydraulic are set early in the modeling study and specifyconductivity and storage coefficient, streambed standards to measure the appropriateness of dataconductance, and recharge from precipitation. If acquisition, modeling approach, model construction,significant reduction in streamflow is predicted, repeat calibration, use, and presentation. Examples of criteriathe analysis for well locations of 300 m and 700 m include: the basis for zones of homogeneous aquifernorth of the river. properties, limits on the magnitude of allowable

(b) The overall purpose of this study is to calibration targets, and type and degree of sensitivitydetermine groundwater flow travel times and directions analysis testing. These serve as a basis for evaluatingbeneath Swan Lake Landfill. Pollution from the model performance. Criteria are developed and agreedlandfill may contaminate nearby supply wells. upon between the modeling team and the customer. InEstimate the groundwater pore velocities and flow certain cases, a high degree of unknowns prior to thedirections in the unconfined aquifer beneath the Swan modeling effort requires the specification of criteria asLake Landfill at the northeast property corner, the model development progresses. southeast property corner, and at the midpointbetween. Estimate pore velocities directly down- b. Initial interpretation of geologic/hydrologicgradient from these three points every 50 m until environment.intersecting the western property boundary of thelandfill. Estimate overall groundwater travel times (1) Field reconnaissance. A site investigationfrom these three points to the western property should be scheduled for all relevant personnel involvedboundary in the form of “best estimate, and expected ± in the project. Field reconnaissance will provide a30 percent confidence interval values reflecting more complete understanding of site hydrogeology anduncertainties in hydraulic conductivities and boundary project objectives. Additionally, it will aid in theconditions. determination of the feasibility of proposed methods

(3) Objectives and code selections. Modeling documented by photographs and a trip log include theobjectives should be set before conceptual model following:development and numerical code selection. Differingobjectives lead to different modeling approaches. For (a) General character of local geology.example, data for a particular site may indicate that thewater table elevations vary seasonally and interact with (b) Prominent topographic features.the levels of a nearby reservoir. If modeling objectivesincluded determining the effects of reservoir level (c) Location and flow rates of wells and adequacychanges on the water table throughout the year, a of local wellhead protection.conceptual model may describe the changing watertable in a step-wise manner (e.g., monthly averages). (d) Nature, volume, flow, and location of surfaceThis approach would lead to the construction of a waters.model with time-varying boundary conditions andwould require a software code with this capability. (e) Nature, volume, and location of any potentialHowever, if the modeling objective is to determine surface and sub-surface contamination.effects only during that period of low reservoir levels, asimpler conceptual model describing only the typical (f) Nature and location of any significantlow reservoir conditions may suffice. This latter case impermeable areas.would allow construction of a much simpler steady-state numerical model. Additional information on (g) Nature and location of areas of significantproper code selection is presented in Chapter 5. vegetative ground cover.

calibration residuals, number and location of

and use of equipment. Objectives which should be

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(2) Literature search, accessing existing data. associated with the particular groundwater investiga-Existing data should be assessed completely as a first tion. Such recommendations will be consistent withstep to any hydrogeologic site investigation. Much of the level of detail required. The investigator shouldthe data necessary for developing a conceptual model choose the investigative methods which provide themay already have been collected during previous most valuable data within time and cost constraints.investigations of the site. Geologic, hydrologic, The following is a list of some available sources.geographic, and other data can be obtained fromelectronic databases and from reports by the Corps, the (1) Geologic information.U.S. Geological Survey, other federal agencies, andstate, local, and private organizations. The level of (a) Surficial structures and deposits. detail desired will also affect the data needs. All datashould be critically reviewed to validate their accuracy (b) Drilling samples.and applicability to investigation purposes. Data thatshould be reviewed include the following: (2) Hydrologic data.

(a) Regional hydrogeologic reports. (a) Distribution of groundwater levels

(b) Previous investigations of aquifer and/orsurface waters. (b) Flow to/from wells.

(c) Available information on groundwater use, (c) Slug tests.including purpose, quantities, and future projections.

(d) Boring log data.

(e) Cone penetrometer log data. fluctuations in surface water.

(f) Monitoring well data. (f) Response of groundwater levels to loading

(g) Production well data.

(h) Well construction characteristics. hydrology).

(i) Geophysical data. (h) Artificial tracers.

(j) Geologic, hydrologic, and topographic maps (3) Geophysical data.and cross sections of study area.

(k) Aerial photographs.

(l) Land use maps.

(m) Soil maps.

(n) Long-term climatic data. d. Conceptual model development.

c. Acquisition of additional data. Data require-ments should be assessed by the investigator as a (1) Definition. A conceptual model is a simpli-function of cost and the level of acceptable uncertainty fied description of the groundwater system to be

(horizontally and vertically).

(d) Laboratory tests of drilling samples.

(e) Response of groundwater levels to

events.

(g) Water chemistry (geochemistry and isotope

(a) Borehole.

(b) Surface methods.

(c) Ground penetrating radar.

(d) Cone penetrometers.

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Figure 3-2. Example of an integrated approach to asite characterization study

studied. Development of a conceptual model is the (d) Does some of the available data add littlemost important step in developing a computer model. value toward meeting study objectives?Natural area boundaries, hydrostratigraphy, waterbudget, aquifer properties, potentiometric surfaces and (e) What aspects of the conceptual model lackother features are described in a level of detail adequate definition?commensurate with the ability of the data to representthe system. In other words, a highly heterogeneous (f) If data are not available for a particularsystem requires more (and/or higher quality) data to feature, is a computer model expected to be sensitiveprovide for the same level of detail in representing a to that feature?more homogeneous system. Features often describedin conceptual models include the following: (3) Integrated interpretation. During conceptual

(a) Relationship and extent of hydrogeologic units integrated interpretation of all the data available to(hydrostratigraphy, hydrofacies). produce the most accurate assessment of site

(b) Aquifer material properties (porosity, site characterization assesses data from multiplehydraulic conductivity, storativity, isotropy). sources, and combines the data to produce a more

(c) Potentiometric surfaces. accuracy of the model will depend on the accuracy of

(d) Water budget (inflows and outflows such as: were collected, and the expertise of the specialists insurface infiltration, lateral boundary flux, leakage combining and interpreting the data. through confining units, withdrawals and injections).

(e) Boundary locations (depth to bedrock,impermeable layer boundaries, etc.).

(f) Boundary conditions (fluxes, heads, naturalwater bodies).

(g) System stresses (withdrawal wells, infiltrationtrenches, etc.).

(h) Dynamic relationships varying through time.

(i) Water chemistry (varies with purpose;drinking, irrigation, pumping, etc.).

(2) Data requirements.

(a) What is the physical extent of the system to bestudied (horizontally and vertically)?

(b) What are the distinct measurable components (4) Presentation of conceptual model. Graphicof the system? descriptions of the conceptual model can include

(c) What data are currently available?

model formulation, technical specialists perform an

conditions (Figure 3-2). The integrated approach to a

accurate interpretation of the site characteristics. The

the available data, the time frame in which the results

simplified hydrogeologic cross sections,

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potentiometric surface maps, structure maps of during a specific condition. Thus, fluctuations mayhydrogeologic units, three-dimensional graphics, and occur through time, and misleading data could arise.schematic water balance diagrams. Graphics shouldcomplement a written description. (g) Cross-sectional maps. These maps are

(a) Topographic maps. Topographic maps aid in graphy of the subsurface is mapped out using multipledelineating drainage areas, locating desired cross boreholes spaced in a horizontally planar manner.sections, and locating boundaries for other maps Water table, aquifer, and other variances in the sub-(including geologic, depth to water, flow gradients, surface can be identified and mapped out.recharge and discharge areas, and other relatedfeatures). Many different scales are available ranging (h) Fence diagrams. These maps are similar tofrom 1:126,700 to 1:4,800. cross-sectional maps, except they illustrate the surface

(b) Aerial photographs. Aerial photos are oftenused as substitutes for topographic maps. Multiple (i) Hydrographs. Hydrographs show water levelphotographs may be used with a stereoscope to obtain changes for individual wells over time. a three-dimensional view of the area. The Departmentof Agriculture and the U.S. Geological Survey are (j) Water budget. A description of the inflowsgood sources for these photographs. and outflows (water budget) through the model area

(c) Geologic maps and sections. These maps are through the upper surface, leakage through the lowerhelpful when complex geologic structures and surface, and flux through the sides of the model areavariances occur. When accompanied by analysis should be estimated using methods from hydraulic andreports, they aid in locating aquifers, water level seepage theory. These estimates are required to ensureconditions, structural and stratigraphic control of water that predicted and calculated flux through modelmovement, and other related factors. The boundaries match to an acceptable degree. ExamplesU.S. Geological Survey is the primary source of of inflows into the study area include: subsurface flowsuch materials, although mining companies, from upgradient of the study area, recharge fromuniversities, and other geology-related organizations precipitation, leakage from surface water, and injectionmay also be helpful in locating a map and/or study of a wells. Examples of outflows from the study areaspecific area. include: subsurface flow downgradient of the study

(d) Water table contour maps. These maps are extraction wells.similar to topographic maps, the difference being thatthey show water table elevations as opposed to ground e. Conceptual model use. The conceptualelevations. model, together with the computer modeling objectives,

(e) Piezometric surface maps. Piezometric condition and time variation designation, and setting ofsurface maps are similar to water table contour maps, initial conditions in the numerical model. For example,except they are based on the piezometric potential if the conceptual model describes a simple horizontaldeveloped in piezometers which penetrate a single flow system in an unconfined aquifer above a relativelyconfined aquifer. flat impermeable layer, construction of a simple two-

dimensional mathematical model would likely suffice.(f) Depth-to-water maps. These maps show the

depth from the ground surface to the water table. Careshould be taken when using these maps due to theircondition-specific accuracy. They are usuallydeveloped using a limited number of reference points

developed using borehole data. The vertical strati-

and subsurface in three dimensions.

boundaries is key to the conceptual model. Recharge

area, evapotranspiration, leakage to surface water, and

helps guide code selection, grid design, boundary

If, however, the conceptual model reveals a much morecomplex system, then a quasi three-dimensional orfully three-dimensional model should be considered.The conceptual model also helps to identify data needs.

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f. Uncertainty in conceptual models. Formula- computer model is required, initial analytical analysestion of the conceptual model requires dealing with should be performed for comparison with simulateduncertainty. Most of the conceptual model components results.can be represented either as single values, ranges ofvalues, or as statistical distributions. Where possible, h. Numerical model development. Once athe values should be carried through the analysis as complete conceptual model has been developed, aranges or distributions. This is particularly the case numerical model can be generated. Parametersfor hydraulic conductivity estimates, the variation of determined during conceptual model development arewhich has a relatively large impact on modeling integrated into a computer model. The computer modelresults. The computer modeler's approach in dealing is then calibrated to reproduce measured fieldwith uncertainty depends on the quality and conditions. If model calibration is judged acceptable,completeness of available data, the level of confidence the computer model can be used to predict otherrequired by the modeling objectives, and the quality hydrogeologic changes due to new stresses; forand quantity of resources available to do the modeling instance, the introduction of a pumping well forjob. Eliminating uncertainty altogether is an unlikely groundwater cleanup, within the site. If the numericaland impractical objective for groundwater modeling. model does not produce acceptable results duringManaging uncertainty and communicating its effects calibration, then it may be necessary to completelyare essential to good modeling. During conceptual reanalyze the geologic and hydrogeologic parameters.model development, the following should be considered A complete discussion of numerical model developmentwhen managing uncertainty: is presented in Chapter 5.

(1) Document the quality, quantity, andcompleteness of the data upon which the model isbased.

(2) Document data sources.

(3) Assess additional data needs.

(4) Document the boundary conditionassumptions.

(5) If a component is set at a single value, or if ahydrofacie surface is set as unique, document theassumptions and implications of doing so.

(6) If components are to be carried forward to thenumerical model as a range or a distribution, documenthow these were derived and why doing so meets themodeling objectives.

g. Simplified analysis. In cases where data arelimited or a detailed analysis is not required, studyobjectives can often be met without the use ofcomputer models. In these cases, simplified analyticalcalculations (see Chapters 2 and 6), such as estimatingthe capture zone of a pumping well or using Darcy'sLaw to estimate groundwater flow volumes, mayadequately address study objectives. In cases when a

3-3. Project Management

a. General. A successful modeling analysisinvolves much more than manipulating modelingsoftware. The analysis should develop and presentinformation that answers the questions posed by theproject. This requires proper planning and control.

b. Planning and control. Project managementinvolves project planning and project control. Becausegroundwater models often play a decisive role in watersupply and remediation studies, the modeler should bepart of the project management team and take part insetting the objectives and schedules in the projectmanagement plan.

(1) Project planning. Project planning includesidentification of existing data and data needs, definitionof work requirements, work time frame, and resourcesneeded. Definition of work requirements, primarily inthe form of establishing modeling objectives, is thesingle most important key to project planning forgroundwater modeling studies. Before constructing theconceptual model and before choosing the modelingsoftware, groundwater modelers and their customersneed to understand what exactly the objectives ofperforming a modeling study are. An understanding of

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modeling objectives and some experience with be detailed and closely reviewed by Corps personnelmodeling is also necessary when estimating expected having a high degree of expertise. In Corps officesschedule and resource requirements. There is no “one where expertise in groundwater modeling is limited,size fits all” schedule and technical resource personnel could be sent to several groundwaterrequirements in groundwater modeling. Simple models modeling courses which are available. Corps centerscan be performed in a matter of weeks while complex of expertise and research and development centers canmodels often require months or even years. assist in providing direction and review.

(2) Project control. Project control includesmonitoring progress, measuring performance, andmaking adjustments as necessary. Key intermediatemilestones that can be used to monitor progress are:

(a) Establishment of modeling objectives.

(b) Completion of a conceptual model.

(c) Successful calibration of the modelapplication.

(d) Obtaining preliminary results.

(e) Model testing.

(f) Obtaining final results and reporting.

Measuring the quality of model development andmaking appropriate adjustments to the work scope arenot easy tasks. Typically, a modeler requires outsidereview to aid in assessing the adequacy of modeldevelopment as it progresses. At a minimum, peerreview should be performed at the completion of theconceptual model and then again when interpretingpreliminary results even if the modeler feels that thingsare going well.

c. Maintaining/developing corps technicalexpertise. Performing groundwater modeling studies“in-house” provides the advantage of development ofexpertise within the Corps. Such expertise greatlyincreases the Corps’ capacity to write scopes of workthat give specific and complete direction for both in-house and contracted work. Expertise within the Corpsalso adds flexibility for performing small projects aswell as controlling changes in large projects. Wheremany changes are likely to occur, contracting outwithout adequate control can lead to excessive costs.When it is necessary to contract out groundwatermodeling projects, scope of work specifications should

3-4. Personnel

a. Project team. A groundwater modelingproject truly requires a multidisciplinary approach.Although the modeler performs a key role, alsorequired are the project manager, geologists and/orhydrogeologists, geotechnical engineers, field datacollection personnel, hardware and softwarespecialists, and graphics support personnel. Inaddition, interfaces with hydrologists and hydraulicengineers, meteorologists, chemists, soilengineers/physicists, Geographical InformationSystems specialists, environmental engineers and datamanagement specialists are often required. The basicmodeling team should consist of the followingpositions:

(1) Project manager.

(2) Groundwater modeler.

(3) Geologist, hydrogeologist.

(4) Software/graphics support.

(5) Peer review.

A single individual can perform more than one of theabove roles. It is important that the modeler maintainclose relationships with geologists and other fieldpersonnel who characterize the site. Arranging foroffsite peer review increases the soundness of themodeling approach and adds credibility to the finalproduct.

b. Roles.

(1) Project manager. The project manager isresponsible for overall planning and control. Thesetting of objectives, schedules, and allocation of

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resources require early planning by the project a. Define objectives. A feasibility study wasmanager. Oversight of funds and interaction with performed for construction of a wastewater treatmentvarious larger project elements, customers, and plant that will discharge up to 5 million gallons per dayregulatory agencies are main activities. The project to an aquifer recharge lagoon. Groundwater modelingmanager also monitors progress and actively was used to: (1) make predictions of the highest waterparticipates in making corrective actions to the scope table elevations expected in a typical 10-year timeand schedule. The project manager is also responsible period resulting from maximum natural andfor the assembly of the modeling team and delegating wastewater recharges, and (2) make predictions of thespecific project assignments and responsibilities. groundwater flow paths for the same conditions.

(2) Groundwater modeler. The groundwater objectives were agreed upon by the parties involved. modeler is responsible for developing the conceptualmodel, designing the model grid, determining b. Form study team. To perform this task, aparameter inputs, model calibration, model execution, study team was assembled consisting of a projectand interpretation of results. Because of the highly manager, a geologist, a groundwater modeler/subjective nature of the modeling process, it is hydrogeologist, a hydrologist, and a graphics supportimportant that the modeler have a strong background in technician; several of these tasks can be performed byhydrogeology, along with an intimate understanding of the same person. A knowledgeable modeler fromsite geology. another District agreed to provide peer review. The

(3) Geologist/hydrogeologist. The responsibilities milestones for tracking progress.of the geologist can include direct gathering of fielddata, interpretation of site characterization information, c. Develop conceptual model. A conceptualand development of the conceptual model with the understanding of site hydrogeology was initiallymodeler. compiled from several existing well logs, water table

(4) Software and graphics support. These and field observations. These sources indicated severalpersonnel provide assistance in code installation and data gaps that led to the installation of three additionaltesting, linking programs, and developing formulation wells and performance of a pumping test. Using theof output. Graphics support is important in model additional data gathered, a conceptual model wasdocumentation and presentation of model results. developed that described the hydrogeologic units,

(5) Peer review. A highly qualified expert in the table surface, and aquifer transmissivities.field of groundwater modeling should be retained toprovide periodic technical oversight along with critical d. Simplified analysis. Darcy's Law (see Chap-review of the final model. Review of the conceptual ter 2) was applied to provide an initial estimate ofmodel is essential. To provide a different perspective seepage rates from the recharge lagoon to thein the modeling effort, it is helpful that this person be groundwater table.somewhat removed from the daily modeling projecteffort. e. Select computer model. Having defined the study objectives and groundwater flow system,3-5. Example of Site Characterization andModeling Process

This example outlines simplified steps in performing agroundwater investigation and modeling study. Anoverview of the technical aspects of groundwatermodeling is presented in Chapter 5.

Specific detailed statements defining modeling

team defined the modeling objectives, schedule, and

measurements, climate records, a topographic map,

hydrogeologic boundaries, water budget, existing water

modeling software with the capability of computingwater table elevations and flow paths was thenselected. The software had the capability to perform atwo-dimensional, steady-state approach that wasdetermined to be consistent with the modelingobjectives.

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f. Develop the initial model input files. At this j. Model application. The calibrated model waspoint the features of the conceptual model were then used to simulate the “worst case” conditiontransferred to the modeling software input file where, (highest water table elevations expected) that includedwith help from the software, they were represented on a maximum wastewater discharge plus natural rechargetwo-dimensional grid. This grid was superimposed on from the 10-year storm. The highest typical seasonala site map which aided the assignment of water table condition and the lowest estimates oftransmissivities and recharge locations. The grid transmissivities for the hydrogeologic units were alsostructure and zonation of aquifer properties was kept used. as simple as possible; i.e., the complexity of the modelshould be commensurate with the ability of the data to k. Produce modeling results. The modelingrepresent the system. The boundaries of the grid software produced output in the form of water tablerequired special attention to ensure that flows and maps and flow-line graphics. When compared withheads within the model area realistically matched those observed conditions, the simulated output presentedof the surrounding areas. expected changes in groundwater flow directions as a

g. Model calibration. After a software input file demonstrated that several low-lying areas at the sitecontaining the “best estimate” representation of the may be inundated by raised groundwater levels for thenatural system was created, the modeling software was conditions tested.run repeatedly to resolve any obvious anomalies. Thisprocess of iteratively running the modeling software, l. Final report. The modeling study reportcomparing the output to observed site conditions, then documented the purpose, approach, and results of theadjusting inputs within specified ranges is called analysis. The report fully addressed the followingcalibration and was continued until the computed heads topics:and boundary flows matched field conditions.

h. Sensitivity analysis. Sensitivity analysis is themeasure of uncertainty in the calibrated model caused (2) Data acquisition.by uncertainty in aquifer parameters and boundaryconditions. Sensitivity analysis was performed by (3) Summary of geologic and hydrologicsystematically changing the calibrated values of conditions.hydraulic parameters by defined factors (such as 0.5and 2.0), while holding all other model parameters (4) Development of conceptual model.constant. Sensitivity analysis identifies parametersmost important in conceptual model development, and (5) Computer code selection.can be used as a guide for additional data acquisition.

i. History matching. Model simulations wererun and results were compared with field data which (7) Boundary and initial conditions.were not used in the calibration process. For example,if the model was calibrated to simulate seasonal water (8) Determination of hydrogeologic propertieslevel fluctuations for 1994, a comparison between (calibration).measured and simulated water levels from 1993 can beperformed if data are available. A favorable (9) Sensitivity analysis.comparison lends greater validity to model predictivecapability. An unfavorable comparison indicates that (10) Model application.further calibration (and perhaps data acquisition) isnecessary.

result of wastewater plant discharge. The simulations

(1) Definition of model objectives.

(6) Definition of model grid and model layer.

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(11) Interpretation of results. m. Post audit. Following development of theinitial numerical model, the predictive capability of the

(12) Recommendations for future monitoring anddata gathering.

A complete explanation of the physical basis or otherjustification for all parameters used in modeldevelopment was included. Additionally, a discussionof how uncertainty was dealt with was included in themodeling report. (Approaches for dealing withuncertainty are discussed in Chapter 5). Tabularcomparisons of computed and observed values used forcalibration and for results of the sensitivity analysiswere included. Graphical representation, includingcolor graphics, were included for conveying thecomplexities of spatially distributed information.Time-varying graphics in the form of videopresentations were provided.

model was periodically monitored as new field databecame available. Model recalibration should beperformed if it is judged that the additional data allowfor a significantly more accurate conceptualization ofsite conditions.

3-6. Conclusion

The purpose of this chapter was to present a generaloverview of performing a groundwater siteinvestigation and modeling study from a projectmanagement perspective. The following chaptersprovide technical information on investigative methods,and numerical modeling of groundwater flow.Additionally, a detailed summary of a specificgroundwater site investigation and modeling study ispresented as Appendix C.

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Chapter 4Field Investigative Methods

4-1. General

a. Adequate conceptualization of a hydrogeologicsystem often requires the acquisition of new field data.This chapter provides an overview of different methodswhich can be employed to gain a better understandingof subsurface conditions pertaining to the occurrenceand flow of groundwater. Key references are providedto allow for a more detailed understanding of conceptsand applications. Hazardous, toxic, and/or radioactivewaste (HTRW) investigations often require specialconsideration beyond the scope of this text.

b. Initially, information that can be obtained in theprocess of, and as a product of, the construction of awell is described. The construction and developmentof wells can provide a wealth of information onsubsurface conditions. Geologic logging duringdrilling of a borehole enables the delineation of high-conductivity and low-conductivity strata. Boreholegeophysical methods can provide information on thelithology, porosity, moisture content, permeability, andspecific yield of water-bearing rocks; additionally,borehole geophysical methods can also help define thesource movement and chemical characteristics ofgroundwater. Completed wells offer information onhydraulic head and water quality. Finally, wellsprovide a conduit through which stress can be placedupon an aquifer by the extraction or injection of water.Aquifer properties, such as transmissivity and storagecoefficient, can then be estimated by the aquiferresponse to these stresses.

c. An overview of surface geophysical methods isthen presented. Surface geophysical methods allow forthe nonintrusive gathering of information onsubsurface stratigraphy and hydrogeologic conditions.Surface geophysical methods include seismic refractionand reflection, electrical resistivity, gravitationalmethods, electromagnetic methods, and ground-penetrating radar. A section on cone penetrometers isthen included. Cone penetrometers often provide acost-effective method for gathering significant data onsubsurface stratigraphy. Finally, overviews on the useof geochemistry, and the response of water levels to

loading events to gain information on subsurfaceconditions are included.

d. An additional method for acquiring newhydrologic data is studying the interaction betweensurface water and groundwater. For example, theeffects of surface water fluctuations on groundwaterlevels can be used to estimate the aquifer transmissivityand storage coefficient. Analytical methods forquantifying interaction of surface water andgroundwater are presented in Chapter 6.

4-2. Wells

a. Well drilling methods.

(1) General. The overriding objectives in pumpingwell design and construction are as follows: theattainment of the highest yield possible with minimumdrawdown in pumping wells, good water quality,minimizing environmental effects, ensuring boreholeintegrity, minimizing siltation, and reasonable short-and long-term costs. Various well drilling methodshave been developed in response to the range ofgeologic conditions encountered, and the variety ofborehole depths and diameters that are required. Themost common methods employed in drilling deep wellsare direct and reverse circulation mud rotary, directand reverse circulation air-rotary with casing drive,hollow stem auger drilling, and the cable tool method.The terms direct and reverse refer to the direction inwhich the drilling fluid (mud or air) is circulated. Indirect drilling, the drilling fluid is circulated down thestring of drill tools out the bit and up the annulusbetween the tool string and the borehole wall. Inreverse, as the name implies, the direction ofcirculation is reverse that of direct drilling. An in-depth description of drilling methods can be found inDriscoll (1986).

(2) Mud rotary. The rotary methods provide arapid means for drilling in a wide range of geologicconditions. In direct mud rotary, a hollow rotating bitis used, through which a mixture of clay and water,known as drilling mud, is forced out under pressurizedconditions. This drilling mud serves the dual purposeof transporting cuttings to the surface along withsealing the borehole wall, thus allowing the hydrostatic

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pressure of the drilling mud to hold the borehole open. samplers to be inserted through the center of theAdvantages in using the direct mud rotary method augers. The hollow stem of the augers also acts toinclude its rapid drilling rate, and the non-requirement temporarily case the borehole, so that the well screenfor placing casing during drilling operations in and casing may be inserted down through the center ofunconsolidated material. Disadvantages include mud the augers once the desired depth is reached,disposal, the need to remove mud lining from the minimizing the risk of possible collapse of the boreholeboring walls during well development, and difficulty in that might occur if it is necessary to withdraw theidentifying when the water table is encountered. augers completely before installing the well casing and

screen. The hollow-stem auger drilling technique is not

(3) Air rotary. In air-rotary drilling, air, ratherthen drilling mud, is used to remove cuttings and coolthe bit. Air rotary drilling can be done open-hole(semi- and consolidated formations) or in conjunctionwith simultaneously driving the casing (unconsolidatedformation). Air for drilling is supplied either by an on-board or auxiliary air compressor. Air is circulated atvolumes up to 57 m /min at pressure up to 2,400 kpa;3

however, in unconsolidated formations pressure above1,000 kpa is unnecessary and can cause excessiveborehole erosion and borehole instability. The airshould be filtered to remove compressor oil and othercontaminants prior to use in drilling. When drilling inunconsolidated formations, air rotary drilling istypically done in conjunction with driving the casing tostabilize the borehole. The advantages of air rotarydrilling are its rapid drilling (penetration) rate, lack ofdrilling mud and associated clean-up, and the accuracywith which the water table can be located when drillingat low pressures (i.e., < 700 kpa). Disadvantagesinclude higher cost, access for larger equipment, andnoise.

(4) Hollow stem auger. Hollow stem augerdrilling is a rotary drilling method that does not requirecirculation of a fluid medium. Rather, the borehole isadvanced and cuttings removed by a cutter headfollowed by a continuous flight or helix of auger rampswhich can be likened to a wood screw. Modern hollowstem auger drills can install wells to depths greaterthan 80 m in unconsolidated formation (hollow stemaugers are not for use in semi- or consolidatedformations). When drilling, a cutting head is attachedto the first auger flight, and as the auger is rotateddownward, additional auger flights are attached, one ata time, to the upper end of the previous auger flight.As the augers are advanced downward, the cuttingsmove upward along the continuous flighting. Thehollow stem or core of the auger allows drill rods and

without problems. These are more completelydescribed in Aller et al. (1989), but generally include:

(a) Heaving: Sand and gravel heaving into thehollow stem may be difficult to control, and maynecessitate adding water to the borehole.

(b) Smearing of silts and clays along the boreholewall: In geologic settings characterized by alternatingsequences of sands, silts, and clays, the action ofthe augers during drilling may cause smearing ofclays and silts into the sand zones, potentially resultingin a considerable decrease in aquifer hydraulicconductivity along the wall of the borehole. Thesmearing of clays and silts along the borehole wallmay, depending on the site-specific properties of thegeologic materials, significantly reduce well yield orproduce unrepresentative groundwater samples evenafter the well has been developed.

(c) Management of drill cuttings: Control ofcontaminated drill cuttings is difficult with the augermethod, especially when drilling below the water table.

(5) Cable tool method.

(a) The cable tool method is one of the oldest andmost versatile drilling techniques. Penetration into thesubsurface is achieved by lifting and dropping a stringof tools suspended from a cable, with the weight of thefalling tools providing the driving force. The string oftools generally consists of four sections: the swivelsocket, the drilling jars, the drill stem, and the drill bit.The swivel socket rotates the bit, allowing it to strike adifferent area of the hole bottom with each stroke. Thedrilling jars consist of two loosely interconnected rods.Their purpose is to enable a reverse hammering effectto free the bit and stem, should they become lodged inthe borehole. The drill stem keeps the drill bit driving

Filter Pack

Annular Seal

Screen

Casing (6 in.)

Backfill (10-in. hole)

GroutGround Level

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Figure 4-1. Basic well components

straight, while also providing additional weight. The b. Well design and completion.bit crushes and mixes any materials in the drilling path.The debris is removed by the addition of water (whenabove the water table) into the borehole to produce aslurry that can then be pumped out. Cable tool drillingis usually limited to borehole diameters less than 75 cm(30 in.) and drilling depths less than 600 m (2,000 ft).

(b) The advantages of this type of drilling are lowcost and ability to drill into a variety of mediums inmany conditions. Additionally, this method providesfor an accurate logging of formation changes. It issensitive to any medium changes, allowing the driller toadjust sample increments. This method also uses lesswater than other drilling methods, which is convenientwhen drilling in desolate arid regions. The majordisadvantages are a slow drilling progress, thelimitation in borehole sizes and depths, and the need todrive casing coincident with drilling when drilling inunconsolidated materials.

(1) General. Well design should address thefollowing factors: the depth of the well screen orscreens; diameter of screen and casing; type of material(e.g. mild steel, stainless steel, etc.); the type of wellscreen (mill slot, shutter slot, continuous slot, etc.);gradation of the filter pack (formation stabilizer)surrounding the well screen; and the type andcomposition of annular seals (e.g. conventional neatcement versus high-solids bentonite grout). Wellcompletion involves setting and positioning casing andwell screens, placing filter pack, sealing the annularspace, and constructing well-head features at theground surface. While each of these design elements isdependent upon site-specific conditions such as thepurpose of the well and available funding, there aresome general guidelines that need to be incorporatedinto every design. Figure 4-1 illustrates basic wellcomponents. Driscoll (1986) presents a more completediscussion of well design and completion procedures.

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(2) Casing. Casing should be of sufficientstrength to withstand not only the depth of installation,but also a certain amount of abuse during handling andinstallation. Casing should be of sufficient diameter toaccept a pump at least one size larger than currentlyrequired in order to account for potential lowering ofthe water table.

(3) Filter pack. The filter pack commonly con-sists of a graded sand which is artificially placedaround the well screen to stabilize the aquifer,minimize sediment entering the well, permit the use ofa large screen slot size, and provide an annular zone ofhigh permeability. The filter pack is a key element inthe hydraulic efficiency of the well. The filter packneeds to provide a smooth gradation transition from theformation. Essentially, the gradation of the filter packis based upon the uniformity coefficient (a measure ofhow well it is sorted) and the D (70 percent passing70

sieve size) of the formation. These parameters areobtained from sieve analyses of formation samplesobtained during exploratory drilling. Depending uponthe uniformity coefficient, the D of the formation is70

multiplied by a factor from 3 to 9. The resulting valueis the new D for the filter pack. Utilizing the new70

D , the filter pack gradational curve is constructed70

such that it roughly parallels the formation gradationalcurve.

