Technical feasibility of centrifugal techniques for evaluating hazardous waste migration

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Technical feasibility of centrifugal techniques for evaluating hazardous waste migration
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Thesis (Ph. D.)--University of Florida, 1986.
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Includes bibliographical references (leaves 112-116).
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by Gary F.E. Goforth.
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Vita.

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TECHNICAL FEASIBILITY OF CENTRIFUGAL TECHNIQUES
FOR EVALUATING HAZARDOUS WASTE MIGRATION














By

Gary F. E. Goforth


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1986















ACKNOWLEDGEMENTS


I am grateful to each member of my research committee for their

individual contributions. The guidance and support over the past 5

years of Drs. Jim Heaney and Wayne Huber have been very helpful to my

professional and academic career development. The enthusiasm and

direction provided by Dr. Frank Townsend during the day-to-day

adventures in the laboratory were instrumental in the success of this

project. The resources and experiences of Drs. Dinesh Shah and Jim

Davidson were called upon and generously provided during the course of

this inter-disciplinary research project.

Comments and suggestions of numerous individuals at the University

of Florida have contributed to this project and are collectively

acknowledged and appreciated. Dr. Siresh Rao furnished valuable

information on contaminant migration as well as imparted natural

enthusiasm for research. The experience and assistance of Dr. Dave

Bloomquist was invaluable in resolving daily mechanical and design

problems. The ideas and laboratory assistance provided by Rob Vicevich

are appreciated. The guidance of Pete Michel in the Engineering Machine

Shop was indispensable during the fabrication of the permeameters.

The continual encouragement from my entire family is sincerely

appreciated. I am especially indebted to my wife, Karen, for all the

sacrifices she has made during the course of this research, as well as

for preparation of the manuscript.









This investigation was part of the University of Florida research

project No. 124504050, funded by the U. S. Air Force, Capt. Richard

Ashworth, Ph.D., Technical Officer and Dr. Paul Thompson, Project

Manager, Engineering Services Center, Tyndall Air Force Base, Florida.

The support of the Water Resources Engineering Group, directed by

Dr. Michael Palermo, of the U. S. Army Engineer Waterways Experiment

Station, Vicksburg, Mississippi, is greatly appreciated.
















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS . ... . ii

LIST OF TABLES . .... . vi

LIST OF FIGURES . .... .. ..... vii

KEY TO SYMBOLS USED IN TEXT . .... ix

ABSTRACT . .. . .. x

CHAPTERS

I INTRODUCTION . .... .. .. 1

Scope . . . 1
Objectives . . .. 2

II BACKGROUND .... .. . .. 5

Contaminant Migration . .. .. .. 5
Advection ...... .. ........... 10
Flow in Unsaturated Media ................. 14
Immiscible Fluid Flow . . 17
Methods of Prediction . .... .. 19

III CENTRIFUGE THEORY . .... .. ... 25

Historical Use of Centrifugation . .. ... 25
University of Florida Centrifuge Equipment ... 31
Fluid Mechanics and Hydraulics in a Centrifuge 31
Dimensional Analysis . .... 43

IV TESTING PROGRAM . ......... 46

Objectives . . .. .. 46
Materials . . . 48
Testing Equipment . ..... .. .. 53
Bench Testing Procedures . ... .. .... 66
Centrifuge Testing Procedures . .... ... 68
Unsaturated Testing . . .. 69
Data Analysis .. . . 77









V RESULTS AND DISCUSSION . . ... 84

Saturated Hydraulic Conductivity Tests .... .85
Unsaturated Soil Tests . . ... 100
Discussion . . .. 105

VI CONCLUSIONS . . ... ...... 107

VII RECOMMENDATIONS ....................... 111

REFERENCES . . . .. 112

APPENDIX DERIVATION OF VARIABLE HEAD PERMEABILITY EQUATIONS 117

BIOGRAPHICAL SKETCH . . ... .122















LIST OF TABLES


Table Page

1. Classification of the Top 216 Installation Restoration
Program Sites by Type of Waste Area . 2

2. Fundamental Relationships Between the Potential Gradient and
Hydraulic Conductivity .... . 12

3. Field Methods of Estimating Hydraulic Conductivity .. 21

4. Laboratory Methods of Estimating Hydraulic Conductivity 22

5. Advantages of Centrifugal Modeling. . ... 33

6. Limitations of Centrifugal Modeling . .... .33

7. Summary of Scaling Relationships for Centrifugal Modeling 45

8. Summary of Permeability Testing Matrix . .... 47

9. Comparison Between Properties of JP-4, Decane and Water 49

10. Characteristics of the Sand Used in the Testing Program 51

11. Characteristics of the Clay Used in the Testing Program 52

12. Evaluation of Laboratory Tests for Determining Unsaturated
Hydraulic Conductivity ... .. . 70

13. Summary of Simulated Drainage Test Results ... .105















LIST OF FIGURES


Figure Page

1. Flow Pattern of a Soluble Contaminant Beneath a Waste Source 7

2. Transport Processes of a Soluble Contaminant Within a Soil
Volume . ............ 8

3. Radial Movement of Moisture in a Uniformly Dry Soil 16

4. Flow Pattern of an Insoluble Contaminant Beneath a Waste
Source . .... . . 18

5. Number of Journal Articles on Centrifuge Applications .... 32

6. Schematic of the U. F. Geotechnical Centrifuge ... 34

7. Photograph of the U. F. Geotechnical Centrifuge ... 35

8. Definition Sketch for Analysis of Forces Acting on a Fluid
Volume in a Centrifuge .... . 37

9. Hydrostatic Equilibrium in the Centrifuge .... .40

10. Definition Sketch of Soil Volume in a Centrifuge ... 41

11. Moisture Retention Curves for the Sand, Sand/Clay and Clay
Samples . .... . .. 54

12. Photograph of a Commercial Triaxial Apparatus ... 56

13. Comparison of Confining Stress Profiles . .... 58

14. Schematic of Apparatus Used in the Saturated Hydraulic
Conductivity Tests . .... . 61

15. Photograph of the Saturated Conductivity Apparatus Attached to
the Centrifuge Arm a) Front View; b) Rear View ...... 62

16. Time History of the Suction Gradient During Drainage Test 74

17. Schematic of the Proposed Test Apparatus for the Instantaneous
Profile Method. ... . 76

18. Definition Sketch for the Variable Head Permeability Equation -
Bench Test . .... .. . 79









19. Definition Sketch for the Variable Head Permeability Equation -
Centrifuge Test . .. . .. 81

20. Hydraulic Energy Profile During the Variable Head Test 86

21. Permeability of Water Through Sand as a Function of Pore
Volume . . ... ..... 88

22. Permeability of Water Through Sand as a Function of Initial
Gradient . . ... ... 88

23. Comparison of Centrifuge and Bench Results of Permeability of
Water through Sand . .... ..... 89

24. Comparison of Centrifuge and Bench Results of Permeability of
Decane through Sand . . ... 91

25. Permeability of Decane Through Sand as a Function of Initial
Gradient . ... ... 91

26. Comparison of Centrifuge and Bench Results of Permeability of
Water through Sand/Clay . .... 93

27. Comparison of Permeability of Water Through Sand/Clay as a
Function of Acceleration Level . .. 93

28. Comparison of the Permeabilities of Decane and Water Through
Sand/Clay a) Sample 1; b) Sample 2 . .... 94

29. Permeability of Decane Through Sand/Clay as a Function of
Initial Gradient a) Sample 1; b) Sample 2 ... 96

30. Comparison of the Permeabilities of Decane and Water Through
Clay; Initial Water Content 29% a) Sample 1; b) Sample 2 98

31. Comparison of the Permeabilities of Decane and Water Through
Clay; Initial Water Content 327 a) Sample 1; b) Sample 2 99

32. Characteristics of the Sand Used in the Drainage Simulations
a) Hydraulic Conductivity; b) Moisture Retention
Characteristic . . ... ..... 102

33. Comparison of Drainage Sequence in a Soil Sample a) Bench
Simulation Results; b) Centrifuge Simulation Results .... .103

34. Comparison of the Pressure Profiles in a Soil Sample a) Bench
Simulation Results; b) Centrifuge Simulation Results .... .104


viii
















KEY TO SYMBOLS USED IN TEXT


ar
A,a
b
C
c
D
d
f
g
H
HL
ha
J
K
k
L
M
N
n
e
P


Pe
q
Re
r
S
a
t
u
V
v
w
X
z


acceleration acting on control mass
cross-sectional area
contact angle
solute concentration
minor energy loss coefficient
hydrodynamic dispersion coefficient
representative length
friction factor
acceleration due to gravity
total hydraulic energy
energy loss between two points
air entry pressure
convective-dispersive solute flux
hydraulic conductivity
intrinsic permeability
representative length
representative mass
ratio of model to prototype acceleration
nominal porosity of soil
volumetric water content
pressure
mass density
Peclet number
specific discharge
Reynolds number
representative radius
sum of source/sink components
surface tension
representative time
dynamic (absolute) viscosity
average fluid velocity
kinematic viscosity
angular velocity
ratio of prototype to model length
representative elevation


(L/T2)
(L2)
(rad)
(M/L2)
dimensionlesss)
(L2/T)
(L)
dimensionlesss)
(L/T2)



(L)
(M/L2T)

(L2)
(L)
(M)
dimensionlesss)
dimensionlesss)
(L3/L3)
(M/LT2)
(M/L3)
dimensionlesss)
(L/T)
dimensionlesss)
(L)
(M/L2T)
(M/T2)
(T)
(M/TL)
(L/T)
(L2/T)
(rad/T)
dimensionlesss)
(L)
















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


TECHNICAL FEASIBILITY OF CENTRIFUGAL TECHNIQUES
FOR EVALUATING HAZARDOUS WASTE MIGRATION

By

Gary F. E. Goforth

May 1986


Chairman: Dr. James P. Heaney
Cochairman: Dr. Frank C. Townsend
Major Department: Environmental Engineering Sciences



This study was designed and executed to assess the technical

feasibility of using centrifugal techniques to predict the transport

characteristics of hazardous waste through soil. Advection is generally

the major mechanism of contaminant migration from a waste source. For

soluble contaminants, advection occurs within the aqueous phase. For

immiscible fluid contaminants, such as the jet fuel JP-4, migration

rates are often independent of the rates of water movement. Advection in

saturated and unsaturated soils can be predicted from physical models or

from measurements of the hydraulic conductivity in conjunction with

knowledge of existing hydraulic gradients.

A flexible wall permeameter was designed and utilized for

determining saturated hydraulic conductivity of soil samples in the

centrifuge and on the laboratory bench. Fundamental relationships of









hydrodynamic pressure distribution and fluid kinematics within a soil

volume undergoing radial acceleration were derived and verified during

the study. Reagent grade decane was utilized as a surrogate for JP-4

jet fuel. Estimates of the hydraulic conductivity for water and decane

were obtained in sand, sand/clay and 100 percent kaolinite samples.

Testing conducted in the centrifuge reproduced bench test results,

including the deviation from Darcy's law observed in the sand samples

above a gradient of ten. A possible benefit of centrifugal techniques

for saturated soils was the more accurate reproduction of soil stresses

within the sample.

Several laboratory techniques to determine the unsaturated

hydraulic conductivity as a function of soil moisture content were

evaluated. The instantaneous profile method (IPM) was selected as the

technique which would be most conducive to adaptation for use in the

centrifuge. An apparatus was designed and fabricated for conducting the

IPM tests on the laboratory bench and in the centrifuge. Computer

results indicated that a significant decrease in the testing time and a

greater range of moisture contents can be realized by conducting the IPM

test in the centrifuge. However, the use of the centrifuge for

physical modeling of unsaturated phenomena, such as leachate from a

waste pit, offers no advantage over laboratory bench models because of

the dominance of soil moisture suction gradients over gravity gradients

in unsaturated soils.














CHAPTER I
INTRODUCTION


Scope

The assessment of local and regional impacts on groundwater

resources due to leachate of hazardous wastes from confined disposal

areas and accidental spills necessitates the prediction of contaminant

migration. In general, either a physical or numerical model can be

applied to depict the mass transport phenomena.

Tyndall Air Force Base was considering the construction of a

large-scale centrifuge for structural, geotechnical and environmental

research applications. The U.S. Department of Defense Installation and

Restoration Program has identified over 200 high priority hazardous

waste sites at Air Force facilities which require mitigative measures

(Heaney, 1984). Categories of waste sources are presented in Table 1.

