development and testing of a capacitor probe to detect

Development and Testing of aCapacitor Probe to Detect

Deterioration in Portland CementConcrete

byBrian K. Diefenderfer

Thesis submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

Master of ScienceIn

Civil Engineering

APPROVED

_______________________Dr. Imad L. Al-Qadi, ChairProfessor of Civil Engineering

___________________________ _____________________Dr. Sedki M. Riad Dr. Gerardo W. FlintschProfessor of Electrical Engineering Assistant Professor of Civil

Engineering

September 1998

Copyright 1998, Brian K. Diefenderfer

ii

Development and Testing of a Capacitor Probe toDetect Deterioration in Portland Cement Concrete

Brian K. Diefenderfer

Chair: Dr. Imad L. Al-Qadi

The Via Department of Civil and Environmental Engineering

Abstract

Portland cement concrete (PCC) structures deteriorate with age and need to be

maintained or replaced. Early detection of deterioration in PCC (e.g., alkali-silica

reaction, freeze/thaw damage or chloride presence) can lead to significant reductions in

maintenance costs. Portland cement concrete can be nondestructively evaluated by

electrically characterizing its complex dielectric constant in a laboratory setting. A

parallel-plate capacitor operating in the frequency range of 0.1 to 40.1 MHz was

developed at Virginia Tech for this purpose. While useful in research, this approach is

not practical for field implementation. In this study, a capacitor probe was designed

and fabricated to determine the in-situ dielectric properties of PCC over a frequency

range of 2.0 to 20.0 MHz. It is modeled after the parallel-plate capacitor in that it

consists of two conducting plates with a known separation. The conducting plates are

flexible, which allows them to conform to different geometric shapes. Prior to PCC

testing, measurements were conducted to determine the validity of such a system by

testing specimens possessing known dielectric properties (Teflon). Portland cement

concrete specimens were cast (of sufficient size to prevent edge diffraction of the

electromagnetic waves) having two different air contents, two void thicknesses, and two

void depths (from the specimen’s surface). Two specimens were cast for each

parameter and their results were averaged. The dielectric properties over curing time

were measured for all specimens, using the capacitor probe and the parallel-plate

capacitor. The capacitor probe showed a decrease in dielectric constant with

increasing curing time and/or air content. In addition to measuring dielectric properties

accurately and monitoring the curing process, the capacitor probe was also found to

detect the presence and relative depth of air voids, however, determining air void

thickness was difficult.

iii

ACKNOWLEDGEMENT

The author expresses his gratitude to his advisor, Dr. Imad L. Al-Qadi for

contributing to this opportunity to conduct research and providing the guidance

necessary to undertake such a research project. In addition, thanks are given to the

committee members, Drs. Sedki M. Riad and Gerardo W. Flintsch, for giving their time

and expertise to help in the completion of this work.

Thanks are given to Jason Yoho for his friendship, hard work, and patience as a

research partner. His help in the author's overall understanding and assistance in

specimen preparation were instrumental to the completion of this work.

The author extends his heartfelt appreciation to his family for their unending

support and understanding. Additionally, the assistance of the author's colleagues,

Amara, Salman, Walid, Alex, Erin, James, Kiran, Ramzi, and Stacey from the Civil

Engineering Materials Program and Iman from the Electrical Engineering Time Domain

Lab greatly contributed to the author's knowledge as well as the progress of this

research.

The author also recognizes the support and interest received from the United

States Air Force Kirtland Base contract # F29650-W0542 under the direction of John

Rohrbaugh and Wes Tucker and the National Science Foundation grant # MSS-

9212318 under the direction of Ken P. Chong.