(4) Well screen. Well screen design encompassesa balance between required strength and desiredhydraulic efficiency. Hydraulic efficiency is basicallya function of the amount of open area in a well screen;the greater the open area, the greater the area availablefor groundwater flow and thus greater hydraulicefficiency. Generally, one strives to maximizehydraulic efficiency at a prescribed strength. A keyelement of well screen design is the size of theopenings, referred to as slot size. The slot size is afunction of the filter pack gradation. The slot size istypically selected to retain 80-90 percent of the filterpack. Well screens are placed at the depths of interestto: hydrologically isolate formations, prevent sandmovement into the well, and minimize hydraulicresistance to water entering the well. Screens areavailable in a variety of materials, diameters, and slotsizes depending on the hydrologic and water qualityparameters of the aquifer, the desired well yield, andaquifer thickness.

(5) Annular seals. In choosing an annularsealant, the following factors should be considered:borehole stability (e.g., an unstable or caving boreholeneeds an easily placed, quick-setting sealant such ashigh-solids bentonite grout); the method with which thewell was drilled; and the type of well casing (e.g., theheat of hydration from thick cement seals candeform/melt PVC casing).

(6) Placement of cement or grout. Wells arecemented, or grouted, in the annular space surroundingthe casing to prevent entrance of water of unsatis-factory quality, to protect the casing from corrosion,and to stabilize caving rock formations. It is importantthat the grout be introduced at the bottom of the spaceto be grouted by use of a tremie pipe to ensure the zoneis properly sealed.

c. Well development. Wells are developed byremoving the finer material from the natural formationssurrounding the screening. A new well is developed toincrease its specific capacity and prevent silting.Development procedures are varied and includepumping, surging, hydraulic jetting, and addition ofchemicals. The basic purpose of all these methods isto agitate the finer material surrounding the well sothat it can be carried into the well and pumped out.Pumping involves discharging water from a well insuccessive steps until clear water is produced. Surgingutilizes a block which is moved in an up-and-downmotion with increasingly faster strokes. Compressedair can also be utilized to create rapid changes in waterlevels within the well casing. Hydraulic jetting utilizesa high-velocity stream of water which is rotated acrossthe full extent of the screened area removing finer-grained material from the gravel packing by turbulentflow. Chemical additives, such as hydrochloric acid,can be employed in open hole wells in limestone ordolomite formations to remove finer particles andwiden fractures.

d. Well efficiency. The objective in well designis to avoid excessive energy costs by constructing awell that will yield the required water with the leastdrawdown. Well efficiency can be defined as the ratioof the drawdown in an aquifer at the radius of the wellborehole (just outside the filter pack in the aquifer) tothe drawdown inside the well. The difference betweenaquifer and well drawdowns is attributed to head losses

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as water moves from an aquifer into a well and up the (3) Adequate well diameter to accommodatewell bore. These well losses can be reduced by appropriate tools for well development, aquifer testingreducing the entrance velocity of the water, which is equipment, and water quality sampling devices. accomplished by installing the maximum amount ofscreen and pumping at the lowest acceptable rate. (4) Surface protection to assure no alteration ofOther factors involved in reducing well loss include the structure or impairment of the data collected fromproper development techniques and proper filter pack the well (Aller et al. 1989). design. c. In essence, one should strive to construct a4-3. Monitoring Wells

a. The primary objectives of a monitoring wellare to provide an access point for measuring ground-water levels and to permit the procurement ofgroundwater samples that accurately represent in situgroundwater conditions at the specific point of 4-4. Geologic Loggingsampling. To achieve these objectives, it is necessaryto fulfill the following criteria: Logs of rock and soil encountered during drilling can

(1) Construct the well with minimum disturbance delineation of high-conductivity and low-conductivityto the formation. strata. The character, thickness, and succession of the

(2) Construct the well with materials that are existing aquifers, aquitards, and aquicludes and thecompatible with the anticipated chemical and interaction between surface water and the subsurface.geochemical environment. All geologic logs should follow procedures listed in

(3) Properly complete the well in the desired zone.

(4) Adequately seal the well with materials thatwill not interfere with the collection of representativewater samples.

(5) Sufficiently develop the well to remove anyadditives associated with drilling and provideunobstructed flow through the well (Aller et al. 1989).

b. In addition to appropriate construction details,the monitoring well must be designed in concert withthe overall goals of the monitoring program. Keyfactors that must be considered include the following:

(1) Intended purpose of the well.

(2) Placement of the well to achieve accuratewater levels and/or representative water qualitysamples.

well that is transparent to the aquifer in which it isconstructed. Aller et al. (1989) and American Societyfor Testing and Materials (ASTM) (1993) provide in-depth guidelines for the design and installation ofgroundwater monitoring wells.

provide the most direct and accurate means for the

underlying formations provide important data as to

Engineer Manual (EM) 1110-1-4000 (1994).

4-5. Measuring Water Levels

a. Data uses. Accurate measurements ofgroundwater levels are essential for conceptualizationof site hydrogeology. Information which can beprovided by water level measurements includes thefollowing:

(1) Rate and direction of groundwater movement.

(2) Status or change in groundwater storage.

(3) Change in water level due to groundwaterwithdrawal.

(4) Amount, source, area of recharge, andestimate of discharge.

(5) Hydraulic characteristics of an aquifer.

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(6) Identify areas where the water table is near the weight is generally attached to the end to aid in plumb-land surface. ness and added feel. A lead weight is less likely to foul

(7) Delineate reaches of losing or gaining streams should be made so that should the weight becomeor canals. lodged in the well, it will break off allowing retrieval of

b. Data sources. Water level data can be the tape is marked with carpenter’s chalk. The amountacquired from a number of sources, including existing submerged into the water will enable a reading to bewells, piezometers, and from surface water/ taken by viewing the wetted portion. Corrections forgroundwater interfaces such as lakes, streams, and thermal expansion of tapes greater than 300 m (1,000springs. Observation wells can be installed at neces- ft) in length should be applied in extreme temperatures.sary locations where other resources do not exist. Two measurements should be taken, with an agreement

c. Data requirements. In addition to water level down the well, or if the water surface is disturbed, itelevation, the following information should be recorded may be impossible to get an accurate reading. If oil iswith each measurement: present on top of the water in depths greater than a

foot, then the thickness of the oil layer must be known(1) Local well name and owner.

(2) Date drilled.

(3) Well use.

(4) Location by legal description, such as latitudeand longitude coordinates.

(5) Approximate location relative to locallandmarks.

(6) Elevation of land surface and measuring point.

(7) Well depth, size and type of casing, locationand type of perforations.

d. Methodology. There are essentially three maintechniques to measuring water levels in non-flowingwells, the graduated steel tape (wetted-tape method),the electrical measuring line, and air lines. All threehave their advantages and disadvantages for measuringunder certain conditions.

(1) Graduated steel tape method. This method iswidely considered to be the most accurate method formeasuring water levels in non-flowing wells. Tapes inlengths of 50, 100, and 300 m, and 100, 200, 500, and1,000 ft are among the most common. They areavailable as either black or chromium-plated, withblack being preferred by most. Tapes up to 150 m(500 ft) in length are usually hand-crank-operated,while longer tapes are often motor-driven. A lead

any pumps due to its soft nature. The attachment

the tape. To acquire a measurement, the lower end of

of less than 0.6 cm (0.25 in.). If water is dripping

to compensate for the lower density; thus, a higherwater level measurement. The oil level can bedetermined by using a water detector paste that willshow both the water and the oil levels.

(2) Electrical method. Electrical measuringdevices generally consist of two electrodes thatcomplete a circuit when immersed in water. Theseelectrodes are attached to a power supply by aconductive cable. There are various other types ofelectrode/cable combinations, with the two-conductorcable and special probe being the most common. Thecable is generally 150 m (500 ft) long and uses a hand-cranked reel. The advantage to the electrode method isthe ability to take multiple measurements withouthaving to fully remove the cable from the well. It alsois more accurate than the steel tape when measuring ina pumping well where the water may be splashing ordripping down the well. These conditions will usuallyfoul a steel tape measurement. They are also saferwhen used in pumping wells because they detect thewater immediately, lessening the chance of loweringthe probe into pump impellers. The disadvantages arethat they are more bulky than the steel tape, and lessaccurate under ideal conditions. The measurementsshould be within 1 cm (0.04 ft) for less than 60-m(200-ft) depths, and about 3 cm (0.1 ft) for 150-m(500-ft) depths. Measurements have been within15 cm (0.5 ft) for depths as great as 600 m (2,000 ft).Adapters can be added to sensing probes to detect oil.After multiple uses, the length of the cable should bechecked because stretching may occur during use.

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(3) Air line. Air pressure lines consist of an recharge events completely. Under certain pretenses,airtight tube that when submerged into the water is infrequent measurements (semi-annual) may suffice. purged by compressed air. The pressure required topurge the tube is related by the depth of the tube in the g. Effect of changes in barometric pressure onwater. Multiplying the pressure in psi by 2.31 ft/psi water levels in confined aquifers. Changes in atmo-will give the depth. In metric, multiplying the pressure spheric pressure can have a significant effect on waterin Pascals by 4,850 m/Pascal will give the depth. That levels in wells penetrating a confined aquifer. In con-distance can then be subtracted from the total length of fined aquifers, well measurements should be correctedthe tube in the well and the depth to water will be to a constant barometric pressure (Section 4-12).determined. This technique works well where thesurface of the water is being disturbed. The durabilityof air lines has historically been a problem, as theybecome clogged with mineral deposits or may formleaks, both leading to false measurements. Theaccuracy of this technique relies mostly on theaccuracy of the gauge being used. Other measuringtechniques should be employed periodically.

e. Recording devices. Automated devices forrecording changes in water levels may be mechanical,electronic, or electromechanical. Electromechanicaldevices usually consist of a float that measures theactual vertical changes in water levels. Mechanical orelectronic devices consist of submerged probes thatmeasure changes in pressure from varying waterdepths. Rapid changes in depth are measured withgreater accuracy with pressure sensing devices sincethey are able to detect the changes more rapidly than afloat. Floats lose most of their accuracy from cablefriction along the well walls. The recording deviceitself is generally a simple mechanism that is able tochart the water level versus time. Due to the delicatenature of the recording device, some sort of housingshould be provided to protect it from weather andvandalism.

f. Measurement frequency. The basic factorsdetermining measurement frequency are the types offluctuations expected, the potential use of the data, andthe available personnel. Fluctuations occur due tomany factors, including: pumping, recharge (from anynumber of sources, manmade and natural), and evapo-transpiration. Use of the data will determine thedesired frequency of measurements, with restraintsfrom equipment and personnel. Automatic recordersare best for high-frequency measurements. Humanerror may cause discrepancies in frequent measure-ments causing the data to skew results. Weekly andmonthly measurements may miss pumping and

4-6. Pumping Tests

a. General. Pumping tests (or aquifer tests) arein situ methods that can be used to determine hydraulicparameters such as transmissivity, hydraulicconductivity, storage coefficient, specific capacity, andwell efficiency. Hydrogeologic values derived frompumping tests are averaged over the spatial zone ofinfluence of the test. The basic steps involved inperforming a pumping test are: (1) backgroundmeasurements; (2) pumping test measurements; and(3) recovery measurements. Depending on data needsand well and geological conditions, two general typesof pumping tests can be performed : constant-ratepumping tests, and step-drawdown pumping tests.Data measured during a pumping test include: flowrates, time, and water levels. Atmospheric pressuremeasurements can be additionally made when perform-ing tests in confined aquifers. Several analyticalmethods for data interpretation are available. Appen-dix D presents an overview of general methods avail-able. Recommended references for a more in-depthdiscussion of pumping tests and accompanying analyti-cal methods are: Dawson and Istok (1991), Krusemanand De Ridder (1983), Driscoll (1986), and Walton(1987).

b. Flow to pumping wells.

(1) General. The study of well hydraulics is acomplicated blend of mathematics, fluid mechanics,and soil physics. It is as much an art as a science. Thefollowing sections present wells from a somewhatidealized perspective, oftentimes greatly simplifying thetrue system. Through this idealization, the resultingequations simplify to solutions that are exact or easilyapproximated to near exact solutions. Generalassumptions for all cases are: (a) that the aquifer isisotropic, homogeneous, and of infinite areal extent;

t1

t0

t1

t0

t1

t0

t1

t0

Low T Low S

High SHigh T

Transmissivity (T) Storage Coefficient (S)

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Figure 4-2. Influence of transmissivity and storagecoefficients on cone of depression for similar aquifersat a constant pumping rate

(b) the well fully penetrates the aquifer; (c) the flow ishorizontal everywhere within the aquifer; (d) the welldiameter is so small that storage within the well isnegligible, and; (e) water pumped from the well isdischarged immediately with decline of piezometrichead. The general governing equation for all idealizedcases is Laplace's equation in cylindrical coordinates.Detailed derivations of these equations are performedin Freeze and Cherry (1979).

(2) Specific capacity. The specific capacity of awell is the yield per unit drawdown, and is determinedby dividing the pumping rate at any time by thedrawdown at the same time. The specific capacity of awell depends both on the hydraulic characteristics ofthe aquifer and on the construction, pumping rate, andother features of the well. Values of specific capacity,available for many supply wells for which aquifer-testdata are not available, are widely used by hydrologiststo estimate transmissivity. c. Types of pumping tests.

(3) Cone of depression. The movement of water (1) Constant-rate test. A constant-rate pumpingfrom an aquifer into a well results in a cone of test consists of pumping a well at a constant rate for adepression (also known as zone of influence). Because set period of time (usually 24 or 72 hr), and monitoringwater must converge on the well from all directions, the response in at least one observation well. Theand because the area through which the flow occurs number and location of observation wells is dependentdecreases toward the well, the hydraulic gradient must upon the type of aquifer and the objectives of theget steeper toward the well. The size of a cone of study. Values of storage coefficient, transmissivity,depression is dependent primarily on the well pumping hydraulic conductivity (if aquifer thickness is known),rate, elapsed time since start of pumping, aquifer type, and specific capacity can be obtained. aquifer transmissivity, and aquifer storativity (Figure4-2). Withdrawals from an unconfined aquifer result in (2) Step-drawdown test. During a step-drainage of water from rocks through which the water drawdown test, the pumping rate is increased at regulartable declines as the cone of depression forms. intervals for short time periods. The typical step-Because the storage coefficient of an unconfined drawdown test lasts between 6 and 12 hr, and consistsaquifer closely approximates the specific yield of the of three or four pumping rates. Because step-aquifer material, the cone of depression expands drawdown pumping tests are typically much shorterslowly. On the other hand, a lowering of the water than constant-rate pumping tests, transmissivity andtable results in a decrease in aquifer transmissivity storativity values are not as accurate for these tests.which will cause an increase in drawdown both in the The primary value of the step-drawdown test is inwell and in the aquifer. Withdrawal from a confined determining the reduction of specific capacity of theaquifer causes a drawdown in artesian pressure and a well with increasing yields. corresponding expansion of water and compression ofthe mineral skeleton of the aquifer. The very small (3) Recovery test. A recovery test consists ofstorage coefficient of a confined aquifer results in the measuring the rebound of water levels towardsrapid expansion of the cone of depression. preexisting conditions immediately following pumping.

The rate of recovery is a valuable source of data

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which can be used for comparison and verification of based on the conceptual geologic model. Nearbyinitial pumping test results. property owners may have wells and can be of some

help, as can local water well drillers.d. Pumping test design.

(1) General. Before implementing a constant-rateor step-drawdown pumping test, the well should bedeveloped adequately to reduce the influence of wellconstruction on aquifer response. Aquifer data from apumping test should be derived from both the pumpingwell and appropriately placed observation wells. Smalldiameter pumping wells are preferable because of theirquicker response to changes in hydraulic head. Theaccuracy of data taken from a pumping well is oftenless reliable because of turbulence created by thepump. Furthermore, drawdown data from anobservation well are required for the accuratecalculation of the storage coefficient of the aquifer.Thus, at least one observation well should be usedwhen practicable. Design of a field pumping test (alsocalled an aquifer test) is as much art as it is science,and requires judgement tempered by experience. Assumptions must be made concerning the type ofaquifer and its characteristics, and a suitable testdeveloped based on those assumptions. The followingprocedure may be followed as a guide to design anaquifer pumping test.

(2) Development of conceptual geologic model.To design a pumping test, it is necessary to have someknowledge (or make assumptions) of the subsurfacestratigraphy. Items of concern include the type, thick-nesses, and dip of strata, as well as the ease with whichthis strata can be drilled. If no borings have beendrilled in the project area, it will be necessary to startwith a geologic literature search of USGS and stateagency documents (see Section 3-2).

(3) Development of conceptual hydrologic model.Items of concern include type and depth of theaquifer(s), as well as the hydraulic conductivity,transmissivity, storativity or specific yield, and yieldand specific capacity of pumping wells. Water qualitymay also be a concern, particularly if a dischargepermit is required for disposal of the pumped water. Ifno wells have been drilled in the project area, it will benecessary to glean this information fromU.S. Geological Survey (USGS) or state agencyreports, or to make assumptions that seem reasonable

(4) Define the test objectives. While it may atfirst seem that the objectives are simply to “learn aboutthe aquifer,” on further examination the questionbecomes “What exactly do you want to learn about theaquifer?” Is this test being conducted as part of awater budget study where the concern is definingtransmissivity and storativity; or is the test part of awater supply study where the concern is specificcapacity and safe well yield; is the test part of agroundwater contaminant transport study where theultimate question is the velocity of the groundwater? Is there any concern between the possible interconnec-tion of two or more separated aquifers, such as a near-surface water table aquifer and a deeper artesianaquifer? A careful definition of the test objectives isessential to ensure a successful test.

(5) Determining the well pumping rate (Q). It isusually desirable to pump at the maximum practicalrate so as to stress the aquifer as much as practical forthe duration of the test. This translates into moredrawdown at the pump well and observation wells, andtherefore more data available for the final analysis. Themaximum rate will be limited by the efficiency of thewell construction and the specific capacity of the well,and should be a rate such that the well will not bedewatered below the pump intake screen during theduration of the test. If a new well is to be drilled forthis pump test, then it will be necessary to initiallyassume a pumping rate based on the conceptualhydrologic model previously mentioned.

(6) Determining the test duration (t). Practicalconstraints usually limit the time available for the test,and at a maximum it is useless to run the test beyondthe point at which a steady-state condition is reached(i.e., no more drawdown) or the point at which thepumping well intake screen begins to dewater.Pumping tests last anywhere from 6 hr to 2 weeks,depending on the objectives and the aquifercharacteristics, but most probably fall between 1 and3 days for the pumping phase of the test, followed byan equal amount of time to monitor the recovery.

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(7) Determining the observation well locations. yield data to refine the earlier estimates of specificObservation wells should be located in areas of capacity, well yield, transmissivity, hydraulicinfluence of the pumping test. However, wells placed conductivity, and aquifer thickness. too close to the pumping well will be influenced by thevertical flows in the immediate vicinity of the pump (9) Refine the conceptual geologic and hydrologicwell and may yield erroneous data. A good rule of models. Use the data obtained from the first wellthumb is to place the observation wells a distance no drilled to reevaluate the pumping rate, test duration,less than (1.5)(b) from the pumping well, where b is and observation well locations. Make changes to thethe aquifer thickness. However, this rule has often field layout as needed. From a practical standpoint,been violated with no apparent ill effects, especially for this may have to be accomplished in a motel room atlow pumping rates. To determine the maximum radial night after working all day in the field with the drillingdistance (r) at which observation wells can be placed crew.from the pumping well, assume a minimal drawdown(s) that you believe to be significant, and solve the (10) Drill the first observation well and perform aappropriate discharging well analytical equations in mini-pumping test. It would be most conservative toreverse. To check for aquifer anisotropy, locate wells drill the closest observation well first, since this wellat equal distances from the pumping well but in will predictably have the greatest drawdown of all thediffering azimuthal directions. To allow for distance planned observation wells. Use the refined conceptualdrawdown solutions and to allow for calculation of the models to predict drawdown in the single observationcone of influence of the pumping well, locate wells at well after a short period of pumping (1 to 4 hrdiffering radial distances from the pumping well. recommended). Measure drawdown in both theProject budgets will usually provide a practical pumping well and the observation well, and compareconstraint for the number of observation wells, so well the measured and predicted values. Further refine thelocations must be optimized to fit the test objectives, conceptual models as necessary and drill the remainingand compromises often must be made. In the event observation wells.that an observation well(s) cannot be optimally located,then the observation well(s) should be replaced with a e. Single well tests. It is also possible to obtaincluster of depth-staggered piezometers. A piezometer useful data from production wells when data fromcluster would have at least one piezometer at (0.25)(b) observation wells are not available. The procedure forand another at (0.75)(b). Using depth-staggered this determination is similar to the Jacob method.piezometers allows the collection of draw-down data Values of drawdown are recorded directly from thewhich can be readily corrected for partial penetration pumping well. However, because of well loss in theand delayed yield. pumping well, the estimates of storativity and

transmissivity derived from the straight-line intercept(8) Drill the pumping well. Since the conceptual

models developed earlier are not absolutes, it is oftennecessary to reevaluate and refine these models asactual field data are obtained. The first well drilledshould be the pumping well, and it should bethoroughly logged as drilled to evaluate the actual sitestratigraphy. A performance test should be conductedon this well as soon as possible after completion, andprior to drilling the observation wells. Down-hole tests g. Aquifer boundaries. Aquifer boundaries canmay be conducted on the open hole prior to be of two types: recharge and impermeable. Aconstructing the well to obtain hydrologic data on recharge boundary is a boundary which serves as aparticular zones. These tests may consist of either potential or actual source of recharge to the aquifer,pump-in (pressure tests) or pump-out (variable head) and has the effect of decreasing the response of antests, and can be analyzed by methods as explained in aquifer to withdrawals. Examples of rechargeU.S. Department of Interior (1977). These tests will boundaries include zones of contact between the

with the line of zero drawdown are a roughapproximation.

f. Well interference. Well interference occurswhen the cones of depression from adjoining wellsintersect. Well interference reduces the availabledrawdown, and the maximum yield of a well.

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aquifer and rivers, lakes, and mountain-front recharge determination of physical parameters of the adjacentareas. An impermeable boundary is a zone of contact rock and fluids contained in that rock. This isacross which minimal flow occurs. Impermeable accomplished by the propagation or detection ofboundaries have the effect of increasing the response of electrical currents, radiation, thermal flow, or soundthe aquifer to withdrawals. One of the assumptions of waves through the surrounding subsurface.analytical methods used to analyze pump test data is Geophysical well logs can be interpreted to determinethat the aquifer to which they are applied is infinite in the lithology, geometry, resistivity, formation factor,extent. This assumption is commonly met for practical bulk density, porosity, permeability, moisture content,purposes in aquifers that are aerially extensive to a and specific yield of water-bearing rocks, and to definedegree where pumping will not have an appreciable the source, movement, and chemical and physicaleffect on recharge and discharge, and most water is characteristics of groundwater. Borehole geophysicalderived from groundwater storage. In situations wherelateral boundaries have an appreciable influence onaquifer response, the hydraulic effect can be assumed,for analytical convenience, to be due to the presence ofother pumping wells, called image wells. A rechargeboundary has the same effect on drawdowns as arecharging image well, and an impermeable boundaryhas the same effect on drawdowns as a dischargingimage well.

4-7. Slug Tests

Slug tests are applicable to a wide range of geologicsettings as well as small-diameter piezometers orobservation wells, and in areas of low permeabilitywhere it would be difficult to conduct a pumping test.A slug test is performed by injecting or withdrawing aknown volume of water or air from a well andmeasuring the aquifer’s response by the rate at whichthe water level returns to equilibrium. Hydraulic con-ductivity values derived relate primarily to the horizon-tal conductivity. Slug tests have a much smaller zoneof infiltration than pumping tests, and thus are onlyreliable at a much smaller scale. A general overviewof slug tests can be found in Fetter (1994).Recommended references for in-depth discussions ofslug tests and accompanying analytical methods are:Bouwer and Rice (1976); Bouwer (1989); Hvorslev(1951); Cooper, Bredehoeft, and Papadopulos (1967);and Papadopulos, Bredehoeft, and Cooper (1973).

4-8. Borehole Geophysics typically contain a clause which states that they are not

a. General. is part of the larger concept of a quality assurance/

(1) Subsurface geophysical logging involves the logging QA/QC program should consider thelowering of a sensing device within a borehole for the following:

logs provide a continuous record of various natural orinduced properties of subsurface strata and of the porefluids contained within those strata. Boreholegeophysics also provide information about the fluidstanding within the borehole and well construction.These data, when interpreted in a conjunctive manner,can provide accurate and detailed information aboutsubsurface conditions.

(2) A general overview of borehole geophysicalmethods is presented in this section. For a morein-depth discussion, the following references arerecommended: EM 1110-1-1802, Keys and MacCary(1971), and Taylor, Hess, and Wheatcraft (1990).

b. Planning a well logging program. Theobjective of any well logging program should be toacquire data on a real-time basis and to develop thebackground data to be able to monitor changes in theborehole environment over time. Borehole geophysicallogs require calibration in the geologic environment inwhich they will be run. This is because logs have non-unique response, and there are no published orstandard correction factors for many geologic mediacommon to groundwater studies, such as all igneousrocks, metamorphic rocks, and certain sedimentaryrocks such as conglomerates. Calibrating for ageologic environment in which little or no data isavailable will require that core samples be obtainedand tested for physical properties such as density,porosity, and saturation. Logging company contracts

responsible for the quality of the data. This principle

quality control (QA/QC) program. At a minimum, a

Lithology Logging Device

ImpermeableClay

PermeableSands and Gravel

ImpermeableShale

Dense Rock

Dense andImpermeable

Electrical

Resistivity SP Nuclear

Limestone

PermeableSands and Gravel

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Figure 4-3. Conjunctive use of borehole geophysicallogs

(1) Calibration. When was the tool last calibratedand how? Tools should be calibrated at standard pitson a regular basis. These pits are located at theUniversity of Houston and at the U.S. GeologicalSurvey Denver Field Center. Calibration also meansthe use of field standards to check the tool at thebeginning and end of each day.

(2) Core analysis. Preferred, necessary in newarea.

(3) Water analyses. Essential, also includes mudanalyses.

(4) Well construction details. Essential if logginginside existing well.

(5) Local hydrogeology. Essential for understand-ing logs and anticipating problems and/or anomalies.

(6) Logging procedures. Essential, requires onsitepresence. An example is logging speed. Some logsshould run at speeds as low as 7.5 m/min (25 ft/min).

(7) Data processing. All logs need somecorrection. Depth is commonly ±5 m (15 ft), scales offup to ±20 units. Additionally, borehole effects need tobe corrected for. In order to perform this type of erroranalysis, the data (log) must be digitized so correctionscan be made and the data replotted.

(8) Drilling. Carry out drilling operations in amanner that produces the most uniform hole and leastdisturbance to the formation.

The final principle to keep in mind is that logs shouldalways be interpreted collectively, on the basis of athorough understanding of the principles andlimitations of each type of log, and a basicunderstanding of the hydrogeology of the study area.Table 4-1 summarizes the application of various typesof logs. Figure 4-3 presents an example of theconjunctive use of borehole geophysical logs.

c. Types of logs.

(1) Caliper log.

(a) Principle. A caliper log is a record of theaverage borehole diameter. It is one of the first logs

Table 4-1Applications of various borehole geophysical methods

Parameter Borehole Geophysical Method

Stratigraphy and porosity Natural gamma logGamma-gamma logAcoustic logNeutron logSpontaneous potential log

Stratigraphy Caliper logResistance log

Moisture content Neutron log

Location of zones of saturation Spontaneous potential logTemperature logNeutron logGamma-gamma log

Physical and chemical Resistivity logcharacteristics of fluids Spontaneous potential log

Temperature logFluid conductivity log

Dispersion, dilution, and Fluid conductivity logmovement of waste Temperature log

Gamma-gamma log

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which should be run, and one of the most useful and where filtrate is lost to the formation or where thesimplest tools. The caliper log is necessary for the borehole is gaining or losing fluid. The second, andselection of the size of other tools and for any borehole most significant, is the electrochemical reaction thatcorrections to other logs. Most caliper tools consist of occurs at the interface between dissimilar materials.a body or sonde with from one to four "arms" that Currents tend to flow from the borehole into permeablefollow the borehole wall. beds until sufficient cross-sectional area of a resistant

(b) Application. Caliper logs are utilized foridentification of lithologic horizons, location offractures or other openings in the borehole wall,guidance in well design and construction, and mostimportantly, for the borehole correction needed forother logs such as single point resistance and gamma-gamma.

(2) Fluid conductivity and temperature logs.

(a) Principle. Fluid-conductivity logs provide ameasurement of the conductivity of the fluid within theborehole, which may or may not be related to thefluid(s) in the formation. Generally, the conductivity isderived from measuring the potential drop between twoclosely spaced electrodes.

(b) Application. Fluid-conductivity measurementsare needed for the correction of other logs which aresensitive to changes in the electrochemical nature of theborehole fluid(s) such as spontaneous potential andmost resistance logs. It is good practice to make atemperature log simultaneously with the fluid-conductivity log. This allows the most accurateconversion to specific conductance, which is needed tocalculate equivalent salinity, by avoiding thedisturbance of the fluid column that may be induced by E = potential [volts]running a separate thermal probe prior to the fluid-conductivity probe. Fluid conductivity and I = current [amperes]temperature logs should be run at the beginning of thelogging process. r = resistance [ohms]

(3) Spontaneous potential log. (b) Application. The most common type of

(a) Principle. The spontaneous potential (SP) tool method. Because the radius of investigation is small,measures the natural electric potential between the single point resistance log is strongly affected byborehole fluid and the formation. The SP log must be the conductivity of the borehole fluid and variation ofrun in an uncased borehole filled with a conductive borehole diameter. Single point resistance logging isfluid. Two sources of potential are recognized. The very useful because any increase in formationfirst, and least significant, is the streaming potential resistance produces a corresponding increase in thecaused by dissolved electrolytes such as NaCl, moving resistance recorded on the log and thus deflections on athrough a porous media. This phenomenon occurs single point log can be attributed to changes in

bed is encountered to carry the current.

(b) Application. The SP log can be used forlithologic identification or correlation. As previouslydiscussed, the direction of the deflection of the SP logis an indication of either sand or shale. It is only aqualitative indicator and should never be used alone.Thus, SP should not be used for calculating waterquality during hydrogeologic investigations.

(4) Resistance logging.

(a) Principle. Resistance logging provides acalculation of the resistance, in ohms, of the geologicmaterials between an electrode placed within theborehole and an electrode placed at the surface orbetween two electrodes placed within the borehole.The resistance log must be run in an uncased boreholefilled with a conductive fluid. A potential difference involts or millivolts is measured between the twoelectrodes and the resistance is calculated by Ohm'sLaw when the current I is held constant:

E = I r (4-1)

where

resistance logging is the single point or point resistance

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lithology (although the response is nonlinear). Single porosity, and mud resistivity. Normal logs are thepoint systems do not experience the log reversal at thin most commonly used resistivity tools in groundwaterbeds that multielectrode systems do. These properties investigations. Normal logs measure the apparentmake the single point log one of the better logs for resistivity of a volume of geologic material surroundinglithology or stratigraphic correlation. the electrodes. The records produced by normal

(5) Resistivity logging.

(a) Principle. Though their names are similar,resistivity logging is different from resistance logging.Resistivity includes the dimensions of the materialbeing measured and is an electrical property inherent tothe geologic material. The relationship betweenresistance and resistivity is analogous to that of weightand density. Resistivity is defined by:

R = r × S / L (4-2)

where

R = resistivity [ohm-meters]

r = resistance [ohms]

S = cross-sectional area [L ]2

L = length [L]

The resistivity of sediments depends on the physicalproperties of those sediments and the fluid(s) theycontain. Most sediments are composed of particles ofvery high electrical resistance. All resistivity logs mustbe run in an uncased borehole filled with a conductivefluid. When saturated, the water filling the pore spacesis relatively conductive compared to the sediments.Thus, the resistivity of sediments below the water tableis a function of the salinity of the water filling porespaces and how those pore spaces are interconnected.Resistivity logging devices measure the electricalresistivity of a known (assumed) volume of geologicmaterial using either direct or induced electricalcurrents. Below the water table the resistance of aformation depends on the composition of the waterwithin it, and on the length and shape of interconnectedpores. (7) Gamma-gamma logs.