Of significant concern is the transport characteristics of jet fuel JP-4

through soil. A laboratory research study was designed and executed to

evaluate the feasibility of using centrifugal techniques to determine

hazardous waste migration characteristics. The utilization of a

centrifuge may offer several advantages over traditional physical

modeling apparatus as well as provide the dual capability of performing

as a laboratory instrument capable of testing material properties. The

centrifugal techniques were evaluated on the following criteria:

1. Can they significantly shorten the testing period?

2. Can they reduce the uncertainty associated with estimates of








Table 1. Classification of the Top 216 Installation
Restoration Program Sites by Type of Waste Area

Type of Waste Area Number in Percent in
Top 216 Top 216


Landfills 61 28.2

Surface impoundments, lagoons,
beds and waste pits 57 26.4

Leaks and spills 43 19.9

Fire training areas 28 13.0

Drainage areas 16 7.4

Other 11 5.1

TOTAL 216 100.0

Source: Heaney, 1984


hydraulic conductivity of soil samples?

3. How do the costs compare with conventional techniques?


Objectives

The objective of this study was to assess the technical feasibility

of using a large-scale centrifuge for determining migration rates and

characteristics of hazardous wastes. Centrifugal techniques for

evaluating hazardous waste migration include physical modeling and

material properties testing. While physical modeling has been

successfully conducted under l-g conditions on the laboratory bench,

gravity-dominated phenomena can be accelerated within a centrifuge,

thereby providing an additional scaling factor and attendant reduction

in testing time. Several geotechnical applications have demonstrated the

feasibility of centrifugal modeling for such gravity-dominated phenomena

as sedimentation and consolidation (Bloomquist and Townsend, 1984;









Mikasa and Takada, 1984). An additional advantage of centrifugal

modeling is the accurate reproduction of effective stresses in the

scaled down soil profile as a result of the greater acceleration force

acting on the soil particles. To fully utilize the potential of physical

modeling in the centrifuge, the fundamental relationships of radial

acceleration, hydraulic pressures and pore fluid kinematics within the

centrifuge soil sample needed to be developed and verified. The

execution of concurrent bench and centrifuge hydraulic conductivity

testing provided the opportunity to investigate these fundamental fluid

flow properties as well as allowed the direct assessment of the

feasibility of material properties testing within the centrifuge. The

objective of the laboratory research program was to develop centrifugal

testing methods for determining saturated and unsaturated hydraulic

conductivity of soil samples. The testing program encompassed

1. design, fabrication and analysis of permeameters for use in the

centrifuge;

2. execution of hydraulic conductivity tests in a 1-g environment

to provide a benchmark to compare centrifuge results;

3. derivation of the appropriate equations of motion for fluid flow

in a centrifuge;

4. execution of hydraulic conductivity tests in the centrifuge at

various accelerations;

5. comparison of centrifuge results with 1-g test result; and

6. (if necessary) modification of the centrifuge device, testing

procedures and/or data analysis based on results of the comparison.

A secondary goal of the project was to establish the theoretical and

practical operating limits of centrifugal techniques. The flow and





4


storage characteristics of commercially available n-decane were

evaluated during the course of this study as a surrogate for JP-4.

Results of the testing program will serve as the foundation for

subsequent research in the area of centrifugal modeling of hazardous

waste migration.















CHAPTER II
BACKGROUND


Contaminant Migration

Predicting the migration of jet fuel and its derivatives from

storage areas is a challenging problem. Fluid flow will occur in both

partially saturated and fully saturated soil. Material storage and

transport can be dominated by either the lateral movement of vapors

(Reichmuth, 1984), the advection and dispersion of soluble fractions

within percolating water (Schwille, 1984), interfacial phenomena

occurring between the fuel and the soil matrix, e.g., adsorption and

biodegradation (Borden et al., 1984) or a variety of theological

phenomena associated with multiple phase (e.g, air-water-oil) flow

systems, including the pure advection of the water insoluble fractions.

The cumulative mass transport from the waste source to the water

table and/or a downstream water resource is sensitive to site-specific

advective, dispersive and reactive properties of the soil-fluid system.

In lieu of collecting extensive site-specific data to describe the

transport phenomena, a conservative estimate is often initially

presented which considers only advective transport. The efforts of the

current study are hence directed at techniques for estimating the

advective properties of jet fuel in unsaturated and saturated soil.

Contaminant migration within the soil profile is a complex

phenomenon, reflecting the chemical diversity of contaminants as well as

the variety and heterogeneity of the geohydrologic regimes and soil








matrices encountered. Nonetheless, predictions of the travel rates and

directions of contaminant movement can be formalized based on

generalized transport phenomena. The movement of a soluble contaminant

will in general be governed by the flux of water through the soil

profile. Below a disposal area this fluid movement may resemble the

pattern depicted in Figure 1. Figure 2 presents a schematic of a porous

soil volume through which a solute is passing. Basically, four

fundamental transport phenomena account for all significant movement of

a solute within a soil profile:

1. Advection refers to the movement of a solute by virtue of its

entrainment within the bulk fluid.

2. Mechanical dispersion is the flux of a solute which results from

nonuniform pore fluid velocities, i.e., due to flow path tortuosity

and dead-end channels, the velocities within typical soil volumes

are not uniformly distributed.

3. Molecular diffusion is the movement of a solute solely on the basis

of concentration gradients. Because of their similar influence on

solute movement, mechanical dispersion and molecular diffusion are

often represented by a single term referred to as hydrodynamic

dispersion.

4. Source/sink phenomena, including adsorption. Adsorption phenomena

encompass a variety of interactions of the solute with the surfaces

of the soil matrix. Source/sink phenomena are influenced by many

factors, including soil and bulk fluid pH, the ionic nature of the

soil and solute, and the surface characteristics of the soil.

These phenomena are significant to varying degrees, entirely specific to

the site characteristics. For example, in the transport of




























































Figure 1. Flow Pattern of a Soluble Contaminant Beneath a Waste Source































-
-- 3 --












LEGEND
1. ADVECTION
2. MECHANICAL DISPERSION
3. MOLECULAR DIFFUSION
4. ADSORPTION PHENOMENA









Figure 2. Transport Processes of a Soluble Contaminant Within a Soil
Volume








a low concentration of a nonionic compound through uniformly graded

coarse sand, the advection term would dominate the material transport;

molecular diffusion would be insignificant due to relatively large pore

fluid velocities and the small concentration gradients of the solute;

adsorption phenomena may also be insignificant due to the relatively

large advection component, nonionic nature of the solute and small

specific surface area of the soil. At the other extreme, the movement

of a high concentration of a cationic solute through a thick clay

landfill liner would be governed less by advection and more by

adsorption and diffusion phenomena. The mass transport of a contaminant

can be expressed quantitatively as a composite of these elements

(Davidson et al., 1983)

J = -D 0 dC + qC + S (1)
dz

where J = convective-dispersive solute flux per unit cross-sectional
area (M/L2T);

D = hydrodynamic dispersion coefficient (L2/T);

e = volumetric soil water content (L3/L3);

dC = solute concentration gradient in the z direction (M/L4);
dz
q specific discharge, i.e., the volumetric discharge of bulk
fluid per unit cross-sectional area (L/T);

C = solute concentration (M/L3); and

S = sum of the source/sink components (M/L2T).

The advective component, qC, can be further expanded as

qC = C [-K(e) dH] (2)
dz
where K(e) hydraulic conductivity, which is dependent on the water
content; and

dH E hydraulic potential gradient in the z direction
dz

which explicitly relates the mass transport of a solute to the hydraulic










conductivity and the gradient. In addition, the magnitude of the

hydraulic conductivity is important not only for the advection of a

solute but also for the kinetics of the other components as well. The

hydrodynamic dispersion coefficient in most natural soils with uniform

porosities is dependent on the pore fluid velocity as is the reaction

time for adsorption and other source/sink phenomena (Rao and Jessup,

1983). The relative magnitudes of the transport phenomena can be

expressed by the Peclet number, Pe, a dimensionless quantity defined as

(Bear, 1972)

Pe = qL/eD (3)

where L = representative length. During flow conditions at low Peclet

numbers, the dispersion and diffusion phenomena dominate the transport

process, while advection dominates solute migration under flow

conditions with high Peclet numbers. However, to assess the relative

significance of each term, the influential parameters of the solute,

soil matrix and extant geohydrologic regimes must be evaluated. The

geohydrologic regime of a particular site may be saturated, unsaturated

or some heterogeneous combination. In turn, the character and

significance of each component of the material transport phenomena is

highly influenced by this regime.


Advection

In many cases of pollutant transport, consideration of downstream

risks requires that conservative estimates of travel time through the

medium in question be obtained. In a soil matrix, this conservative

value of contaminant migration is generally the advection term and is

estimated from the saturated hydraulic conductivity of the soil, which








may be three to five orders of magnitude greater than the hydraulic

conductivity of the unsaturated soil at its average moisture content.

However, for engineering design purposes, the average value of the

hydraulic conductivity may be desired, as there may be tremendous

differences in control technologies and economics compared to solutions

using the saturated values.

The rate of bulk fluid movement through the soil profile is the

most fundamental process affecting the migration of soluble or

immiscible contaminants. A fluid moves through the soil matrix in

response to hydraulic energy (potential) gradients. The hydraulic

potential of fluid in the pores of a soil volume has been defined as the

amount of work necessary to transport, reversibly and isothermally, a

volume of pure water from an external reservoir at a known elevation to

the soil volume at a known location and pressure. While the validity of

this definition has been debated, it does convey the fundamental

concepts of hydraulic energy of pore fluid. The flux of fluid through a

soil volume, whether saturated or unsaturated, is proportional to the

existing potential gradient, as stated by Darcy's law, written in one

dimension as

q = -K (dH/dz) (4)

where q = specific discharge, defined as the volume of fluid
passing through a unit area of soil in a unit time (L/T).

The terms hydraulic conductivity and permeability are often used

interchangeably, reflecting the broad range of disciplines which employ

the parameter. The term hydraulic conductivity will be used throughout

this text when referring to the constant of proportionality between the

total hydraulic potential gradient and the specific discharge.









The gradient of the total hydraulic potential provides the driving

force for water movement in soils. The total potential energy can be

expressed on the basis of energy per unit weight, defined as the

hydraulic potential, or head, which has the dimension of length. The

potential energy can also be expressed as energy per unit volume,

defined as the pressure potential, with the dimensions M/LT2; or as

energy per unit mass, defined as the specific energy potential, with the

dimensions L2/T2. The units of hydraulic conductivity must be

dimensionally consistent with the potential energy term; Table 2

summarizes these relationships.


Table 2. Fundamental Relationships Between the Potential
Gradient and Hydraulic Conductivity

Potential Dimensions Example
Gradient of K of K


Hydraulic Potential /T cm/s
Pressure Potential L /M cm2s/g
Specific Energy Potential T sec



Darcy's original work employed the dimension of length for the

hydraulic potential (Darcy, 1856). As a consequence, the dimensions of

the potential gradient were length per unit length and the dimensions of

the hydraulic conductivity were length per time, later expressed as a

function of both the bulk fluid and the soil media (Bear, 1979)

K kg / v (5)

where k = intrinsic permeability of the medium (L2)

g = acceleration due to gravity acting on the fluid (L/T2);
and

v = kinematic viscosity of the fluid (L2/L).

The influence of acceleration due to gravity can be separated by










employing the dimensions of the specific energy potential. The

resulting coefficient of proportionality has the dimension of time, and

still preserves the direct relation between the properties of the medium

and fluid. Accordingly, equation 5 can be modified as

K k / v (6)

Based on this relationship, the hydraulic conductivity, and hence flow

rates, of various bulk fluids in a similar medium theoretically can be

determined from the fluid's kinematic viscosity. This principle is

relevant in predicting the bulk transport of nonaqueous fluids as well

as the advection of solutes in aqueous flow. However, this extrapolation

is based on the implicit condition that chemical interactions between

the bulk fluid and the soil matrix would not alter the intrinsic

permeability. In fact, in investigations of contaminant migration the

solution properties and surface chemistry of the solute and soil need to

be examined. Numerous studies have documented increases or decreases in

the hydraulic conductivity beyond that suggested by equation 5 (Gordon

and Forrest, 1981; Brown et al., 1984). For example, one study reported

an increase in conductivity of three orders of magnitude with the

addition of gasoline to water in a clay soil (Brown et al., 1984). The

viscosity of gasoline is approximately one half that of water, so a two-

fold increase in the conductivity was expected from equation 5. The

tremendous increase was attributed to the surface chemistry properties

of the water/gasoline/clay system. The gasoline apparently displaced

the water molecules separating the clay sheets which in turn created

numerous cracks through which the fluid passed more readily.