iv

TABLE OF CONTENTS

LIST OF FIGURES __________________________________________________ vii

LIST OF TABLES ____________________________________________________ ix

CHAPTER 1 INTRODUCTION___________________________________________ 1

1.1 Background_____________________________________________________ 1

1.2 Problem Statement _______________________________________________ 3

1.3 Objectives of Research____________________________________________ 4

1.4 Scope of Research _______________________________________________ 4

CHAPTER 2 BACKGROUND ___________________________________________ 6

2.1 Portland Cement Concrete _________________________________________ 8

2.1.1 Hydration of Portland Cement _________________________________ 9

2.1.2 Hydrated Cement Paste_____________________________________ 13

2.1.3 Aggregate Phase __________________________________________ 14

2.1.4 Transition Zone ___________________________________________ 15

2.2 Deterioration of PCC_____________________________________________ 16

2.2.1 Corrosion of Reinforcing Steel in PCC __________________________ 16

2.2.2 Alkali-Silica Reaction _______________________________________ 19

2.2.3 Freeze-Thaw Damage ______________________________________ 20

2.3 Dielectric Materials ______________________________________________ 21

2.3.1 Polarization Concepts ______________________________________ 25

CHAPTER 3 PARALLEL-PLATE MEASUREMENT SYSTEM _________________ 31

3.1 System Design and Setup_________________________________________ 31

3.2 Theoretical Background of the Parallel-Plate Capacitor __________________ 32

3.3 Parallel-Plate Capacitor Model _____________________________________ 34

v

3.4 Parallel-Plate Calibration Standards _________________________________ 38

3.4.1 Open Calibration Standard___________________________________ 38

3.4.2 Load Calibration Standard ___________________________________ 38

3.4.3 Short Calibration Standard___________________________________ 39

3.5 Equations Governing the Parallel-Plate System ________________________ 40

3.5.1 Parallel-Plate Measurement System Calibration __________________ 43

3.5.2 Determination of Remaining Unknowns _________________________ 48

3.6 Calibration Schemes _____________________________________________ 52

CHAPTER 4 CAPACITOR PROBE MEASUREMENT SYSTEM ________________ 55

4.1 Physical Construction of the Capacitor Probe__________________________ 57

4.1.1 Capacitor Probe Design _____________________________________ 57

4.2 Capacitor Probe Plate Configurations________________________________ 59

4.3 Capacitor Probe Calibration Standards_______________________________ 60

4.3.1 Open Calibration Standard___________________________________ 60

4.3.2 Load Calibration Standard ___________________________________ 60

4.3.3 Short Calibration Standard___________________________________ 61

4.3.4 Known Dielectric Material Calibration Standard ___________________ 61

4.4 Equations Governing the Capacitor Probe System______________________ 62

4.4.1 Load Calibration___________________________________________ 63

4.4.2 Open Calibration __________________________________________ 65

4.4.3 Calibration Using Material of Known Dielectric Constant ____________ 66

4.4.4 Short Calibration __________________________________________ 67

4.4.5 Determination of Remaining Unknowns _________________________ 69

4.4.6 Correction Function ________________________________________ 75

CHAPTER 5 TESTING PROGRAM______________________________________ 78

5.1 Specimen Preparation____________________________________________ 78

5.2 Dielectric Constant Measurements __________________________________ 80

vi

CHAPTER 6 DATA PRESENTATION AND ANALYSIS_______________________ 83

6.1 Discussion of Data ______________________________________________ 88

6.2 Parallel-Plate Capacitor vs. Capacitor Probe __________________________ 93

6.3 Final Remarks __________________________________________________ 94

CHAPTER 7 SUMMARY AND CONCLUSIONS_____________________________ 95

7.1 Findings ______________________________________________________ 95

7.2 Conclusions____________________________________________________ 96

CHAPTER 8 RECOMMENDATIONS _____________________________________ 97

REFERENCES ______________________________________________________ 98

APPENDIX A ______________________________________________________ 107

APPENDIX B ______________________________________________________ 110

APPENDIX C ______________________________________________________ 114

APPENDIX D ______________________________________________________ 145

APPENDIX E ______________________________________________________ 154

vii

LIST OF FIGURES

Figure 2.1 Typical atom in (a) the absence of and (b) under an applied field (after

Balanis, 1989) ____________________________________________ 22

Figure 2.2 Parallel-plate capacitor in the presence of (a) a vacuum and (b) dielectric

material (after Callister, 1994) ________________________________ 23

Figure 2.3 Representation of dielectric polarization: (a) ionic (b) electronic, (c) dipole,