(b) Application. Resistivity logs are generally (a) Principle. Gamma-gamma logs are records ofused to estimate the physical and chemical the intensity of gamma radiation from a source in thecharacteristics of fluids, formation resistivity and probe after the radiation has been backscattered and

devices are affected by bed thickness as well as bedresistivity. As bed thickness decreases, the resistivitypeak decreases in amplitude.

(6) Natural-gamma logs.

(a) Principle. Some of the most useful loggingmethods involve the measurement of either naturalradioactivity of the geologic media and the fluidswithin it, or the attenuation of induced radiation.Nuclear methods can be used in either open or casedboreholes provided there are not multiple casing stringsand seals. Natural-gamma logs are records of theamount of natural-gamma radiation emitted bygeologic materials. The chief uses of natural-gammalogs are the identification of lithology and stratigraphiccorrelation. Potassium, of which about 0.012 percentis K , is abundant in feldspars and micas which40

decompose readily to clay. Clays also concentrate theheavy radioelements through the processes of ionexchange and adsorption. In general, the natural-gamma activity of clay-rich sediments is much higherthan that of quartz sands and carbonates. The radiusof investigation of a natural-gamma probe is a functionof the probe, borehole fluid, borehole diameter, sizeand number of casing strings and seals, density of thegeologic materials, and photon energy.

(b) Application. The most important applicationin groundwater studies of the natural-gamma log is theidentification of clay- or shale-bearing sediments.Clays tend to reduce the effective porosity andhydraulic conductivity of aquifers, and the natural-gamma log can be used to empirically determine theshale or clay content in some sediments. The natural-gamma log does not have a unique response tolithology. The response is generally consistent for agiven locality.

Porosity '

Grain density & Bulk density (from log)Grain density & Fluid density

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attenuated within the borehole and surrounding the casing. Gamma-gamma logs can also indicategeologic materials. The gamma-gamma probe contains water level and significant changes in fluid densitya source of gamma radiation, generally cobalt-60 or (fresh water-brine interface). A license must becesium-137, shielded from a sodium iodide detector. obtained to use a gamma-gamma log.Gamma radiation from the source penetrates and isscattered and absorbed by the fluid, casing, grout, and (8) Neutron logs. geologic materials surrounding the probe. Gammaradiation is absorbed and/or scattered by all material (a) Principle. The various types of neutron logsthrough which it travels. The radius of investigation of are potentially the most useful techniques in boreholegamma-gamma probes is reported to be about 15 cm geophysics as applied to groundwater studies. This is(6 in.). The bulk density of the geologic material, due to the fact that the measured response is due tofluids, or casing and seals will affect the radius of hydrogen and thus, generally, water. Neutron logs alsoinvestigation. The distance between the source and have advantages over other nuclear logs in that theydetector will also significantly alter the volume of can be run in liquid-filled or dry holes, cased ormaterial investigated. uncased holes, and have a relatively large volume of

influence. In neutron logging, neutrons are artificially(b) Application. The main uses of gamma-gamma

logs are for the identification of lithology, and themeasurement of bulk density and subsequentdetermination of porosity. They may also be used tolocate cavities and grout outside of casing. Gamma-gamma density is widely used for determination of totalporosity by:

(4-3)

Grain density can be derived from laboratory analysesof cores (or, for quartz sands, a value of 2.65 g/cc canbe used). The fluid density for groundwater studies isassumed to be 1 g/cc; however, if the fluid is saline orcontains levels of contaminants high enough to alterfluid density, then laboratory analysis of density isnecessary. In an unconfined aquifer or a partiallydewatered confined aquifer, it should be possible toderive specific yield from gamma-gamma logs.Specific yield should be proportional to the differencebetween the bulk density of saturated and drainedsediments, assuming porosity and grain density do notchange. Bulk density may be read directly from acalibrated and corrected log or derived from chartsproviding correction factors. Errors in bulk densityobtained by gamma-gamma methods are on the orderof ± 2 percent. Errors in the porosity calculated fromlog-derived bulk densities depend upon the accuracy ofgrain and fluid densities used. In addition todetermining porosity, gamma-gamma may be used tolocate casing, collars, or the position of grout outside

introduced into the borehole environment, and theeffect of the environment on the neutrons is measured.Assuming that the vast majority of hydrogen occurs inthe form H O, materials with higher porosity (and thus2

higher water content) will slow and capture moreneutrons, resulting in fewer neutrons reaching thedetector. The converse is true for materials of lowporosity. This assumption does not hold when hydro-carbons, chemically or physically bound water, and/orother hydrogenous materials are present. Neutron logsare affected by changes in borehole conditions to alesser degree than other geophysical logs that measurethe properties of geologic materials. The most markedextraneous effect on neutron logs is caused by changesin borehole diameter.

The volume of influence, which is defined by theradius of investigation, is an important factor in theanalysis of neutron logs. The radius of investigation isa function both of the source-detector spacing, thepetrology of the material, and the water content withinthe volume of influence. The radius of investigation ofneutron tools has been reported to be from 15 cm(6 in.) for high-porosity saturated materials to 60 cm(2 ft) in low-porosity materials. These estimates maybe conservative, as recent laboratory work with semi-infinite models suggests that the radius of investigationin saturated sands was greater than 50 cm (20 in.).

(b) Application. Neutron logs are used chiefly forthe measurement of moisture content in the unsaturatedzone and total porosity (water filled) in the saturatedzone. In most geologic media the hydrogen content is

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directly proportional to the interstitial-water content; of secondary porosity can be identified byhowever, hydrocarbons, chemically or physically cross-plotting data from an acoustic-velocity log and abound water, or any hydrogenous material can give neutron log or a gamma-gamma log.anomalous values. For example, gypsum has a highpercentage of water associated with the crystalstructure which can result in it appearing to be amaterial of high porosity. This has been used todistinguish between anhydrite (high neutron count rate)and gypsum (low neutron count rate). Although aneutron log cannot be used to measure porosity abovethe water table, it is very useful for measuring changesof water content in the unsaturated zone. A license isrequired to use a neutron log.

(9) Acoustic logs.

(a) Principle. Acoustic logging utilizes atransducer to transmit an acoustic wave through theborehole fluid and into the surrounding rocks. Thefour most common types of acoustic logs are: acousticvelocity, acoustic wave form, cement bond, andacoustic televiewer. Acoustic logs can provide data onporosity, lithology, cementation, and fractures.Acoustic logging is appropriate only for consolidated(cemented) material. Acoustic-velocity logs, alsocalled sonic logs or travel-time logs, are a record of thetravel time of an acoustic wave from one or moretransmitters to receivers in a probe. The velocity of theacoustic signal is related to the mineralogy andporosity of the formation. The radius of investigationof an acoustic-velocity probe is reported to beapproximately three times its wavelength; thewavelength is equal to the velocity divided by thefrequency. At a frequency of 20 kHz, this radiusranges from less than 30 cm (1 ft) in unconsolidatedmaterials to about 120 cm (4 ft) in hard rocks.

(b) Application. Acoustic-velocity logs are usefulfor providing information about lithology and porositywhen used in consolidated materials penetrated byuncased, fluid-filled boreholes. Transit times decreasewith greater depth and with increases in cementation.Acoustic velocities may vary with confining pressurefor several hundred feet below the ground surface,most notably in slightly consolidated materials.Secondary porosity will not be detected by an acoustic-velocity log because the acoustic wave will take thefastest path through the formation. Intervals

4-9. Surface Geophysics

a. General. Surface geophysical methodsgenerally do not provide the vertical resolution ofborehole geophysical methods. However, surfacegeophysical methods provide valuable information onsite geology on a greater spatial scale. Thus,conceptual model development often requires theconjunctive use of surface and borehole geophysicalmethods. Additionally, surface geophysical methodsallow for the nonintrusive gathering of information onsubsurface stratigraphy and hydrogeologic conditions.This section presents an overview of: seismic refractionand reflection, electrical resistivity, gravitationalmethods, electromagnetic methods, and ground-penetrating radar. Recommended references areincluded when a more in-depth understanding ofconcepts and principles is desired.

b. Seismic geophysical methods.

(1) The seismic exploration method deals with themeasurement of the transmission, refraction, reflection,and attenuation of artificially generated seismic wavestraveling through subsurface materials. The refractionand reflection methods are the most widely usedseismic methods for hydrogeologic sitecharacterizations. Both of these methods make use ofthe fact that seismic waves travel through differentmaterials, such as soil, weathered rock, intact rock,etc., with differing velocities. Measurements are madeby generating a seismic disturbance at or just below theground surface and measuring the time required for thedisturbance to travel through the ground and to one ormore seismic sensors, called geophones, which arefirmly implanted into the ground surface. With asuitable geometric arrangement of the seismic sourceand geophones, and theory to determine the probabletravel paths, considerable information can be gained onthe geometry and stratigraphy of the underlying soiland rock materials. In some cases, particularly inunconsolidated sediments, the depth to the water tablemay be computed.

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(2) This section provides a brief overview of the unconsolidated materials, whether saturated or not, in aseismic refraction and reflection methods, along with bedrock valley. applications in hydrologic site characterization studies.Also, the strengths and weaknesses of each method will One of the major limitations of the seismic refractionbe assessed. For a more in-depth discussion, the method is that each successive velocity layer must havefollowing references are recommended: EM 1110-1- a velocity greater than the one above it. If a low-1802; Telford et al. (1990); and Zohdy, Eaton, and velocity layer is between layers with greater velocities,Mabey (1974). the low-velocity stratum will not be detected and

erroneous depths to deeper interfaces will be computed.c. Types of seismic geophysical methods. However, in most hydrologic cases an increase in

(1) Seismic refraction. as the case when there is a water table in sediments

(a) Principle. Seismic refraction technology the method is its inability to detect thin intermediateis based on the fact that elastic waves travel velocity layers. An example of this situation is athrough differing earth materials at different velocities. relatively thin saturated zone at the bottom of a thickThe denser the material, the higher the wave sand layer which overlies a high-velocity bedrockvelocity. When seismic waves are propagated through surface. In this case, the refracted arrivals from thea geologic boundary of two layers with separate bedrock arrive prior to those from the top of thedensities, a refracting of propagation direction saturated sand and, as a consequence, the saturatedoccurs. Through the propagation of a set of layer will not be detected. elastic waves, usually through small explosions,and the recording of the time travel at (2) Seismic reflection.differing distances on a seismograph, the layerdepths and their acoustic velocities can be estimated. (a) Principle. The basic principle of seismicSeismic refraction methods are only effective in reflection is that seismic waves are reflected atformations with definite boundaries between strata and interfaces between geologic units with different seismicwhere density increases with each successive lower velocities. Seismic velocities depend upon the elasticlayer. constants of a porous medium. The time required for

(b) Application. The acoustic velocity of a reflecting stratigraphic boundary and back to a definedmedium saturated with water is greatly increased in point on the surface is measured by a geophone (Figurecomparison with velocities in the vadose zone. Thus, 4-4). The geophone detects the reflected signals fromthe refraction method is applicable in determining the the various reflecting horizons and transmits thisdepth to the water table in unconsolidated sediments. information to a seismograph where the times of arrivalThe velocities associated with those of saturated are recorded. By measuring the time the energy takesunconsolidated materials, although indicative of to propagate from the source to a reflecting horizonsaturation, are by no means unique. For example, a and back to the surface and by also knowing thedry, weathered rock layer can exhibit the same velocity velocity of the material along the path of travel, theranges as those normally associated with saturated, depth to the reflecting horizons can be computed. Byunconsolidated materials. The refraction method is recording the output of each geophone in a seismic line,also applicable in determining the depth and extent of a a visual representation of the local pattern of groundrock aquifer as well as the thickness of overlying motion called a seismogram is obtained (Figure 4-5).unconsolidated materials. Common hydrologic prob- By displaying the seismogram for each geophone sidelems that relate to this situation are that of mapping by side, a vertical profile of the subsurface may beburied channels or determining the thickness of obtained.

velocity as a function of depth can be expected (such

which are underlain by bedrock). Another limitation of

an acoustic signal to travel from the source to the

Ground Surface

Receiver

Layer 1

Layer 2

Layer 3

Layer 4

Source

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Figure 4-4. Reflected energy from three layers

Figure 4-5. Illustration of seismic section for ahypothetical geologic model

(b) Application. One important advantage the plumes. Other applications of electrical resistivityreflection method has over the refraction method is that include: determination of depth to bedrock, cavernsucceeding layers do not have to increase with velocity. location in karst regions, permafrost mapping, andThe reflection method is more accurate, has better geothermal exploration.resolution, and can determine the depths to more layersthan the refraction method. It also uses shorter (2) Gravitational methods. geophone lines and uses smaller energy sources.Seismic reflection methods are capable of producing (a) Principle. Gravitational methods are based ondetailed information on subsurface structure. measurement of small variations in the gravitationalHowever, interpretation of seismic reflection data field at ground surface. If subsurface rocks ofrequires analysis by a trained geophysicist using differing density are present in the study area, thepowerful computer techniques; moreover, the collection resulting irregularity in mass distribution will be

of data requires expensive field equipment and largefield teams (Smith and Wheatcraft 1991).

d. Additional surface geophysical methods.

(1) Surface electrical resistivity.

(a) Principle. Resistivity of a material is definedas the ability of that material to impede the flow ofelectric current through the material. In a surfaceresistivity survey, a direct current or low-frequencyalternating current is sent through the ground betweenmetal stakes or electrodes. The accompanying drop inelectric potential is measured at a point between thecurrent electrodes. Electrical resistivity displays awider range of values than any other physical propertyin rocks (Zohdy, Eaton, and Mabey1974). Resistivitydepends primarily on the amount, distribution, andsalinity of water in the rock being studied. Saturatedrocks have lower resistivities than unsaturated and dryrocks. Electrical resistivity methods are most useful indetermining depth to rock and evaluating stratifiedformations where a denser stratum overlies a less densestratum. Clays and conductive materials also reducethe rock's resistivity. An in-depth discussion of surfaceelectrical resistivity can be found in EM 1110-1-1802.

(b) Application. Electrical resistivity methodshave a variety of applications. Although the fieldtechniques are relatively time-consuming, it is often thechosen method because surface resistivity surveying isone of the less costly geophysical techniques.Resistivity surveying is commonly used in groundwaterstudies for determining the water table depth, locatingfreshwater aquifers, mapping confining clay layers,and mapping saltwater intrusion and contaminant

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Figure 4-6. Concept of gravity anomaly and definitionof residual gravity anomaly

reflected in a corresponding change in gravity intensity determination of fundamental hydrogeologicon the surface. Geophysical gravity surveys involve parameters or properties. Gravity surveys can be usedmeasurement of the magnitude and spatial variation of for monitoring gravity changes associated withthe earth's gravity field using a gravity meter. If the groundwater level changes; if the bulk porosity isearth were perfectly spherical and radially uniform, the known, the elevation change can be determined fromacceleration of gravity would be constant over the the gravity change, or if the elevation change is knownearth; however, this is not the case. Measurement, from a monitor well, a representative bulk porosity candefinition, and geological interpretation of the be determined from the gravity change. An emergingdepartures from radial uniformity are the objectives of application area for gravity surveys is to monitorgravity surveys; some of the departures are global or gravity changes associated with a pumping well.regional in scale, while some of the departures are local Theoretically, if gravity surveys are conducted beforein nature. Local departures from radial uniformity in and during well pumping, the shape of the drawdownthe subsurface are referred to as anomalies and give curve can be determined, flow heterogeneity can berise to local gravity variations or gravity anomalies. mapped, and estimates of bulk hydraulic conductivityThe concept of a gravity anomaly is illustrated in can be determined from the gravity data. Telford et al.Figure 4-6, where the terms total or measured gravity, (1990) and Carmichael and Henry (1977) discussregional gravity trend, residual gravity, and gravity standard gravity survey procedures in detail, andanomaly are defined. Butler (1980) discusses procedures for microgravity

(b) Application. For hydrogeologic investigations, with electromagnetic techniques.gravity surveys have two primary applications. Thefirst of these applications contributes to the definition Natural variations in subsurface conductivity mayof local- to regional-scale geology and is a standard or be caused by changes in soil moisture content,classical use of gravity surveys. Gravity surveys can groundwater specific conductance, depth of soil coverbe used to map “bedrock” topography, detect and map over rock, and thickness of soil and rock layers.buried river channels (Figure 4-7), detect and map Changes in basic soil or rock types, and structurallarge fracture zones, and detect truncations or features such as fractures or voids may also produce“pinchouts” of major aquifers or aquitards. The changes in conductivity. Localized deposits of naturalsecond application area for gravity surveys in organics, clay, sand, gravel, or salt-rich zones will alsohydrogeologic investigations involves the affect subsurface conductivity.

surveys.

(3) Electromagnetic methods.

(a) Principle. The electromagnetic (EM) methodinvolves the propagation of time-varying, low-frequency electromagnetic fields in and over the earth.The electromagnetic method provides a means ofmeasuring the electrical conductivity of subsurfacesoil, rock, and groundwater. Electrical conductivity is afunction of the type of soil and rock, its porosity, itspermeability, and the fluids which fill the pore space.In most cases the conductivity (specific conductance)of the pore fluids will dominate the measurement.Accordingly, the electromagnetic method is applicableboth to assessment of natural hydrogeologic conditionsand to mapping of many types of contaminant plumes.Additionally, trench boundaries, buried wastes anddrums, as well as metallic utility lines can be located

Distance

SurfaceClay till

Sand and gravelBuried valley

Valley traindeposit

2 4 6

8

10 12

1416 18 20

2

4 68 10 12 14 16 18

20

(a) Results of gravity traverse -- bedrock profile

(b) Subsurface geology

Bedrock

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Figure 4-7. Illustration of Gravity Anomaly above a Buried Channel

(b) Application. There are two basic techniques above the ground and below. Electromagnetic noiseavailable for electromagnetic surveying. Profiling is may be caused by nearby power lines, powerful radioaccomplished by making fixed-depth electromagnetic transmitters, and atmospheric conditions. In additionmeasurements along a transverse line to detect lateral to other forms of electromagnetic noise, instrumentvariations. Sounding is accomplished by making responses from subsurface or surface metal may makeconductivity measurements to various depths at a given it difficult to obtain a valid measurement. Uniquelocation to detect vertical variations. interpretation of subsurface conditions generally

Electromagnetic systems are susceptible to signal alone; it must be supported by drilling data or otherinterference from a variety of sources, originating both geologic information.

cannot be obtained from electromagnetic sounding data

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(4) Ground-penetrating radar theory. contrast in electrical properties to the host environment

(a) Principle. Ground-penetrating radar (GPR) reflected, or scattered. The host material must beutilizes high frequencies of electromagnetic waves qualified in two ways. First, the electrical properties ofwhich are propagated in a straight line into the ground the host must be defined. Second, the degree andto depths which vary from a few feet to tens of feet, spatial scale of heterogeneity in the electrical propertiesdepending on the electrical conductivity of the terrain. of the host must be estimated. If the host materialThe use of GPR is similar to the seismic reflection exhibits variations in properties which are similar totechnique because both methods record the time the contrast and scale of the target, the target may notrequired for a wave to travel to an interface between be recognizable from the responses generated by thetwo formations and then reflect to the surface. In host environment. Lastly, the area where the survey isgeneral, electromagnetic methods lack the resolution to be performed should be free of the presence ofand depth penetration of resistivity surveys, but have extensive metal structures and of radio frequencythe advantage of being rapid and less expensive. electromagnetic sources or transmitters.

In geologic materials, the presence of water is oneof the most important factors determining electricalproperties. In addition, ions dissolved in the water giverise to an electrical conduction mechanism which is amajor factor in most soils and rock. Basically theconductivity is roughly proportional to the totaldissolved solid content; hence, the more ions dissolvedin the solution, the higher the conductivity. Theelectrical conductivity of a soil is much harder topredict. It is very dependent on the pore-waterconductivity. In addition, it is dependent on the surfaceconduction mechanisms present in the soil matrix.Surface conduction addresses the charge transportassociated with charges moving on the surface of themineral grains. Generally surface conduction is verysmall in clean, coarse-grained material such as quartzsand; however, it is a major factor in fine-grained soilssuch as clays. As a result, clays are very important inGPR investigations because they have a strong impacton electrical conductivity of the medium. Aselectromagnetic waves propagate downward into theground, reflections are generated by changes in theelectrical impedance in the ground.

(b) Application. Before starting a GPR survey,one must determine if the site conditions and desiredtarget are suitable. Of primary concern is the targetdepth; GPR has a very definite and often limited depthof investigation based on the site geology. Clay andsaturated soils attenuate the GPR signal, therebyseverely limiting the depth of penetration. The targetsize should also be qualified as accurately as possible.In order for GPR to work, the target must present a

in order that the electromagnetic signal be modified,

4-10. Cone Penetrometer Testing

a. General. Cone penetrometer testing (CPT)has been utilized in the geotechnical field for at least65 years. Benefits of using the CPT system includelower costs, faster data acquisition, less invasivedisturbance to the subsurface, and no acquisition-derived wastes. A CPT apparatus is typically truck-mounted, similar to a drilling machine. A basic CPTsystem consists of four basic components; the truck,hydraulic thrust system, data acquisition and reductionsystem (computers), and the sensor assembly, i.e. thecone. (Figure 4-8). The truck not only transports theCPT unit, but also supplies the power to drive the CPTsystem. In addition, the truck also provides the massnecessary to counteract the hydraulic thrust. Trucksizes vary anywhere from 4,400 to 28,500 kg, with17,500 kg being most common.

b. Hydraulic thrust system. The hydraulicthrust system provides the force to push the soundingrod(s)/cone assembly into the ground. The depth ofpenetration is a function of several factors; truckweight, soil density and cementation skin friction onrods, and deviation (from vertical) of rods. Dependingupon the interaction of these factors, CPT has beendone at depths up to 100 m (300 ft), with depths of 25to 30 m (80 to 100 ft) routine. This makes CPT atruly practical alternative to drilling.

c. Data acquisition system. The data acquisi-tion and reduction system receives the signals from thesensor in the cone assembly and processes them,

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Figure 4-8. Components of cone penetrometer testing system

providing both digital and hard copy of raw data and d. Sensor assembly. The cone assembly housesbasic interpretation. Interpretations are in the form of all the sensor elements. The sensors within the conesoil behavior types, which are based upon a database are connected to the data acquisition and reductionrelating the ratio of skin friction to the tip resistance to system by a multi-lead electrical cable which runssoil type. In addition, the data acquisition and through the center of the sounding rods. Whenreduction system performs system monitoring to ensure sampling soil, groundwater, or soil gas, the conethe sensors are functioning properly. The type of data containing the sensor elements fig4-8is replaced with athat can be acquired and processed is limited only by “dummy.” The dummy has a tip which is pushedthe selection of sensors. Currently, there are proven ahead of the sounding rods, exposing the annulus of thesensors for soil type (stratigraphy), pore pressure rods to the environment, allowing the insertion/use of(water content/water table), soil electrical resistance, various soil, water, and gas samplers.seismic velocity, radiation (gamma), laser-inducedflorescence, temperature, pH, and soil gas and e. Limitations. Limitations of the CPT methodgroundwater sampling. The CPT system does not include:produce samples for direct observation. Thus, it ispreferable for the CPT to be used in conjunction with (1) Smaller trucks require an anchoring systemlithologic data obtained from standard drilling which is sometimes difficult to get.methods.

C 6 protons, 6 electrons, 6 neutrons

C 6 protons, 6 electrons, 8 neutrons

12

6

14

6

Mass Number

Atomic Number

(Isotope)*18O '

(18O/16O)sample & (18O/16O)standard

(18O/16O)standard

× 1,000

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Figure 4-9. Example of carbon isotope C14

(2) Large trucks with reaction mass pose accessproblems.

(3) Rocks/debris in the near surface can interferewith data acquisition.

f. Site characterization and analysispenetrometer system (SCAPS). SCAPS is a resourceto be used by all Corps districts and laboratories forthe investigation of HTRW sites. An in-depthexplanation of SCAPS capability, along with points ofcontact, can be found in ETL 1110-1-171.

4-11. Isotope Hydrology

a. General. Isotopes are atoms of the sameelement that have different masses; they have the samenumber of protons and electrons, but a differentnumber of neutrons (Figure 4-9). The 92 naturalelements give rise to more than 1,000 stable andradioactive isotopes. These are often calledenvironmental isotopes. Environmental isotopes arecommonly categorized into two general groups: stableisotopes and unstable isotopes. Stable isotopes are notinvolved in radioactive decay. Most stable isotopes donot react chemically in the subsurface environment andare of particular use in determining the source ofgroundwater. Unstable isotopes are undergoing decay.Unstable isotopes are of particular use in determiningthe age of water. The relative abundance of isotopes ofhydrogen, oxygen, and carbon in the hydrologic cycleis presented as Table 4-2. An in-depth discussion onthe use of environmental isotopes can be found in Fritzand Fontes (1980).

Table 4-2Relative Abundance of Isotopes of Hydrogen, Oxygen, andCarbon in the Hydrologic Cycle (Freeze and Cherry 1979)

Atom Relative Abundance (%) Type1H 99.984

H (deuterium) 0.016 Stable2

isotope

H (tritium) 0-10 Radioactive3 -15

isotope(½ life 12.3 yr)

O 99.7616

O (oxygen-17) 0.04 Stable17

isotope

O (oxygen-18) 0.20 Stable18

isotope

C (radiocarbon) <0.001 Radioactive14

isotope(½ life 5,730 yr)

b. Stable isotopes.

(1) General. Stable isotopes can serve as naturaltracers that move at the average velocity ofgroundwater, and are of particular use in determiningthe recharge areas, degrees of mixing between watersof different origin, and hydrograph separation. Themost common stable isotopes used in hydrologicanalysis are O and H (also known as deuterium18 2

or D).

(2) Isotopic fractionation. In lighter elements,such as hydrogen (H), and oxygen (O), the differencesin mass produced by isotopes is significant to the totalmass of the atom. These differences in mass causeisotopic fractionation in nature. Isotopic fractionationis any process that causes the isotopic ratios inparticular phases or regions to differ from one other.For example, the ratio of O/ O in rain is different 16 18

from the ratio in the oceans. This ratio is representedby *:

(4-4)

&dMdt

' kM

t1/2 'ln 2

k

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Similarly, the isotopic fractionation ratio of H where2

(deuterium-D) is represented by *D. For a specificarea, the relationship between * O and *D in rainfall M = mass of unstable isotope18

is approximately linear and can be plotted on ameteoric water line, an empirically derived relationship k = decay constantfor continental precipitation.

(3) Use of stable isotopes as natural tracers. period in which half of the initial amount of unstableIsotopic fractionation of * O and *D during phase isotopes have decayed and can be calculated by the18

changes enriches one isotope relative to another. Water following formula: that has been subject to evaporation is enriched in H2

(D) relative to O because of its lower atomic weight.18

Fractionation is temperature-dependent. For example,winter precipitation is depleted in O and H18 2

compared with summer precipitation. Additionally,precipitation at the beginning of a storm is often higherin O and H than at the end of the storm, as the18 2

heavier isotopes are selectively removed from the vaporphase. These processes provide watermasses with unique signatures that can be used asnatural tracers in groundwater studies. Hence, thesource areas of different waters, and the mixingpatterns between waters can be assessed.

(4) Use of stable isotopes for hydrographseparation. Stable isotopes have also been used inhydrograph separation (Sklash 1990). Rivers have twoprincipal sources of water: surface runoff, andgroundwater. In rivers where runoff is the majorsource of water, large seasonal variations in * O and18

*D are measured. In rivers where groundwater(baseflow) is the major source, these variations in* O and *D are much less significant due to a much18

longer retention period and aquifer mixing.

c. Unstable isotopes.

(1) General. Unstable isotopes are of particularuse in determining the age of water. Radioactive decayis the conversion of atomic mass to energy in the formof gamma rays, alpha particles, etc., over time:

(4-5)

The half-life (t ) of an isotope is defined as the time½

(4-6)

The two most commonly used unstable isotopes ingroundwater hydrology are H (tritium) and C3 14

(radiocarbon). Cl (radiochloride) is also used for the36

dating of very old groundwater.

(2) H (tritium). Tritium has a half-life of3

12.3 years. Small amounts are produced naturally inthe atmosphere. Between 1952 and 1969 nucleartesting in the atmosphere raised the tritium content inrainfall from 5-10 TU (tritium units) in the 1940's to100-1,000 (or more) TU in the 1960's. The peak oftritium levels occurred in 1963 (Figure 4-10).Currently (in 1996) the tritium content in rainwater isapproximately 10-30 TU. Tritium in groundwater isnot significantly affected by chemical processes.Common uses of tritium analysis include:

(a) Distinguishing between water that entered intothe aquifer prior to 1952 (pre-bomb), and water thatwas in contact with the atmosphere after 1953.

(b) Estimating recharge rates by locating thedepth of the tritium peak which occurred in 1963(Robertson and Cherry 1989).

(c) Estimating groundwater flow velocity.

Because of hydrodynamic dispersion, mixing of aquiferwaters, and the variable tritium source, age estimatesare best viewed as one more input in theformulation of a hydrogeologic conceptual model,

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Figure 4-10. Variations of tritium (TU) in precipitation at Ottawa, Canada (“Groundwater,” by Freeze/Cherry, ©1979. Reprinted by permission of Prentice-Hall, Inc., Upper Saddle River, NJ.)

rather than an exact determination of residence time groundwater as old as 30,000 years (Davis and(Smith and Wheatcraft 1992). Table 4-3 provides an Murphy 1987). Hydrogeologic settings with residenceestimate of groundwater residence time as of 1987 times of this magnitude include large-scale regional(Davis and Murphy 1987). flow systems, and systems in thick low-permeability

Table 4-31987 Relationship Between Tritium Concentration andGroundwater Age (Davis and Murphy 1987)Concentration, TU Interpretation (1987)< 0.2 Water is older than 50 yr

0.2 - 2.0 Water is older than 30 yr

2 - 10 Water is likely at least 20 yr old

10 - 100 Water is less than 35 yr old, may bemodern

> 100 Probably related to peak fall-outperiod of 1960-1965

(3) C (radiocarbon). C has a half-life of 5,73014 14

years. Like tritium, small amounts of C are also14

produced naturally in the atmosphere; and like tritium,much higher concentrations of C were introduced into14

rainfall by atmospheric nuclear testing. Because of itslonger half-life, C can be a useful tool for dating14

sediments. The measurement of C along several14

points in a regional flow system allows for aninterpretation of age differences, areas of recharge, andflow velocities. Complications which can occur whenusing radiocarbon analysis include:

(a) Dissolution of carbonate minerals or oxidationof organic matter may add “dead” (no detectable C)14

carbon to water, giving an erroneously old age. Anumber of correction techniques exist. Phillips et al.(1989) review six methods and apply age dating as atool on modeling groundwater flow in the San JuanBasin.

(b) Mixing of aquifer waters. A low C content14

can be indicative of either old water, or a mixture ofyoung water and “dead” water. Therefore, low C14

measurements can be interpreted for age of ground-water only in flow scenarios where mixing isinsignificant.

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(4) Cl (chloride-36). Cl has a half-life of However, the “isotopically aware hydrogeologist”36 36

300,000 years. Cl is produced by cosmic ray interac- would consider the following approach:36

tion with the atmosphere. Cl has been used to date36

very old groundwater up to 1 million years old (Phillips Use isotopic analysis to determine if such a connectionet al. 1986). Disadvantages are that abundance is exists.very small, and the analytical techniques required arecomplex and expensive. (4) Hypothetical results:

d. Approximate cost (1988) of isotopic analysis. (a) Tritium ( H ) concentrations more than 5.0 TUHendry (1988) made the following cost estimates for were encountered in the piezometers above and belowisotopic analysis: the clay layer.

Isotope CostH $402

O $3018

H $45-$1003 1

C $70-$21514 1

Range of costs reflects degree of accuracy required.1

Collecting samples of O, H, and H is simple. C is18 2 3 14

not as simple, but is relatively easy, requiring only theprecipitation of the dissolved inorganic carbon.

e. Example of the use of isotopes ingroundwater studies.