Darcy's law is generally regarded as valid in laminar flow ranges,

that is, where viscous forces predominate over inertial forces acting on










the fluid. By analogy to open channel hydraulics, a Reynolds number,

Re, has been defined for flow through porous media as (Bear, 1979)

Re = q d /v (7)

where d = representative length of the porous matrix (L). Often d is

taken as either the mean grain diameter or the diameter such that 10

percent by weight are smaller. Experimental evidence suggests that

Darcy's law becomes invalid at some point in the range of Re between 1

and 10 (Bear, 1979).


Flow in Unsaturated Media

The infiltration of leachate from a waste storage pond, an

accidental spill or other source will generally encounter unsaturated

soil directly below the site. As is the case in saturated media,

hydraulic potential gradients determine the flow conditions in

unsaturated soils. The unsaturated hydraulic gradient is composed of

similar components such as pressure potential and gravitational

potential; also, thermal gradients can exist which influence fluid

movement. However, unlike the positive pressures acting on pore fluid

in saturated media, pressures which are less than atmospheric are

exerted on fluid volumes within unsaturated soil. By convention these

pressures are considered negative, and the positive (in sign) terms soil

moisture suction and matric potential are widely used. Soil suction

increases rapidly as the pore water content decreases. The relationship

between soil suction and water content is referred to as a moisture

retention curve and exhibits a hysteretic effect between the wetting

imbibitionn) and desorption (drainage) paths. In association with the

wide range of moisture contents and cycles of imbibition and drainage,









the hydraulic gradient in the unsaturated zone can be dominated by any

one of the components during specific flow conditions.

As the soil dries, the influence of gravity on the movement of pore

fluid decreases. For the majority of the time fluid flux in natural

soils is dominated by suction gradients, which can typically be 1000 to

10,000 times greater than the gradient due to gravity (Hillel, 1982). In

a uniformly dry soil, water movement below an influent source will occur

in a radial pattern, as in Figure 3, demonstrating the negligible

influence of gravity. Thus, in the scenario of percolation of leachate

from a hazardous waste site overlaying an unsaturated soil profile, the

movement of fluid will be dominated by the soil suction gradients.

Another consequence of decreasing soil moisture content as the soil

dries out is the attendant decrease in the hydraulic conductivity.

Reductions of up to five orders of magnitude from the saturated

hydraulic conductivity value have been documented (Hillel, 1982). This

reduction may be attributed to several phenomena: (1) the first pores

to empty are the larger ones which offer the least flow resistance; (2)

as the center of the pores lose water first, the adsorption influence of

the soil particles on the water film further increases the resistance

to flow; (3) the tortuosity of the flow paths increases as the pores

drain; and (4) the total cross-sectional area of flow decreases, thereby

requiring a larger gradient to maintain a given specific discharge.












WATER SOURCE



I


Figure 3. Radial Movement of Moisture in a Uniformly Dry Soil











Immiscible Fluid Flow

Two fluids are mutually immiscible if their solubility in the other

is very low. Decane and JP-4 jet fuel are immiscible in water; decane

has a solubility of 0.009 mg/l at 200C. The movement of these fluids

through soil, as depicted in Figure 4, is vastly different than the

transport of a soluble contaminant. The advection and hydrodynamic

dispersion within the water phase are negligible due to their limited

solubility. In soils that are initially water-saturated, insoluble

wastes must displace extant water from soil pores in order to migrate

through the voids. The energy required to displace the existing liquid

from the pores is termed the interfacial energy (Adamson, 1982). An

analogous situation occurs when saturating a porous media (e.g., a

porous stone) originally filled with air. In that case, the interfacial

energy is commonly expressed as the air entry pressure or bubble

pressure (Brooks and Corey, 1964). The magnitude of the interfacial

energy is inversely proportional to the diameters of the pore, or

(Adamson, 1982)

ha = 2 s cos(b) /(dp r g) (8)

where ha = air entry pressure (L);

s = surface tension (M/T2);

b = contact angle (rad);

dp = difference in fluid densities (M/L3); and

r = radius of the pores (L).

For flow to occur, the hydraulic energy gradient across a sample must be

sufficient to satisfy the interfacial energy requirements. The smaller

the soil pores, the greater the driving force required to displace the

water.





























































Flow Pattern of an Insoluble Contaminant Beneath a Waste Source


Figure 4.








In unsaturated soil, a three-phase flow system exists, composed of

air, water and the immiscible fluid. The movement of each fluid occurs

only after the volume of that fluid attains a minimum value, referred

to as the residual saturation. The residual saturation is specific to

the fluid and soil type. Most components of JP-4 are less dense than

water; hence, any of these lighter fluids which reaches the water table

will spread on the surface. The travel distance is limited by the

residual saturation flow requirement. Migration into and along with the

surficial aquifer fluid will be limited by the solubility of the various

fractional components of JP-4.


Methods of Prediction

A wide variety of analytical, numerical and physical techniques

have been developed to predict hazardous waste transport (Anderson-

Nichols, 1984). In all cases, an estimate of the hydraulic conductivity

is paramount to estimating the migration rate of a material through the

soil. Literature from soil physics, groundwater hydraulics,

geohydrology and geotechnical engineering publications was reviewed to

provide a comprehensive information base of field and laboratory methods

used to estimate hydraulic conductivity. In general, all the lab tests

provide an estimate of hydraulic conductivity for one-dimensional flow,

whereas field conditions are often two- or three-dimensional.


Field Tests

Field tests are often preferred over laboratory tests for saturated

soils because they generally utilize a larger volume of soil, which

includes the effects of the soil macrostructure, e.g., worm holes, roots

and fissures, which contribute to the overall anisotropy of the flow









region. Field tests also are generally designed to account for three-

dimensional flow. Discrepancies of three orders of magnitude have been

observed between field and laboratory tests (Day and Daniel, 1985). A

summary of field methods for measuring hydraulic conductivity is

presented in Table 3.


Laboratory Tests

Laboratory tests can be conducted to determine the physical and

chemical properties of the soil medium and the contaminant. These data

can be used in subsequent analysis of migration rates and/or evaluation

of appropriate mitigative measures. In the classical treatment of a soil

volume as a physical continuum, the concept of a representative

elementary volume (REV) emerges when conducting laboratory tests. The

REV is defined as the smallest volume of soil which accurately

characterizes the extrinsic and intrinsic variability of the parameter

in question. A summary of laboratory techniques for determining the

hydraulic conductivity of a soil specimen is presented in Table 4.


Saturated hydraulic conductivity tests

Laboratory procedures for determining saturated hydraulic

conductivity of soil specimens have been standardized by several

organizations. The American Society for Testing Materials (ASTM), the

U. S. Geological Survey (USGS), the U. S. Army Corps of Engineers

(USCOE) and others have documented techniques for specific soil types.

The principle of the test has remained essentially unchanged from the

famous Dijon, France sand filter experiments conducted by Henri Darcy in

1855. However, the apparatus used to conduct the test has been modified









Table 3. Field Methods of Estimating Hydraulic Conductivity
Physical Moisture
Method Scale Content Reference(s)
Range

Unsteady Flow Tests


1. Instantaneous Point
Profile


2. Theta method Point


3. Flux method Point


4. Pump test Regional
nonsteady flow

5. Double tube Point
method

6. Auger hole Point


7. Piezometer Point
method

Steady Flux Tests

8. Crust- Point
imposed flux

9. Sprinkler- Point
imposed flux

10. Tracer Field
transport

11. Double-ring Point
infiltrometer

12. Pump test Regional
steady flow

13. Dry auger Point
hole method

14. Carved Point
column

15. Permeameter Point
method


Moist to
saturated


Moist to
saturated

Moist to
saturated

Unconfined
aquifer

Saturated


Saturated


Saturated




Moist to
saturated

Moist to
saturated

Saturated


Saturated


Unconfined
aquifer

Saturated


Saturated


Saturated


Green et al., 1983
Dane and Hruska, 1983
Chong et al., 1981

Libardi et al., 1980
Jones and Wagenet, 1984

Libardi et al., 1980
Jones and Wagenet, 1984

Bear, 1979


Bouma et al., 1982
USGS, 1982

Bouma et al., 1982
USGS, 1982

Boersma, 1965b
USGS, 1982



Green et al., 1983


Green et al., 1983


Bear, 1979


Chong et al., 1981


Bear, 1979


Boersma, 1965a
Bouma et al., 1982

Bouma et al., 1982


Boersma, 1965a









Table 4. Laboratory Methods of Estimating Hydraulic
Conductivity
Flow Moisture
Method Condition Content Reference(s)
Range


Constant head
permeameter

Falling head
permeameter

Triaxial
cell test

Low-gradient
constant flux

Constant
pressure

Method of
van Genuchten

Outflow
method

Centrifuge
balance

Steady flux


Pressurized
steady flux

Consolidation
testing

Instantaneous
profile

Crust-
imposed flux

Sprinkler-
imposed flux

Centrifuge
flow through


Steady


Unsteady


Unsteady


Steady


Steady


Unsteady


Unsteady


Unsteady


Steady


Steady


Unsteady


Unsteady


Steady


Steady


Unsteady


Saturated


Saturated


Saturated


Saturated


Moist to
saturated

Moist to
saturated

Moist to
saturated

Moist to
saturated

Moist to
saturated

Moist to
saturated

Saturated


Moist to
saturated

Moist to
saturated

Moist to
saturated

Moist to
saturated


ASTM, 1974
Olson and Daniel, 1981

Bear, 1972
Olson and Daniel, 1981

Edil and Erickon, 1985
USAEWES, 1970

Olsen, 1966


Olson and Daniel, 1981


Dane, 1980


Kirkham and Powers, 1972


Alemi et al., 1976


Klute, 1965a


Klute, 1965a


Cargill, 1985
Znidarcic, 1982

Olson and Daniel, 1981


Green et al., 1983
Dunn, 1983

Dunn, 1983
Green et al., 1983

This study









as appropriate to test a wide range of soil specimens under a variety of

soil stress conditions.

Permeameters in general consist of a sample cell, a fluid conduit

system and may or may not incorporate a pressurized air system. The

sample cell can be a rigid vall container; however, to prevent short

circuiting of permeant along the wall of the sample container, some

sample cells utilize a flexible membrane in association with an applied

external pressure.


Unsaturated hydraulic conductivity tests

In contrast to the numerous techniques and apparatus available to

conduct a saturated hydraulic conductivity test, only a few methods

exist for determining the relationship between hydraulic conductivity

and water contents below saturation. However, this is commensurate

with the commercial demand for such methodology. For many engineering

purposes, including many aspects of contaminant migration, the highest

rate of flux is of concern; for these applications the saturated

hydraulic conductivity tests are appropriate.

A variety of techniques have been developed for estimating

unsaturated hydraulic conductivity. Along with steady flow tests,

transient flow methods have been developed which yield estimates of

unsaturated hydraulic conductivity over a range of moisture contents.

Estimates can be obtained during the imbibition (wetting) and/or

desorption (drainage) cycle. As in the tests for saturated hydraulic

conductivity, these methods generally yield an estimate of hydraulic

conductivity for one-dimensional flow.

Laboratory techniques for determining unsaturated hydraulic

conductivity are preferred over field tests for several reasons (Hillel,










1982, Christiansen, 1985):

1. the flow during unsaturated conditions is dominated by the film of

water along soil particles, hence the influence of macrostructures

is much less than during saturated conditions;

2. better control of initial and boundary conditions is provided in

the lab and more sensitive measurements can be obtained, yielding

more accurate interpretation of data; and

3. lab tests are generally less expensive.


Physical Modeling

Another approach to predicting contaminant migration and

evaluating treatment alternatives is to construct a prototype of the

field site and conduct appropriate dynamic tests. The results can

subsequently be extrapolated to field conditions by use of appropriate

scaling relationships. The choices of materials and testing conditions

are governed by geometric, mechanical and dynamic similitude between the

model and field prototype.














CHAPTER III
CENTRIFUGE THEORY



Historical Use of Centrifugation

Centrifuges have been used as laboratory apparatus by soil

physicists and geotechnical engineers since the turn of the century.

Centrifugal techniques have been developed for performing physical

models of field-scale prototypes and for testing the physical properties

of materials. A brief history of centrifugal applications is presented

below; specific areas of interest include soil moisture retention, soil

moisture movement and solute transport. An overview of past and current

centrifuge projects is presented below to emphasize the wide range of

practical and research applications.


Soil Moisture Capacity

Centrifugal techniques have been developed to quantify the moisture

retention capacity of soils. Briggs and McLane (1907) presented the

development of experimental procedures and test results of a centrifugal

method for determining a soil parameter they designated as moisture

equivalent. They were after a way to quantitatively compare disturbed

soil samples and elected to compare samples on the basis of capillary

equilibrium in a sample undergoing a constant rotational velocity. The

centrifuge they designed was driven by a steam turbine and was capable

of rotating eight 0.5 cm soil samples up to 5500 rpm (approximately 3550









times the force of gravity, or 3550 g's). Their experimental assessment

included the influence of test duration, angular velocity and initial

water content on the moisture content after centrifugation. They

presented moisture equivalent values for 104 soil types.