(d) heterogeneous (after Jastrzebski, 1977) _____________________ 26

Figure 2.4 A model representation the molecular interaction effect (after Debye,

1929) ___________________________________________________ 28

Figure 3.1 Schematic setup for the parallel-plate capacitor___________________ 32

Figure 3.2 Electric field distribution between the two plates of the parallel-plate

capacitor_________________________________________________ 33

Figure 3.3 Parallel-plate capacitor with and without specimen under test ________ 35

Figure 3.4 Parallel-plate load calibration standard__________________________ 39

Figure 3.5 Large height calibration standard base _________________________ 39

Figure 3.6 Small height calibration standard base__________________________ 40

Figure 3.7 Short calibration standard____________________________________ 40

Figure 3.8 Schematic of parallel-plate measurement system and model. ________ 41

Figure 3.9 (a) General parallel-plate system model and (b) general S-parameter

model ___________________________________________________ 43

Figure 3.10 (a) Load parallel-plate system model and (b) load S-parameter model _ 44

Figure 3.11 (a) Open parallel-plate system model and (b) open S-parameter model 46

Figure 3.12 (a) Short parallel-plate system model and (b) short S-parameter model_ 47

Figure 3.13 (a) MUT parallel-plate system model and (b) MUT S-parameter model _ 50

Figure 3.14 Real part of dielectric constant of nylon using different calibrations____ 53

Figure 3.15 Imaginary part of dielectric constant of nylon using different calibrations 54

Figure 4.1 The capacitor probe ________________________________________ 55

Figure 4.2 Schematic of EM field distribution at (a) high frequency and (b) low

frequency ________________________________________________ 56

Figure 4.3 Capacitor probe load calibration standard _______________________ 60

Figure 4.4 Capacitor probe short calibration standard_______________________ 61

viii

Figure 4.5 (a) General capacitor probe model, (b) general S-parameter model of the

interface network, and (c) general S-parameter model of the combined

network__________________________________________________ 63

Figure 4.6 (a) Load capacitor probe model and (b) load S-parameter model _____ 64

Figure 4.7 (a) Open capacitor probe model and (b) open S-parameter model ____ 65

Figure 4.8 (a) Material capacitor probe model and (b) material S-parameter model 67

Figure 4.9 (a) Short capacitor probe model and (b) short S-parameter model ____ 68

Figure 4.10 (a) MUT capacitor probe model and (b) MUT S-parameter __________ 74

Figure 5.1 Schematic of Styrofoam placement in PCC slabs _________________ 80

Figure 5.2 Dielectric properties of PCC measured with capacitor probe comparing

Styrofoam and an Air Bag used to apply a systematic and repeatable

pressure _________________________________________________ 81

Figure 5.3 Dielectric properties of Teflon measured with parallel-plate capacitor __ 82

Figure 6.1 Average dielectric properties (real part) for type A specimens at 42 days

after mixing_______________________________________________ 83

Figure 6.2 Average dielectric properties (imaginary part) for type A specimens at 42

days after mixing __________________________________________ 84

ix

LIST OF TABLES

Table 3.1 Reflection coefficients from the measured calibration standards ______ 49

Table 4.1 Plate size and spacing of the different capacitor probes ____________ 59

Table 4.2 Reflection coefficients from the measured calibration standards ______ 69

Table 5.1 Mix design and specimen characteristics ________________________ 79

Table 6.1 Dielectric constant for type A specimens (2% air content, w/c = 0.45)

measured using capacitor probe a _____________________________ 84

Table 6.2 Dielectric constant for type C specimens (6% air content, w/c = 0.45)


Table 6.3 Dielectric constant for type A specimens (2% air content, w/c = 0.45)

measured using the parallel-plate capacitor______________________ 85

Table 6.4 Dielectric constant for type C specimens (6% air content, w/c = 0.45)