(1) Setting. The year is 1996. A disposal site islocated above the water table in a shallow phreaticaquifer (Figure 4-11). This aquifer is underlain by aclay layer which appears to confine an underlyingaquifer. The lower aquifer is used for domestic watersupplies. Water-level measurements show that water ismoving laterally from site A to site B in both aquifers.Hydraulic gradients also indicate that there is thepotential for downward flow from the phreatic aquiferto the underlying aquifer.

(2) Question. Will the clay layer, which appearsto separate the two aquifers between sites A and B,prevent flow from the upper aquifer to the lower one?

(3) Solution. The “non-isotopically inclinedhydrogeologist” might answer: “How many test holesneed to be drilled to make sure the clay layer iscontinuous?” and “What tests can we perform todetermine the vertical hydraulic conductivity of theconfining layer?” This can be at a considerable cost.

3

(b) Analysis: Post-bomb (1953) water hasentered both the phreatic and underlying aquifer andthe clay layer is not an effective barrier to watermovement. Thus, any contaminants that might migratefrom the waste site could enter the lower aquifer andcontaminate local water supplies.

(c) Tritium ( H ) concentrations in piezometers3

in the deep aquifer were measured at less than 0.1 TU.

(d) Analysis: The age of the water is greater than50 years, although this provides little information as tothe degree to which the clay layer acts as a barrier.

(e) C analyses were conducted in the deep14

piezometers at sites A and B, and results indicated agedates on the order of tens of thousands of years.

(f) Analysis: The clay layer is continuous andacts as a barrier to separate the phreatic aquifer fromthe deeper aquifer.

4-12. Response of Groundwater Levels toLoading Events

a. General. It is possible to estimate values ofhydraulic properties of aquifers from the frequencyresponse of the water-level fluctuations. Short-termfluctuations in confined aquifers can be caused bychanges in atmospheric pressure of the atmosphere,earth tides, seismic events, and external loads such aspassing trains. In many cases, there may be more thanone mechanism operating simultaneously, withatmospheric pressure changes and earth tidalfluctuations being the two common natural events.These fluctuations offer evidence that confined aquifersare not rigid bodies, but are elastically

ground surface

potential confining layer

shallow aquifer

deep aquifer

disposal site

flow paths

flow path

potential flow to deep aquifer??

CA

Bdomestic water well

289.6

289.4

289.2

288.6

288.1

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4-27

Figure 4-11. Hypothetical proposed disposal site

compressible. Earth tides can lead to water-level water surface of the piezometer, tending to displacechanges of 1 or 2 cm; atmospheric pressure changes water from the piezometer into the aquifer. On themay cause fluctuations of several tens of centimeters, other hand, the increased atmospheric pressure alsodepending upon the elastic properties of the aquifer and increases the load on the confined aquifer, which tendsthe magnitude of change in atmospheric pressure. to displace water from the aquifer into the piezometer.Hydraulic properties, such as storage coefficient Part of this increased atmospheric load is born by the(storativity) and porosity, can be calculated from the mineral skeleton of the aquifer, however, and the netresponse of measured water levels to these natural result of an increase in barometric pressure is toloading events. These types of water-level changes are decrease the water level in the piezometer. Conversely,damped in unconfined aquifers. decreases in atmospheric pressure produce increases in

piezometer water levels. For an unconfined aquifer,b. Effects of changes in atmospheric pressure on

water levels.

(1) General. Although variations in barometricpressure have no significant effect on the water tablelevels in unconfined aquifers, the variations do causewell water levels for confined aquifers to fluctuategreatly. This is explained by recognizing that aquifersare elastic bodies. In a confined aquifer, an increase inatmospheric pressure is transmitted directly to the

atmospheric pressure changes are transmitted directlyto the water table, both in the aquifer and a well;hence, no fluctuation results. Thus, when measuringwater levels in confined aquifers, the effect ofatmospheric pressure should be considered.

(2) Barometric efficiency. In confined aquifers,when atmospheric pressure changes are expressed interms of columns of water, the ratio of water levelchange to pressure change expresses the barometric

B ')h(w

)pa

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4-28

Figure 4-12. Response of water level in a well penetrating a confined aquifer to atmospheric pressure changes. (Robinson, ©1939, reprinted by permission of the American Geophysical Union)

efficiency of an aquifer. In Figure 4-12, the upper (ft of water) (12in./ft) (1 in. Hg/13.6 in. water)curve indicates observed water levels. The lower curve (1/barometric efficiency) = in. Hgshows atmospheric pressure (inverted) in feet of waterand multiplied by 0.75. A close correspondence of In metric units, (Hg, inches)(2.54) = (Hg,major fluctuations exists in the two curves. Thus, centimeteters)Figure 4-12 illustrates a measured barometricefficiency of approximately 0.75 for an aquifer. (b) Barometric efficiency can be definedTypical barometric efficiencies in confined aquifers mathematically by:range from 0.20 to 0.75. The units of measurement (SIor metric) for water levels and atmospheric pressureused in Figure 4-12 are not important, but they must beconsistent with each other.

(a) To convert the values on the right y-axis ofFigure 4-12 into values we are familiar with from theevening news weather report, the units must bechanged from feet of water to inches of mercury,considering the factor of barometric efficiency:

(4-7)

where

B = barometric efficiency of an aquifer

)h = change in measured water level

B 'nEs

nEs % Ew

$ 'n

Ew

%1Es

S ' $(wb

S 'n(wb

EwB

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4-29

( = specific weight of water wherew

)p = change in atmospheric pressure $ = aquifer compressibilitya

(c) In confined aquifers, well measurements can n = porositybe corrected to a constant atmospheric pressure by:

• Deriving barometric efficiency.

• Correcting changes in water levels forcorresponding changes in atmospheric (a) The storage coefficient of a confined aquiferpressure. can be defined as:

(d) Jacob (1940) derived an expression for relatingthe barometric efficiency of an aquifer to aquiferproperties:

(4-8)

where

B = barometric efficiency of an aquifer

n = porosity

E = bulk modulus of compressibility for waterw

E = modulus of elasticity of the aquifer solidss

(e) Thus, barometric efficiency is directlyproportional to the rigidity of an aquifer. Barometricefficiency approaches one for rigid aquifers, and issmall for flexible unconsolidated aquifers. Abarometric efficiency of one suggests that the well is aperfect barometer, in which all changes in stress on theaquifer are borne by the mineral skeleton. The rightside of Equation 4-8, and therefore barometricefficiency, is constant for a given aquifer.

(3) Relationship between barometric efficiencyand storage coefficient. The compressibility of anaquifer can be expressed as:

(4-9)

E = bulk modulus of compressibility for waterw

E = modulus of elasticity of the aquifer solidss

(4-10)

where

S = storage coefficient

$ = aquifer compressibility

( = specific weight of waterw

b = aquifer thickness

(b) By combining Equations 4-8, 4-9, and 4-10, arelationship between barometric efficiency and aquiferstorage coefficient can be derived:

(4-11)

where

S = storage coefficient of the confined aquifer

n = porosity

( = specific weight of water [1,000 kg/m ]w3

b = aquifer thickness [m]

E = bulk modulus of compression of waterw

[2.07 × 10 N/m ]9 2

B = barometric efficiency of the aquifer

100 mWell A Well B

confining layer

S 'n(wb

EwB

Te ')h(w

)Ft

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4-30

Figure 4-13. Hypothetical well locations

(4) Example problems. Therefore, the change in water levels = 0.25 m;

(a) If the confined aquifer in Figure 4-12 is 40 mthick and has a porosity of 0.2, what is its estimated c. Earth tides. storage coefficient?

S = (0.2)(1,000)(30)(9.8)/(2.07 × 10 )(0.75) =9

3.8 × 10-5

Note: the value of 9.8 (gravity) in the aboveequation is required to convert from units of Newtonsto units of kilograms.

(b) As illustrated in Figure 4-13, well A andwell B are screened beneath a confining layer. Well Awas measured on 3/1/90 to be 301.0 ft above mean sealevel (msl); well B was measured on 3/3/90 to be300.75 m above msl. The barometric efficiency of theaquifer is 0.50. When well A was measured, thebarometric pressure was 756 cm (of water column).When well B was measured, the barometric pressurewas 806 cm (of water column). What is the gradientbetween the two wells?

The change in barometric pressure = 50 cm ofwater column.

The barometric efficiency = 0.5.

therefore, the gradient = 0.

(1) General. Water level changes in response totidal fluctuations can occur in confined aquifers as aresponse to gravity, or in confined aquifers whichoutcrop to the ocean. In the latter case, changes inpressure heads due to tides are transmitted directly tothe water in the aquifer at the outcrop. In confinedaquifers not adjacent to the ocean, the effect ofgravitational forces on water levels is a function of therigidity of the aquifer. As discussed in the previoussection, atmospheric pressure acts not only on the rockmatrix and its contained water, but also on the waterlevel in an open observation well. Gravitational forcesact only on the rock matrix and its contained water.Earth tides are predominantly the result of thegravitational pull of the moon; and to a lesser extent,the result of the gravitational pull of the sun. Earthtides cause small (1-2 cm) water-level fluctuations inwells located in confined aquifers.

(2) Tidal efficiency. The tidal efficiency of anaquifer is defined as the ratio between change in headin a confined aquifer and change in tidal force:

(4-12)

where

T = tidal efficiency of an aquifere

)h = change in measured water level [ft]

( = specific weight of waterw

)F = change in tidal forcet

The tidal efficiency is inversely proportional to therigidity of an aquifer. Tidal efficiency approaches zerofor rigid aquifers, and approaches one for flexibleunconsolidated aquifers. A tidal efficiency of onesuggests that the well is perfectly flexible, in which allchanges in stress on the aquifer are born by the porewater. The relationship between barometric efficiencyB and tidal efficiency T is:e

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B + T = 1 (4-13) Often, site characterization studies focus on pumpinge

4-13. Conclusion

Investigation of the subsurface is a dynamic andinexact science; but is essential to the success of agroundwater study. Aquifer characterization isdependent upon the quality and quantity of datagathered and the interpretation of that data to obtain agood understanding of the hydrogeologic setting.

tests and borehole geophysics, and neglect othervaluable and cost-effective investigative methods suchas cone penetrometers, surface geophysics, andisotopic analyses. Due to time and financialconstraints, it is important for the study manager to befamiliar with all potential sources of data, and plan thesite investigation in the most efficient manner to meetstudy objectives.

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Chapter 5Computer Modeling of Groundwater Flow

5-1. General

a. Chapter organization. In Chapter 3, an over-view of planning and management considerations inperforming a groundwater site characterization andmodeling study was presented. This chapter provides atechnical overview of the theory, development, and useof computer models for simulating groundwater flow.Initially, the criteria to be used in the selection of acomputer code are discussed. An overview of the com-ponents of a groundwater model is then presented,followed by a discussion on model calibration, execu-tion, and interpretation of results.

b. What is a groundwater model? A ground-water model is a replica of some real-world ground-water system. A groundwater model can be as1,2,3,4

simple as a construction of saturated sand packed in aglass container or as complex as a three-dimensionalmathematical representation requiring solution of hun-dreds of thousands of equations by a large computer.The term “modeling” refers to the formation of concep-tual models and manipulation of modeling software(codes) to represent a site-specific groundwater system.The resulting representation is referred to as a “model”or a “model application.” The accuracy of a model isdependent upon the level of understanding of the system

the model is to represent. Thus, a complete siteinvestigation and accurate conceptualization of sitehydrogeology are necessary precursors to a successfulmodeling study.

c. Components. As discussed in Chapter 3, basiccomponents of a groundwater modeling project are:

(1) A statement of objectives.

(2) Data describing the physical system.

(3) A simplified conceptual representation of thesystem.

(4) Data processing and modeling software.

(5) A report containing written and graphicalpresentations.

d. Protocol. General protocol for performingmodeling studies is discussed in Chapter 3, and typicallyfollows a process that includes the following steps:

(1) Determination of modeling objectives.

(2) Data gathering and organization.

(3) Development of a conceptual model.

(4) Numerical code selection.

(5) Assignment of properties and boundary condi-tions to a grid.

(6) Calibration and sensitivity analysis.

(7) Model execution and interpretation of results.

(8) Reporting.

The following sections in this chapter will focus onsteps 4-7; i.e., the technical aspects of developing acomputer model of groundwater flow.

5-2. Code Selection

a. Identifying needs. Selecting the appropriatecode for a modeling job involves matching modeling

The International Groundwater Modeling Center1

defines a model as “a non-unique, simplified, mathe-matical description of an existing groundwater system,coded in a programming language, together with aquantification of the groundwater system, the codesimulates in the form of boundary conditions, systemparameters, and system stresses” (U.S. Environmental Protection Agency (USEPA) 1993). “A model is a simplified description of a physical2

system” (U.S. Department of Energy 1991). “A groundwater flow model is an application of a3

mathematical model to represent a site-specific flowsystem” (ASTM 1992). “A mathematical model is a replica of some real4

world object or system” (Nuclear RegulatoryCommission 1992).

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5-2

needs with the capabilities and controls of available b. Types of codes. Four ways of describingcodes. Before selecting a code for use, the modeling groundwater models are (USEPA 1993): objectives, the conceptual model, and project time andcost constraints should be well-defined. Use this (1) Objective-based: groundwater supply, wellinformation to develop a list of needs. Purchasing a field design, prediction, parameter estimation, and edu-code first, then defining the problem second may cause cation models.insurmountable problems. Table 5-1 lists some ques-tions helpful in determining needs and matching these (2) Process-based: saturated flow, unsaturatedwith appropriate codes. flow, contaminant transport, and flow path models.

Table 5-1Determination of Model NeedsCode attributes

What is the general type of problem to be solved (flow in anunconfined aquifer, flow in a fractured confined aquifer, wellfield design)?

Does the code have the capability to adequately model thehydrologic/geologic features of the site (i.e., wells, rivers,reservoirs, precipitation, watershed runoff,evapotranspiration, variable-density flow, vertical gradients,faults, etc.)?

What are the dimensional capabilities needed (1-D, 2-DHorizontal, 2-D Vertical, quasi 3-D, 3-D)?

What is the best-suited solution method (analytical, finitedifference, integrated finite difference, finite element, matrixsolver)?

Is a particular mathematical basis needed (empirical vs.mechanistic, deterministic vs. stochastic)?

What grid discretization features are needed?

Will unusual grid size or computational capabilities berequired?

What pre- and post-processors are available?

Code administration

Who developed, distributes, and supports the code?

What is the quality of the support?

What is the quality of the user’s manual?

What is the cost?

Is the code proprietary?

Is a list of user references available?

Is the code widely used and well verified?

(3) Physical-system-characteristics based: uncon-fined aquifer, confined aquifer, porous media, fracturedrock, steady-state, time varying, multi-layer, andregional scale models)

(4) Mathematical-based: dimensionality of solutionequations, analytical, numerical, empirical, deter-ministic, and stochastic models.

The above categories are not exclusive. Typically, amodel application is labeled using a combination ofadjectives from the above categories; for example, a“two-dimensional transient numerical model of ground-water flow in porous media for the prediction of flowpaths” is one possible label.

c. Solution methods. Differing solution methodsaffect the difficulty of use and overall flexibility ofmodeling software. The three most common solutionmethods used in groundwater modeling, listed inincreasing complexity are: analytical, finite difference,and finite element. Each method solves the governingequation of groundwater flow and storage, but differ intheir approaches, assumptions, and applicability toreal-world problems.

(1) Analytical methods. Analytical methods useclassical mathematical approaches to resolve differentialequations into exact solutions. They provide quickresults to simple problems. Analytical solutions requireassumptions of homogeneity and are limited to one-dimensional and two-dimensional problems. They canprovide rough approximations for most problems withlittle effort. For example, the Thiem equation can beemployed to estimate long-term drawdown resultingfrom pumping in a confined aquifer.

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(2) Finite difference methods. Finite difference e. Pre- and post-processors.methods solve the partial-differential equations describ-ing the system by using algebraic equations to approxi- (1) General. Some pre-processors allow superpo-mate the solution at discrete points in a rectangular grid. sition of the grid and the site map, and then allowThe grid can be one-, two-, or three-dimensional. The interactive assignment of boundary conditions, aquiferpoints in the grid, called nodes, represent the average for properties, etc. Post-processors allow the numericalthe surrounding rectangular block (cell). Although adja- output to be presented as contour maps, raster plots,cent nodes have an effect on the solution process, the flow path plots, or line graphs. Choosing a code thatvalue for a particular node is distinct from its neigh- does not have, or cannot be easily linked to, pre-andboring nodes. Grids used in finite difference codes gen- post-processors should be avoided. Hundreds oferally require far less set-up time than those of finite simulation runs are typically performed for a modelingelement codes, but have less flexibility in individual job, each requiring adjusting input files and interpretingnode placement. Many common codes, such as results. Lack of tools to aid in these tasks canMODFLOW (McDonald and Harbaugh 1988), use the cumulatively result in large amounts of additional timefinite difference solution method. spent. An effective link to quality output graphics is

(3) Finite element methods. Finite element methods sented pictorially. Systems that include groundwaterdiffer from finite difference methods in that the area (or modeling as just one application in an overall datavolume) between adjacent nodes forms an element over modeling and representation system are beingwhich exact solution values are defined everywhere by developed. Such systems reduce overall modeling timemeans of basis functions. A main practical difference is by reducing manual data manipulation requirements.that finite element codes allow for flexible placement ofnodes which can be important in defining irregular (2) The Department of Defense Groundwaterboundaries. However, defining a unique location for Modeling System. The Department of Defense Ground-each finite element node requires a more labor-intensive water Modeling System (GMS) provides a compre-grid setup than that of finite difference. FEMWATER hensive graphical environment for numerical modeling,(Lin et al. 1996) is a common code using the finite tools for site characterization, model conceptualization,element solution method. mesh and grid generation, geostatistics, and sophisti-

d. Code references. Selection of a code ideally numerical codes are supported by GMS. The currentrequires knowing the capabilities, attributes, and (1996) version of GMS provides a complete interfacenuances of all available codes, then selecting the most for the codes MODFLOW, MT3D (a contaminantsuitable one. There are numerous commercial codes for transport model), and FEMWATER (a finite elementuse in groundwater modeling. Practically, the modeler model). Many other models will be supported in theoften lacks up-to-date information on all available codes future. Tools and features of GMS include theand lacks sufficient time to sort through code details. following:An extensive list of codes, their respective charac-teristics and contact addresses, and an assessment of (a) Graphical user interfaces to MODFLOW,their usability and reliability is found in the “model MT3D, and FEMWATER groundwater flow andinformation database” of the International Groundwater transport codes.Modeling Center. A selected listing from that databaseis found in “Compilation of Groundwater Models” (b) Site characterization using solid modeling of(USEPA 1993). Additional help in selecting a short list earth masses defined from borehole data.of potential codes can be provided by various publi-cations and databases provided by professional organ- (c) Surface and terrain modeling using Triangularizations and institutes such as the National Groundwater Irregular Networks.Association, the International Groundwater ModelingCenter, and research offices of the CE, USEPA and (d) Automated two- and three-dimensional finiteUSGS, among others. element and finite difference grid generation.

critical because many modeling results are best pre-

cated tools for graphical visualization. Several types of

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(e) Geostatistical tools for two-dimensional inter- data can be measured much easier than flux data,polation and three-dimensional interpolation of scattered making specified head boundary conditions more desir-data, including kriging and natural neighbor able for natural features that vary over the length ofinterpolation. boundary or vary through time. One caution is that a

specified head boundary allows an inexhaustible amount(f) Three-dimensional graphics, including contours,

vector arrows, shaded images, iso-surfaces, crosssections, and cut-away views.

(g) Animation of steady-state and transient data.

(h) Site maps can be displayed simultaneously withmodel simulation results.

(i) Intuitive and modular user interface takesadvantage of graphical display, and point and clickediting.

(j) Available for MS Windows and UNIXplatforms.

5-3. Initial Model Development

a. Basic components. After construction of theconceptual model (Chapter 3) and selection of themodeling software, the features of the conceptual modelare transferred to an input file that defines the mathe-matical model. Boundary conditions, grid dimensionsand spacing, initial aquifer properties, and time-steppingfeatures are specified according to the particularrequirements of the selected code. Input file develop-ment can be expedited by use of a pre-processor thatallows direct assignment of values to a grid that issuperimposed on a site map. At the end of this initialdevelopment phase, the model will be ready forcalibration.

b. Boundary conditions.

(1) Boundary conditions are constraints imposed onthe model grid that express the nature of the physicalboundaries of the aquifer being modeled. Boundaryconditions have great influence on the computation offlow velocities and heads within the model area. Threetypes of boundary conditions are commonly used ingroundwater flow models:

(a) Specified head. A specified head boundary canbe used when expressing the constraints imposed by alake, a reservoir, or a known phreatic surface. Head

of water flow.

(b) Specified flux. A specified flux boundaryexpresses the effects of a feature that constrains flowinto or out of a boundary or a location where the fluxcan be estimated. Examples include: zero flux from asubsurface barrier, surface infiltration, leakage across aconfining layer, or a “no-flow” boundary chosen tocoincide with a groundwater divide or a groundwaterflow line so that lateral flux is negligible. Cautionshould be used in the latter case because natural ground-water divides and “no-flow” lines can move when theaquifer is stressed.

(c) Value-dependent flux. A value-dependent fluxallows flux through the boundary according to someexternal constraint. Examples include infiltration froma pond dependent upon pond levels, and injection of wellwater dependent upon injection pressure. This type ofboundary is used commonly in transient simulations.

(2) Boundary location and orientation. The type ofboundary chosen should be fully consistent with thewater budget and boundary conditions identified in theconceptual model. Choosing an observable natural fea-ture such as a lake, river, or a groundwater divide as agrid boundary allows the boundary condition to approx-imate a constraint that can be quantified by measure-ment (reservoir levels) or reasonable estimate (fluxacross a groundwater divide). When a natural feature isnot available, orienting the boundary to run parallel witha groundwater flow line allows for designation of aboundary with a specified flux of zero. Although theboundaries can be placed anywhere, wise placementreduces uncertainty, thus contributing to more realisticmodel outcome.

(3) Boundary type variation. Simple models oftenhave uniform conditions for each whole boundary.More detailed models often have boundaries broken intosubregions having varying values or differing types ofboundary conditions altogether. The type of boundaryconditions applied can greatly affect modeling results.A study on boundary condition effects showed that three

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groundwater models, the same in all respects except for analyses can predict general aquifer response to specialtheir boundary conditions, responded very differently to stresses. However, another method, such as spreadsheetan imposed stress. The study emphasized that when analysis of well drawdown equations, is necessary tocalculated heads match those of the natural system, it simulate the local effect of pumping mainly becausedoes not guarantee that the model boundary conditions node spacing in most site models is typically many timesmatch those of the natural system (USGS 1987). greater than the diameter of the well.

(4) Boundary and system stresses. The location d. Grid design. Model grids discretize the contin-and magnitude of stresses applied to the model affect the uous natural system into segments (i.e., cells, elements,appropriate choice of boundary conditions. For exam- blocks) that allow numerical solutions to be calculated.ple, if a groundwater divide is chosen as a zero-flux The grid should be superimposed on a map of the areaboundary condition, the natural boundary and the model to be modeled. Grid boundaries should be located con-boundary may match closely in an unstressed steady sistent to the conceptual model and following the guide-state. If, however, an extraction well is placed near this lines discussed in the boundary condition section. Inboundary in the computer simulation, the original flow finite difference modeling, grid nodes lying outside thesystem is no longer being modeled and the original boundary are often designated as non-computational toboundary condition and its alignment may need to be minimize computation volume. When designatingchanged. A rule of thumb is to avoid placing boun- boundary nodes, the modeler must be aware of whetherdaries close to where stresses will be applied. the modeling software uses a block-centered or mesh-

(5) Water table boundary. The water table boun- The flux boundary for the mesh-centered nodes is cal-dary is typically specified three ways: (a) as a depen- culated on the line (or plane) directly between the nodes.dent variable using the Dupuit assumptions (commonly The flux face is calculated at the midpoint between theused in two-dimensional and three-dimensional appli- nodes when using the block-centered convention.cations), (b) as a designated no-flow boundary (usually Flexible placement of finite element boundary nodesused in three-dimensional and profile applications), or allows exact placement of nodes along the boundary.(c) as a dependent variable in an unsaturated/saturatedmodel application. The Dupuit assumptions are: that e. Grid resolution and geometry. The followingflow in an unconfined aquifer is horizontal, the head guidelines should be followed when constructing adoes not change with depth, and that horizontal flow is numerical model grid:driven by the water table gradient at all depths. Codesusing the Dupuit assumptions allow for treating the (1) Node spacing. The spacing between nodes,water table as the feature to be computed by the model called grid resolution, should be responsive to sharpwhich is often exactly what is desired. The response of changes in physical features, temporal conditions, and,the water table to pumping from a well or variations in numerical stability and overall model size constraints.reservoir stages can be solved with codes using the Generally, node spacing is finer where the dependentDupuit assumptions. Generally speaking, codes using variables, usually the hydraulic gradient and flux, arethe Dupuit assumptions are more simple and less labor subject to greater change. The areas near extractionintensive than those requiring the water table to be wells, infiltration trenches, and confined aquifer flowdesignated (fixed). Codes requiring an unsaturated/ channels are examples. Finer node placement may alsosaturated zone interface have complex and detailed be required where curved surfaces or irregular boun-requirements and are generally only used for localized daries are being represented. Where definition of irreg-applications because of the detailed definition required. ular surfaces is required, use of a code not allowing for

c. System recharge and withdrawal stresses. result in a grid with an excessively large number ofGroundwater models are useful in predicting the effects nodes. Sensitivity to grid resolution should be checkedfrom special recharge and withdrawal stresses, usually when performing a thorough analysis because differinginjection and extraction wells, that cause a relatively grid resolutions can affect modeling results.large water exchange in a relatively small area. These

centered convention and place the nodes accordingly.

flexible node placement should be questioned as it could

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(2) Selection of model layers. In three-dimensional fluctuating lake level is an example, and could be simu-models, model layers allow for the simulation of flow in lated using specified head nodes that vary according toseparate hydrographic units, leakage between aquifers, some predetermined schedule. and vertical flow gradients. Typically, one model layeris selected for each hydrostratigraphic unit; however, if g. Aquifer material properties. Aquifer materialthere are significant vertical head gradients, two or more properties refer to those aquifer properties, such aslayers should be used to represent a single hydrostrati- hydraulic conductivity and anisotropy, that govern flowgraphic unit (Anderson and Woessner 1992). rate and flow direction. Table 5-2 presents basic aqui-

(3) Avoiding numerical errors. Numerical errorand unintended biases in solution of the flow equationscan be minimized by avoiding large variations in nodespacing and large aspect ratios. The aspect ratio is themaximum dimension of a block or element divided bythe minimum dimension. An aspect ratio of one is usu-ally ideal for minimizing numerical errors. As a rule ofthumb, aspect ratios up to 10:1 in non-sensitive areas ofa grid are usually acceptable and expanding block orelement sizes by 1.5 times the adjacent block sizesshould be avoided.

(4) Grid sizes. The overall size of the grid (i.e.,total number of nodes) should be adequate to define the Aquifer storage (pumping tests, geophysical methods).

problem and produce results consistent with modelingobjectives, but not so large as to cause excessive runpreparation and computation requirements. Severalhundred iterations of adjusting the model input, runningthe model executable code, and interpreting the resultsare often required in a modeling job. An excessivelylarge grid will expand the time requirements for eachiteration, resulting in a cumulatively large impact to themodeling quality or schedule.

f. Initial conditions. Initial conditions refer to thevalues of the dependent variables defined at thebeginning of the simulation. For steady-state models(no time variation), initial conditions need only approx-imately match the natural system because the solutionfor each dependent node can be found eventuallythrough repeated iteration. In contrast, transient models(time variation included) require initial conditionsclosely matching natural conditions at the beginning ofthe simulation. To do this, it is often necessary to firstrun a steady-state model, or alternately, run the transientmodel for a lead-up period of time before beginning theinterval of interest. Transient models commonly haveboundary conditions that vary as the model simulates anaquifer system response through time. A seasonally

fer properties and typical data sources.

Table 5-2Aquifer Properties and Data SourcesHydraulic conductivity (pumping tests, slug tests, sluginterference tests, grain size analysis, laboratorypermeameter tests, tracer tests).

Transmissivity (pumping tests, calculation from hydraulicconductivity).

Porosity (grain size analysis, observation at trenching oroutcrop sites, geophysical tests).

Anisotropy (tracer tests, geologic conceptualization andhistory).

h. Assignment of aquifer material properties togrid. The aquifer properties previously listed areassigned throughout the model grid by use of a pre-processor or directly into an input file. A simple modelmay assign uniform hydraulic conductivity in all nodeswhile complex models may have many different nodegroups, layers, or zones, each with differingconductivity values. The discretization of zones ofhomogeneous aquifer properties should be basedprimarily on site geology. The discretization of zonesbased on water levels should only be considered in areaswhere a high quantity (and quality) of data presentscompelling physical evidence of distinct hydrogeologicconditions. Geostatistical methods may be employed todistribute the properties to all nodes based on the dataknown at only a few nodes. However, geostatisticsprovides a systematic method for distributing theproperties and does not account for site geologicalconditions. The total number of zones of homogeneityshould be kept at the minimum required to adequatelyrepresent the system within data constraints.

i. Representing uncertainty. The inherent uncer-tainty in the information describing aquifer properties

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should be recognized and preserved throughout the the model should be ready for use to simulate the flowanalysis. Most properties should be represented as system.ranges because of the uncertainty associated withgathering, interpreting, and extrapolating the data to the b. Calibration methods. Methods of calibratingmodel. Aquifer properties are usually gross, large-scale can be grouped into two categories: manual trial-and-representations of properties that are increasingly vari- error calibration and automated calibration. The stateable when viewed at increasingly smaller scales. Deal- of the practice is that most modeling is performed bying with uncertainty in model inputs is discussed in trial and error while automated methods are becomingSection 5-6 on modeling application. increasingly usable and accepted. The method is code-

j. Time-stepping. Time-stepping is the discretiz- greater use of automated calibration are expected. ing of the flow equations through time and is used intransient simulations. Like node spacing, time-stepping (1) Manual trial and error. This method of cali-should be fine enough to define the problem adequately, bration is labor-intensive. The modeler makes succes-but not too small to exceed practical computation con- sive cycles involving interpreting prior results tostraints. Time-stepping should be finer at those times determine where inputs need adjustment, makingwhen new stresses are introduced. Changes in boundary speculative adjustments to the input code, re-running theconditions usually control the time-step requirement. model and output software, and then comparing theInitial time-stepping designation should be estimated by computed results to the natural system. Typically, hun-experience and refined with a time-stepping sensitivity dreds of iterations are made before an acceptableanalysis. Some codes combine time-steps into groups calibration is achieved, the specific number dependingcalled stress periods. on model complexity, experience of the modeler, and the

5-4. Model Calibration and Sensitivity Analysis

a. Calibration defined. Calibration is the processof adjusting model inputs to achieve a desired degree ofcorrespondence between the model simulations and thenatural groundwater flow system. A flow model is con-sidered calibrated when it can reproduce, to an accept-able degree, the hydraulic heads and groundwater fluxesof the natural system being modeled. This is accom-plished by finding a set of values for the boundaryconditions, aquifer properties, and stresses that result incomputed heads and fluxes matching their natural coun-terparts at target locations. In other words, calibrationmethods solve a problem inversely by iteratively adjust-ing the unknowns (hydraulic conductivities, certainboundary fluxes, etc.) until the solution matches theknowns (usually the hydraulic heads). Multiple calibra-tions of the same system are possible using differentboundary conditions and aquifer properties. There isnot one unique calibration that is “correct” for anymodel because exact solutions cannot be computed withthis multi-variable approach. Furthermore, becausemodel zones of homogeneous aquifer properties shouldhave a strong physical basis, the most accurate model isoften not the model which most closely simulates cali-bration targets. At the end of the calibration process,

dependant. Advances in modeling software allowing for

acceptableness criteria applied. Typically, the inputsbeing adjusted are hydraulic conductivity (or transmis-sivity), storage, leakage across a confining layer used asa boundary, flux to and from a surface water body, anddesignation of boundary conditions. A typical manualtrial-and-error calibration process includes the followingsteps:

(a) Complete initial model development andassignment of properties as outlined in this chapter.