In 1935 the American Society of Testing and Materials (ASTM)

adopted a standard test method for determining the moisture equivalent

of soils (ASTM, 1981). The moisture content of an air-dried and

reconstituted sample after centrifugation at 1000 g's for one hour was

suggested as an approximation for the air-void ratio, also referred to

as the water holding capacity or the specific retention. Additional

testing development was conducted by Johnson et al. of the U. S.

Geological Survey (1963).

Bear (1972) presented a simple method to rapidly obtain the

moisture retention curves of thin soil samples by repeated

centrifugation periods at different rotational speeds. Corey (1977)

discussed the use of gamma radiation attenuation during centrifugation

to obtain an entire segment of the moisture retention curve during the

course of a single test.


Soil Moisture Movement

Alemi et al. (1976) presented the theoretical development and

experimental design of two methods for determining the unsaturated

hydraulic conductivity of undisturbed soil cores by centrifugation. The

potential savings in time was a major advantage of the proposed method.

A closed system method was based on describing the redistribution of

moisture within a sample after centrifugation by means of the mass

shift, as detected by a pair of analytical balances. Relevant

assumptions included constant hydraulic conductivity along the sample










during redistribution and a linear relation between moisture content and

soil-water pressure head. Acceleration levels between seven and 285 g's

were imposed on a 5-cm long sample for durations of 60, 70 and 100

minutes. Estimates of conductivities from two cores of Yolo loam

compared well to field and other lab results.

Alemi et al. (1976) proposed a pressure outflow method for

determining the unsaturated hydraulic conductivity from a centrifuged

sample. Estimates of conductivity could be obtained from the record of

total outflow resulting from a specific increase in rotational velocity.

No experimental results were available to assess the method.

Cargill and Ko (1983) presented details of a centrifugal modeling

study of transient water flow in earthen embankments. The total

hydraulic head was monitored with miniature pressure transducers fitted

with porous tips. Their results suggested the movement of fines (clay

to silt grain sizes) caused anomalous increases in conductivity via

development of channelized flow paths. Comparison of centrifuge model

results with a finite element program indicated very similar heights of

the phreatic surface at the headwater end with a gradual discrepancy

toward the tailwater side of the embankment.


Solute Transport

Arulanandan et al. (1984) presented cursory details of a study

utilizing a centrifuge to execute a simple physical model of

infiltration below a ponded water surface. Breakthrough curves of

electrical resistivity in saturated sand samples were obtained under

steady water flux conditions. Acceleration levels between 1 g and 53

g's were imposed on sand samples with a saturated hydraulic conductivity









in a l-g environment of 0.01 cm/sec. A constant head was maintained

throughout the tests. The authors suggested that centrifugal modeling

"may have significant application" in determining the advective and

dispersive components of contaminant transport (1984, p. 1). However,

careful review of their testing procedure and results indicated that

only a single aspect of centrifugal techniques offers a possible

advantage over laboratory bench (i.e., l-g) physical models.

The paper described a prototype scenario of fresh water

infiltrating into a saltwater stratum of soil under a constant ponded

depth, although the conditions actually constructed were appropriate for

the much simpler one-dimensional model of a constant head saturated

hydraulic conductivity test. The breakthrough curve of fresh water was

determined at multiple acceleration levels by means of an electrical

resistivity probe located within the soil specimen. A comparison of

modeled breakthrough curves at 1 g and 53 g's indicated a reduced pore

fluid velocity at the higher acceleration. While this lag may be an

artifact of the delayed response of the resistivity probe, the results

possibly reflected lower flow rates due to an increase in effective

stress on the soil particles, caused by the increasing acceleration

level with sample depth. The accurate reproduction of the prototype

effective stress profile would be a definite advantage of centrifugal

models over laboratory bench models.

The assumption of a reduction in model length by a factor of N (the

ratio of accelerations between model and prototype) to maintain dynamic

similitude resulted in a proportionate increase in the hydraulic

gradient across the sample. This led to a major pronouncement of the

paper, i.e., that test durations will decrease proportionately by the









square of the acceleration ratios. While this result is valid in the

reference frame of the conceptually simple tests conducted, the

suggestion that the results are generally valid and uniquely a

characteristic of centrifugal modelling is misleading. The reduction in

testing time realized by centrifugal modeling can be readily duplicated

on a bench model. The equivalence in terms of hydraulic potential of

fluid pressure forces and gravity-induced body forces allows

reproduction of centrifuge acceleration potential in bench models by

merely increasing the pressure on the fluid delivery systems. Thus, the

centrifuge does not offer a unique capability for decreasing the testing

time of physical models.

The authors' suggestion that dispersive characteristics of soil

media can be modelled at accelerated velocities was apparently disputed

by the study results. Hydrodynamic dispersion coefficients reflect the

nonuniform pore fluid velocity distribution within a soil volume.

Accordingly, the dispersion coefficient has been observed to vary

significantly with the velocity of the bulk fluid, demonstrating greater

variation in soils with a wide distribution of pore sizes. While the

breakthrough curve results presented clearly demonstrated the dependence

between the dispersion coefficient and pore fluid velocity, the authors

failed to recognize this and optimistically suggested that estimates of

this parameter can indeed be determined at accelerated velocities.

Extrapolation of dispersion coefficients determined by centrifuge tests

to field conditions and pore velocities would be severely restricted to

laboratory media with an extremely uniform pore size distribution such

that hydrodynamic dispersion would be independent of pore fluid

velocity.









In summary, the study highlighted a principal feature of physical

modeling in a centrifuge, that of increasing the body forces imposed on

fluid and soil particles. However, the testing conditions were too

narrow in range to warrant the authors' general conclusion that

centrifugal modeling is superior to bench models in determining

advective characteristics of contaminant transport. In addition, the

breakthrough curve results disputed their suggestion that dispersive

characteristics of soils under field conditions can be determined in a

centrifuge model. Because the prototype condition was never executed,

there was no independent base with which to compare the model results.


Geotechnical Engineering Applications

The use of centrifuges in geotechnical engineering research has

increased at an accelerated rate in the last decade. From the earliest

reference in American literature (a study of mine roof design)

centrifuges have been utilized to investigate a wide spectrum of

problems, including landfill cover subsidence, soil liquefaction, slope

stability, cellular coffer dam performance, bearing capacity of footings

in sand, tectonic modeling, explosive and planetary impact cratering,

sinkhole collapse and evaluation of sedimentation and consolidationof

fine-grained materials.

Research centers specializing in centrifuge projects have developed

in many nations, notably England (Cambridge University), the United

States (University of California Davis, University of Florida,

University of Colorado, University of Kentucky, NASA Ames Research

Center, and others), Japan (four research centers) and France. A

recent review of the state of the art ambitiously projected "the day

will come when every well-equipped geotechnical research laboratory will









include a centrifuge for model testing .. ." (University of California,

1984, p.36). The growth curve presented in Figure 5 demonstrates the

increase in interest in centrifugal applications. A summary of

advantages and limitations of centrifugal techniques compiled from

several articles is presented in Tables 5 and 6.


University of Florida Centrifuge Equipment

The University of Florida geotechnical centrifuge has a 1-m radius

and can accelerate 25 kg to 85 g's (2125 g-kg capacity). Figure 6

presents a schematic drawing of the centrifuge and photographic

equipment. A photograph of the centrifuge is presented in Figure 7. A

window on the centrifuge housing allows visual observations of the model

in flight. A photo-electric pick-off and flash delay augment the system

for visual observation and photographic recording. Two hydraulic slip

rings supply fluid to the apparatus, while 32 slip rings are available

for transmission of electrical current.



Fluid Mechanics and Hydraulics in a Centrifuge

All laboratory systems utilized as a permeameter or physical model

inherently entail fluid flow through conduits and through porous media.

The design and analysis of such an apparatus necessitated an

understanding of fluid flow in both regimes as well as any

modifications of their behavior under the influence of radial

acceleration. In this context fluid flow is discussed below.


Flow Through Conduits

During the execution of a laboratory hydraulic conductivity test,

the hydraulic energy at the sample boundaries is determined by the











40



35



J 30
0


25
J
Z
D 20-
0

IL
0 15-
hi

S 10



5



0
0 10 20 30 40 50 60 70 80

YEAR (1900's)

Figure 5. Number of Journal Articles on Centrifuge Applications










Table 5. Advantages of Centrifugal Modeling

1. It is the only means for subjecting laboratory models to
gravity-induced self-weight stresses comparable to those
in the full-scale field prototypes.
2. Many gravity-dominated phenomena take place at
dramatically increased rates.
3. It allows for verification of model to prototype scaling
relationships by repeating the tests at various
acceleration levels, a technique referred to as modeling
of models.
4. A single model configuration can be used to evaluate
many different prototype configurations by varying the
acceleration levels.
5. It is the only realistic way to model large-scale
phenomena such as nuclear explosive effects and
planetary impacts.





Table 6. Limitations of Centrifugal Model Testing

1. The acceleration level in the centrifuge varies with the
radius of rotation, in contrast to the essentially
constant gravitational force field at the earth's
surface.
2. Coriolis effects may have an influence if movements occur
within the model during rotation.
3. The start-up period, when model acceleration is
increased, has no counterpart in the prototype.
4. Tangential acceleration effects may be significant if
centrifuge speeds are changed too rapidly.
5. Grain size similarity is difficult to achieve.
6. There is a risk of injury and/or property damage during
operation of a large centrifuge due to the large forces
that are developed.
7. They can be more expensive than conventional apparatus.






























































Schematic of the U. F. Geotechnical Centrifuge


Figure 6.
































































Photograph of the U. F. Geotechnical Centrifuge


Figure 7.









influent and effluent reservoir conditions and the flow characteristics

of the conduit system. Under the influence of the earth's gravitational

acceleration, the one-dimensional relationship between the pressure

distribution and fluid kinematics in a conduit flowing full between two

points is the Bernoulli equation (Fox and McDonald, 1978)

(P/p + V2/2 + gz)1 = (P/p + V2/2 + gz)2 (9)

where P = pressure acting on the fluid (M/LT2);

p = mass density of the fluid (M/L3);

V = velocity of the fluid (L/T); and

z = elevation of the point (L).

The Bernoulli equation is an integrated form of the Euler equations of

motion. An analogous equation was derived to describe the same

relationship within a centrifuge. The equations of fluid motion were

evaluated in the reference frame of a centrifugal permeameter. For the

elementary mass of fluid in a tube (see Figure 8), motion is parallel to

the radial acceleration. The forces acting on the element in the

direction of flow are

1. hydraulic pressures acting on the surfaces of the control element;

2. shearing forces of adjacent elements and/or the walls of the tube;
and

3. centrifugal body forces acting on the element.

For a control volume in a centrifuge, the acceleration, ar, acting on

the mass is a function of the radius, r, expressed as

ar = rw2 (10)

where w = angular velocity (rad/T), which is constant at all distances

from the axis of rotation. Newton's second law of motion in one





































-- dr ----


-- dFS


weight a W (pdrdA) r w2


--- (P + dP)dA


I

Figure 8. Definition Sketch for Analysis of Forces Acting on a Fluid
Volume in a Centrifuge


PdA ---


W
--0


111








dimension can be expressed as

F Mar M(dV/dt) p dr dA dV/dt (11)

where F = sum of the forces acting on the control volume (ML/T2);

M = mass of the element (M); and

A = cross-sectional area of the element (L2)

Substituting in the forces acting on the element, equation 11 becomes

PdA (P+dP)dA dFs + p ard A dr = p dr dA dV/dt (12)

where P = pressure acting on the control surface of the element; and

dF = total shear forces.

Dividing equation 12 by (pdA) and simplifying yields

(-dP/p) (dFs/pdA) + ardr = dr dV/dt (13)

Replacing dr/dt with the fluid velocity, V, (dF,/pdA) with dHL and

incorporating equation 10 yields

(-dP/p) dHL + w2 rdr = VdV (14)

Collecting terms,

-w2 rdr + dP/p + dBL + VdV = 0 (15)

For an incompressible fluid equation 15 is integrated across the element

to yield

-w2(r2 r )/2 + (P2- P1)/p + L + (V2 V)/2 0 (16)

Separating terms yields the centrifugal equivalent of the Bernoulli

equation:

(V2/2 + P/p v2r2/2)1 = (V2/2 + P/p w2r2/2)2 + HL (17)

Defining the specific energy hydraulic potential as

H V2/2 + P/p w2r2/2 (18)

Equation 17 can be written as

H1 = B2 + BL (19)









The dimensions of the specific energy potential are energy per unit

mass. For a system in hydrostatic equilibrium, the velocity and hence

the frictional losses are zero. The relationship between the pressure

distribution and the radial location is thus

P2 1 + P2(r22 r12)/2 (20)

This relationship is demonstrated in Figure 9.