Table 6.5 Dielectric constant for type D specimens (6% air content, w/c = 0.45,

and 7.5 mm thick void at 25 mm depth) measured using capacitor probe a

________________________________________________________ 86

Table 6.6 Dielectric constant for type E specimens (6% air content, w/c = 0.45,

and 7.5 mm thick void at 50 mm depth) measured using capacitor probe a

________________________________________________________ 86

Table 6.7 Dielectric constant for type F specimens (6% air content, w/c = 0.45,

and 15 mm thick void at 25 mm depth) measured using capacitor probe a

________________________________________________________ 87

Table 6.8 Dielectric constant for type G specimens (6% air content, w/c = 0.45,

and 15 mm thick void at 50 mm depth) measured using capacitor probe a

________________________________________________________ 87

Table 6.9 Dielectric constant for type D specimens (6% air content, w/c = 0.45)


Table 6.10 Dielectric constant for type F specimens (6% air content, w/c = 0.45)


Table 6.11 Difference in dielectric constant due to air content as measured using

capacitor probe a __________________________________________ 90

x

Table 6.12 Difference in dielectric constant due to void depth (7.5 mm thick void) as


Table 6.13 Difference in dielectric constant due to void depth (15 mm thick void) as


Table 6.14 Change in dielectric constant due to void thickness (25 mm void depth) as


Table 6.15 Change in dielectric constant due to void thickness (50 mm void depth) as


Table 6.16 Change in dielectric constant of type A specimens (6% air, 0.45 w/c) due

to different capacitor probes__________________________________ 93

Table 6.17 Change in dielectric constant of type G specimens (6% air, 0.45 w/c, 15

mm thick void at 50 mm depth) due to different capacitor probes _____ 93

1

CHAPTER 1 INTRODUCTION

The ability of any industrialized nation to produce and sustain economic growth

is directly related to its ability to transport the goods and services that it creates.

Without a viable infrastructure system, basic public services (e.g., food distribution,

water supply, waste removal, and medical facilities) cannot be effectively disbursed.

The success of such a system depends on the ability of government policy makers to

strike a balance between available funds and the need for repair or replacement of

infrastructure components. This balance often proves difficult to achieve in a political

climate that gauges success and progress with the creation of new facilities and not the

rehabilitation of existing ones.

In the United States there are more than 581,000 bridges in the national

highway infrastructure system. Nearly 32% of these bridges are listed as “structurally

deficient or functionally obsolete” (ASCE, 1998). Approximately forty-five percent of the

bridges in the United States were constructed between the end of World War II and

1975. As these older structures approach (and exceed) their designed service life, a

plan must be implemented to categorize the need for repair or rehabilitation, based on

the level of deterioration associated with a given structure.

1.1 Background

Portland cement concrete (PCC) is the most widely used construction material in

the world due to its ease of preparation and molding, its low price (relative to other

construction materials), and the abundance of its constituent materials (cement,

aggregate, and water). However, there is more to PCC than simply mixing a collection

of materials together and placing the resultant composition in a form. When properly

designed, consolidated, and cured, PCC (with adequate reinforcing steel) will provide

excellent structural properties in the field. Improper design, preparation or placement

2

can yield an inferior quality PCC of low strength and high porosity. Poor quality control

can produce various forms of deterioration.

The main causes of deterioration in PCC are chloride-induced corrosion of the

reinforcing steel, freeze-thaw damage, and alkali-silica reaction. Chlorides found in

PCC structures, often come from the use of salts as a deicing agent on roads, their

presence in spray areas near salt-water bodies, and their inclusion during mixing.

Freeze-thaw damage in PCC results from the expansion of moisture caused by

freezing temperatures. This cyclic process exerts destructive tensile pressures within

the PCC. Alkali-silica reaction occurs when an aggressive reaction takes place

between alkalis in the PCC pore water and silica ions (from amorphous, high-silica

content aggregate). This also causes tensile pressures to build within the PCC.