(b) Identify the parameters to be adjusted duringcalibration and the appropriate range for each. Theseare determined from the initial sensitivity analysis andfrom the conceptual model.

(c) Identify the locations and values for the targetpoints forming the calibration set. Groundwater flowmodels are usually calibrated to a set of observed poten-tiometric head levels.

(d) Iteratively run the modeling software and adjustinput parameters until an acceptable match betweenobserved and calculated values at the target points isachieved. If the model is being calibrated to a set ofobserved head values, the computed and estimatedboundary fluxes must also be compared.

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(e) Repeat steps (c) and (d) for different calibration These questions can usually be answered by having aconditions if desired. For example, a model can be complete conceptual model and observing the changes tocalibrated to the seasonal low and seasonal high calibra- the set of target values over time.tion conditions or to conditions where the aquifer isstressed by pumping or injection. d. Types of comparisons.

(2) Automated calibration. This method utilizes an (1) Spatial graphic comparisons. This methodobjective function, such as minimization of the sum of often uses superimposed contoured water table surfacesthe squared differences between observed and computed or raster plots to show locations and magnitude of theheads (residuals), to govern automatic iterative differences between computed and observed valuesadjustment of values that would otherwise be adjusted (residuals). These methods provide the modeler with anmanually. Automated codes do this in a systematic understanding of spatial variation of the residuals andfashion and typically require constraints on sets of input can be key to selecting where further input parametervalues in the form of probability functions, conditional adjustments are required. bounds, or weighted values. These constraints requirethe modeler to better define the uncertainty and variation (2) Tabular comparison at target nodes. Thiswithin parameters, such as hydraulic conductivity, method provides a quantifiable comparison of valuesbefore code execution begins. Particular requirements point by point.for automated calibration codes vary.

(3) Comparison of calibration methods. Automatedcalibration methods have some potential advantagesover trial-and-error methods. They can provide asystematic approach to calibration, allowing for effi-ciencies within individual modeling jobs and a basis forcomparison between different modeling jobs. Statisticalmeasurements are available from some automatedapproaches that are not usually performed in trial-and-error approaches. And finally, practitioners report that,because less time was spent on manual iteration, moretime was available to refine the calibration and exploremodel sensitivity to various calibration options.

c. Matching computed values with target values.A key to calibration is the comparison of computedvalues, usually the computed heads, with observedvalues, often called “target values,” to determine theappropriateness of the calibration. Questions to beconsidered when compiling a set of target values includethe following:

(1) Do the target values reflect a steady-state ortransient condition?

(2) Are there effects from local anomalies?

(3) Are the wells screened comparably?

(4) Are the measurement errors acceptable?

(3) Lumped-sum comparison. These methods lumpresidual measurements into single values and often takethe form of: (a) mean error of the residuals,(b) absolute mean error to the residuals, and (c) root-mean-squared error of the residuals. Using the root-mean-squared error method provides a commonly usedoverall comparison.

e. Calibration cautions. Successful calibration toone model component does not guarantee a soundmodel.

(1) Head calibrations and boundary conditions.When model head results match observed head results,the groundwater flow system is not necessarily simu-lated accurately. As discussed in the “BoundaryConditions” section, research shows that modelsdiffering only by their boundary conditions can becalibrated to the same hydraulic head set, yet performdifferently when stressed. Similarly, models that differonly by magnitude of hydraulic conductivity values canbe calibrated to the same water table head set, yetproduce differing flow velocities and boundary fluxes.These potential difficulties can be overcome to somedegree by development of a sound conceptual model andensuring the mathematical model appropriatelyrepresents key conceptual components. Estimatedfluxes should be compared with calculated fluxes forany calibration using hydraulic heads as target values.Boundary conditions play an important role in sound-ness of modeling.

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(2) Experience required. Model calibration ± 20 percent due to the reasonably expected range ofrequires extensive knowledge of the natural groundwater site hydraulic conductivities, then interpretation of finalsystem being modeled. Understanding how to best model results should reflect this.achieve an adequate calibration and when the matchbetween results is “good enough” depends on modelingobjectives and expectations of the customers. Freyberg(1988) documents a study where nine groups, using thesame model and input data, individually calibrated themodel and produced widely varied final results. “Thegroup achieving the best prediction chose to zone theconductivity field into a relatively few homogenousregions, while the group producing the worst predictionchose to ‘tweak’ the conductivity field grid block bygrid block to achieve a good (in fact, the best) local fitto the observed data.” This study showed that anapparently “good” calibration does not necessarilyresult in accurate predictive results for othersimulations.

f. Sensitivity analysis defined. A sensitivityanalysis is a quantitative evaluation of the influence onmodel outputs from variation of model inputs. A sensi-tivity analysis identifies those parameters most influen-tial in determining the accuracy and precision of modelpredictions (USEPA 1992). During sensitivity analysis,numerous model runs are performed, each having onlyone parameter varied by some specified percentage.Both positive and negative variance is tested.

g. Use of sensitivity analyses. Sensitivity analy-ses can be used to aid in model construction by identi-fying inputs requiring more definition. For example, thesensitivity analysis may show that existing hydraulicconductivity data ranges so widely that additionalpumping tests are needed to obtain the desired level ofaccuracy in modeling results. Sensitivity analyses alsoaid in interpreting results. For example, uncertaintyabout the head values at a boundary may not be a con-cern if the analysis shows that output of interest isinsensitive to these head values. Typically the analysiswill show that sensitivity of groundwater flow to vari-ation in hydraulic conductivity is relatively high.

h. Level of effort. Commonly, a small-scale anal-ysis is performed during early model calibration, as acalibration aid; then a more rigorous analysis is per-formed after calibration as an indicator of model per-formance. If, for example, the results from a sensitivityanalysis show that computed velocities vary

5-5. History Matching

Following calibration and sensitivity analyses, the modelapplication can be tested with the concept of historymatching. The concept of history matching is that amodel's predictive capability can be shown to residewithin acceptable limits by comparing model predictionswith a data set independent of the calibration data. Ifthe comparison is unfavorable, the model needs furthercalibration. If the comparison is favorable, it givesweight to the argument that the model application canbe used for prediction with a reasonable assurance ofaccuracy. This assurance does not, however, extend toconditions other than those tested and thus does notaccount for unforeseen stresses. History matchingshows how the model application can simulate pastconditions. It does not necessarily indicate accuracy forpredictive simulations.

5-6. Model Execution and Interpretation ofResults

a. Model execution. After successfully perform-ing the calibration and sensitivity analysis, the modelapplication is ready for use in performing simulations.This step usually takes less time than the calibrationstep. Model output is usually produced in the form ofhydraulic heads and flow vectors at grid nodes. Fromthese, head contour maps, flow field vector maps,groundwater pathline maps, and water balance calcula-tions can be made using post processors. Some combi-nation of these simulation results can be used to answerthe questions posed by the modeling objectives.

b. Dealing with uncertainty. One key issue ishow to constrain the modeling runs to account foruncertainty while still meeting the modeling objectives.This can be accomplished by using one of the followingapproaches:

(1) Best estimate. Producing “best estimate”results by using the most representative input valuesusually provides a useful indicator of groundwatervelocities, heads, and fluxes. However, single valuemodeling results do not, by themselves, give muchassurance of accuracy.

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(2) Worst case. One possible modeling objective is modeling results a greater understanding of how overallto determine if a certain groundwater level or flow rate model performance varies according to inputmay arise given the most unfavorable conditions pos- uncertainty.sibly expected. In this case, the model is calibratedusing the best estimates from the ranges of input values, (5) Using uncertainty distributions. Variousbut simulations are performed using input values from methods, such as inverse modeling and Monte Carlothe most unfavorable end of the input ranges. For analysis, can be used to more fully analyze the effects ofexample, field estimates for transmissivities are identi- uncertainty on modeling results. Usually these methodsfied at 500-800 m /d-m. If model simulations predict require the modeler to bound the range of uncertainty or3

that a well field design will meet its production goals define a probability distribution for the associatedeven when using transmissivities as low as 400 m /d-m, variable. Results are returned in bounded or distri-3

this gives some assurance that the design is adequate. bution form. The level of effort and computation time

(3) Best estimate with sensitivity analysis adjust- than those of earlier described approaches. Advances inment. Best estimate results can be coupled with the software are expected to increase the usability of theseresults from the sensitivity analysis to provide a range approaches in the future.of expected aquifer performance. For example, ifmodeling objectives were to predict whether head fluc-tuations at a location could exceed 5 m, and, if the bestestimate results plus additional adjustment from thesensitivity analysis results predict only a total of 2 mexpected fluctuation, then further analysis may not bewarranted.

(4) Bracketed ranges. In this case, two or morecalibrations of the model are made. Each uses a differ-ent set of values for key input parameters. The resultsshould bracket the expected possible range of results.For example, if field data defined a dominant hydro-geologic unit at a site, but the only two pumping testsfor this unit produced differing estimates of itshydraulic conductivity, a model could be calibratedtwice using the two different estimates. These twocalibrations would differ in boundary flux and flowvelocities which should be checked against observed orestimated values. Bracketing gives those interpreting

required for these types of analyses are much greater

5-7. Post Audit

A post audit is similar to history matching described inSection 5-5, but differs in that it assesses the accuracyof past predictions compared with data gathered in theinterim period (usually over a long period of time). Postaudits usually provide insights into model improvementsthat can be made and weaknesses in making modelingassumptions. Anderson and Woessner (1992) report onfour post audits reported in widely available literaturenone of which accurately predicted the future. Theyconcluded that inaccurate predictions were based onerrors in the conceptual models and also on failure touse appropriate values for assumed future stresses.When modeling is viewed as an iterative process con-tinuing over long periods of time, then modeling per-formed today will provide a basis for future modelingwhich will be improved by larger data sets andimproved technology.

Precipitation

Overland Flow

Infiltration

Interflow

Unconfined Aquifer

Well

River

Base FlowBank

Confined Aquifer

Water Table

Storage

Confining Layer

Reservoir

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Figure 6-1. Flow components of the surface-groundwater system

Chapter 6Interaction Between Surface Water andGroundwater

6-1. General

This chapter will provide an overview of the distributionand movement of water between the surface and thesubsurface. Practical analytical methods which quan-tify the interaction between surface water and ground-water are provided. Additionally, an overview on com-puter modeling of the interaction of groundwater withsurface water is presented.

6-2. System Components

a. General. Surface and groundwater systems arein continuous dynamic interaction. In order to properlyunderstand these systems, the important features in eachsystem must be examined. These features are groupedinto components referred to as the surface component,the unsaturated zone component, and the groundwater(saturated) component. The flow of water on thesurface, and in the unsaturated and saturated zone, isdriven by gradients from high to low potentials.Figure 6-1 presents the basic flow components of asurface-groundwater system.

b. Surface water. Surface water is water thatflows directly on top of the ground. Surface waterincludes obvious features of streams, lakes, and

reservoirs, and the less obvious features of sheet flow,and runoff from seeps and springs. Runoff across thesurface occurs whenever the accumulation from precip-itation (either as rain or snow) exceeds the infiltrationcapacity of the subsurface strata and the evapo-transpiration rate, or whenever the rate of groundwaterdischarge exceeds that which is evapotranspired.

c. Subsurface water.

(1) Water infiltrating through the unsaturated zoneis from direct precipitation, from overland flow, andfrom leakage through streambeds. Flow in the unsatu-rated zone generally is assumed downward in responseto gravity. However, poorly permeable strata (forexample, a clay layer) can create barriers to downwardflow that can limit the amount of water reaching theunderlying saturated zone by deflecting flow laterallyuntil it is discharged as evapotranspiration or as seepageto the surface (referred to as interflow).

(2) Groundwater is an important component in thehydrologic cycle as it acts as a large storage reservoirthat accepts and releases water from and to the surface.In places where streams flow over permeable strata, thepeak flow of a flood is attenuated because of leakagefrom the stream into the subsurface. Most of this waterreturns to the stream as the stage decreases, resulting inprolonged flow. This relatively short-term flow ofwater into and out of the subsurface during a floodevent commonly is called bank storage. Additionally,many streams throughout the country have sustainedflows during extended dry periods as a result of leakagefrom groundwater. This contribution to streamflow iscalled baseflow.

(3) Groundwater flow is complicated by variationsin the water-transmitting properties of strata. Forexample, groundwater can be confined beneath poorlypermeable layers of strata (clay or unfractured, denserock) only to discharge to the surface where landsurface cuts through the confining layers or discharge tothe surface through fractures that extend through theconfining layers (such as a spring). Additionally,pumping of groundwater from permeable sediments neara stream can decrease flow in the stream either byreducing leakage of groundwater to the stream or byinducing leakage from the stream into the subsurface.

q v ' &KvM(R % z)

Mz

MMz

K(2v)MRMz

%MzMz

'M2Mt

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Figure 6-2. Typical relationship between moisturepotential (RR), hydraulic conductivity (K) and watercontent (22 ) for an identical clay samplev

6-3. Infiltration

a. General. Infiltration is the process by whichwater seeps from the surface into the subsurface. Theunsaturated zone consists of soil, air, and water (whichmay be in the form of ice or vapor). The pore spacewithin the soil medium is filled with varying amounts ofair and water. Quantifying flow in the unsaturated zoneis a much more complicated process than that of thesaturated zone primarily because soil properties whichcontrol infiltration rates, such as hydraulic conductivityand soil moisture content, tend to change with time.

b. Concepts. Both gravity and moisture potentialact to pull water from the surface into the unsaturatedzone. Gravity potential is equivalent to elevation (orhydraulic) head. Moisture potential is the negativepressure (or suction) exerted by a soil due to soil-waterattraction. The total potential h in unsaturated flow isdefined as:

h = Q(2) + Z (6-1)

where

Q(2) = moisture potential

Z = gravity potential

Downward flow through the unsaturated zone is con-trolled by the vertical hydraulic conductivity K(2 ) ofv

the soil medium, and moisture potential. The valueK(2 ) increases as the moisture content increases. Atv

saturation, the vertical hydraulic conductivity K(2 )v

equals the saturated hydraulic conductivity described byDarcy's Law (Section 2-11), and downward flow iscontrolled by hydraulic conductivity and elevation head.Moisture potential varies with the moisture content andpore size of the medium. When soil is dry, the moisturepotential is typically several orders of magnitude greaterthan gravity potential. A dry soil will have a higherinitial infiltration rate than that of a moist soil, dueprimarily to free surfaces within the pore space. Thepores act as capillary tubes to draw in water, and asthey fill, the capillary forces decrease along with theinfiltration rate. Figure 6-2 provides an illustration ofthe relationship between moisture potential, hydraulicconductivity, and water content for a clay sample.

Groundwater flow is described by Darcy's Law:

q = -K (dh/dl) (6-2)

where

q = flow rate of groundwater

K = hydraulic conductivity

dh/dl = gradient over which flow occurs

By substituting R+z in Equation 6-1 for h in Equa-tion 6-2, infiltration can be described as a function ofvertical hydraulic conductivity and moisture potential:

(6-3)

As discussed earlier, infiltration and flow in theunsaturated zone are controlled by moisture potentialR(2) as well as hydraulic conductivity K(2 ). Thus,v

any change in the infiltration rate requires a change inmoisture content 2. This is described by the one-dimensional Richard's equation:

(6-4)

fo

fc = Kv

Infiltration Rate

Cumulative Infiltration0

EM 1110-2-142128 Feb 99

6-3

Figure 6-3. Infiltration capacity curve

The solution to Richard's equation indicates a decreasein moisture potential with cumulative infiltration, and asmoisture potential approaches zero, the infiltration ratedecreases to a rate equivalent to saturated verticalhydraulic conductivity; i.e.,

q (at saturation) = -K (dz/dz) = -K (6-5)v v

Infiltrating moisture from rainfall events tends to movevertically downward as a wave front of saturated soil.Eventually, this wave front reaches the water table andmoisture conditions in the soil profile stabilize andreturn to their pre-rain state.

c. Infiltration capacity curve. The decrease inmoisture potential with cumulative infiltration is illu-strated by an infiltration capacity curve (Figure 6-3).The initial (or antecedent) infiltration capacity f is0

typically controlled by the moisture content of the soil.The final (or equilibrium) infiltration capacity f isc

equivalent to the saturated vertical hydraulic conduc-tivity of the soil K .v

Other factors affecting soil infiltration include: rain-water chemistry, soil chemistry, organic matter content,and presence of roots and burrowing animals. Fieldconditions that encourage a high infiltration rate include:low soil moisture, course/porous topsoil, well-vegetatedland (inhibited overland flow, lower soil moisture due totranspiration), and land use practices that reduce soilcompaction.

6-4. Stream-Aquifer Interaction

Water is transmitted from a basin to a channel systemthrough the following three basic mechanisms (Figure 6-1):

• Overland flow occurs when the rate ofprecipitation exceeds the infiltration capacity of thelocal soil.

• Interflow occurs when infiltrating subsurfaceflow above the water table is diverted towards a channelbed by stratigraphic changes.

• Base flow occurs when the potentiometric sur-face (or elevation of the water table) proximate to thechannel bed exceeds stream elevation.

Seasonal conditions may control the groundwater eleva-tion and thus the direction of flow between the streamand aquifer. When the hydraulic gradient of the aquiferis towards the stream, groundwater discharges to thestream, and the stream is a gaining or effluent stream.When the hydraulic gradient of the aquifer is away fromthe stream, the stream is losing or influent. The rate ofthis water loss is a function of the depth of water, thehydraulic gradient towards the groundwater, and thehydraulic conductivity of the underlying alluvium. Thechannel system can be hydraulically connected to theaquifer, or have a leaking bed through which water caninfiltrate to the subsurface. The extent of this interac-tion depends on physical characteristics of the channelsystem such as cross section and bed composition.Streams commonly contain a silt layer in their bedswhich reduces conductance between the stream and theaquifer.

6-5. Interaction Between Lakes andGroundwater

The hydrologic regime of a lake is strongly influencedby the regional groundwater flow system in which it islocated. This interaction plays a critical role inevaluating the water budget for the lake. A method ofclassifying lakes hydrogeologically can be based on thedomination of the annual water budget on surface wateror groundwater. Lakes dominated by surface watertypically have inflow and outflow streams, whileseepage lakes are groundwater dominated. Large

Q ' Q0e&kt

EM 1110-2-142128 Feb 99

6-4

permanent lakes almost always provide areas of dis- The slope of baseflow recession is consistent for eachcharge from the local groundwater. The rates of watershed and independent of such things as magnitudegroundwater inflow are controlled by watershed topo- of the precipitation event or peak flow. When an aqui-graphy and the hydrogeologic environment. Winter fer contained by a watershed is homogeneous, the(1976) concluded that if the water table is higher than hydrograph of a stream at a critical time following athe lake level on all sides of a seepage lake, groundwater precipitation event (when all discharge to the stream iswill seep into the lake from all sides, including upward contributed by groundwater) will decay following anseepage through the lake bottom assuming a homogen- exponential curve. This baseflow recession is describedeous flow system. However, should an aquifer of much by:higher conductivity underlie the lake, this zone ofupward seepage can be eliminated. Three-dimensionalnumerical analysis of the lake/groundwater interactionsystem indicated that upward seepage tends to occuraround the lake edges, while seepage out of the laketends to occur in the middle of the lake.

6-6. Analytical Methods

a. General. This section will provide physicallybased analytical methods for:

(1) Estimating aquifer diffusivity (Section 2-16)from the response of groundwater levels to fluctuationsin surface-water levels.

(2) Estimating the groundwater contribution ofrecharge from a storm event to streamflow.

(3) Using streamflow records to estimate aquiferdiffusivity.

(4) Estimating the effects of pumping wells onstream depletion.

b. Baseflow recession. A stream hydrographdescribes the flow at a certain point on a river as a func-tion of time. While the overall streamflow shown on ahydrograph gives no indication of its origin, it is pos-sible to break down the hydrograph into componentssuch as overland flow, interflow, and baseflow. After acritical time following a precipitation event whenoverland flow and interflow are no longer contributingto streamflow, the hydrograph of a stream will typicallydecay exponentially. Discharge during this decayperiod is composed entirely of groundwater contribu-tions as the stream drains water from the declininggroundwater reservoir. This baseflow recession for adrainage basin is a function of the overall topography,drainage patterns, soils, and geology of the watershed.

(6-6)

where

Q = flow at some time t after recession has started

Q = flow at the start of baseflow recession0

k = recession constant for the basin

t = time

The value for k, the recession constant, is typicallyestimated empirically from continuous hydrographrecords over an extended period. Rorabaugh (1964)developed a physically based method for estimating therecession constant for the basin based upon aquiferdiffusivity (Section 2-17) and basin topography. Thisallowed for the estimation of baseflow recession instreams with limited continuous data, and also allowedfor the estimation of adjacent groundwater propertiesbased upon measured streamflow records.

c. Assumptions. To analyze a stream-aquifer sys-tem analytically, many simplifying assumptions need tobe made. Assumptions used throughout Sections 6-7,6-8, and 6-9 include the following:

(1) Darcy's law applies.

(2) The aquifer is homogenous, isotropic, and ofuniform thickness.

(3) The rocks beneath the aquifer are impermeable.

(4) The surface-water body fully penetrates thegroundwater system, and flow is considered horizontal.

MhMt

'TS

M²hMx²

hgw'2Hswe&d BS

PT

EM 1110-2-142128 Feb 99

6-5

(5) The lateral boundaries of the aquifer are S = aquifer storage coefficientimpermeable.

(6) Distances from the stream to groundwaterdivides or geologic boundaries of flow are for each T/S = aquifer diffusivity [L /T]stream reach; when this distance is termed semi-infinite,this boundary has minimal influence on the analytical c. Review of solutions. The solution to the gov-solution. erning equation (Equation 6-7) subject to a fluctuating

(7) The river is not separated from the aquifer by authors (Ferris 1951; Cooper and Rorabaugh 1963;any confining material. Pinder, Bredehoeft, and Cooper 1969; Hall and Moench

6-7. Estimating the Transient Effects of FloodWaves on Groundwater Flow

a. Introduction. Accurate estimation of the trans-missivity and storage coefficient of an aquifer is criticalto the prediction of groundwater flow patterns. If anaquifer is adjacent to a river or surface reservoir whichexperiences periodic stage fluctuations, it may be pos-sible to calculate these parameters from an analysis ofthe aquifer response to the fluctuations.

b. Principle. The idealized flow domain is shownin Figure 6-4. The aquifer is represented as a semi-infi-nite, horizontal confined aquifer of uniform thicknessbounded on the left by a reservoir (open boundary).The surface-water body is assumed to completely pene-trate the aquifer. The water level in the reservoirfluctuates and causes a corresponding fluctuation in thepiezometric head within the aquifer. The one-dimensional flow system is described by the governingequation for linear, non-steady flow in a confined aqui-fer (see Equation 2-28):

(6-7)

where

h = rise or fall of piezometric head in the aquifer[L]

x = distance from aquifer-surface bodyintersection [L]

t = time [T]

T = aquifer transmissivity [L /T]2

2

boundary condition has been presented by several

1972). Each of the solutions was derived for the semi-infinite flow domain described above subject to theassumptions listed in Section 6-6. The solutions arederived for confined conditions, although satisfactoryresults for unconfined conditions will be obtained if:

(1) The location of the computed head is suffi-ciently far enough from the surface water intersection sothat it is unaffected by vertical components of flow.

(2) The range in cyclic fluctuation at the computedlocation is only a small fraction of the saturated thick-ness of the formation.

d. Uniform fluctuations. Ferris (1951) observedthat wells near bodies of tidal water often exhibitsinusoidal fluctuations of water level in response toperiodic changes in tidewater stage. An analogousresponse was suggested for wells situated adjacent tolarge surface-water bodies. When the stage of thesurface body fluctuates as a simple harmonic motion, aseries of sinusoidal waves is propagated outward fromthe surface body-aquifer intersection through theaquifer. Expressions were developed to determineaquifer diffusivity (T/S) based on the observed values ofamplitude, lag, velocity, and wavelength of thesinusoidal changes in groundwater level. If the range ofthe fluctuation in surface water and an adjacent well isknown, aquifer parameters can be derived by:

(6-8)

If the lagtime in occurrence between surface andgroundwater maximum or minimum stages is known,then:

Land Surface

Piezometric Surface

h (x,t)Initial Piezometric Surface

AquiferReservoir

Maximum Stage

h (x,0)

h0

x

tlag'd PS4BT

EM 1110-2-142128 Feb 99

6-6

Figure 6-4. Representation of simplified one-dimensional flow as a function of surface-water stage

(6-9)

where

h = maximum rise in groundwatergw

H = maximum rise in surface-water bodysw

d = distance from well to surface water

S = aquifer storage coefficient

T = aquifer transmissivity

P = period of uniform tide or stage fluctuation

t = lag time in occurrence of maximumlag

groundwater stage following the occurrenceof a similar surface stage

As shapes of the stage hydrographs for flood waves insurface streams and reservoirs vary widely, a solution ofthe governing equation satisfying a boundary conditiondescribed by a uniform sine wave will generally notapproximate the actual domain adequately.

e. Example problem. Sunny Bay has tidal fluctu-ations every 12 hr with a total tidal change of 3 m. Ascreened monitoring well 200 m from the shoreline islocated within a confined aquifer that is 10m thick. Theamplitude of the groundwater change due to the tides is1 m. S was estimated to be 0.001. Estimate the hydrau-lic conductivity K of the aquifer.

Given

h = 1 mgw

H = 3 msw

d = 200 m

hgw ' 2Hswe&d BS

PT

1m ' 2(3 m) e&200 m B(0.001)

(0.5 days)(10 m)(K)

ln 0.1667 ' ln(e&200 m B(0.001)

(0.5 days)(10 m)(K))

&1.79 ' &200 mB(0.001)

(0.5 days)(10 m)(K)

0.0090 m&1 '0.0006 m&1days&1

K

0.0001 m&2 '0.0006 m&1days&1

K

K ' 6 ft/day

h (0, t) '0 when t ˜ 0)Hm when t ™ 0

h (4, t) ' 0

h (x, 0) ' 0 when x š 0

)hm ' )Hmerfc x

2 (T/S)t

erfc(x)'m4

xe &t 2

dt

hp '

p

jm'1

)Hm erfc u

2 p&m

u 'x

(T/S))t

EM 1110-2-142128 Feb 99

6-7

S = 0.001

b = 10 m

P = 12 hr (0.5 day)

Determine K by using Equation 6-8, and substituting Kbfor T (Equation 2-9).

f. Representation of fluctuations by discretesteps. Pinder, Bredehoeft, and Cooper (1969)developed solutions to the governing equation using adiscrete approximation of the surface body stagehydrograph. This discrete approach allows the use of astage hydrograph of any shape (i.e., one not restricted tosinusoidal or uniform asymmetric curves). For eachincrement in reservoir stage, the head in the adjacentsemi-infinite aquifer is given by the solution of Equation6-7 subject to the boundary and initial conditions

(6-10)

(6-11)

(6-12)

where

)h = instantaneous rise in surface-water stage at timem

t = m)t where m is an integer

The solution to the problem is given by:

(6-13)

The complementary error function (erfc) is unique foreach value of x:

(6-14)

Values of erfc can be found in tables from manysources.

To compute the change in aquifer head (h ) at the end ofp

any number of stage increments, the change in surface-water stage )H after each successive increment timem

)t must be obtained. The change in groundwater headis given by summing the values of )h computed form

each )H over the period (p-m))t, giving:m

(6-15)

where

h = head at a distance x from the reservoirp

intersection at time p)t;

p)t = total time since beginning the period ofanalysis, where p is the number of timeintervals.

(6-16)

Equation 6-16 can be used to generate type curves fordifferent values of diffusivity. Each set of curves there-fore represents the computed change in hydraulic head

q ' 2T(h0

a)(e &B2Tt/4a 2S % e &9B2Tt/4a 2S %...)

q ' 2T(h0

a)e &B2Tt/4a 2S

q ' h0STtB

tc '0.2a 2S

T

V ' 2ql( 4a 2S

B2T)

EM 1110-2-142128 Feb 99

6-8

due to a change in the surface-water stage when selecteddiffusivities are assumed. The diffusivity of the aquiferis then obtained by choosing from the set of type curvesthe one which best matches the response observed inadjacent observation wells.

6-8. Estimating Baseflow Contribution fromStorm Events to Streamflow

a. Instantaneous recharge.

(1) For flood event scenarios where the precipita-tion event is of short duration, the assumption ofinstantaneous recharge can often be made. Rorabaugh(1964) derives an equation which describes base-flowrecession at a critical time after an instantaneousuniform increment of recharge ceases to calculategroundwater discharge to a stream:

(6-17 )

where

q = groundwater discharge [cfs] per foot of streamlength (one side) at any time

t = time ”days› after recharge ceases [L/T]

h = an instantaneous water table rise, in feet [L]0

T = aquifer transmissivity, in ft /day [L /T]2 2

S = storage coefficient [dimensionless], a commonestimate for this value in an alluvial aquifer is0.20

a = distance from stream to groundwater divide, in feet [L]

(2) This relationship assumes the initial conditionthat groundwater levels are equal to stream level, andwater table fluctuations are small compared to totalaquifer thickness.

(3) When Tt/a S> 0.2, the terms in the series of2

Equation 6-17 become very small and may be neglected(Rorabaugh 1964):

(6-18)

Conversely, when Tt/a S < 0.2, Equation 6-17 can be2

estimated as (Rorabaugh 1964):

(6-19)

(4) Equation 6-19 is for time sufficiently small sothat the aquifer response has not reached the ground-water divide, and therefore may be applied to semi-infinite conditions.

(5) The term ‘critical time’ is defined as the timerequired in a recession for the profile shape to stabilize,allowing for a straight plot on semi-log graph ofstreamflow versus time (water levels fall exponentiallywith time). From stream records, the logarithmic slopeof the baseflow recession can be derived after criticaltime. Critical time (t ) defines the point on a flowc

hydrograph where water moving into a stream followinga recharge event is derived solely from groundwater(i.e., overland flow in the watershed is no longer acomponent). Mathematically this term was defined byintegrating Equation 6-17 with respect to time:

(6-20)

(6) The total groundwater remaining in storage Vfrom the recharge event, which will eventually be trans-mitted to a stream at any time after t along an entirec

stream reach l, can be estimated by:

(6-21)

b. Constant rate of recharge. For the case of aconstant rate of recharge (or constant rate of change inriver stage), Rorabaugh (1964) derived the followingequation:

q ' CaS 1&8

B2(e &B2Tt/4a 2S %

19

e &9B2Tt/4a 2S

%1

25e &25B2Tt/4a 2S%...)

q ' CaS

q ' C(2/ B) TSt

q ' CaS(8/B2) e &B2Tt )/4a 2S & e &B2Tt/4a 2S

%19

e &9B2Tt )/4a 2S &19

e &9B2Tt/4a 2S % ...