Flow Through Porous Media

For flow through porous media, the velocity component of the

hydraulic potential is negligible compared to the pressure and elevation

terms. In reference to the control volume in Figure 10, Darcy's law

within a centrifuge sample can be expressed using the specific energy

potential gradient by introducing equation 18 into equation 4 as


q = -K d (P/p w2r2/2) (21)
dr


Consistent with the units of the hydraulic potential, the hydraulic

conductivity, K, has the units of time. This dimensional definition

retains the basic relationship of flow conductivity to the soil matrix

and fluid properties, i.e.,

K k / v (22)

This definition of K is not a function of the gravity induced

acceleration acting on the fluid mass. Expanding equation 21 yields


q = -K [d(P/p) w2(r + dr)2 r2]] (23)
dr 2 dr

expanding the quadratic term yields











4



3.5-


3 300 RPM
L
4-
o 2.5

E00
%O 2-
Io 200 RPM

Id
1.5


1

100 RPM

0.5-




40 60 80 100

RADIUS (cm)

Figure 9. Hydrostatic Equilibrium in a Fluid Sample in a Centrifuge


















AXIS OF ROTATION


dr
-*114


r+dr


Definition Sketch of a Soil Volume in a Centrifuge


Figure 10.










q = -K [d(P/p) 2[r2 + 2rdr + dr2 r2]]
dr 2 dr


(24)


q = -K [d(P/p) w2(2rdr + dr2)] (25)
dr 2 dr
Evaluating equation 25 at a point and neglecting the second order

differential yields


q -K [d(P/p) rw2] = -K [d(P/p) ar]
dr dr


(26)


This result is plausible; in a l-g environment, the second term in

brackets is equal to unity, while in a multiple-g environment, it is

equal to the acceleration acting on the fluid mass. Assuming that the

pressure gradient component is not influenced by the acceleration

induced by the centrifuge, the hydraulic potential gradient within the

centrifuge will increase over a 1-g sample by an amount equal to (ar-1).

This additional gradient will result in a proportionate increase in the

fluid flux through the soil, i.e., the flux at a radius, r, will

increase by an amount equal to

q = -K (ar 1) (27)

where ar is given by equation 10. However, it is important to note from

equation 26 that the increase in specific discharge is directly

proportional to the acceleration level only if the pressure gradient

equals zero.


Energy Losses in The Permeameter


Along with the

mechanical energy is

tubing walls, and,

expansions and bends.

of the Darcy-Weisbach


energy loss induced across the soil sample,

lost in the permeameter due to friction along the

of minor importance, due to flow contractions,

These losses are generally expressed in the form

equation










HL (f + C) LV2/2D (28)

where HL = lost mechanical energy per unit mass (L2/T2)

f = friction factor dimensionlesss);

C = coefficient for minor energy losses (dimensionless)t

L = length of the conduit (L); and

D = inside diameter of the conduit (L).


Dimensional Analysis

When used to conduct physical modeling of prototype behavior,

appropriate relationships between the forces acting on the control

volume must be preserved in the centrifuge model. Scaling relationships

between the fundamental dimensions, mass, length and time, of the

prototype and centrifuge model are determined by dimensional analysis.

Historically, three methods of determining scaling factors have been

utilized. Croce et al. (1984) employed an approach based on Newton's

original definition of mechanical similarity requiring proportionality

of all the forces acting on similar systems. Cargill and Ko (1983)

derived scaling relationships from a method of dimensional analysis

incorporating the Buckingham Pi Theorem. Others have based scaling

relations on the differential equations governing the phenomena. Each of

these methods, when properly applied,yields identical scaling factors

for the same phenomena and assumptions. Verification of the scaling

factors is accomplished by comparing results of tests with various

geometrical and/or acceleration ratios; this latter process is referred

to as modeling of models and can be readily executed by spinning the

same sample at various speeds and comparing results. An apparent

discrepancy concerning the scaling of hydraulic conductivity was based










on an inconsistent definition of the total potential gradient. When the

potential is defined as the hydraulic potential, with the dimension of

length, K scales as 1/N, where N is the ratio of acceleration in the

model to that in the prototype. When the potential is defined as the

pressure potential or the specific energy potential, K scales as unity.

The reason for the difference in scaling is that the definition of K in

the latter cases is independent of the acceleration acting on the fluid.

A general set of scaling factors is presented in Table 7; however,

individual analysis of the hydraulic conditions specific to the model

under consideration should be conducted.










Table 7. Summary of Scaling Relationships for Centrifugal Modeling

Property Scaling Factor


Potential gradient
(specific energy potential) 1/N

Potential gradient
(hydraulic potential) 1

Potential gradient
(pressure potential) 1/N

Hydraulic conductivity
(specific energy potential) 1

Hydraulic conductivity
(hydraulic potential) 1/N

Hydraulic conductivity
(pressure potential) 1

Time XN

Pressure X/N

Darcian flux in saturated soil 1/N

Darcian flux in unsaturated soil 1

Volumetric flow rate X2/N

Capillary rise N

Note: N (acceleration of model)/(acceleration of prototype)
X (unit length of prototype)/(unit length of model)














CHAPTER IV
TESTING PROGRAM

Centrifugal techniques for evaluating hazardous waste migration

include physical modeling and material properties testing. To fully

utilize the potential of physical modeling in the centrifuge, the

fundamental relationships of radial acceleration, hydraulic pressures

and pore fluid kinematics within the centrifuge soil sample needed to be

developed and verified. The execution of concurrent bench and centrifuge

hydraulic conductivity testing provided the opportunity to investigate

these fundamental fluid flow properties as well as allowed the direct

assessment of the feasibility of material properties testing within the

centrifuge. A secondary objective of the project was to establish the

theoretical and practical operating limits of centrifugal techniques.

The design and execution of the laboratory testing program is discussed

below.


Objectives

The laboratory research program was designed and implemented to

develop centrifugal testing methods for determining saturated and

unsaturated hydraulic conductivity of soil samples. The testing program

encompassed:

1. the analysis, design and fabrication of permeameters for use in the

centrifuge;

2. execution of hydraulic conductivity tests in a 1-g environment to

provide a benchmark for comparing centrifuge test results;








3. derivation of the appropriate equations of motion for fluid flow in a

centrifuge;

4. execution of hydraulic conductivity tests in the centrifuge at

various accelerations;

5. comparison of centrifuge results with 1-g test results; and

6. if necessary, modification of the centrifuge device, testing

procedures and/or data analysis based on results of the comparison.

The technical feasibility of centrifugal techniques for evaluating

hazardous waste migration was assessed based on the results obtained.

Results of the testing program will also serve as the foundation for

subsequent research in the area of centrifugal modeling of hazardous

waste migration. A summary of the testing program is presented in Table

8.





Table 8. Summary of Permeability Testing Matrix..

Soil Moisture Condition
Soil Saturated Unsaturated
Type Water Decane Water Decane


Bench tests
Sand La L C
Sand/clayb L L
Kaolinitec L L
Kaolinited L L

Centrifuge tests
Sand L L C
Sand/clayb L

Notes: a L indicates a laboratory test; C indicates analysis
by computer model
80 percent sand, 20 percent kaolinite, by weight
c initial moisture content was 29 percent by weight
d initial moisture content was 32 percent by weight








Materials

Permeants

Saturated and unsaturated hydraulic conductivity tests were

performed using water and decane as the permeants. A survey of current

hydraulic conductivity studies and published testing procedures

indicated that distilled water was the most common permeant, although

most agree that so-called native water should be used. Several studies

have documented reductions in the estimates of hydraulic conductivity

through clays using distilled water of up to two orders of magnitude

lower than estimates from tests using native water or a weak electrolyte

solution (Uppot, 1984; Olson and Daniel, 1981). The discrepancy has been

attributed to electric double layer interaction of the clay particles

with the fluid (Dunn, 1983; Uppot, 1984; Olson and Daniel, 1981). When

distilled water flows past clay particles with high surface potentials,

the electric double layer of diffuse ions expands as the number of

counter ions anionss in this case) in solution decreases, increasing the

surface viscosity and resulting in reduced estimates of hydraulic

conductivity (Adamson, 1982). The use of distilled water did not

present a problem in this study because the initially dry kaolinite was

prepared to an initial moisture content with distilled water. In

essence, distilled water was the "native" water for these clays.

Reagent grade, i.e. at least 99 percent pure, decane was used as the

nonaqueous permeant. Decane is a straight chain hydrocarbon with

similar properties to the U. S. Air Force jet fuel JP-4. A comparison

of physical and chemical properties of water, JP-4 and decane is

presented in Table 9. Like jet fuel, decane is flammable in specific

mixtures with air. The lower and upper explosive limits for decane in








Table 9. Comparison Between Properties
Water (at 250C)


of JP-4, Decane and


Property JP-4 Jet Fuela n-Decaneb Waterc


Fluid density 0.774 0.686 0.997
(g/cc)

Kinematic viscosity 0.01184 0.01195 0.00900
(cm2/s)

Surface tension 24.18 18.59 72.14
(dyne/cm)

Freezing point -60.000 -29.661 0.000
(c)

Boiling point not available 174.123 100.00
(c)

Vapor pressure not available 3.240 32.69
(cm water)

Solubility in not available 0.009
water (mg/1)

Polarity Nonpolar Nonpolar Polar

Sources: a Ashworth, 1985
b Chemical Rubber Company, 1981
c Giles, 1962


air are 0.67 and 2.60 percent by volume, respectively. The auto-

ignition temperature of decane is greater than 2600C, while the closed

cup open flame flash point is 460C. However, decane is not susceptible

to spontaneous heating (Strauss and Kaufman, 1976). Suitable

extinguishing agents include foam, carbon dioxide and dry chemicals.

Because of the explosive potential and otherwise hazardous nature of

decane, safety procedures in handling and disposal were implemented.

Recommended precautions for safe handling of decane include the use of

rubber gloves, lab coats, face shields, good ventilation and a

respirator. Recommended disposal procedures consist of absorbing in









vermiculite, collection in combustible boxes, transferal to open pit and

burning (Strauss and Kaufman, 1976). During the course of the testing

program waste decane and water were separated by density differences;

the waste decane was decanted into the original shipping containers and

picked up by a University of Florida hazardous waste removal group.

The potential existed for atomizing substantial volumes of decane

during centrifugation, which could have resulted in a potentially

explosive atmosphere. The presence of elevated hydraulic pressure under

high acceleration could cause a rapid efflux of decane from the

permeameter should a seal in the apparatus fail. Depending on the

location of the seal failure, the amount of decane released could result

in a concentration in the centrifuge atmosphere between the lower and

upper explosive limits, and hence present a combustion hazard if an

ignition source was present. The decane could be sprayed and

subsequently condensed on the walls of the centrifuge housing. The

relatively cool temperature (250C) of the housing is well below the

auto-ignition point (2600C) and below the open flame flash point of

460C. In summary, the actual combustion behavior of decane released

during centrifugation is not definitively predictable. However, general

calculations of explosive potential coupled with a concerted exercise of

caution suggest that there is little potential of combustion during

centrifuge testing.


Soils

Four soil preparations were utilized in the testing program. The

soils were chosen to span the wide range of pore fluid velocities of

natural soils as well as for their low degree of reactivity:

1. fine-grained silica sand;









2. 80% sand 20% kaolinite (by weight);

3.1007 kaolinite prepared to an initial water content of 29%; and

4.100% kaolinite prepared to an initial water content of 32%.

The uniform fine-grained silica sand used in the laboratory tests was

obtained from the Edgar Mine Company of Edgar, Florida. A summary of

the physical and chemical characteristics of the sand is presented in

Table 10.


Table 10. Characteristics of the Sand Used in the Testing Program


Parameter


Value


Chemical Composition
Si02
Other minerals

Particle Size Distribution
1.00 mm
0.25 mm
0.20 mm
0.125 mm
0.07 mm

Specific surface area
(based on spherical grain)

Specific Gravity


99.3 percent by weight
< 1 percent by weight

Cumulative percent undersize
100.0
93.0
50.0
10.0
0.6

0.01 m2/g


2.64


The kaolinite employed for the laboratory tests was also obtained

from the Edgar Mine of Edgar, Florida. A summary of the physical and

chemical characteristics of the clay is presented in Table 11.

Kaolinite was selected as a representative fine-grained soil with

extremely low values of hydraulic conductivity, with the advantage that

its shrink/swell and reactivity tendencies are small compared to other

clays such as illite. The hydrogen bonding and Van der Waal forces

which hold the silica and alumina sheets together are sufficiently










Table 11. Characteristics of the Clay Used in the Testing Program

Parameter Value


Chemical Composition Weight percent, dry basis
Si02 46.5
A12 37.6
Other minerals < 2
Loss on ignition 13.77

Mineral Content (x-ray diffraction)
Kaolinite (A1203 2SiO2 2H20) 97 percent

Particle Size Distribution Cumulative percent undersize
40 micron 100
10 micron 90
5 micron 78
3 micron 68
1 micron 49
0.5 micron 40
0.2 micron 20

Specific Surface Area 11.36 m2/g

Specific Resistivity 35,000 ohms/cm

Oil Absorption 47.3 g oil/100 g clay

pH
5% solids 6.05
10% solids 6.07
20% solids 5.85
30% solids 5.89

Cation Exchange Capacity 5.8 Meq/100 g

Specific gravity 2.50



strong to restrict interlayer expansion (Mitchell, 1976). A net

negative charge is present on the edges of kaolinite particles resulting

in a relatively low cation exchange capacity of 3-13 milliequivalents

per 100 grams. Relative to other clay, e.g., montmorillonite and

illite, kaolinite has a small specific surface area of 5-12 square

meters per gram. The particular kaolinite employed in the laboratory

tests had an average specific surface area of 11.36 m2/g as determined











by the nitrogen method. The clay samples were prepared at two initial

water contents, one below the optimum water content of 30 percent by

weight and one above the optimum water content. Theory and practical

experience indicated that the resulting pore structures would differ

enough to produce discernible differences in hydraulic conductivity

values (Mitchell, 1976).

A mixture of sand and clay was prepared to create a soil with

intermediate values of hydraulic conductivity. The mixture was prepared

to the ratio of 4 parts sand to one part kaolinite by weight.

The relationship between the moisture content and the soil moisture

suction of a soil volume is referred to as a soil moisture retention

curve, or moisture characteristic curve. The curves are specific to

each soil type and generally exhibit a hysteretic response during the

absorption and drainage cycles. Moisture retention curves were prepared

for each soil during a drainage cycle using water covering the range

from saturation to 15 bars suction. The results, presented in Figure 11,

were used in the unsaturated hydraulic conductivity analysis.


Testing Equipment

Evaluation of Current Technology

A preliminary task was the design of the permeameter for the

testing program. A review of current research revealed that two major

types of permeameters are utilized for determining the hydraulic

conductivity of water and nonaqueous fluids in saturated samples.

Historically, sample containers had rigid walls. Mechanical simplicity,

ease of sample preparation and ability to facilitate field cores were

among the reasons for their popularity. However, sidewall leakage,











0.5

CLAY (32%)


0.4
,. +^ \ (LAY (29s)





S\I SAND/CLAY
z







0 0.2


W SAND
3-J-
0 0.1




0
0 2 4

SOIL MOISTURE SUCTION Iog(cm of water)

Figure 11. Moisture Retention Curves for the Sand, Sand/Clay and Clay
Samples











i.e., flow along the wall rather than through the sample, has been

documented, raising the question of validity of results for a rigid wall

apparatus (Daniel et al., 1985). Prevention of sidewall leakage was

addressed by various remedial measures, as exemplified by the practice

of sealing the top of the sample adjacent to the wall with sodium

bentonite. Another practical problem encountered in rigid wall apparatus

has been volumetric change of reactive soils when exposed to nonaqueous

permeants. Reports of tremendous increases in the hydraulic

conductivity of soils to organic solvents have been criticized because

the rigid wall apparatus utilized were conducive to unrestrained

shrinking resulting from chemical reaction between the fluid and the

soil matrix (Brown et al., 1984). With the advent of triaxial apparatus

(see Figure 12), used for measurements of soil strength, an alternative

to the rigid wall container developed. The triaxial apparatus confines

the soil sample in a flexible membrane which allows transmittal of

confining pressures to the soil specimen. Flow along the wall outside

the specimen is prevented by the continuous contact between the sample

and the flexible wall. Review of current research indicated that

flexible wall permeameters are the preferred laboratory apparatus for

saturated hydraulic conductivity measurements of nonaqueous permeants

(Dunn, 1983; Uppot, 1984; Daniel et. al., 1985).

The flexible wall apparatus also has the advantage over rigid wall

permeameters in that complete saturation of the soil sample can be

ensured by applying high pressure from both ends of the sample. In the

process of introducing water into the sample, air is entrapped in the

interior voids, preventing complete saturation of the sample. These air

pockets effectively block the flow of water through the sample, reducing


















































































Figure 12.


Photograph of a Commercial Triaxial Apparatus


' -







the observed value of the hydraulic conductivity. By applying high back

pressures, the trapped air dissolves into the pore fluid. Attempts to

utilize back pressure saturation in rigid wall permeametershave

exacerbated the sidewall leakage problem (Edil and Erickson, 1985). A

related advantage of flexible wall apparatus over rigid wall

permeameters is the ability to verify complete saturation of the sample

before testing begins. Application of an incremental increase in the

confining pressure, transmitted to the sample by the flexible membrane,

will cause an equal incremental increase in pore fluid pressure when the

sample is fully saturated. The ratio of the observed pore pressure

increase to the applied increment of confining pressure is referred to

as the "B" value, and is equal to unity for complete saturation. It is

not possible to check for "B" values in a rigid wall device

(Christiansen, 1985).

Another benefit of the flexible wall apparatus is the ability to

control the effective stresses acting on the sample particles. During

back pressure saturation, the external applied pressure is

proportionately increased to maintain specified effective stresses on

the soil particles. Neglecting the weight of the overlaying sample, the

effective stress of a sample in a flexible membrane is the net pressure

difference between the pore fluid pressure and the external chamber

pressure. This unique capability allows the sample to be tested under

similar effective stress conditions as exist in the field, e.g., fifty

feet below the surface. A comparison between the confining stress

distribution in a flexible wall and a rigid wall container is presented

in Figure 13. Flexible wall permeameters also allow direct measurement

of sample volume change during testing.

































































Figure 13.


Comparison of Confining Stress Profiles








Disadvantages of a flexible vall apparatus include higher equipment

costs, possible reactivity of the flexible membrane with nonaqueous

permeants, and the inability to reproduce zero effective stress at the

top of the sample, a condition which exists at the soil surface. When

exposed to the atmosphere, desiccation cracks open up in clay soil and

liners due to shrinkage. The resulting fissures significantly increase

the rate of liquid movement through the layer. Currently, there is no

way to reproduce this condition of zero effective stress at the surface

in the flexible wall permeameter. A study comparing field seepage rates

of a carefully compacted clay liner with rates determined in a flexible

wall apparatus documented a difference of three orders of magnitude (Day

and Daniel, 1985). Rigid wall field apparatus (double-ring

infiltrometers) recorded values within an order of magnitude of observed

field rates.

A carefully controlled investigation of the effects of permeameter

type concluded that there was no significant difference in saturated

hydraulic conductivity measurements for water in clay (Boynton and

Daniel 1985). However, estimates of hydraulic conductivity of

concentrated organic were an order of magnitude higher for tests

conducted in rigid wall containers than in a flexible wall permeameter.

In that study results from a flexible wall apparatus were compared to

estimates from a standard consolidation cell and compaction mold.


Design of the Hydraulic Conductivity Apparatus

Separate permeameters were designed for use in the saturated and

unsaturated hydraulic conductivity tests. After a review of current

technology, the saturated hydraulic conductivity permeameter was

designed as a modular apparatus to facilitate uncomplicated sample








preparation and for the convenience of incorporating possible future

design revisions. The device incorporated the current best technology

in permeameters, including

1. incorporation of a flexible membrane;

2. capability for de-airing the permeant and sample via vacuum;

3. capability for back pressure saturation; and,

4. capability to check for complete saturation by means of the "B" value

test.

The design also included constraints brought about by its intended use

in the centrifuge. These included

1. size constraint the device must fit on the 75-cm long lower flat

portion of the centrifuge arm, while at the same time, be narrow

enough so that the radial acceleration forces act in nearly parallel

directions;

2. the weight must remain balanced in flight hence the apparatus must

have a self-contained permeant system;

3. the permeameter is limited to two hydraulic slip rings on the

centrifuge assembly; and

4. the permeant tubing system should be as large as possible to minimize

flow velocities and hence minimize the energy losses due to friction.

A schematic of the completed device is presented in Figure 14. A

photograph of the apparatus attached to the centrifuge arm is presented

in Figure 15. The unit consisted of 1.25-cm thick, 11.43-cm inside

diameter acrylic cylinders separated by 2.54-cm thick acrylic plates.

Conduits were drilled in the plates to conduct the test permeant. 0-

rings between the individual elements provided high pressure seals,

and the entire apparatus was unified by six 0.95-cm diameter steel rods.














0.95-cm


FROM


I ?23 cm


-I


Figure 14. Schematic of Apparatus Used in the Saturated Hydraulic
Conductivity Tests





























































Figure 15. Photograph of the Saturated Hydraulic Conductivity Apparatus
Attached to the Centrifuge Arm a) Front View; b) Rear View









Permeant flow between the reservoirs and the soil sample was controlled

by a three-way solenoid valve. Material and fabrication of the

permeameter cost approximately $1000. Pressure transducers, attendant

voltage meters, pressure controls and miscellaneous hardware cost an

additional $4000.

The soil specimens were confined in a flexible membrane within the

upper water-filled acrylic cylinder. Stainless steel porous discs and

filter fabric were used to contain the soil sample, subject to the

criterion that the pore sizes be small enough to prevent particle

emigration from the sample, and yet large enough to avoid becoming

limiting to flow. The flexible membrane must be free of leaks,

nonreactive with the permeant and relatively impermeable to the

confining fluid to ensure hydraulic isolation. Reactivity and

permeability of the membrane can be tested by stretching a piece of the

membrane over the top of a beaker containing the fluid in question,

inverting, and monitoring the subsequent fluid loss (Uppot, 1984).

Initial tests with decane revealed significant leakage and interaction

between the latex rubber membrane and decane. After several hours of

exposure to decane, the surface of the latex membranes was transformed

into a wrinkled covering, similar in pattern to the convolutions on the

surface of the brain. A similar wrinkle pattern was observed in a

previous study using benzene with a latex membrane (Acar et al., 1985).

It has been suggested that decane and other nonpolar hydrophobic

organic penetrate the polymers comprising the latex membrane, resulting

in molecular relaxation and hence an increase in the surface area of

the membrane. The wrinkles result from the confining pressure

restricting the volumetric expansion of the membrane. As an










intermediate solution to the leakage problem, a sheet of polyethylene

food wrap was sandwiched between two latex membranes. However, this

measure did not prevent the surface convolutions on the inner membrane.

Single neoprene rubber membranes were subsequently utilized and found to

be relatively nonreactive to decane. All of the saturated hydraulic

conductivity tests reported herein using decane as the permeant utilized

the neoprene rubber membranes.

The conduit system consisted of the tubing and valves connecting

the sample cell to the pressure control and flow measurement components.

Along with the energy loss induced across the soil sample, mechanical

energy is lost in the permeameter due to friction along the tubing

walls, and, of minor importance, due to flow contractions, expansions

and bends. The conventional constant head saturated hydraulic

conductivity test is conducted under steady flow conditions, and as

such, the appropriate head loss can be obtained by pressure transducers

located at each end of the sample; no correction is needed to account

for other energy losses. However, hydraulic conductivity tests with

variable boundary conditions, such as the falling head or variable head

test employed here, result in transient boundary conditions, and the

gradient across the sample is constantly changing; hence pressure

transducers seldom are used at the ends of the sample. Rather, the

transient boundary conditions are incorporated directly into the

derivation of the equation for K. Generally the energy losses due to

friction, etc., are neglected, which is acceptable when flow velocity in

the tubing is small, as it may be for flow through clays and sand/clay

composites as well as for gravity flow through sand. However, for sand

samples under pressure and permeameters with small diameter tubing,










energy losses became significant as flow velocities increased.

Extremely high energy losses due to friction were observed in the small

(0.25 cm inside diameter) tubing of the commercial triaxial device.

Larger tubing (0.64 cm inside diameter) was used in the new permeameter

and as large as practical valves were employed in the permeameter to

minimize energy losses due to flow restrictions. Energy losses were

monitored during tests. Nylon tubing, which is nonreactive to most

organic, was used in the permeameter. The presence of decane did not

noticeably affect the nylon tubing nor the acrylic chambers of the

permeameter.

Elaborate multiphase systems have been utilized to accurately

measure inflow/outflow rates (Dunn, 1983). However, visual observation

of water surface elevations were utilized in this study to determine

fluid flux in the current hydraulic conductivity device.