TS

'0.933a 2log(h1/h2)

(t2&t1)

a 2ST

')t/log cycle

0.933

tc '0.2()t/log cycle)

0.933

EM 1110-2-142128 Feb 99

6-9

(6-22)

where

C = dh/dt, which is the rate of rise of the watertable associated with constant recharge

For values of Tt/2aS > 2.5, the exponential termsbecome insignificant, and flow approaches the steady-state condition:

(6-23)

For early time when Tt/a S < 0.2, effects will not have2

reached the boundary and the flow is the same as thatfor a semi-infinite case:

(6-24)

c. Constant rate of recharge over a specifiedtime. For the case of constant rate recharge beginningat time t=0, and stopping at time t', Rorabaugh (1964)derived the following equation:

(6-25)

Analytical methods presented in Section 6-8 assume thatprecipitation instantaneously recharges the water table.Thus, flow in the unsaturated zone is not addressed. Amore accurate estimation of baseflow contribution tostreamflow from a storm event can be derived byaccounting for soil moisture conditions in the unsatu-rated zone. However, this accounting requires a numer-ical complexity that can only be addressed by computermodels. These equations also allow for the estimation of

baseflow recession if average values of aquifer diffu-6-9. Estimating Aquifer Diffusivity fromStreamflow Records

a. Theory. When critical time is reached, therecession curve on a semilog graph becomes a straight

line. Rorabaugh (1960) developed an equation for esti-mating aquifer diffusivity (T/S) from the slope of thewater level recession in a stream or observation wellafter critical time:

(6-26)

where

a = distance from stream to groundwater divide[L]

T = aquifer transmissivity [L /T]2

S = storage coefficient [dimensionless]

h = initial water level [L], at time t [T]1 1

h = water level [L], at time t [T]2 2

This equation is applicable for the condition whererecharge is instantaneous and evenly distributed.Assumptions in addition to those stated in Section 6-6include that the aquifer is thick relative to the change inwater level and that the aquifer is wide relative to thethickness. If the base-flow recession curve is evaluatedafter critical time to determine the time required forstreamflow to decline through one log cycle ()t/logcycle), Equation 6-26 reduces to:

(6-27)

Combining Equations 6-20 and 6-27 yields a criticaltime of:

(6-28)

sivity and the distance from the stream to the ground-water divide can be estimated.

b. Methodology. To determine T/a S from a2

recession curve which is declining exponentially with

a 2ST

')t/log cycle

0.933;

(1,000 m)2(0.20)T

'32 days0.933

T ' 5,800 m2/day

EM 1110-2-142128 Feb 99

6-10

time, the following procedure can be followed (Bevans 0.20. The stream is located in a valley bounded by1986): bedrock approximately 1,000 m on each side of the

(1) The time that recharge occurred is assumed tobe at the point at which streamflow hydrographs reachtheir peak.

(2) The slope of the baseflow recession curve(days/log cycle) is determined from the recession curveafter it becomes a straight line, either by the observeddecrease through one log cycle, or by extrapolating thestraight line part of the baseflow recession curvethrough one log cycle.

(3) The slope of the base-flow recession curve isinserted into Equation 6-28 as )t/log cycle, and thecritical time t (days) is computed.c

(4) The computed critical time is checked againstthe streamflow hydrograph. The computed critical timeneeds to be equivalent to the period from the hydrographpeak to the point on the recession curve where the curvebecomes a straight line. If computed and observed criti-cal times are the same, then the slope of the baseflowrecession curve can be used in Equation 6-27 tocompute T/a S (1/days). If the computed and observed2

critical times differ significantly, then extraneous fac-tors probably are affecting the slope of the baseflowrecession curve and that particular streamflow record isnot appropriate for determining T/a S.2

(5) T/a S values should be determined from several2

baseflow recession curves, representing different rangesof baseflow rate, and compared to see if T/a S is con-2

stant. If the values are constant within a narrow range,then T/a S can be considered a stream-aquifer constant.2

Once aquifer diffusivity (T/S) is estimated, the value oftransmissivity can be estimated by approximating Sfrom tables; i.e., S . 0.20 for typical sand aquifers.

c. Example problem.

Given: Extrapolated slope of baseflow recessionequals 32 days/log cycle (Figure 6-5). The aquifer isunconfined and consists of shallow sands underlain bybedrock. Assume the aquifer storage coefficient equals

stream. Estimate aquifer transmissivity.

Solution:

6-10. Estimating Effects of Pumping Wells onStream Depletion

a. Assumptions. Jenkins (1968) created a seriesof dimensionless curves and tables which can be appliedto a stream-aquifer system under the followingassumptions:

(1) The aquifer is isotropic, homogeneous, andsemi-infinite.

(2) Transmissivity remains constant.

(3) The stream is of constant temperature, repre-sents a straight boundary, and fully penetrates theaquifer.

(4) Water is released instantaneously from storage.

(5) The pumping rate is steady during any rate ofpumping.

(6) The well is screened through the full saturatedthickness of the aquifer.

b. Applications. Computations can be made of:

(1) The rate of stream depletion at any time duringthe pumping period or the following non-pumpingperiod.

(2) The volume of water induced from the streamduring any period, pumping or non-pumping.

0 8005 2818.383

10 75015 1548.81720 200025 60030 20035 15040 10045 7050 5055 4060 2065 1570 1075 580 1085 3590 10095 400

100 800105 600110 500115 300

Streamflow Hydrograph

1

10

100

1000

10000

0 10 20 30 40 50 60 70 80 90 100 110 120 130

Time (days)

Str

eam

flo

w (

cub

ic m

eter

s p

er s

eco

nd

)

EM 1110-2-142128 Feb 99

6-11

Figure 6-5. Hypothetical streamflow hydrograph

(3) The effects, both in volume and rate of stream d. Methodology. A simple application of deter-depletion, of any pattern of intermittent pumping mining the effects of a well, located a given distance a(Jenkins 1968). from a stream, pumping at a constant rate Q for a given

time t on the volume of stream depletion v can bec. Stream depletion factor. Stream depletion

means either direct depletion of the stream or reductionof groundwater flow to the stream. In his report,Jenkins introduces a 'stream depletion factor' (sdf) term.If the system meets the above assumptions:

sdf = a S/T (6-29)w2

where

a = distance from the stream to the pumping wellw

In a complex system, sdf can be considered an effectivevalue of a S/T. This value is dependent upon the inte-w

2

grated effects of irregular impermeable boundaries,stream meanders, areal variation of aquifer properties,distance from the stream, and imperfect connectionsbetween the stream and aquifer.

derived from Figure 6-6. First compute the value of sdf,then estimate the ratio of v/Qt from Figure 6-6.Additionally, the effects of pumping on the rate ofstream depletion at a given time t after pumpingcommenced can be easily determined by using Fig-ure 6-6 to determine the ratio q/Q. Conversely, the timeafter pumping begins in which stream depletion willequal a predetermined percentage of the pumping ratecan be determined by first computing the ratio of t/sdf.Computations for estimating the effects on the riverafter pumping has stopped, intermittent pumping, andthe volume of water induced from the stream during anypumping or non-pumping period can be derived fromadditional charts and tables in the Jenkins (1968) report.

EM 1110-2-142128 Feb 99

6-12

Figure 6-6. Curves to determine rate and volume of stream depletion (Jenkins 1968)

Figure 6-7. Hypothetical stream and pumping well

e. Example problem.

(1) The potential influence of aquifer pumping onan effluent stream must be determined. The depth of thestream is 10 m, and depth of the aquifer is 30 m.Assume the stream fully penetrates the aquifer. Thehydraulic conductivity of the aquifer is 50 m/day, andspecific yield is 0.25. A recently constructed well islocated 500 m from the stream (Figure 6-7) and beginspumping at a rate of 1,000 m /day.3

(2) How much is the total volume of flow in thestream reduced by the pumping well after 2 weeks ofpumping?

EM 1110-2-142128 Feb 99

6-13

(a) Given: one-dimensional problems because of rigid boundaryconditions and simplifying assumptions. However, for

Unconfined aquiferK = 50 m/day b = 30 mQ = 1,000 m /day3

a = 500 m S = 0.25

(b) Find transmissivity:

T = Kb = (50 m/day)(30 m) = 1,500 m /day2

(c) Find stream depletion factor (sdf):

sdf = a S/T = (500 m) (0.25)/(1,500 m /day)2 2 2

= 41.7 days

(d) Estimate ratio of v/Qt from Figure 6-6:

t/sdf = 14 days/41.7 days = 0.33

This gives a v/Qt value of approximately 0.09

(e) Solve for v (total stream depletion)

v = (Q)(t)(0.09) = (1,000 m )(14 days)(0.09)3

v = 1,260 m3

(3) What is the rate of stream depletion after2 weeks of pumping?

(a) The rate of streamflow depletion can besolved by:

t/sdf = 0.3, q/Q = 0.22

(b) q = (0.22)(Q). The streamflow is depleted by arate of 1/5 the pumping rate (220 m /day) after 2 weeks3

of pumping.

(c) Therefore, the total flow in the stream will bedepleted by a total of 1,260 m during the first 2 weeks3

the well is pumping.

6-11. Numerical Modeling of Surface Waterand Groundwater Systems

a. General. Although mathematically exact, ana-lytical models generally can be applied only to simple

many studies, analysis of one-dimensional flow is notadequate. Complex systems do not lend themselves toanalytical solutions, particularly if the types of stressesacting on the system change with time. Numericalmodels allow for the approximation of more complex equations and can be applied to more complicatedproblems without many of the simplifying assumptionsrequired for analytical solutions. Computer simulationof the interrelationships between surface water andgroundwater systems requires the mathematical descrip-tion of transient effects on potentially complex watertable configurations. Ideally, a computer model of thesurface-water/groundwater regime should be ableto simulate three-dimensional variable-saturated flowincluding: fluctuations in the stage of the surface-waterbody, infiltration, flow in the unsaturated zone, and flowin the saturated zone. Additionally, simulation ofwatershed runoff, surface-water flow routing, andevapotranspiration will allow for completeness. How-ever, this is often a complex task, and no matter howpowerful the computer or sophisticated the model,simplifying assumptions are necessary.

b. Modeling stream-aquifer interaction.

(1) General. Numerical models provide the mostpowerful tools for analysis of the surface-water/groundwater regime. Commonly, interaction betweensurface water and groundwater is only addressed in themost rudimentary terms. The perspective of the modelis of primary importance. In surface-water models, theinteraction between surface water and groundwater isoften represented as a “black box” source/sink term.Conversely, in groundwater models, surface water isoften represented as an infinite source of water, regard-less of availability. However, a more precise simulationof the impacts of this interaction can be necessarydepending on the objectives of the modeling study.

(2) Theory. From the groundwater perspective, acommon simplifying assumption made to ease numericalsimulation is that simulation of unsaturated flow is notaddressed, and leakage from surface water to an aquiferis assumed to be instantaneous; i.e., no head loss occursin the unsaturated zone. This assumption is usuallyreasonable in the common situation where the thicknessof the unsaturated zone between the stream and aquifer

MMx

KxxMhMx

%MMy

KyyMhMy

%MMz

KzzMhMz

& W ' SsMhMt

Q ' CRIV(hriv&hgw)

EM 1110-2-142128 Feb 99

6-14

is not large. The interaction between surface water and Section 5-3. In this type of boundary condition, thethe underlying aquifer can be represented by the flow which is computed at the stream-aquifer interfacepartial differential equation of groundwater flow is computed as a function of the relative water levels for(Equation 2-20): each stress period. This functional relationship is both

(6-30)

where

W = flow rate per unit volume of water added to ortaken from the groundwater system

Most, but not all, interaction between groundwater andsurface water is lumped into the “W” term.

(3) Specified head and specified flux boundaries.The simplest approach in modeling stream-aquiferinteraction is to represent surface water as a specified(constant) head or a specified (constant) flux boundarywithin the groundwater model grid (Section 5-3). In thecase of a specified head boundary, the head at thesurface-water location is specified as the elevation ofwater surface. The flow rate to or from the boundary iscomputed from heads at adjacent grid points usingDarcy's law. This type of boundary does not require a'W' term in the partial differential equation of ground-water flow. For the case of the constant, or specifiedflux boundary, the flow rate is specified in the modelgrid as a “known” value of recharge or discharge, andthe model computes the corresponding head valuethrough the application of Darcy's law. This type ofboundary requires the "W" term in the partial differ-ential equation of groundwater flow.

A major disadvantage to specified head and flux streamboundary representations is that they do not allow for alower hydraulic conductivity across the seepage inter-face, or account for the elevation of the streambedbottom. Thus, leakance from the river continues toincrease as the water table drops below the streambed.

(4) Head-dependent flux boundary. A secondapproach is to represent the stream as a head-dependentflux boundary. A head-dependent flux boundary is acommon type of value-dependent boundary discussed in

included in the “W” term of the partial differentialequation of groundwater flow and is typically derivedfrom Darcy's law. Thus, the value of groundwater headoccurs in the “W” term, and in the space derivatives,which can add difficulty to the solution.

(a) Most groundwater flow models incorporate oneor more functions built in to handle this functionalrelationship. For stream-aquifer relationships, this canbe represented as:

(6-31)

where

Q = flow between the stream and the aquifer

CRIV = streambed conductance

h = river stageriv

h = groundwater elevationgw

The streambed conductance term represents the productof hydraulic conductivity K and cross-sectional area offlow LW divided by the length of the flow path M:

CRIV = KLW/M (6-32)

Formulation of a streambed conductance term isillustrated in Figure 6-8. If reliable field measurementsof stream seepage are available, they may be used tocalculate effective conductance. Otherwise, a conduc-tance value must be chosen more or less arbitrarily andadjusted during model calibration. Values for the cross-sectional area of flow can typically be utilized to guidethe initial choice of conductance. In general, however, itshould be recognized that formulation of a single con-ductance term to account for three-dimensional flowprocesses is inherently an empirical exercise, and thatadjustment during calibration is almost always required(McDonald and Harbaugh 1988).

(b) An important assumption common in head-dependent flux boundaries of stream-aquifer

EM 1110-2-142128 Feb 99

6-15

Figure 6-8. Determination of streambed conductance

relationships is that the head differential between the Package first computes river stage from Manningsstream and the aquifer is never greater than the sum of equation (assuming a rectangular channel), then uses thestream depth and streambed thickness. In other words, MODFLOW River Package head-dependent fluxthe value of leakage to groundwater does not increase as boundary condition (Equation 6-32) for computingthe groundwater elevation drops below the streambed, leakage to groundwater flow.and recharge is instantaneous to groundwater. Thevalue of stream bottom elevation is thus also entered Additionally, the U.S. Geological Survey groundwaterinto the computational process. flow model MODFLOW has also been coupled to the

(5) Relationship between cell size and stream model BRANCH (Schaffranek et al. 1981). Thewidth. In groundwater modeling, the smallest unit of BRANCH surface flow model simulates flows inhomogeneity is represented by the grid cell. Thus, flow networks of open channels by solving the one-between a stream and aquifer is distributed equally over dimensional equations of continuity and momentum forthe area of the cell face. For example, if a stream has a river flow. These equations are appropriate forwidth of 50 ft, and the model cell has a width of 300 ft, unsteady (changing in time) and nonuniform (changingthe same total flow between the stream and the aquifer in location) conditions in the channel. It was developedwill be distributed over 36 times the area. Therefore, in independent of MODFLOW to simulate flow in riverssituations where the interaction between a stream and an without consideration of interaction with the aquifer.aquifer is of interest, it is important to discretize cell BRANCH was modified to function as a module forsize to approximate river geometry. MODFLOW (Swain and Wexler 1993). Leakance

between stream and aquifer is computed through use of(6) Streamflow routing. As discussed previously,

the interaction between surface water and groundwateris usually treated as a constant head, constant flow, oras a head-dependent flow boundary. The quantity ofsurface water in a river, stream, lake, etc., is notaccounted for in most groundwater flow simulations. (1) General. Groundwater flow models used toThis approach is reasonable for lakes and large rivers quantify flow between reservoirs (and lakes) andwhere changes in groundwater flow do not appreciably groundwater typically use a specified head to representaffect the quantity of water in the lakes or rivers. But the average elevation of the reservoir. However, reser-this approach may not be reasonable for conditions voir levels often show long- and short-term transience inwhere the amount of surface water is sensitive to stage and area of inundation. Thus, a model using

changes in groundwater flow. Streamflow routing pro-grams can be used in situations so as not to allow moreleakage from streams than there is streamflow.Streamflow routing programs can also allow for thecomputation of stream stage by inputting an inflow termon the upper reach.

Prudic (1989) developed a simple stream routingcomputer program, called the “Stream Package,” for theU.S. Geological Survey three-dimensional finite-difference flow model MODFLOW. Basic assumptionsof the Stream Package are that streamflow entering themodeled area is instantly available to downstreamreaches during each time period, leakage between astream and aquifer is instantaneous, and all stream lossrecharges the groundwater system (ET, precipitation,and overland runoff is not accounted for). The Stream

U.S. Geological Survey unsteady, open-channel flow

a head-dependent flow boundary, Equation 6-31.

c. Modeling interaction between reservoirs (andlakes) and groundwater.

CRB 'KLW

M

Qres ' CRB(hres&hgw)

EM 1110-2-142128 Feb 99

6-16

specified heads may not provide reliable estimates of (3) Computation of flow between reservoir andgroundwater fluxes and reservoir fluctuations over time. groundwater. Leakage between the reservoir and theAs stage increases in reservoirs, a spreading out of the underlying aquifer is simulated for each model cellimpoundment occurs. Thus, increases in leakage to or corresponding to the inundated area by multiplying thefrom a reservoir are dependent on stage and area of head difference between the reservoir and the aquifer byinundation. An algorithm entitled the “Reservoir Pack- the hydraulic conductance. Hydraulic conductanceage” (Fenske, Leake, and Prudic 1996) was developed between the reservoir and the aquifer is given by:for the U.S. Geological Survey three-dimensional finite-difference groundwater flow model MODFLOW toautomate the process of specifying head-dependentboundary cells during the simulation. The packageeliminates the need to divide the simulation into manystress periods while improving accuracy in simulatingchanges in groundwater levels resulting from transientreservoir levels. The package is designed for caseswhere reservoirs are much greater in area than the arearepresented by individual model cells.

(2) Description. More than one reservoir can besimulated using the Reservoir Package. Figure 6-9illustrates the specification of the area of potentialinundation for two reservoirs. Only those cells specifiedin the array represented by Figure 6-9 can be activatedduring model simulations. In cases where areas ofhigher land-surface elevation separate areas of lowerelevations in a reservoir, part of the reservoir may fillbefore spilling over to an adjacent area. The packagecan simulate this process by specifying two or morereservoirs in the area of a single reservoir. The area ofpotential inundation is represented by values ofreservoir-bed elevation, layer number, reservoir-bedconductance, and reservoir-bed thickness. Reservoir-bed elevation is the elevation of the land surface withinthe specified area of potential inundation for eachreservoir. Typically, the reservoir-bed elevation at eachmodel cell is equivalent to the average land-surfaceelevation of the cell.

Reservoir stage is used to determine whether a modelcell is activated for each time-step. Whenever stageexceeds land-surface elevation of a cell within the areaof potential inundation of a reservoir, the cell is acti-vated. Similarly, whenever reservoir stage is less thanthe land-surface elevation of a cell, the cell is notactivated.

(6-33)

where

CRB = reservoir-bed conductance [L /T]2

K = vertical hydraulic conductivity of thereservoir bed [L/T]

L = cell length [L]

W = cell width [L]

M = reservoir-bed thickness ”L]

Values of reservoir-bed conductance and reservoir-bedthickness can be entered into the Reservoir Package as asingle parameter or an array.

Reservoir-bed thickness is subtracted from reservoir-bed(or land-surface) elevation to obtain the elevation of thereservoir-bed bottom. The reservoir-bed bottom eleva-tion is used in computing leakage. When the head in theaquifer is above the reservoir-bed bottom, leakage fromor to the aquifer is computed by:

(6-34)

where

Q = leakage from the reservoir [L /T]res3

h = head in the reservoir [L] res

h = aquifer head [L] gw

TributaryStreams

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 00 00 0

0 00 00 00 00 00 00 00 00 0

0 00 00 0

0 00 00 0

0 00 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

1 11 1 1 1 11 1 1111

1 1 1 1 1 1 1

111

1 1 1 1 111

111111111

11

11 1

1 11 1 11 1 1 1 1

0 0 0 0 00

00000

00

00

000000 0

0

0000000 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

222222

22

222222

222 2 2 2

2222 2 2

0000

00

00

000000

00

Maximumareal extentof reservoir 2

Maximumareal extent

of reservoir 1

Qres ' CRB(hres&hresbot)

EM 1110-2-142128 Feb 99

6-17

Figure 6-9. Definition of maximum areal extent of reservoir(s)

When the head in the aquifer is less than the elevation of subsurface is instantaneous, and it is assumed that therethe reservoir-bed bottom, leakage from the reservoir to is no significant head loss between the bottom of thethe groundwater is computed by: reservoir bed and the water table. Water exchange

takes place across the horizontal faces of model cells.(6-35)

where

h = elevation of the reservoir-bed bottom [L]resbot

(4) Reservoir package applicability and limitations.Water exchange between surface and

Thus, bank flow is not directly simulated. The effectsof bank flow can be approximated by dividing thereservoir into multiple layers. Changes in reservoirstage are transmitted instantly across the reservoir.Implied in this assumption is that the reservoir has noslope and there is no flow across the reservoir. Thisassumption may not be valid for large reservoirs.Additionally, head-dependent flow boundaries are

EM 1110-2-142128 Feb 99

6-18

specified for all cells having a land-surface elevation adjacent lower-lying areas. The package can simulateless than the reservoir stage, even if areas of higher this process by having two or more reservoirs specified.land-surface elevations separate areas of lower Neither precipitation on nor evapotranspiration from theelevations. This assumption may be unreasonable for reservoir is directly simulated; however, both can bereservoirs in which the land surface is uneven and where included by adding or subtracting an equivalent volumeparts of the reservoir fill before spilling into of water per unit area from the flood stage.

EM 1110-2-142128 Feb 99

A-1

Appendix AReferences

A-1. Required Publications

ER 1110-1-263Chemical Data Quality Management for HazardousWaste Remedial Activities

ER 1110-2-1150Engineering and Design for Civil Works Projects

ER 1165-2-132Hazardous, Toxic, and Radioactive Waste (HTRW)Guidance for Civil Works Projects

EM 200-1-3Requirements for the Preparation of Sampling andAnalysis Plans

EM 1110-1-1802Geophysical Exploration for Engineering and Environ-mental Investigations

EM 1110-1-1804Geotechnical Investigations

EM 1110-1-4000Monitor Well Design and Installation and Documen-tation at Hazardous and/or Toxic Waste Sites

EM 1110-2-1901Seepage Analysis and Control for Dams

EM 1110-2-1914Design Construction and Maintenance of Relief Wells

ETL 1110-1-171Tri-Service Site Characterization and AnalysisPenetrometer

A-2. Related Publications

Aller, Bennett, Hackett, Petty, Lehr, Sedoris,Nielsen, and Denne 1989Aller, L., Bennett, T. W., Hackett, G., Petty, R. J.,Lehr, J. H., Sedoris, H., Nielsen, D. M., and Denne,J. E. 1989. “Handbook of Suggested Practices for theDesign and Installation of Ground-Water MonitoringWells,” EPA 600/4-89/034, Environmental ProtectionAgency and National Water Well Association, Dublin,VA.

American Society for Testing and Materials 1992American Society for Testing and Materials. 1992.“Annual Book of Standards, Vol. 04.08, Soil andRock,” ASTM Pub., Philadelphia, PA.

American Society for Testing and Materials 1993American Society for Testing and Materials. 1993. “Design and Installation of Ground Water MonitoringWells in Aquifers,” ASTM D-5092.

Anan 1992Anan, A. P. 1992. “Ground Penetrating Radar Work-shop Notes,” Sensors and Software Inc., Mississauga,Ontario.

Anderson and Woessner 1992Anderson, M. P., and Woessner, W. W. 1992. “Applied Groundwater Modeling-Simulation of Flowand Advective Transport,” Academic Press, Inc.,San Diego, CA.

Appel and Reilly 1988Appel, C. A., and Reilly, T. E. 1988. “SelectedReports that Include Computer Programs Produced bythe U.S. Geological Survey for Simulation of Ground-Water Flow and Quality,” U.S. Geological SurveyWater Resources Investigation Report, 87-4271,U.S. Department of Interior, Reston, VA.

EM 1110-2-142128 Feb 99

A-2

Bear 1972 Carmichael and Henry 1977Bear, J. 1972. “Dynamics of Fluids in a Porous Carmichael, R. S., and Henry, G. 1977. “GravityMedia,” American Elsevier Publishing Co., New York, Exploration for Groundwater and Bedrock TopographyNY. in Glaciated Areas,” Geophysics 42, pp 850-859.

Bear and Verruijt 1987 Cooley, Harsh, and Lewis 1972Bear, J., and Verruijt, A. 1987. “Modeling Ground- Cooley, R. L., Harsh, J. F., and Lewis, D. C. 1972.water Flow and Pollution,” D. Reidel Publishing Co., “Principles of Ground-Water Hydrology,” U.S. ArmyBoston, MA. Corps of Engineers Hydrologic Engineering Center -

Hydrologic Engineering Methods for Water ResourcesBennet 1976Bennet, G. D. 1976, “Introduction to Ground-WaterHydraulics,” Techniques of Water-Resources Investiga-tions of the United States Geological Survey, Book 3,Chapter B2.

Bevans 1986Bevans, H. E. 1986. “Estimating Stream-AquiferInteractions in Coal Areas of Eastern Kansas UsingStreamflow Records,” U.S. Geological Survey WaterSupply Paper 2290, p. 51-64.

Bouwer 1989Bouwer, H. 1989. “The Bouwer and Rice Slug Test -An Update,” Ground Water 27(3), pp 304-309.

Bouwer and Rice 1976Bouwer, H., and Rice, R. C. 1976. “A Slug Testfor Determining Hydraulic Conductivity of UnconfinedAquifers with Completely or Partially PenetratingWells,” Water Resources Research 12(3), pp 423-428.

Bredehoeft and Konikow 1993Bredehoeft, J. D., and Konikow, L. F. 1993. “Ground-water Models: Validate or Invalidate,” Ground Water31(2), 2 p.

Bureau of Reclamation 1977Bureau of Reclamation. 1977. “Ground WaterManual,” U.S. Government Printing Office, Washing-ton, DC.

Butler 1980Butler, D. K. 1980. “Microgravimetric Techniques forGeotechnical Applications,” Miscellaneous PaperGL-80-13, U.S. Army Engineer Waterways ExperimentStation, Vicksburg, MS.

Development 10.

Cooper and Jacob 1946Cooper, H. H., and Jacob, C. E. 1946. “A GeneralizedGraphical Method for Evaluating Formation Constantsand Summarizing Well-Field History,” Transactions,American Geophysical Union, Vol 27.

Cooper and Rorabaugh 1963Cooper, H. H., Jr. and Rorabaugh, M. I. 1963.“Ground-Water and Bank Storage Due to Flood Stagesin Surface Streams,” U.S. Geological Survey Water-Supply Paper, 1536-J, pp 343-366.

Cooper, Bredehoeft, and Papadopulos 1967Cooper, H. H, Bredehoeft, J. D., and Papadopulos, I. S.1967. “Response to a Finite Diameter Well to anInstantaneous Charge of Water,” Water ResourcesResearch 3, pp 263-269.

Daniel 1976Daniel, J. F. 1976. “Estimating Groundwater Evapo-transpiration from Streamflow Records,” WaterResources Research 12(3), pp 360-374.

Darcy 1856Darcy, H. 1856. “Les fontaines publiques de la ville deDijon,” Victor Dalmont, Paris.

Davis and DeWiest 1966Davis, S. N., and DeWiest, R. J. M. 1966. “Hydroge-ology,” John Wiley and Sons, New York.

Davis and Murphy 1987Davis, S. N., and Murphy, E. 1987. “Dating Ground-water and the Evaluation of Repositories for Radio-active Waste,” U.S. Nuclear Regulatory Commission,NUREG/CR-4912.

EM 1110-2-142128 Feb 99

A-3

Dawson and Istok 1991 Fiats 1993Dawson, K. J., and Istok, J.D. 1991. “Aquifer Testing: Fiats, C. 1993. “Well Discharge Optimization UsingDesign and Analysis of Aquifer Tests,” Lewis Analytical Elements,” Proceedings of the 1993 GroundPublishers, Inc., Chelsea, MI. Water Modeling Conference, International Ground

Domenico and Schwartz 1990Domenico, P. A., and Schwartz, F.W. 1990. “Physicaland Chemical Hydrogeology,” John Wiley and Sons, France, O. D., Reilly, T. E., and Bennett, G. D. 1987.New York. “Definition of Boundary and Initial Conditions in the

Driscoll 1986Driscoll, F. G. 1986. “Groundwater and Wells,” gations of the United States Geological Survey,2nd ed., Johnson Screens, Wheelabrator Water U.S. Government Printing Office, Washington, DC.Technologies Inc., St. Paul, MN.

El-Kadi 1989El-Kadi, Aly I. 1989. “Watershed Models and Their Prentice-Hall Inc., Englewood Cliffs, NJ.Applicability to Conjunctive Use Management,” WaterResources Bulletin 25(1), pp 125-137.

Fair and Hatch 1933Fair, G. M., and Hatch, L. P. 1933. “Fundamental 26(1).Factors Governing the Streamline Flow of Waterthrough Sand,” Journal of American Water ResourcesAssoc. 25, pp 1551-1565. Fritz, P., and Fontes, J. C., eds. 1980. “Handbook of

Fenske, Leake, and Prudic 1996Fenske, J. P., Leake, S. A., and Prudic, D. E. 1996.“Documentation of a Computer Program to SimulateLeakage from Reservoirs using the Modular Finite- Goerlick, S., Freeze, A., Donohue, D., and Keely, J.Difference Ground-Water Flow Model,” U.S. Geo- 1993. “Groundwater Contamination, Optimal Capturelogical Survey Open-File Report, 96-364. and Containment,” Lewis Publishers, FL.

Ferris 1951 Grubb 1993Ferris, J. G. 1951. “Cyclic Fluctuations of Water Grubb, S. 1993. “Analytical Model for Estimation ofLevels as a Basis for Determining Aquifer Transmissi- Steady-State Capture Zones of Pumping Wells inbility,” Int. Assoc. Sci. Hydrol., Pub. 33, pp 148-155. Confined and Unconfined Aquifers,” Ground Water

Fetter 1993Fetter, C. W. 1993. “Contaminant Hydrology,”Department of Geology, University of Wisconsin- Haeni, F. P. 1988. “Application of Seismic-RefractionOshkosh, Macmillan Publishing Company. Techniques to Hydrologic Studies,” Techniques of

Fetter 1994Fetter, C. W. 1994. “Applied Hydrogeology,” Office, Washington, DC.Charles E. Merrily Pub., Columbus, OH.

Water Modeling Center, Golden, CO.

France, Reilly, and Bennett 1987

Analysis of Saturated Ground-Water Flow Systems-AnIntroduction,” Techniques of Water-Resources Investi-

Freeze and Cherry 1979Freeze, R. A., and Cherry, J. A. 1979. “Groundwater,”

Freyberg 1988Freyberg, D. L. 1988. “An Exercise in Ground-WaterModel Calibration and Prediction,” Ground Water

Fritz and Fontes 1980

Environmental Isotope Geochemistry, Vol. 1,” Elsevier,Amsterdam.

Goerlick et al. 1993

31(1), pp 27-32.

Haeni 1988

Water-Resources Investigations of the United StatesGeological Survey, 02-D2, U.S. Government Printing

EM 1110-2-142128 Feb 99

A-4

Hall and Moench 1972 Jenkins 1968Hall, F. R., and Moench, A. G. 1972. “Application of Jenkins, C. T. 1968. “Computation of Rate andthe Convolution Equation to Stream Aquifer Relation- Volume of Stream Depletion by Wells,” U.S. Geologi-ships,” Water Resources Research 8(2), pp 487-493. cal Survey Techniques of Water-Resources Investiga-

Hantush 1964Hantush, M. S. 1964. “Hydraulics of wells,” Advancesin Hydrosciences, Vol. I, V. T. Chow, ed., Academic Jenkins, C. T. 1970. “Computation of Rate and Vol-Press, New York. ume of Stream Depletion by Wells,” U.S. Geological

Heath 1984Heath, R. C. 1984. “Ground-Water Regions of the DC.United States,” United States Geological SurveyWater-Supply Paper, 2242, U.S. Government PrintingOffice, Washington, DC. Johnson, A. I. 1967. “Specific Yield-Compilation of

Helm 1975Helm, D. C. 1975. “One-Dimensional Simulation ofAquifer System Compaction Near Pixley, CA;Volume 1, Constant Parameters,” Water Resources Keys, W. S., and MacCary, L. M. 1971. “ApplicationResearch 11(3), pp 465-478. of Borehole Geophysics to Water-Resources Investiga-

Hem 1992Hem, J. D. 1992. “Study and Interpretation of the Printing Office, Washington, DC.Chemical Characteristics of Natural Water,” UnitedStates Geological Survey Water-Supply Paper, 2254,United States Government Printing Office, Washington, Krumbein, W. 1943. “Manual of Sedimentary Petro-DC. graphy,” Appleton-Century, New York.

Hendry 1988 Kruseman and De Ridder 1983Hendry, M. J. 1988. “Do Isotopes have a Place in Kruseman, G. P., and De Ridder, N. A. 1983.Groundwater Studies?” Ground Water 26(4), pp 410- “Analysis and Evalution of Pumping Test Data,”415. NILRI, the Netherlands.

Huling and Weaver 1991 Lin et al. 1996Huling, S. G., and Weaver, J. W. 1991. “Dense Non- Lin, H. J., Richards, D. R., Yeh, G., Cheng, J.,aqueous Phase Liquids,” EPA/540/4-91/002, Robert S. Cheng, H., and Jones, N. 1996. “Femwater: A Three-Kerr Environmental Research Laboratory, Ada, OK. Dimensional Computer Model for Simulating Density

Hvorslev 1951Hvorslev, M. J. 1951. “Time Lag and Soil Permeabil- Vicksburg, MS.ity in Ground Water Observations,” Bulletin 36,U.S. Army Corps of Engineers Waterways ExperimentStation, Vicksburg, MS. Lohman, S. W., et al. 1972. “Definitions of Selected

Ground-Water Terms-Revisions and Conceptual Refine-Jacob 1940Jacob, C. E. 1940. “On the Flow of Water in anElastic Artesian Aquifer,” Am. Geophys. Union, Trans.21st Ann. Mtg., Part 2, pp 574-586.

tions, D1-4.

Jenkins 1970

Survey Techniques of Water-Resources Investigations,04-D1, U.S. Government Printing Office, Washington,

Johnson 1967

Specific Yields for Various Materials,” U.S. GeologicalSurvey Water-Supply Paper, 1662-D.

Keys and MacCary 1971

tions,” U.S. Geological Survey Techniques of Water-Resources Investigations, 02-E1, U.S. Government

Krumbein 1943

Dependent Flow and Transport,” unpublished report,U.S. Army Engineer Waterways Experiment Station,

Lohman et al. 1972

ments,” U.S. Geological Survey Water-Supply Paper1988, U.S. Government Printing Office, Washington,DC, 21 p.

EM 1110-2-142128 Feb 99

A-5

McDonald and Harbaugh 1988 Ozbilgen and Dickerman 1984McDonald, M. G., and Harbaugh, A. W. 1988. “A Ozbilgen, M. M., and Dickerman, D. C. 1984. “AModular Three-Dimensional Finite Difference Ground- Modification of the Finite-Difference Model for Simu-Water Flow Model,” U.S. Geological Survey Open-File lation of Two-Dimensional Ground-Water Flow toReport 83-875. Include Surface-Ground Water Relationships,”

Mercer and Faust 1981Mercer, J. W., and Faust, C. R. 1981. “Ground-WaterModeling,” National Water Well Association, Colum-bus, OH. Pacific Northwest Laboratory 1993. “Hanford Site

Molz et al. 1986Molz, F. J., Oktay, G., Melville, J. G., and Keeley, J. F. Prepared for the U.S. Department of Energy, Richland1986. “Performance and Analysis of Aquifer Tracer Office, by Pacific Northwest Laboratory, Richland,Tests with Implications for Contaminant Transport WA.Modeling,” EPA/600/2-86/062, U.S. EnvironmentalProtection Agency, Robert S. Kerr EnvironmentalResearch Laboratory, Ada, OK. Papadopulos, I. S., Bredehoeft, J. D., and Cooper,

Molz et al. 1990Molz, F. J., Oktay, G., Melville, J. G., Javandel, I.,Hess, A. E., and Paillet, F. L. 1990. “A NewApproach and Methodologies for Characterizing the Phillip, J. R. 1969. “Theory of Infiltration,” AdvancesHydrogeologic Properties of Aquifers,” EPA/600/ in Hydroscience, Vol. 5, V. T. Chow, ed., Academic2-90/002, U.S. Environmental Protection Agency, Press, New York, pp 215-296.Robert S. Kerr Environmental Research Laboratory,Ada, OK.

National Research Council 1992National Research Council 1992. “A Review of gation of Groundwater in the Central San Juan Basin,Ground Water Modeling Needs for the U.S. Army,” New Mexico: Carbon 14 Dating as a Basis of Numeri-Water Science and Technology Board, National cal Flow Modeling,” Water Resources ResearchResearch Council, Washington, DC. 25(10), pp 2259-2273.

Neuman 1974 Pinder, Bredehoeft, and Cooper 1969Neuman, S. P. 1974. “Effect of Partial Penetration on Pinder, G. F., Bredehoeft, J. D., and Cooper, H. H.Flow in Unconfined Aquifers Considering Delayed 1969. “Determination of Aquifer Diffusivity fromGravity Response,” Water Resources Research 10(2), Aquifer Response to Fluctuations in River Stage,”pp 303-312. Water Resources Research 5(4), pp 850-855.

Neuman 1975 Prudic 1989Neuman, S. P. 1975. “Analysis of Pumping Test Data Prudic, D. E. 1989. “Documentation of a Computerfrom Anisotropic Unconfined Aquifers Considering Program to Simulate Stream-Aquifer Relations UsingDelayed Gravity Response,” Water Resources a Modular, Finite-Difference, Ground-Water FlowResearch, 11(2), pp 329-342. Model,” U.S. Geological Survey Open-File Report,

U.S. Geological Survey Water Resources InvestigationsReport 83-4251.

Pacific Northwest Laboratory 1993

Ground-Water Model: Geographic Information SystemLinkages and Model Enhancements, FY 1993,”

Papadopulos, Bredehoeft, and Cooper 1973

H. H. 1973. “On the Analysis of Slug Test Data,”Water Resources Research 9, pp 1087-1089.

Phillip 1969

Phillips et al. 1989Phillips, F. M., Grisak, G. E., Avis, J. D., Belanger,D. W., and Thury, M. 1989. “An Isotopic Investi-

88-729.

EM 1110-2-142128 Feb 99

A-6

Reynolds 1987 Simons and Rorabaugh 1971Reynolds, R. J. 1987. “Diffusivity of a Glacial- Simons, W. D., and Rorabaugh, M. I. 1971. “Hydrol-Outwash Aquifer by the Floodwave-Response Tech- ogy of the Hungry Horse Reservoir, Northwesternnique,” Ground Water 25(3), pp 290-299. Montana,” U.S. Geological Survey Professional Paper

Robertson and Cherry 1989Robertson, W. D., and Cherry, J. A. 1989. “Tritium asan Indicator of Recharge and Dispersion in a Ground- Sjögrenm, B. 1984. “Shallow Refraction Seismics,”water System in Central Ontario,” Water Resources Chapman and Hall, New York.Research 25(6), pp 1097-1109.

Robinson 1939Robinson, T. W. 1939. “Earth-Tides Shown by of Storm and Snowmelt Runoff Generation,” SurfaceFluctuations of Water Levels in Wells in New Mexico and Subsurface Processes, M.G. Anderson and T.P.and Iowa,” Trans. Amer. Geophysical Union, Vol 20, Burt, eds., Wiley, Sussex, England. pp 912-917.

Rocky Mountain Arsenal 1993Rocky Mountain Arsenal 1993. “Draft Final, South Flow,” Handbook of Hydrology, Chapter 6, McGrawPlants/Basin A Groundwater Flow Model,” Version 2.0, Hill, Inc., New York.Prepared for U.S. Army Program Manager's Office forthe Rocky Mountain Arsenal, Denver, CO.

Rorabaugh 1960Rorabaugh, M. I. 1960. “Use of Water Levels in Esti- Survey Open-File Report 92-63.mating Aquifer Constants,” Internat. Assoc. Sci.Hydrology, Pub. no. 52, pp 314-323.

Rorabaugh 1964Rorabaugh, M. I. 1964. “Estimating Changes in Bank Simulation of Stream-Aquifer Interaction,” U.S. Geo-Storage and Ground-Water Contribution to Stream- logical Survey Open-File Report, 92-138.flow,” Internat. Assoc. Sci. Hydrology, Pub. No. 63,pp 432-441.

Rutledge and Daniel 1994Rutledge, A. T., and Daniel, C. C. 1994. “Testing an nation of Water in the Upper Floridian Aquifer, West-Automated Method to Estimate Ground-Water Central Florida, 1986-1989,” U.S. Geological SurveyRecharge from Streamflow Records,” Ground Water Water-Supply Paper, 2409.32(2), pp 180-190.

Schaffranek 1987Schaffranek, R. W. 1987. “Flow Model for Open- ation of Selected Borehole Geophysical Methods forChannel Reach or Network,” U.S. Geological Survey Hazardous Waste Site Investigations and Monitoring,”Professional Paper, 1384. EPA/600/4-90/029, U.S. Environmental Protection

682.

Sjögrenm 1984

Sklash 1990Sklash, M. G. 1990. “Environmental Isotope Studies

Smith and Wheatcraft 1992Smith, L., and Wheatcraft, S. W. 1992. “Groundwater

Solley and Pierce 1992Solley, W. B., and Pierce, R. R. 1992. “Estimates ofWater Use in the United States, 1990,” U.S. Geological

Swain and Wexler 1993Swain, E. D., and Wexler, E. J. 1993. “A CoupledSurface-water and Ground-Water Flow Model for

Swancar and Hutchinson 1995Swancar, A., and Hutchinson, C. B. 1995. “Chemicaland Isotopic Composition and Potential for Contami-

Taylor, Hess, and Wheatcraft 1990Taylor, K., Hess, J., and Wheatcraft, S. 1990. “Evalu-

Agency, Las Vegas, NV.

EM 1110-2-142128 Feb 99

A-7

Telford et al. 1990 U.S. Army Engineer Hydrologic Engineering CenterTelford, W. M., Geldart, L. P., Sheriff, R. E., andKeys, D. A. 1990. “Applied Geophysics,” Cambridge U.S. Army Engineer Hydrologic Engineering Center.University Press. 1992. “A Review of Surface-Groundwater Interaction

Theis 1935Theis, C. V. 1935. “The Relationship Between theLowering of the Piezometric Surface and the Rate andDuration of Discharge of a Well Using Ground-Water U.S. Department of Energy. 1991. “Description ofStorage,” Transactions of the American Geophysical Codes and Models to be Used in Risk Assessment,”Union Sixteenth Annual Meeting, Part I, pp 519-524. DOE/RL-91-44, prepared for the U.S. Department of

Todd 1964Todd, D. K. 1964. “Ground Water Hydrology,” JohnWiley and Sons, Inc., New York. U.S. Department of Energy. 1992. “Draft Remedial

Todd 1980Todd, D. K. 1980. “Ground Water Hydrology,” the U.S. Department of Energy, Richland Office,2nd ed., John Wiley and Sons, Inc., New York. Richland, WA.

U.S. Army Corps of Engineers 1993 U.S. Department of Interior 1977U.S. Army Corps of Engineers. 1993. “Army Ground- U.S. Department of Interior. 1977. “Ground Waterwater Modeling Use and Needs Workshop,” Technical Manual - A Water Resources Technical Publication,”Report IRRP-93-1, prepared by the U.S. Army Engi- U.S. Government Printing Office, Washington, DC.neer Waterways Experiment Station for Headquarters,U.S. Army Corps of Engineers, Washington, DC.

U.S. Army Corps of Engineers 1994U.S. Army Corps of Engineers. 1994. “Hydrologic surface,” EPA/625/4-89/019, Environmental ProtectionFlow Model for Tooele Army Depot, Utah,” U.S. Army Agency, Robert S. Kerr, Environmental Laboratory,Corps of Engineers Hydrologic Engineering Center, Ada, OK.Davis, CA.

U.S. Army Engineer Hydrologic Engineering Center1981U.S. Army Engineer Hydrologic Engineering Center. ance Document,” OSWER-9950.1, EPA, Washington,1981. “HEC-1, Flood Hydrograph Package, Users DC.Manual,” U.S. Army Engineer Hydrologic EngineeringCenter, Davis, CA.

U.S. Army Engineer Hydrologic Engineering Center1991U.S. Army Engineer Hydrologic Engineering Center. Heijde, Aly I. El-Kadi, and Stan A. Williams, for the1991. “Importance of Surface-Ground Water Interac- Robert S. Kerr Environmental Research Laboratory,tion to Corps Total Water Management: Regional and Office of Research and Development, Ada, OK. National Examples,” Research Document 32,U.S. Army Engineer Hydrologic Engineering Center,Davis, CA.

1992

Models,” U.S. Army Engineer Hydrologic EngineeringCenter, Davis, CA.

U.S. Department of Energy 1991

Energy, Richland Office, Richland, WA.

U.S. Department of Energy 1992

Investigation/Feasibility Study for the 1100-EM-1Operable Unit,” Hanford, DOE/RL-92-67, prepared for

U.S. Environmental Protection Agency 1989U.S. Environmental Protection Agency. 1989.“Transport and Fate of Contaminants in the Sub-

U.S. Environmental Protection Agency 1986U.S. Environmental Protection Agency. 1986. “RCRAGround-water Monitoring Technical Enforcement Guid-

U.S. Environmental Protection Agency 1988U.S. Environmental Protection Agency. 1988.“Groundwater Modeling: An Overview and StatusReport,” EPA/600/2-89/028, by Paul K. M. van der

EM 1110-2-142128 Feb 99

A-8

U.S. Environmental Protection Agency 1992 Walton 1987U.S. Environmental Protection Agency. 1992. “Qual- Walton, W. C. 1987. “Groundwater Pumping Tests:ity Assurance and Quality Control in the Development Design and Analysis,” Lewis Pub., Chelsea, MI.and Application of Ground-Water Models,” EPA/600/R-93/011, prepared for the Robert S. Kerr Environ-mental Research Laboratory, U.S. Environmental Pro- Walton, W. C. 1970. “Groundwater Resource Evalu-tection Agency, Ada, OK. ation,” McGraw Hill Pub., New York.

U.S. Environmental Protection Agency 1993 Wang and Anderson 1982U.S. Environmental Protection Agency. 1993. Wang, H. F., and Anderson, M. P. 1982. “Introduction“Compilation of Ground-Water Models,” EPA/600/R- to Groundwater Modeling-Finite Difference and Finite93/118, prepared for the Robert S. Kerr Environmental Element Methods,” W. H. Freeman and Co., San Fran-Research Laboratory, U.S. Environmental Protection cisco, CA.Agency, Ada, OK.

U. S. Geological Survey 1977U. S. Geological Survey. 1977. “National Handbook Impact Assessment Report for the 1325-N Liquidof Recommended Methods for Water-Data Acquisi- Waste Disposal Facility,” prepared for thetion,” U.S. Department of Interior, Reston ,VA. U.S. Department of Energy, Richland Office, by

U.S. Geological Survey 1987U.S. Geological Survey. 1987. “The Effects of Boun-dary Conditions on the Steady-State Response of Three Winter, T. C. 1976. “Numerical Simulation of Analy-Hypothetical Ground-Water Systems - Results and sis of the Interaction of Lakes and Ground Water,”Implications of Numerical Experiments,” U.S. Geo- U.S. Geological Survey Professional Paper 1001.logical Survey Water Supply Paper 2315, USGSFederal Center, Denver, CO.

van der Heijde, El-Kadi, and Williams 1988van der Heijde, P. K., El-Kadi, A. I., and Williams, Acid Precipitation Impacts, J. Schnoor, ed., pp 89-119,S. A. 1988. “Groundwater Modeling: An Overview Butterworth Publishers, Boston, MA.and Status Report,” EPA/600/2-89/028, EnvironmentalProtection Agency, Robert S. Kerr EnvironmentalLaboratory, Ada, OK. Zohdy, A. A. R., Eaton, G. P., and Mabey, D. R.

van Overmeeren 1981van Overmeeren, R. A. 1981. “A Combination of Techniques of Water-Resources Investigations, U.S.Electrical Resistivity, Seismic Refraction, and Gravity Government Printing Office, Washington, DC.Measurements for Groundwater Exploration in Sudan,”Geophysics 46, pp 1304-1313.

Venetis 1970Venetis, C. 1970. “Finite Aquifers: CharacteristicResponses and Applications,” Journal of Hydrology 12,pp 53-62.

Walton 1970

Westinghouse Hanford Company 1993Westinghouse Hanford Company 1993. “Groundwater

Westinghouse Hanford Company, Richland, WA.

Winter 1976

Winter 1984Winter, T. C. 1984. “Modeling Interrelationships ofGroundwater and Surface Water,” Modeling of Total

Zohdy, Eaton, and Mabey 1974

1974. “Application of Surface Geophysics to Ground-Water Investigation,” U.S. Geological Survey

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Appendix BGlossary

ADVECTION. The process by which solutes aretransported by the motion of flowing groundwater.

ALLUVIUM. Sediments deposited by flowing water.Deposits can be made by streams on river beds, floodplains, and alluvial fans.

ANISOTROPY. The condition under which one ormore of the hydraulic properties of an aquifer varyaccording to the direction of flow.

AQUICLUDE. A low-permeability unit that formseither the upper or lower boundary of a groundwaterflow system.

AQUIFER. Rock or sediment in a formation, group offormations, or part of a formation that is saturated andsufficiently permeable to transmit significant quantitiesof water to wells and springs.

AQUIFER, CONFINED. An aquifer that is overlainby a confining bed. The hydraulic conductivity of theconfining bed is significantly lower than that of theaquifer.

AQUIFER, PERCHED. A region in the unsaturatedzone where the soil may be locally saturated because itoverlies a low-permeability unit.

AQUIFER, SEMICONFINED. An aquifer confinedby a low-permeability layer that permits water to slowlyflow through it. During pumping of the aquifer,recharge to the aquifer can occur across the confininglayer. Also known as a leaky artesian or leaky confinedaquifer.

AQUIFER, UNCONFINED. Also known as water-table and phreatic aquifer. An aquifer in which thereare no confining beds between the zone of saturationand the surface. The water table is the upper boundaryof unconfined aquifers.

AQUIFUGE. An absolutely impermeable unit that willneither store nor transmit water.

AQUITARD. A low-permeability unit that can storegroundwater and also transmit it slowly from one aqui-fer to another.

BASEFLOW. The part of stream discharge that orig-inates from groundwater seeping into the stream.

BASEFLOW RECESSION. The declining rate ofdischarge of a stream fed only by baseflow for anextended period. Typically, a baseflow recession willbe exponential.

BOREHOLE GEOCHEMICAL PROBE. A devicefor monitoring water quality that is lowered into a wellon a cable and can take direct readings of suchparameters as pH, Eh, temperature, SP, and specificconductivity.

BOREHOLE GEOPHYSICS. The general field ofgeophysics developed around the lowering of variousprobes into wells.

BORING. A hole advanced into the ground by meansof a drilling rig.

CALIBRATION. The process of refining the modelrepresentation of the hydrogeologic framework, hydrau-lic properties, and boundary conditions to achieve adesired degree of correspondence between the modelsimulations and observations of the groundwater flowsystem.

CALIPER LOG. A borehole log of the diameter of anuncased well.

CAPILLARY FORCES. The forces which act on soilmoisture in the unsaturated zone, caused by the molec-ular attraction between soil particles and water.

CONCEPTUAL MODEL. A simplifiedrepresentation of the physical hydrogeologic setting.This includes the identification and description of thegeologic and hydrologic framework, media type,hydraulic properties, and sources and sinks of flow.

CONFINING LAYER. A body of relatively imper-meable material that is statigraphically adjacent to oneor more aquifers. It may lie above or below the aquifer.

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DARCY'S LAW. An empirical equation developed to EQUIPOTENTIAL SURFACE. A surface in a three-compute the quantity of water flowing through an dimensional groundwater flow field such that the totalaquifer. hydraulic head is the same everywhere on the surface.

DENSITY. The mass or quantity of a substance per EVAPOTRANSPIRATION. The sum of evaporationunit volume. Units are kilograms per cubic meter or and transpiration.grams per cubic centimeter.

DIRICHLET CONDITION. Also known as a that the unsaturated zone of a soil can hold against theconstant head boundary. A boundary condition for a downward pull of gravity. groundwater computer model where the head is knownat the boundary of the flow field.

DIFFUSIVITY. The ratio of transmissivity to storage that sets the boundaries of the model and the nodescoefficient in an aquifer. where the model will be solved.

DISCHARGE. The volume of water flowing in a FINITE-ELEMENT MODEL. A digitalstream or through an aquifer past a specific point in a groundwater-flow model where the aquifer is dividedgiven period of time. into a mesh formed of a number of polygonal cells.

DISCHARGE AREA. An area in which there are FLOW NET. The set of intersecting equipotential linesupward components of hydraulic head in the aquifer. and flowlines representing two-dimensional steady flow

DISPERSION. The phenomenon by which a solute inflowing groundwater is mixed with uncontaminated FLOW, STEADY. The flow that occurs when, at anywater and becomes reduced in concentration. Disper- point in the flow field, the magnitude and direction ofsion is caused by differences in the velocity that the flow are constant in time.water travels at the pore level and differences in the rateat which water travels through different strata in theflow path.

DRAWDOWN. A lowering of the water table of anunconfined aquifer, or of the potentiometric surface of aconfined aquifer. Drawdown is the result of pumping ofgroundwater from wells.

DUPUIT ASSUMPTIONS. The following assump-tions for flow in an unconfined aquifer: (a) hydraulicgradient is equal to the slope of the water table,(b) streamlines are horizontal, and (c) equipotential linesare vertical.

EFFECTIVE GRAIN SIZE. The grain size corre-sponding to the one that is 10 percent finer by weightline on the grain-size distribution curve.

EQUIPOTENTIAL LINE. A line in a two-dimensional groundwater flow field such that the totalhydraulic head is the same for all points along the line.

FIELD CAPACITY. The maximum amount of water

FINITE-DIFFERENCE MODEL. A particular kindof digital computer model based upon a rectangular grid

through porous media.

FLOW, UNSTEADY. Also called transient flow. Theflow that occurs when, at any point in the flow field, themagnitude or direction of flow changes with time.

GAMMA-GAMMA RADIATION LOG. A boreholelog in which a source of gamma radiation as well as adetector are lowered into the borehole. This log mea-sures bulk density of the formation and fluids.

GHYBEN-HERXBERG PRINCIPLE. An equationthat relates the depth of a saltwater interface in a coastalaquifer to the height of the freshwater table above sealevel.

GLACIAL OUTWASH. Well-sorted sand, or sandand gravel, deposited by the meltwater from a glacier.

GLACIAL TILL. Unsorted and unstratified depositsby melting ice without reworking by meltwater. Tillmay consist of a mixture of clay, silt, sand, gravel, andboulders.

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GRAVITY POTENTIAL. A potential due to the HYDRAULIC GRADIENT. The change in total headposition of groundwater or soil moisture above a datum. with a change in distance in a given direction which

GROUND-PENETRATING RADAR. A surfacegeophysical technique based upon the transmission of HYDROGRAPH. A graph that shows some propertyrepetitive pulses of electromagnetic waves into the of groundwater or surface water as a function of time.ground. Some of the radiated energy that is reflectedback to the surface is captured and processed.

GROUNDWATER. The water contained in intercon- ultimately back to the ocean.nected pores located below the water table.

GROUNDWATER DIVIDE. The boundary between law of mass conservation for purposes of water budgets.two adjacent groundwater basins. The divide is repre- It may be stated as inflow equals outflow plus or minussented by a high in the water table. changes in storage.

GROUNDWATER FLOW MODEL. An application INFILTRATION. The flow of water downward fromof a mathematical model to represent a site-specific the land surface into and through the upper soil layers.groundwater flow system.

HATTUSH-JACOB FORMULA. An equation to which infiltration can occur under specific conditions ofdescribe the change in hydraulic head with time during soil moisture. For a given soil, the infiltration capacitypumping of a leaky confined aquifer. is a function of the water content.

HEAD, TOTAL HYDRAULIC. The sum of the INTERFLOW. The lateral movement of water in theelevation head, the pressure head, and the velocity head unsaturated zone during and immediately after a pre-at a given point in an aquifer. cipitation event. The water moving as interflow dis-

HETEROGENEOUS. A medium which consists ofdifferent (nonuniform) characteristics in different ISOTROPY. The condition in which hydrauliclocations. properties of the aquifer are equal in all directions.

HOMOGENEOUS. A medium with identical JACOB STRAIGHT-LINE METHOD. A graphical(uniform) characteristics regardless of location. method using semilogarithmic paper and the Theis equa-

HYDRAULIC CONDUCTANCE. A term whichincorporates model geometry and hydraulic conductivity KARST. The type of geologic terrain underlain by car-into a single value for simplification purposes. Controls bonate rocks where significant solution of the rock hasrate of flow to or from a given model cell, river reach, occurred due to the flowing groundwater. Karst topo-etc. graphy is frequently characterized by sinkholes, caves,

HYDRAULIC CONDUCTIVITY. The rate at whichwater of a specified density and kinematic viscosity can LAMINAR FLOW. That type of flow in which themove through a permeable medium. fluid particles follow paths that are smooth, straight,

HYDRAULIC DIFFUSIVITY. A property of anaquifer or confining bed defined as the ratio of thetransmissivity to the storativity.

yields a maximum rate of decrease in head.

HYDROLOGIC CYCLE. The circulation of waterfrom the oceans through the atmosphere to the land and

HYDROLOGIC EQUATION. An expression of the

INFILTRATION CAPACITY. The maximum rate at

charges directly into a stream or lake.

tion for evaluating the results of a pump test.

and underground drainage.

and parallel to the channel walls. In laminar flow, theviscosity of the fluid damps out turbulent motion.

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LAPLACE EQUATION. The partial differential NUMERICAL MODEL. A model of groundwaterequation governing steady-state flow in a homogeneous, flow in which the aquifer is described by numericalisotropic aquifer. equations, with specified values for boundary

LEAKANCE. Controls vertical flow in a modelbetween cells in adjacent layers. Equivalent to effectivevertical hydraulic conductivity divided by the vertical OBSERVATION WELL. A nonpumping well useddistance between layer midpoints. to observe the elevation of the water table or the

LEAKY CONFINING LAYER. A low-permeabilitylayer that can transmit water at sufficient rates to fur-nish some recharge to a well pumping from an under-lying aquifer. Also known as an aquitard.

LINEAMENT. A regional topographic feature ofregional extent that is believed to reflect crustalstructure.

LYSIMETER. A field device containing a soil columnand vegetation; used for measuring evapotranspiration.

MANNING EQUATION. An equation that can beused to compute the average velocity of flow in an openchannel.

MODEL CALIBRATION. The process by which theindependent variables of a numerical model are adjustedto produce the best match between simulated andobserved data, usually water-level values.

NATURAL GAMMA RADIATION LOG. Aborehole log that measures the natural gamma radiationemitted by the formation rocks. It can be used todelineate subsurface rock types.

NEUMANN CONDITION. Also called a constantflux boundary. The boundary condition for agroundwater-flow model where a flux across theboundary of the flow region is known.

NEUTRON LOG. A borehole log obtained bylowering a radioactive element, which is a source ofneutrons, and a neutron detector into the well. Theneutron log measures the amount of water present;hence, the porosity of the formation.

conditions, that are usually solved on a digitalcomputer.

potentiometric surface. An observation well is generallyof larger diameter than a piezometer and typically isscreened or slotted throughout the thickness of theaquifer.

PACKER TEST. An aquifer test performed in anopen borehole; the segment of the borehole to be testedis sealed off from the rest of the borehole by inflatingseals, called packers, both above and below thesegment.

PERMAFROST. Perennially frozen ground, occurringwherever the temperature remains at or below freezingfor two or more years in a row.

PIEZOMETER. A nonpumping well, generally ofsmall diameter, that is used to measure the elevation ofthe water table or potentiometric surface. A piezometergenerally has a short well screen through which watercan enter.

POROSITY. The ratio of the volume of void spaces ina rock or sediment to the total volume of the rock orsediment.

POROSITY, EFFECTIVE. The volume of the inter-connected void spaces through which water or otherfluids can travel in a rock or sediment divided by thetotal volume of the rock or sediment.

POROSITY, PRIMARY. The porosity thatrepresents the original pore openings when a rock orsediment formed.

POROSITY, SECONDARY. The porosity that hasbeen caused by fractures or weathering in a rock orsediment after it has been formed.

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POTENTIOMETRIC SURFACE. A surface that SAFE YIELD. The amount of naturally occurringrepresents the level to which water will rise in tightly groundwater that can be economically and legally with-cased wells. The water table is a particular poten- drawn from an aquifer on a sustained basis withouttiometric surface of an unconfined aquifer. impairing the native groundwater quality or creating an

PUMPING TEST. Also known as an aquifer test. Atest made by pumping a well for a period of time andobserving the change in hydraulic head in the aquifer. Apumping test may be used to determine the capacity ofthe well and the hydraulic characteristics of the aquifer. SATURATED ZONE. The zone in which the voids in

RECHARGE BOUNDARY. An aquifer systemboundary that adds water to the aquifer. Streams andlakes are typically recharge boundaries.

REGOLITH. The fragmented and unconsolidated rockmaterial that forms the surface of the land and overliesthe bedrock.

RESIDUAL. The difference between the computedand observed value of a variable at a specific time andlocation.

RESISTIVITY LOG. A borehole log made bylowering two current electrodes into the borehole andmeasuring the resistivity between two additionalelectrodes. It measures the electrical resistivity of theformation and contained fluids near the probe.

ROCK, IGNEOUS. A rock formed by the cooling andcrystallization of a molten rock mass called magma.

ROCK, METAMORPHIC. A rock formed by theapplication of heat and pressure to preexisting rocks.

ROCK, SEDIMENTARY. A layered rock formedfrom the consolidation of sediment. Includes clasticrocks (such as sandstone), rocks formed by chemicalprecipitation in water (such as limestone), or rocksformed from organic material (such as coal).

ROCK, VOLCANIC. An igneous rock formed whenmolten rock called lava cools on the earth's surface.

undesirable effect such as environmental damage. Itcannot exceed the increase in recharge or leakage fromadjacent strata plus the reduction in discharge, which isdue to the decline in head caused by pumping.

the rock or soil are filled with water at a pressuregreater than atmospheric. The water table is the top ofthe saturated zone in an unconfined aquifer.

SEEPAGE VELOCITY. Also known as pore watervelocity. The rate of movement of fluid particlesthrough porous media along a line from one point toanother.

SEISMIC REFRACTION. A method of determiningsubsurface geophysical properties by measuring thelength of time it takes for artificially generated seismicwaves to pass through the ground.

SENSITIVITY ANALYSIS. The measurement of theuncertainty in a calibrated model as a function of uncer-tainty in estimates of aquifer parameters and boundaryconditions.

SIMULATION. One complete execution of a ground-water modeling computer program, including input andoutput.

SLUG TEST. An aquifer test made either by pouringa small instantaneous charge of water into a well or bywithdrawing a slug of water from the well.

SPECIFIC CAPACITY. The ratio of the rate of dis-charge of water from the well to the drawdown of thewater level in the well. Specific capacity should bedescribed on the basis of the number of hours of pump-ing prior to the time the drawdown measurement ismade. It will generally decrease with time as thedrawdown increases.

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SPECIFIC DISCHARGE. Also known as Darcian UNSATURATED ZONE. Also known as the zone offlow velocity. An apparent velocity calculated from aeration and the vadose zone. The zone between theDarcy's law; represents the flow rate at which water land surface and the water table. It includes the rootwould flow in an aquifer if the aquifer were an open zone, intermediate zone, and capillary fringe. The poreconduit. spaces contain water at less than atmospheric pressure,

SPECIFIC RETENTION. The ratio of the volume ofwater the rock or sediment will retain against the pull ofgravity to the total volume of the rock or sediment.