The air pressure system consisted of both vacuum and positive

supplies, regulators, gages, pressure transducers and calibrated

voltmeters. Desiring the permeants and the sample were facilitated by

the vacuum. Appropriate pressure gradients were established and

maintained across the sample via independent control of the air

pressures in the influent and effluent reservoirs. Air pressure was

introduced at the top of the influent and effluent reservoirs through

the conduits in the upper acrylic plates. During preliminary testing,

the inability of pressure regulators to hold constant pressures above

the influent and effluent reservoirs as their water levels fluctuated

resulted in inaccurate estimates of hydraulic conductivity. Adequate

regulators were appropriated for subsequent testing. The accuracy of

pressure gages, regulators and transducers is paramount due to their










role in establishing boundary conditions on the sample. Individual and

differential pressure tranducers were utilized to monitor the "B" value

of the sample before testing and the air pressure above the permeant

surfaces during the tests. External confining pressure was maintained

on the sample throughout the test by pressurizing the water in the

surrounding chamber. This design allowed for flow-through back pressure

saturation of the soil sample within the flexible membrane, reported to

be the most efficient method of saturating the specimen (Dunn, 1983).


Bench Testing Procedures

Similar testing procedures were followed for all the saturated

hydraulic conductivity tests. The saturated hydraulic conductivity tests

of the sand and the sand/clay samples used for comparing bench and

centrifuge results were conducted in the new permeameter. The clay

samples were tested with water and decane in the triaxial apparatus. For

the sand and sand/clay samples, the specimens were prepared dry. The

initially dry kaolinite samples were prepared to designated water

contents (29 and 32 percent by weight) and allowed to cure for six

weeks. For each test, the clay samples were compacted to a specified

volume, yielding bulk densities of approximately 100 pounds per cubic

foot.

Several measures were performed to ensure that the samples were

completely saturated. Prior to saturating the sample a vacuum was

applied to the top of the water reservoir until the bubbling ceased.

Water was subsequently introduced into the samples from the bottom while

a vacuum of approximately 13 psi was maintained at the top. When air

bubbles ceased to flow out the top of the sample, the pressures on the









influent and effluent reservoirs were increased to 40 psi for sands, 50

psi for the sand/clay mixtures and 70 psi for the clay samples. A

slight gradient was established to allow flow through the sample. After

a pressurization period of approximately one day for the sand and two to

three days for the sand/clay and clay samples, "B" values of unity were

recorded, indicating complete saturation.

A range of gradients was established during the saturated

hydraulic conductivity testing. Of primary interest was the possibility

of determining the critical value of the Reynolds number above which

Darcy's law was invalid. Preliminary estimates of pore fluid velocities

indicated that only the sand specimens could exhibit a deviation from

Darcy's law. In fact, a previous investigation used gradients of over

800 on clay specimens to reduce the testing time, with no discernible

deviation from Darcy's law (Uppot, 1984). Deviations from Darcy's law

can be attributed to:

1. the transition from laminar to turbulent flow through the pores; and

2. the tendency for flow to occur in the larger pores as the velocity

increases, thus decreasing the total cross-sectional area of flow.

When the desired initial pressure boundary conditions were

established and fluid levels in the reservoirs recorded, the solenoid

valve was opened and flow through the sample commenced. When the

solenoid valve was closed, the elapsed time and fluid levels were

recorded. For the sand specimens, the pressure differential during the

test was recorded to quantify the friction and minor energy losses.

This was not necessary for the slower fluid velocities present in the

sand/clay and clay tests. The testing procedure was repeated until

sufficient data were collected. Boundary conditions were verified and










real time data analysis was conducted on a microcomputer during the

execution of the tests.

Tests with decane were performed immediately following tests using

water. Water was removed from the influent lines and decane was

introduced into the influent reservoir.

The viscosity of a permeant varies with temperature. The

temperature of the main permeant reservoir was recorded during each

test. The temperature in the air conditioned laboratory was maintained

within a 50C range throughout the duration of the testing program.


Centrifuge Testing Procedures

Saturated hydraulic conductivities were determined for sand and

sand/clay soil specimens in the centrifuge. The high influent

pressures, 120 psi, required for the clay samples were too high to

safely perform replicate tests in the acrylic chambers within the

centrifuge. The centrifuge tests were conducted on the same soil

specimen immediately following the bench tests. The pressure transducers

were recalibrated before each centrifuge test to compensate for line

noise in the electrical slip rings. During the centrifuge tests,

pressures in the sample and fluid reservoirs were controlled by

regulators external to the centrifuge, which supplied air through

hydraulic slip rings. When the desired initial pressure boundary

conditions were established and fluid levels in the reservoirs recorded,

the solenoid valve was opened and flow through the sample commenced.

When the solenoid valve was closed, the elapsed time and fluid levels

were recorded. For the sand specimens, the pressure differential during

the test was recorded to quantify the friction and minor energy losses.

This was not necessary for the slower fluid velocities present in the











sand/clay tests. The testing procedure was repeated until sufficient

data were collected. Boundary conditions were verified and real time

data analysis was conducted on a microcomputer during the execution of

the tests.


Unsaturated Testing

Centrifugal techniques for physical modeling and material testing

of unsaturated soil samples were evaluated in this study. A variety of

applications were investigated, including several laboratory techniques

for determining the relationship of hydraulic conductivity as a function

of moisture content, as well as physically modeling the advection of a

conservative leachate through a partially saturated soil profile. The

results are presented below.


Physical Modeling

As the soil dries, the influence of gravity on the movement of pore

fluid decreases. In fact, for the majority of the time, fluid flux in

natural soils is dominated by suction gradients, which can typically be

1000 to 10,000 times the gradient due to gravity. In a uniformly dry

soil, water movement below an influent source will occur in a radial

pattern, reflecting the negligible influence of gravity. Thus, in the

scenario of percolation of leachate from a hazardous waste site, the

movement of fluid will be dominated by the extant suction gradients.

Because the influence of gravity on the flow is small, there is no

feasible advantage of physically modeling unsaturated flow conditions in

the gravity-accelerated environment within the centrifuge.











Material Testing

Laboratory tests for determining the unsaturated hydraulic

conductivity as a function of pore water content of soils have been

developed for both steady and nonsteady flow conditions. Six of the

most common methods were evaluated with the intention of determining a

feasible centrifuge technique. The following criteria for assessing the

different techniques were compiled;

1. The gravity component of the hydraulic potential gradient should be

at least of the same order of magnitude as the suction component;

preferably the gravity component will dominate.

2. The testing procedure should be appropriate for a wide variety of

soil types.

3. The test should not present undue safety concerns with the use of

decane as the permeant.

The results of the evaluation are summarized in Table 12.

Table 12. Evaluation of Laboratory Tests for Determining
Unsaturated Hydraulic Conductivity

Gradient Suitable For a Allows Centrifuge
Test Dominated Wide Range Use of Offers
by Gravity? of Tests? Decane? Advantage?

Steady Flow
1. Impeding
Crust Yes No Yes No
2. Sprinkler Yes No Yes Yes
3. Pressurized
Steady Yes No Yes No
4. Ambient
Steady Yes Yes Yes Yes

Transient Flow
1. IPMa Yes Yes Yes Yes
2. Pressure
Outflow No No Yes No

Note: a IPM refers to the Instantaneous Profile Method







Steady Flow Tests

Steady state methods of determining the hydraulic conductivity as a

function of moisture content establish and maintain a constant pressure

gradient (greater than or equal to zero) across the soil sample and

monitor the rate and volume of discharge. The four tests evaluated

herein were the impeding crust method, the sprinkler-induced steady flux

method and two generic methods, the pressurized steady flux method and

the ambient pressure steady flux method.

In the pressurized steady flux method, application of an air

pressure to the sample can be used to increase the gas phase volume, and

hence decrease the moisture content (Klute, 1965a). This technique is

limited to soils with low permeabilities due to the restriction on the

air entry value of the porous discs at the ends of the samples. The

porous discs must have small enough pores such that the pressurized air

in the soil sample cannot displace the liquid occupying the pores.

However, as the pore diameter is reduced, the hydraulic conductivity of

the disc also decreases. For example, a commercially available ceramic

disc with an air entry value of 7.3 psi suction has an associated

hydraulic conductivity on the order of 10-5 cm/sec (Soilmoisture

Equipment Corporation, 1978).

In the ambient pressure steady flux method, atmospheric pressure is

allowed to enter a horizontal or vertical sample through air holes in

the rigid wall container. The water content is regulated by the soil

suction at the entrance and exit (Klute, 1965a). This removes the

restriction of limiting conductivity of the porous disc, but introduces

the restriction that suctions must be less than the cavitation pressure

of the fluid. For water this corresponds to a practical range of 200 cm







to 800 cm of water (Klute, 1965a). When the sample is vertical and the

entrance and exit sections are equal, the resulting soil moisture flux

is driven by gravity.

Steady flow can also be achieved by placing a thin layer of flow-

restricting material on top of the vertical soil and maintaining a

shallow head of water (Green et al., 1983; Dunn, 1983). The crust

material must have a saturated hydraulic conductivity less than the

hydraulic conductivity of the test soil at the test suction. Plaster of

Paris, gypsum and hydraulic cement have been used for this purpose.

Extended periods of time are required to obtain steady flow, since the

gradient is composed almost entirely of the gravitational potential

gradient.

In the sprinkler-induced steady flux method, a constant rate of

inflow is supplied by a source located above the vertical sample (Green

et al., 1983). As long as the rate of application is lower than the

saturated hydraulic conductivity the sample will eventually achieve a

uniform soil moisture content, specific to the application rate. Since

the gradient is composed almost entirely of the gravitational potential

gradient, this method can be adapted for use in the centrifuge.


Unsteady Flow Techniques

Transient flow techniques for measuring the hydraulic conductivity

have a time advantage over steady state methods in that they yield

estimates of K over a range of moisture contents during a single test.

Two nonsteady flow techniques were evaluated as a potential centrifuge

candidate. The instantaneous profile method (IPM) entails monitoring

the change in soil suction with time along the sample profile as the

sample is exposed to specified boundary conditions (Green et al., 1983;









Olson and Daniel, 1981). Concurrent or independent information on the

moisture retention characteristic is incorporated in obtaining estimates

of K as a function of moisture content. Soil suction profiles can be

obtained during drainage from initially saturated soil or during

imbibition as water is introduced into a dry sample. When the test is

conducted during the drainage cycle, the gravity component of the

hydraulic gradient is greater than the soil moisture suction gradient; a

comparison of these two components during a test of Lakeland Series soil

ispresented in Figure 16 (Dane et al., 1983). The soil moisture and

potential data presented therein were collected during the

redistribution of moisture following surface ponding. Thus the IPM test

for the drainage cycle is a good candidate for adaptation to the

centrifuge.

The other major transient flow technique is the pressure outflow

method. The pressure outflow method relates the unsaturated hydraulic

conductivity to the volume of water discharged from a sample resulting

from an incremental increase in air pressure (Kirkham and Powers, 1972).

Again, the restriction of porous discs with sufficient air entry values

limits this procedure to materials with low conductivity. Alemi et al.

(1976) proposed a theory for revising this test which utilizes a

centrifuge to increase the hydraulic gradient via the gravitational

head. However, no experimental results were available to assess this

method.









1.6

1.4-

1.2

1-

0.8
z

ir 0.4

Z 0.2
0n


-0.2
.-t ,,------

-o., \--


-0.4-

-0.6

-0.8-

-1
0 100 200 300
ELAPSED TIME (hr)
Figure 16. Time History of the Suction Gradient During the Drainage Test








Development of the Centrifugal Technique

The IPM was selected as the most feasible test procedure to

determine the unsaturated hydraulic conductivity of a soil sample within

the centrifuge. The apparatus utilized in the saturated test was

readily modified for use in the IPM testing. A schematic of the

apparatus is presented in Figure 17. Miniature pressure transducers

were placed within the sample during preparation and monitoredthe soil

moisture suction of the pore fluid during the test.



Computer Model

A computer program was developed and utilized to evaluate the

influence of elevated and nonuniform acceleration levels on soil

moisture movement in unsaturated soils. The model incorporated the

centrifuge version of Darcy's law presented in equation 26 into theone-

dimensional continuity expression referred to as Richard's equation

de/dt -dq/dz (29)

where de/dt is the time change in volumetric water content. The model

assumes that the soil is homogeneous. A moisture retention curve and

the relationship between the unsaturated hydraulic conductivity and the

soil suction are entered as input data for each soil type of interest.

The program can simulate the wetting and/or drainage of a soil sample

under constant flux or constant potential boundary conditions. The

model was designed to simulate bench (i.e., 1 g) or centrifuge

acceleration levels, allowing direct evaluation of the influence of

acceleration on soil moisture movement.