SPECIFIC STORAGE. The amount of water per unitvolume of a saturated formation that is expelled from VISCOSITY. The property of fluid describing itsstorage due to compression of the mineral skeleton and resistance to flow. Units of viscosity are newton-the pore water. seconds per meter squared or pascal-seconds. Viscosity

SPECIFIC YIELD. The ratio of the volume of waterthat a given mass of saturated soil or rock will yield by WATER BUDGET. An evaluation of all the sourcesgravity to the volume of that mass. of supply and the corresponding discharges with respect

STORAGE COEFFICIENT (STORATIVITY).The volume of water that a conductive unit will expel WATER TABLE. The surface in an unconfinedfrom storage per unit surface area per unit change in aquifer or confining bed at which the pore waterhead. In a confined aquifer, it is computed as the pressure is atmospheric. It can be measured byproduct of specific storage and aquifer thickness. In an installing shallow wells extending just into the zone ofunconfined aquifer, it is equal to specific yield. saturation and then measuring the water level in those

THEIS EQUATION. An equation for the unsteadyflow of groundwater in a fully confined aquifer to a WELL DEVELOPMENT. The process whereby apumping well. well is pumped or surged to remove any fine material

TOPOGRAPHIC DIVIDE. The boundary betweenadjacent surface water boundaries. It is represented bya topographically high area. WELL EFFICIENCY. The ratio of idealized draw-

TORTUOSITY. The actual length of a groundwaterflow path, which is sinuous in form, divided by thestraight-line distance between the ends of the flow path.

TRANSMISSIVITY. The rate at which water istransmitted through a unit width of aquifer of confiningbed under a unit hydraulic gradient. The product ofsaturated thickness and hydraulic conductivity.

as well as air and other gases. Saturated bodies, suchas perched groundwater, may exist in the unsaturatedzone.

VADOSE ZONE. See unsaturated zone.

is also known as dynamic viscosity.

to an aquifer or a drainage basin.

wells.

that may be blocking the well screen or the aquiferoutside the well screen.

down in the well, where there are no losses resultingfrom well design and construction factors, to actualmeasured drawdown in the well.

WELL, FULLY PENETRATING. A well drilled tothe bottom of an aquifer, constructed in such a way thatit withdraws water from the entire thickness of theaquifer.

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WELL, PARTIALLY PENETRATING. A well WELL SCREEN. A tubular device with either slots,constructed in such a way that it draws water directly holes, gauze, or continuous-wire wrap; used at the endfrom a fractional part of the total thickness of the of a well casing to complete a well. The water entersaquifer. The fractional part may be located at the top or the well through the well screen.bottom or anywhere in between in the aquifer.

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Appendix CSummary of the Hydrogeologic FlowModel for Tooele Army Depot, Utah

A summary of the steps taken in the computer modeldevelopment for the Tooele Army Depot follows. Thissummary serves as an example of what is involved in asite characterization using computer modelingtechniques. The original document is not reproduced inits entirety; the most important details for each sectionare mentioned, using the table of contents from theoriginal document as the format.

1 Introduction

1.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

A three-dimensional finite difference flow model wasused to simulate groundwater flow at a TCE-contaminated site within the Tooele Army Depot inUtah.

1.2 Acknowledgements . . . . . . . . . . . . . . . . . . . . . 1

1.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

The groundwater below the site was contaminated bytrichloroethylene (TCE) flowing through four unlinedditches to an unlined industrial waste lagoon. The Corpswas requested to develop a groundwater flow modelincorporating the most reliable past and current datafrom a number of wells installed onsite for applicationto system design enhancement.

Figure 1. Location MapFigure 2. Project Site Map

1.4 Purpose and Scope . . . . . . . . . . . . . . . . . . . . . 2

The primary objective of this modeling effort is toprovide a tool for determining scientifically based opti-mum pumping rates and locations which will ensure thehydrodynamic isolation of the TCE plume below and tothe north of the closed Industrial Waste Lagoon (IWL).The model should also have the ability to reflect hydro-geologic responses of future stresses placed upon thesite under various potential scenarios,

i.e., the impact of future extraction or injection wells atvarious site locations on flow direction, flow velocity,and contaminant containment.

2 Regional Geology and Hydrology

2.1 Topography . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

The Tooele Valley encompasses approximately250 square miles within a 400-square-mile drainagebasin. It is bordered by the Oquirrh Mountains on theeast, by the Stansbury Mountains on the west, and bySouth Mountain and Stockton Bar on the south. To thenorth, the valley fronts on the Great Salt Lake.

2.2 Climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

The climate of the Tooele Valley drainage basin rangesfrom semiarid in the salt flats near the Great Salt Laketo humid in the higher mountains. The average precipi-tation at the town of Tooele for the period 1897-1977 is16.49 in.

Figure 3. Normal Annual Precipitation of TooeleValley

2.3 Regional Geology . . . . . . . . . . . . . . . . . . . . . . 7

The Tooele Valley is typical of the basin and rangephysiography in which fault block mountains rise aboveflat, intermontaine valleys (Figure 4). The bulk of thisvalley fill consists of inter-fingering clays, silt, sand,and gravel. The fill was emplaced in a complex sedi-mentation pattern of lake bottom, lake shore, stream,and alluvial fan deposits, making it difficult to correlatebeds from one part of the valley to another (38). Thereare areas of faulting and folding.

Figure 4. Geologic Map of Tooele Valley

2.4 Regional Hydrology . . . . . . . . . . . . . . . . . . . . . 8

Groundwater in the Tooele Valley drainage basin occursin the consolidated rocks of the mountains and in theunconsolidated valley fill. As shown in Figures 5 and 6,regional groundwater flow trends from the mountainrecharge areas towards the northern valley front withthe Great Salt Lake.

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Figure 5. Regional Groundwater Flow of Tooele TCE is considered to be the contaminant of primaryValley concern. The plume, defined by the 5-µg/R isoconcen-Figure 6. Regional Groundwater Table of Tooele tration contour was estimated by JMM to be 400 ftValley thick and to contain an estimated 36 billion gallons of

3 Development of Conceptual Model movement of groundwater in the contaminated area to

3.1 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . 12

From 1982-1992, 162 monitoring wells and piezometers 3.5 Hydraulic Properties . . . . . . . . . . . . . . . . . . . 21were installed at the TEAD study site to help charac-terize potentiometric surfaces, groundwater flow direc- Field measurements of hydraulic conductivity show ations, hydraulic gradients, and chemical characteristics broad variance from less than 1 ft/day in the bedrock(Appendices B, C, and H). Additional hydrogeologic areas, to over 1,000 ft/day in the northern alluviuminformation on the Tooele site indicated evidence of (11,12,41). The wide range of hydraulic conductivityfaulting on the northern and western areas of the values derived from tests provided additional evidenceuplifted bedrock block. of the heterogeneous nature of the alluvium on a local

3.2 Geologic Framework . . . . . . . . . . . . . . . . . . . 12

Two physiographic features dominate site geology: anuplifted bedrock block of quartzite, sandstone, and lime- 4.1 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . 23stone located beneath and to the northeast of the IWL,and unconsolidated, poorly sorted alluvial deposits of The purpose of the TEAD groundwater model is tovarying thickness located to the north, west, and south serve as a practical aid in the design of a pump-and-of the bedrock. Extensive, yet highly variable fracturing treat system. exists throughout the bedrock system.

Figure 7. Transverse Hydrogeologic SectionsFigure 8. Longitudinal Hydrogeologic Sections The U.S. Geological Survey (USGS) models

3.3 Hydrologic Framework . . . . . . . . . . . . . . . . . 17

Groundwater flow trends in a northwest direction acrossthe TEAD site (Figures 5 and 6). Broadly speaking, the 4.3 Accompanying Models . . . . . . . . . . . . . . . . . 26TEAD study site can be divided into three separatehydraulic units: the steep flow gradients of the frac- A computer program for calculating sub-regional watertured bedrock and adjoining low conductive (low K) budgets using results from MODFLOW (47) will bealluvium in the central area of the site, the highly included in the modeling package to allow the user totransmissive alluvium to the north, and the shallow easily determine volumetric flow budgets in specifiedalluvium at the southern, upgradient end of the site. sub-regions of the modeled area. Additionally, a com-The uplifted, fractured bedrock block and adjoining low puter program was written which estimates steady-stateconductive alluvium are the hydraulically controlling drawdown at a pumping well using output fromfeatures of the study area due to the steep gradients MODFLOW (Appendix I).required for flow across this area.

Figure 9. Observed Groundwater Table3.4 Groundwater Quality . . . . . . . . . . . . . . . . . . . 19

groundwater (11). JMM (11) estimated the rate of

range from 700 to 1,200 ft/year in the areas of greatestgroundwater flow velocity.

scale.

4 Computer Code

4.2 Model Selection . . . . . . . . . . . . . . . . . . . . . . . 23

MODFLOW and MODPATH were judged to best meetthe criteria and were thus selected for use in the TEADgroundwater modeling project.

4.4 Accompanying Software . . . . . . . . . . . . . . . . 26

5 Construction of Groundwater Flow Model

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Figure 10. Migration of TCE Plume, Tooele Army Depot

5.1 Initial Two-Dimensional Model . . . . . . . . . . . 27

The modeling effort proceeded in a deliberate fashionfrom a simple two-dimensional grid aligned with the Figure 11. Model Layersobserved groundwater flow direction to the final 52 ×80 three-dimensional grid. A constant head boundary, 5.3 Creation of Final Model Grid . . . . . . . . . . . . . 28corresponding to measured water level elevations, waslocated at the southeastern end of the site. A constant The model grid was oriented in a southeast-northwestflux boundary, which represented the total flow through direction with columns being oriented in the direction ofthe site area, was located on the northwestern boundary. groundwater flow (Figure 12, Plate 2). The grid area

5.2 Selection of Model Layers . . . . . . . . . . . . . . . 27

Because of minimal evidence of well-defined continuous delineate the hydrologic structures and prevent thelayering occurring in the alluvium, three layer divisions combination of two wells per grid cell. The final grid

were selected to allow for the simulation of vertical headgradients measured across the site.

was designed to be large enough to encompass anypertinent data points and the extent of the contaminantplume, with the interior grid being fine enough to

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design was then entered into the MODELCAD pre- The northwestern constant flux boundary regulates theprocessor along with the surveyed locations of the wells total flow through the site. The flux boundary values(Appendix C) and oriented in the direction of were determined by first estimating the total flowgroundwater flow. through the modeled area, and then partitioning flow

Figure 12. Model Grid

5.4 Model Calibration . . . . . . . . . . . . . . . . . . . . . 31

The model was calibrated using measured values. Some model boundaries to the northwest and southeastdata values were varied through multiple model runs to through the use of head-dependent flux boundaries. Thebest characterize the site. distance to extend the boundaries of model influence

Table 1. Water Level Vertical/Horizontal Correc- giving a more realistic response to groundwatertions for Model Calibration discharge/recharge scenarios.

5.5 Solution Convergence . . . . . . . . . . . . . . . . . . 33

The Strongly Implicit Procedure (SIP) was used to According to Gates (34), precipitation on the TEAD siteiteratively solve for unknown heads at each grid cell. ranges from 13 in./year on the southeastern end toThe goal of this modeling effort is to consistently pro- 11 in./yr. in the area of the northwestern boundaryduce a mass balance input/output flow differential of (Figure 3). Razem and Steiger (38) estimated theless than 0.1 percent. percentage of this amount of precipitation that infiltrates

Figure 13. Location of Water Level CalibrationPoints 6.5 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . 43

6 Boundary and Initial Conditions After calibration under the no-action scenario, the

Initial boundary conditions consisted of a constant head starting heads in pumping scenarios for the purpose ofboundary at the southeastern side of the grid, a constant computing drawdowns.flux boundary at the northwestern end of the model grid,and no-flow boundaries on the northeastern and south- 7 Determination of Hydrogeologic Propertieswestern sides of the model grid. A constant rechargerate was assigned to all cells in the upper model layer tosimulate infiltration from precipitation. The base of thelower model layer was simulated as a no-flow boundary.Flow across this boundary is assumed to be insignificantrelative to the flow in the upper 600 ft of the system.

6.1 Constant Head Boundary . . . . . . . . . . . . . . . . 35

A constant head boundary specifies a potentiometricsurface elevation at a given location which provides anunlimited supply of water depending on gradient andconductivity values of the system.

6.2 Constant Flux Boundary . . . . . . . . . . . . . . . . 35

values among the three layers.

6.3 Head-Dependent Flux Boundaries . . . . . . . . . 41

The solution to this problem is to, in effect, extend the

should correspond to the regional flow system, thus

6.4 Recharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

to groundwater to range from 1-3 percent.

steady-state head solutions were saved and used as

7.1 Hydraulic Conductivity . . . . . . . . . . . . . . . . . 45

The TEAD site was divided into spatial zones of homo-geneous hydraulic conductivity values. The complexityof the model was considerable to be commensurate withthe ability of data to represent the system. Modelresults complement field evidence of the existence of afault zone that is trending northeast to southwest alongthe northwest side of the bedrock (Figure 15).

Figure 14. Recharge ZonesFigure 15. Hydraulic Conductivity Zones, Layer 1Figure 16. Hydraulic Conductivity Zones, Layer 2Figure 17. Hydraulic Conductivity Zones, Layer 3Table 2. Values of Hydraulic Conductivity

Layer 1 Hydraulic Conductivity (K)

Zone 4

Zone 8

Zone 7

Zone 5

Zone 1

Zone 2

Zone 3

Zone 6

K=.10 ft/day

K=35 ft/day

K=3.0 ft/day

K=1.5 ft/day

K=60 ft/day

K=200 ft/day

K=385 ft/day

K=160 ft/day

Injection

Extraction

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Figure 15. Hydraulic Conductivity Zones, Layer 1

Table 3. Extraction Well Data budget and head files created by MODFLOW, zonalTable 4. Injection Well Data values of effective porosity, and the starting locations of

particles (46). Effective porosity values were derived in7.2 Leakance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Vertical hydraulic conductivity is a difficult charac-teristic of an aquifer system to measure or estimate, yetit is a sensitive and significant parameter for multi-layered models.

Figure 18. Leakance Zones, Layers 1-2Figure 19. Leakance Zones, Layers 2-3

7.3 Storativity/ Porosity . . . . . . . . . . . . . . . . . . . . 57

Storage coefficient values were derived and entered inthe MODELCAD preprocessor for future transient Figure 23. No-Action Potentiometric Surfaceapplications. Effective porosity was set equal to the Elevation, Layer 1specific yield value for each hydrologic soil type and Figure 24. Water Particle Migration Ratewas input into the MODPATH MAIN.DAT input file Figure 25. Profile of Water Particle Pathlines,as a tool for determining particle flow velocities. Layer 3

Figure 20. Storativity/Porosity Zones, Layer 1 10.2 Well Field Optimization . . . . . . . . . . . . . . . 70

Figure 21. Storativity/Porosity Zones, Layer 2Figure 22. Storativity/Porosity Zones, Layer 3

8 Sensitivity Analysis

8.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 63

Sensitivity analysis is used to measure the uncertainty inthe calibrated model caused by uncertainty in the esti-mates of aquifer parameters and boundary conditions.The accompanying changes in head values, relative tothe calibrated head values, are then analyzed as ameasure of the sensitivity of the model to that particularparameter. The systematic varying of calibrated flowparameters indicated that the most sensitive parametersin model calibration were the hydraulic conductivityvalues and the flows determined at the head-dependentflux boundaries.

9 MODPATH Input Parameters

9.1 Input Parameters . . . . . . . . . . . . . . . . . . . . . . 65

Input requirements for the MODPATH particle trackingprogram include the WELL and RCH packages used inthe MODFLOW analysis, unformatted cell-by-cell flow

the Storativity/Porosity section. Effective porosityvalues are directly proportional to the velocity of parti-cle flow, and are thus important in determining particlelocations at specified time increments.

10 Model Application

10.1 No-Action Scenario . . . . . . . . . . . . . . . . . . . 67

Initially, the flow model was run under a no-action scen-ario to present a description of static water elevations,and particle flow paths.

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Figure 26. Particle tracking for optimization of plumeremoval, Layer 1

Sixty-four computer runs were completed to optimize providing additional physical evidence to corroboratewell pumping rates and ensure the simulated 100-per- the existence of displaced sediments. cent capture of the 5-ppb TCE contaminant plumedowngradient from the IWL. Much of the optimization 12 Future Applicationsprocess was performed by trial and error.

10.3 Recommendations . . . . . . . . . . . . . . . . . . . . 71

Installation of three additional wells (E13,14,15) was compared with simulated results. Future recalibrationrequired for 100-percent capture of the 5-ppb TCE con- efforts should employ transient simulations as expand-taminant plume downgradient of the IWL (Figure 26). ing cones of depression from pumping wells are com-

Figure 26. Optimized Pumping Scenario, pumping rates and well locations recommended in thisLayers 1-3 report are for long-term steady-state capture of theTable 5. Optimized Extraction Well Locations/ contaminant plume. A transient, three-dimensionalPumping Rates/Drawdowns particle tracking computer program is in the final stagesTable 6. Optimized Injection Well Locations/ of development by the USGS. The application of thisPumping Rates/Drawdowns program to the Tooele site will enable the prediction of

11 Additional Data Needs and on the northeast and southwest sides of the model

11.1 Additional Data Needs . . . . . . . . . . . . . . . . 75

Additional data gathering should focus on further delin- correlation with the migration rate of the contaminanteating the boundaries of the bedrock block, and plume. Assuming a retardation factor of 2.0 for TCE,

12.1 Future Applications . . . . . . . . . . . . . . . . . . . 76

Work on this project will continue as new field data are

pared with simulated water levels. The optimized

time requirements for complete capture of thecontaminant plume, approximate percentage capture ofthe plume as a function of time, and will allow for theevaluation of transient capture efficiency by adding newwells. This model can be used to predict long-termeffects of the pump-and-treat system on contaminantmitigation and overall project completion time require-ments, and simulate the transport of contaminantsoff-site.

13 Conclusion

13.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 77

The three-dimensional finite-difference modelMODFLOW (44) was selected to simulate groundwaterflow across the TEAD site. The modeled area of15,600 ft by 24,000 ft was overlain by a 52 x 80 grid ofsquare cells 300 ft on each side. The model was con-structed in three layers simulating unconfined andconfined flow conditions. Boundaries of the flow modelconsisted of head-dependent fluxes at the northwest andsoutheast ends of the model grid, recharge at the top oflayer 1, and no-flow conditions at the bottom of layer 3

grid.

Estimated water particle linear velocities showed good

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the computed travel time for the TCE plume to reach the simulated water levels after pumping begins, thenorthern TEAD boundary from the IWL was application of a three-dimensional, transient particle20-25 years. The recalibration effort determined the tracking program to provide an estimate of total con-likely existence of displaced sediments from seismic taminant capture as a function of time, and theactivity as the likely cause of the zone of low hydraulic development of a simple contaminant transport model asconductivity located to the southwest of the bedrock additional improvements are made in the groundwaterblock. The recalibrated model provided a simpler, more flow model and more water quality data becomeaccurate representation of the hydrogeologic system as available.evidenced by the more substantial physical basis forzone delineation, the over 50-percent reduction in 14 References . . . . . . . . . . . . . . . . . . . . . . . . . 79hydraulic conductivity zones, and the reduction in theaverage residual error between measured and simulated Appendiceswater levels from 5.3 to 3.1. A. Terminology

According to model simulations, the construction of C. Surveyed Well Locationsthree additional wells is required to ensure the simulated D. Analysis of Long Term Pumping Test,capture of the 5-ppb TCE contaminant plume down- Popadopolus Inc.gradient from the IWL. The total extraction rate E. Hydrologic Characterization of Bedrock,required for these wells is 1,500 gpm. JMM

Additional data-gathering efforts should focus on G. Profile of Thermal and Total Dissolved Solidsfurther delineating the bedrock block and displaced Gradients, JMMsediments which are the hydrogeological controls of the H. Compilation of TEAD Groundwater Qualitysite, defining the spatial extent of vertical flow gradients Assessmentsin the northern alluvium, and the monitoring of water I. A Computer Program Which Estimateslevels adjacent to extraction wells for the determination Steady-State Drawdown at a Pumping Well Usingof aquifer properties. Output from MODFLOW

Future recommended work to be performed on the Dependent Flux Boundary Conditions Under aTooele Army Depot groundwater flow modeling study No-Action Scenarioincludes the transient calibration of measured versus

B. 1992 Water Levels, Geomatrix

F. Pneumatic Slug Test, Reynolds

J. Output of Calibrated Model Using Head-

h0 - hi

h0 hi hw b

ri

rw

Q

Original

surfacePotentiometricConfining layer

surfacepotentiometric

Confining layer

Q ' 2BbKhi & hw

lnri

rw

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D-1

Figure D-1. Parameters used in solution for radial flow to a well in a confined aquifer

Appendix DGeneral Analytical Solutions forApplication to Pumping Test Data

This appendix contains equations dealing with theeffects of pumping on aquifers, both confined andunconfined, as well as the analysis of pump test results.

D-1. Flow Equations for Aquifer Pumping

a. Steady-state solution in a confined aquifer.For a pumping well similar to that shown in Figure D-1,the magnitude of radial flow to a well is calculated bythe Thiem equation:

(D-1)

where

Q = flow into the well [L /T]3



h = head at observation well (distance r away) [L]i i

h = head at well [L] w

r = radius from center of well to observation welli

[L]

r = radius of well [L]w

In the design of pump-and-treat systems, it is oftendesired to estimate the lateral width of the influence ofthe well. The capture zone of a pumping well understeady-state conditions and assuming uniform flow canbe estimated by:

h2h1

r1

Q

tableWater

Confining layer

Aquifer

r2

yc 'Qvb Q '

BK(h 22 & h 2

1 )

lnr2

r1

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D-2

Figure D-2. Parameters used in solution for radial flow to a well in an unconfined aquifer

(D-2)

where

y = capture zone perpendicular to antecedent flowc

direction [L]

Q = flow into the well [L /T]3

v = specific discharge = -Kdh/dl [L/T]


b. Steady-state solution in an unconfined aquifer.

(1) The solution of the Laplace equation for anunconfined aquifer is similar to that for the confinedaquifer, except that change in aquifer thickness must beaddressed. Figure D-2 presents a graphical representa-tion of flow to a well in an unconfined aquifer. Themagnitude of radial flow can be calculated by:

(D-3)

where

Q = flow to well

h = head at point 1 [L]1

h = head at point 2 [L]2

r = radial distance from well to point 1 [L]1

r = radial distance from well to point 2 [L]2

Assumptions (known as the Dupuit assumptions) inher-ent in this equation are: 1) flow lines are horizontal andequipotentials are vertical; and 2) the hydraulic gradientis equal to the slope of the water table and is invariantwith depth. Equation D-3 is useful for approximatingthe hydraulic conductivity of an aquifer.

s 'Q

4BTW(u)

W(u) ' m4

u

e &u

udu

u 'r 2S4Tt

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D-3

(2) If observation wells are not available, the field (2) Drawdown is defined as the distance from theapplication for Equations D-1 and D-3 can be simplified original piezometric surface to the new surface at aby allowing r to equal the radius of the well (r ), and r point a distance r from the center of the pumping well.1 w 2

to be approximated by the radius of influence of thewell, i.e., the radial distance at which drawdown W(u) = well function term, which is defined as:approaches zero.

c. Unsteady flow solution in confined aquifers.

(1) The solution of flow to a well under transient(non-steady) conditions is complicated. Assumptionsused in simplification are: a) that the aquifer isisotropic, homogeneous, and of infinite areal extent;b) the well fully penetrates the aquifer; c) the flow ishorizontal everywhere within the aquifer; d) the welldiameter is so small that storage within the well isnegligible, and; e) water pumped from the well isdischarged immediately with decline of piezometrichead. Theis, in 1931, gave the following solution forthis problem:

(D-4) T = transmissivity [L /T]

where

s = drawdown [L]

(D-5)

(D-6)

where

r = radial distance in feet [L]

S = storativity coefficient [dimensionless]

t = duration of pumping [T]

2

(3) Table D-1 is a tabulation of W(u) given u,which is easily calculated if S and T are known. Unfor-tunately, these aquifer parameters are usually unknownand pumping tests must be performed. By observing

Table D-1Tabulation of W(u) Values for Use in Theis Equation

Values of W(u) for values of u

u 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

x 1 0.219 0.049 0.013 0.0038 0.0011 0.00036 0.00012 0.000038 0.000012

x 10-1 1.82 1.22 0.91 0.70 0.56 0.45 0.37 0.31 0.26

x 10-2 4.04 3.35 2.96 2.68 2.47 2.30 2.15 2.03 1.92

x 10-3 6.33 5.64 5.23 4.95 4.73 4.54 4.39 4.26 4.14

x 10-4 8.63 7.94 7.53 7.25 7.02 6.84 6.69 6.55 6.44

x 10-5 10.94 10.24 9.84 9.55 9.33 9.14 8.99 8.86 8.74

x 10-6 13.24 12.55 12.14 11.85 11.63 11.45 11.29 11.16 11.04

x 10-7 15.54 14.85 14.44 14.15 13.93 13.75 13.60 13.46 13.34

x 10-8 17.84 17.15 16.74 16.46 16.23 16.05 15.90 15.76 15.65

x 10-9 20.15 19.45 19.05 18.76 18.54 18.35 18.20 18.07 17.95

x 10-10 22.45 21.76 21.35 21.03 20.84 20.66 20.50 20.37 20.25

x 10-11 24.75 24.06 23.65 23.36 23.14 22.96 22.81 22.67 22.55

x 10-12 27.05 26.36 25.96 25.67 25.44 25.26 25.11 24.97 24.86

x 10-13 29.36 28.66 28.26 27.97 27.75 27.56 27.41 27.28 27.16

x 10-14 31.66 30.97 30.56 30.27 30.05 29.87 29.71 29.58 29.46

x 10-15 33.96 33.27 32.86 32.58 32.35 32.17 32.02 31.88 31.76

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D-4

the drawdown over a period of time, the Theis equation and storativity) before the development of new steady-can be solved for S and T. This solution is not explicit state conditions resulting from pumping. The assump-and the solution is usually obtained graphically. tions inherent in the Theis equation include:

d. Unsteady flow in an unconfined aquifer. In depression, well discharge is derived entirely frompractice, drawdowns in unconfined aquifers can be sig- aquifer storage and is discharged instantaneously withnificant and the assumption that water released from decline in head, the discharging well penetrates thestorage is discharged immediately with decline of piezo- entire thickness of the aquifer, and well diameter ismetric head is breached. Unconfined aquifers generally small in comparison with the pumping rate. Theseexhibit a behavior called delayed yield in which water is assumptions are best met by confined aquifers at sitesreleased from storage and specific yield at a time after remote from their boundaries. The Theis equation is ofpumping has started. Flow to a pumping well in an a form which cannot be solved directly, and is solvedunconfined (phreatic) aquifer occurs in three phases. In through the use of a graphic method of solution calledthe first phase, pumping has just started, and a phreatic type curves. Analysis of aquifer-test data involvesaquifer behaves like a confined aquifer. Water is plotting the test data (drawdown versus time) onderived from storage i.e., expansion of water and com- logarithmic graph paper and aligning this curve with apression of the aquifer. The time-drawdown plot for corresponding type curve from which values ofthis phase emulates the Theis curve. In the second transmissivity and storativity can be calculated. Thephase, the phenomenon of delayed yield occurs. During Theis equation can be used for unconfined aquifersthis phase, water remaining in the pores is drained by under the following two considerations: (1), if thegravity (specific yield). This gravity drainage repleni- aquifer is relatively fine-grained, water is not releasedshes that portion of the aquifer supplying water to the instantaneously with the decline in head; thus, the valuewell, resulting in a reduction in the rate of drawdown of storativity determined from a short-period test mayover the first phase. This appears as the time-draw- be too small; and (2) the effect of dewatering the aquiferdown plot flattens in response to the secondary source decreases aquifer thickness and thus transmissivity.of water. In the third phase, the rate of drawdown and This dewatering effect can be addressed by thethe time-drawdown again emulate a Theis curve. The following equation:duration of either of the first two phases is a function ofthe ratio of storage (S) to specific yield (S ). If this ratio s' = s - (s /2b) (D-7)y

is in the range of 10 and 10 , it is an indication that S-1 -2

is relatively large and that one can anticipate a signifi- wherecant first phase. The type of materials you wouldexpect to exhibit this behavior are sandy silts, silty-, s = observed drawdown in the unconfined aquiferclayey-, or fine-grained sands. When S/S is in the [L]y

range of 10 to 10 it is an indication that S is-4 -6y

relatively large and that one can anticipate a significant b = aquifer thickness [L]second phase. The type of materials you would expectto exhibit this behavior are clean sands and gravels. In s' = drawdown that would have occurred if theaddition to S/S , the geometry of the time-drawdown aquifer was confined [L]y

graph can be affected by the location of the observationwell(s). As the distance to an observation wellincreases, the effects of S diminish.

D-2. Analysis of Pump Test Results

a. Theis method. As discussed in Section D-1,the Theis equation allows for the determination of thehydraulic characteristics of an aquifer (transmissivity

transmissivity is constant to the extent of the cone of

2

b. Cooper-Jacob method. The Cooper-Jacobmethod, developed by C. E. Jacob and H. H. Cooper in1946, simplifies the Theis method. This method usesthe fact that after a sufficiently long pumping time or ata sufficient distance from the well, the test data tend toform a straight line when plotted on a semilog scale.The slope of the line formed allows the calculation oftransmissivity (T) and storativity (S). The key addi-tional assumption in the Cooper-Jacob method is that it

T' 2.3Q4B)s

S'2.25Tt0

r 2

T' 2.3Q2B)s

S' 2.25Tt

r 20

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D-5

is only applicable to that portion of the cone of wheredepression where steady-state conditions prevail, or tothe entire cone only after steady-state conditions have Q = pumping rate [L /T]developed. This assumption is necessary because aftersteady-state conditions have developed, the drawdowns t = time at which the drawdowns were measuredat an observation well begin to fall along a straight line [T]on a semi-log graph. The slope and zero drawdown lineintercept of this line can be entered into the following )s = drawdown across one log cycle [L]analytical equations:

r = radial distance from the pumping well to the

(D-8)

(D-9)

where


)s = drawdown across one log cycle [L]

t = time at the point where a straight line0

intersects the zero-drawdown line [T]

r = distance from the pumping well to theobservation well [L]

c. Distance-drawdown analysis. In the Jacobdistance-drawdown method, drawdowns at a specificmoment, from at least three observation wells located atdifferent distances from the pumping well are plotted ona drawdown (arithmetic) and distance (logarithmic)axis. If the Theis assumptions and Jacob limitations aresatisfied, a straight line will be produced. The slope ofthis line is proportional to transmissivity and pumpingrate. Storativity can then be computed as a function oftransmissivity, time, and the value of the intercept at thepoint of zero drawdown.

(D-10)

(D-11)

3

0

point where there is zero drawdown [L]

d. Corrections for partial penetration. As previ-ously stated, the Theis method assumes that pumpingwells fully penetrate the aquifer and all releases fromstorage are derived directly and solely from the aquiferbeing pumped. Partial penetration of the well into theaquifer causes vertical gradients of head to occur.These vertical gradients in the vicinity of the well vio-late a main assumption inherent in the fully penetratingwell solution. When the well only partially penetratesthe aquifer, the average flow path length is increased sothat a greater resistance to flow is encountered. Therelationship between flow Q and drawdown s betweenthe partially penetrating (subscript p) and fully penetra-ting well is: if Q = Q, then s > s; and if s = s, thenp p p

Q < Q. The effect of partial penetration is negligiblep

on the flow pattern and drawdown if the radial distancefrom the well to a point is greater than 7.5 times thesaturated thickness b of the aquifer.

e. Vertical leakance. In the development of theTheis equation for the analysis of pumping-test data, itwas assumed that all water discharged from a pumpingwell was derived instantaneously from storage in theaquifer. Therefore, in the case of a confined aquifer, atleast during the period of the test, the flow of wateracross the confining beds is considered negligible. Thisassumption is often valid for many confined aquifers.Many other aquifers, however, are bound by leaky con-fining beds which transmit water to the well other thanthat specified by the Theis equation. The analysis ofaquifer tests conducted in these environments requiresthe implementation of algorithms that have been devel-oped for semi-confined aquifers.

EM 1110-2-142128 Feb 99

D-6

f. References. The previously mentioned reader obtain a text such as Dawson and Istok (1991),methods of analysis cover only a small fraction of the Driscoll (1986), Kruseman and DeRidder (1983), andanalytical methods available for a wide range of Walton (1987) for a comprehensive treatment of thegeologic/aquifer settings. It is recommended that the subject matter.

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