A fully implicit finite difference solution scheme was used. The

resulting system of simultaneous equations forms a tridiagonal matrix,













OPEN TO ATMOSPHERE 2.64-cm

PLATE


S0.95-cm
STEEL ROD





-10-cm
DIAMETER
PVC PIPE




FROM BOTTOM
OF SAMPLE
SOLENOID
VALUE








PORT OPEN TO
ATMOSPHERE


I- 23 cm


Figure 17. Schematic of the Proposed Test Apparatus
Profile Method


for the Instantaneous


ENDCAI


76 cm


m
i I









which was solved by the Thomas algorithm for each time step. The model

was written in FORTRAN on a microcomputer using doubleprecision

variables and requires approximately five minutes to simulate an hour of

soil moisture movement. The mass balance is checked each time step by

comparing the total change in mass of the system with the net flux of

mass from the system. Cumulative mass errors were consistently less

than one-half of one percent for a one-hour simulation.

Accuracy of the model was determined by comparing the pressure

profile after drainage ceased to the appropriate analytical expression

of hydrostatic equilibrium. For bench tests, a linear relationship

between sample depth and soil suction (expressed in cm of water),

determined analytically as

h = ho + z (30)

was reproduced by the model. Equation 30 states that, at hydrostatic

equilibrium, the soil suction is equal to the height above a datum of

fixed potential, e. g., a water table. For centrifuge tests, the

pressure distribution at hydrostatic equilibrium was derived earlier as

P2 = P1 + pw2 (r22 r12)/2 (31)

Results from the computer model agreed precisely with this relationship,

thereby verifying the accuracy of the numerical technique.


Data Analysis

Analysis of the test results required initially deriving the

appropriate flow equations based on the acceleration distribution and

boundary conditions imposed during the tests. Because of the variable

permeant levels in the influent and effluent reservoirs, traditional

constant head and falling head permeability equations were inappropriate

for the triaxial apparatus and new permeameter. The correct equation









for the bench tests was derived by incorporating the appropriate

boundary conditions into the equation of motion. Referring to the

definition sketch in Figure 18, the variable head equation for the bench

tests is

K = aL ln(hi/hf) (32)
2At

where a = cross-sectional area of the influent line (L2);

L = length of the sample (L);

A = cross-sectional area of the sample (L2); and

t = duration of the test (T).

hi PM PL + (z z) + L (33)
i MO LO) T
pg
PM PL = air pressures at the permeant surface (M/LT2);

ZMO, ZLO I initial permeant surface elevations (L); and
HL = hydraulic energy loss due to friction, bends, valves,
entrances and exits (L).

hf = hi + 2h (34)

h rise in the right burette water surface (L).

Equation 32 has been written in a form similar to the conventional

falling head equation, the differences being the factor of two in the

denominator and the different definitions of hi and hf. Also, like the

falling head equation, when the applied pressure gradient is high

relative to the change in water levels during the test, equation 32

yields nearly identical results as the constant head equation. This was

verified during data analysis. The complete derivation of the falling

head permeability equation is presented in the Appendix. For comparison

with the centrifuge test results and to investigate the influence of

decane, the intrinsic permeability was calculated as

























AIR
PRESSURE
SUPPLY


Tz




ZZ




ZLO
j_ +


Figure 18.
Bench Test


Definition Sketch for the Variable Head Permeability Equation -


HE
no


L Z=o


&B~I I









k Kv/g (35)

where v = kinematic viscosity of the permeant at the test temperature

(L2/T). As in the conventional falling head test, the variable head

condition resulted in a deviation from steady flow, and hence,

introduced an additional acceleration force acting on the fluid element.

The fluid velocity during the test is proportional to the hydraulic

gradient; hence, this acceleration term is proportional to the time

rate of change in the gradient. During the bench tests, the gradients

were nearly constant, hence this additional acceleration term was

neglected. The derivation of the conventional falling head permeability

test also neglects this term.

The derivation of the variable head hydraulic conductivity equation

for the centrifuge testing necessitated derivation of the fundamental

relationships of fluid flow under the influence of radial acceleration.

Highlights of those derivations were presented in Chapter III. The

appropriate equation for the variable head saturated hydraulic

conductivity test in a centrifuge (see Figure 19) test is



K A In (hl/h2) (in units of time) (36)


hO w2 (rLO + rO) (37)


where rLO, rMO = the initial radii of the water surfaces (L).


P P 2
h + T (r rL) + HL (38)
1 h + h (39)M
h2 h h1 + h0 h (39)


































AIR
PRESSURE
SUPPLY


h











L


I

Figure 19. Definition Sketch for the Variable Head Permeability Equation -
Centrifuge Test


rmo M










where h = increase in radius of the upper fluid surface (L).

Here, BL has the dimensions of energy per unit mass. The complete

derivation of the falling head permeability equation is presented in the

Appendix. Estimates of the intrinsic permeability were calculated from

k = Kv (40)

The data analysis worksheet for the centrifuge tests included

information on the acceleration and hydrostatic pressure profiles in the

permeameter. The real-time data analysis facilitated the establishment

of proper initial boundary pressures.


Sources of Error

Measurement errors are inherent in most laboratory tests. Errors

associated with the hydraulic conductivity tests are discussed below.

During the tests, the flux through the soil sample was determined

as the average change in volume of the inlet and effluent reservoirs.

The levels in the reservoirs were recorded before and after each test.

In the centrifuge, a strobe light illuminated the apparatus directly

below the window in the housing, allowing direct observation of the

water levels in flight. Fluctuation of the permeant surfaces was

observed at all rotational speeds, with severe sloshing (0.5 1.0 cm)

occurring below 150 RPM.

The use of high gradients across the clay and sand/clay samples may

have caused differential consolidation during the test. Also, the exit

end of the sample had higher effective stresses acting on the particles

as a result of the gradient. To minimize the influence of these

transient phenomena, the sample was allowed to equilibrate for a period

of one to ten minutes after changing the boundary conditions before

measurements began.












A sensitivity analysis of the measurement errors was performed by

recording the variation in K as the input parameters were varied.

Maximum practical errors in determining the sample dimensions and the

test duration resulted in a variation of less than 5 percent in

estimates of K. The height of the meniscus varied from zero to 0.2 cm

during the course of the tests. The pressure transducers were

calibrated regularly and had a sensitivity of 0.02 psi. Obviously, the

lower the gradient and smaller the flux during the test, the more

sensitive the estimates of K are to errors in reading the water level

and pressure gradient. To compensate for this sensitivity, tests with

small gradients were run long enough to register at least a one cm

change in the effluent reservoir.

Another possible source of error was the equation used to calculate

K. Both the bench and centrifuge variable head equations were derived

during this study and have not been independently tested. For

comparison, estimates of K were determined using the standard constant

head equation. Under high pressure gradients, the variable head

equation yielded similar results, since under these boundary conditions,

the change in elevation of the permeant reservoir surfaces were

negligible compared to the pressure gradient. The validity of the

variable head equations was carefully scrutinized, and eventually

verified under the extreme range of hydraulic conductivity values,

boundary gradients, acceleration levels and test durations experienced

during the testing program. The validity of the equations and the

permeameter was also supported by nearly identical estimates of the

saturated hydraulic conductivity obtained by performing a conventional

falling head permeability test on the sand.














CHAPTER V
RESULTS AND DISCUSSION




The objective of the laboratory research program was to develop

centrifugal testing methods for determining saturated and unsaturated

hydraulic conductivity of soil samples. The testing program

encompassed

1. the design, fabrication and analysis of permeameters for use in the

centrifuge;

2. execution of hydraulic conductivity tests using water and decane in

a 1-g environment to provide a benchmark for comparing centrifuge

results;

3. derivation of the appropriate equations of motion for fluid flow in a

centrifuge;

4. execution of hydraulic conductivity tests using water and decane in

the centrifuge at various accelerations;

5. comparison of centrifuge results with 1-g test results; and

6. (if necessary) modification of the centrifuge device, testing

procedures and/or data analysis based on results of the comparison.

These were successfully accomplished during the course of the

study. Analysis of the current technology in permeameters resulted in

an appropriate design of apparatus to be utilized in centrifuge

testing. The apparatus was fabricated, tested and employed during the

course of the study. Saturated hydraulic conductivity tests were








conducted on the laboratory bench using commercial triaxial apparatus

and the apparatus designed during the study. Four soil types and two

permeants were utilized to cover a broad range of saturated hydraulic

conductivity values. Centrifuge testing was carried out using the same

soil types, permeants and hydraulic gradients. For the unsaturated

hydraulic conductivity analysis, the influence of acceleration levels on

soil moisture redistribution was evaluated by means of a computer model.

Results of these tests are discussed below.


Saturated Hydraulic Conductivity Tests

Sand Samples

Influence of acceleration level

The saturated hydraulic conductivity testing with sand exposed

several interesting facets of permeability testing and flow through

porous media in general. The initial testing was performed on the

commercial triaxial apparatus. However, after analyzing the results, it

was realized that significant energy losses occurred during the tests.

High energy losses due to friction occurred in the small diameter

tubing (inside diameter of 0.15 cm), which rendered the commercial

triaxial apparatus unsuitable for determining saturated hydraulic

conductivity of sand samples. Results presented herein were obtained

from the new apparatus which was designed with larger diameter tubing to

decrease the frictional energy losses. The hydraulic energy losses

which occurred during the tests weremonitored with differential

pressure transducer. A typical hydraulic energy distribution during a

centrifuge test is presented in Figure 20. The derivation of the

variable head conductivity equation incorporated the energy loss term

directly.











4


3.9
L TOP OF SAMPLE
4-
0 -3.8-


E 3.7
0

o0 3.6-
iuc
W
Zo
hi 3.5-
00
t 3.4
0

> 3.3-
I
J
< 3.2 BOTTOM OF SAMPLE
0
F-

3.1-



0 40 80 120 160 200 240

DISTANCE FROM INFLUENT RESERVOIR (cm)
Figure 20. Hydraulic Energy Profile During the Variable Head Test








The tests were conducted on the bench and then transferred to the

centrifuge for subsequent testing. Approximately 30 minutes were

required for assembly in the centrifuge. Similar gradient ranges were

established in the centrifuge as on the bench. As the permeant shifted

from the influent reservoir to the effluent reservoir, the hydraulic

pressure gradient changed during the course of the tests. Changes in

the gradient of 10 were commonly observed in the centrifuge, while

gradient changes on the bench were rarely greater than 1.

Departure from Darcy's law was observed in both the 1-g and

multiple-g tests with sand. Estimates of the intrinsic permeability, k,

are presented in Figure 21. The extreme variation in estimates of k

were explained when the same data were plotted versus the initial

gradient (see Figure 22), exhibiting a strong dependence on the

hydraulic gradient. An independent estimate of k was obtained by

performing a conventional falling head permeability test on the sand

sample using a low gradient. An average gradient of 2.8 yielded an

average value for k of 8.56 x 107 c 2, which corresponds to a hydraulic

conductivity value of 9.44 x 10-3 cm/s. These results verify the

accuracy of the new permeameter as well as the variable head equation.

As Figure 23 demonstrates, this deviation from Darcy's law was

reproduced in the centrifuge at accelerations of 14.7 and 24.4 g's. The

greater scatter observed in the centrifuge results is attributed to the

observed fluctuations in the reservoir surfaces. Below a gradient of

around ten, somewhat constant values of k were determined. However,

increased gradients resulted in decreased magnitudes of the intrinsic

permeability. Constant values of k were obtained below hydraulic

gradients corresponding to soils Reynolds number of approximately 0.2.















I



U
I'
E

z


1.1

1

0.I

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1


0 20 40
PORE VOLUMES

Figure 21. Permeability of Water Through Sand as a Function of Pore Volume


I



zi


1.1 -

1-

0.9 -

0.3 -





O.b-
0.7 -

0.6 -

0.5 -

0.4 -

0.3-

0.2-

0n


0 20 40 o0 30
INITIAL GRADIENT

Figure 22. Permeability of Water Through Sand as a Function of Initial
Gradient


D


Th

8(6
fifr


.1


00
100










1.1 -


1-


0.9-


0.8-


0.7-


0.6-


0.5-


0.4-


0.3-


0.2-

n -


D BENCH TESTS


A CENTRIFUGE TESTS


A




A A
IA
8^ A
6A


E
0





-hi
to
so


WE

o"

z

E
I-

z
Zt


V. i I I I I I I I
0 20 40 60 80 1

INITIAL GRADIENT
Figure 23. Comparison of Centrifuge and Bench Results of Permeability of
Water Through Sand


00


I.


a A


A
A W


W a&




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