Generally, the aforementioned deleterious factors are active beneath the PCC’s

surface and cannot be accurately assessed by visual observation. A majority of repair

and rehabilitation funds are therefore used to fix conditions unseen until the work is

contracted and repair work begins or until the deterioration is visible, because it has

reached such an advanced stage that it may hinder the use and function of the

structure. Recognizing the potential for damage before it occurs will help to preserve

the facility’s structural integrity, reduce life-cycle costs, and minimize the disturbance to

facility users.

To asses the physical condition of large PCC structures without causing further

damage, nondestructive evaluation (NDE) methods have been developed. Their

importance results from the noninvasive nature of the techniques used and the

anticipated rapidity of the measurements. However, not all NDE methods have been

welcomed (or understood) by many practicing civil engineers, who do not have the

interdisciplinary background or the inclination to learn how to properly transform

noninvasive methods into an operational tool. Consequently, although the concept of a

noninvasive measurement technique is attractive these engineers, there is a gap

between laboratory concept and field application.

Portland cement concrete is a composite containing a variety of materials each

with different electrical properties. However, electromagnetic (EM) characterization of

3

PCC using NDE methods can be used to impart information about its constituent

materials, thereby revealing information about the properties of the composite itself.

The EM properties of interest in this regard are conductivity and relative permittivity

(dielectric constant). These electrical properties are related to the composite properties

of the aggregate, aggregate size, cast water to cement (w/c) ratio, chloride content, and

moisture content. As chemical and physical changes occur within PCC due to

deterioration, the local and bulk EM material properties and the propagation of EM

waves in the material also change.

The dielectric properties of PCC have been investigated in a laboratory setting

at Virginia Tech using a parallel-plate capacitor operating in the frequency range of 0.1-

40.1 MHz (Al-Qadi and Riad, 1996). This capacitor setup consists of two horizontal-

parallel plates with an adjustable separation for insertion of a dielectric specimen (e.g.,

PCC). The parallel-plate capacitor has shown that detection of different types of

deterioration in PCC is feasible, but it is frequency dependent. Chloride contamination,

for example, can be easily detected at low radio frequencies (0.1-40.1 MHz), but is

difficult to detect at low microwave frequencies (1-10 GHz). The parallel-plate results

were correlated to the chloride content and different prediction models were

established (Al-Qadi et al., 1997).

1.2 Problem Statement

Civil engineering structures constructed with PCC deteriorate with time and

need to be maintained or replaced. Preventative maintenance procedures can often

reduce the life-cycle cost of such structures. Techniques that would allow civil

engineers to detect subsurface deterioration during routine inspections would aid in

their efforts to prevent major defects from occurring. However, by the time such

deterioration becomes evident on the surface, it is often too late to apply low-cost

maintenance procedures. Early detection and evaluation of deterioration in PCC (e.g.,

alkali-silica reaction, freeze-thaw damage or chloride presence) would allow engineers

to optimize the life-cycle cost of a constructed facility and minimize disturbance to its

users.

4

While useful in research, the parallel-plate capacitor is not practical for field

implementation. Therefore, a new instrument, based on the parallel-plate capacitor,

needs to be developed for civil engineers to detect internal deterioration and to provide

field measurements of the dielectric properties of PCC.

1.3 Objectives of Research

The objective of this research is to develop a capacitor probe that yields

measurement results comparable to those of the parallel-plate capacitor. Since the

parallel-plate capacitor has proved to give accurate and reliable measurements of the

dielectric properties of materials, it has been chosen as the standard measurement

device to which the capacitor probe will be compared. Since it is also desirable to

produce a capacitor probe that is reusable for multiple measurement events, it is to be

an in-situ probe that is lightweight, flexible, durable, and inexpensive.

1.4 Scope of Research

To achieve the objectives of this study, a capacitor probe was developed to

measure the effect of different parameters on the complex dielectric constant of PCC

over low radio frequencies (2-20 MHz). This was accomplished by preparing PCC

mixes with different PCC parameters such as air content. Control mixes were prepared

using a water to cement (w/c) ratio of 0.45 and air contents of 2 and 6%. Deterioration

was induced in some specimens prepared at a 0.45 w/c ratio and 6% air content by

inserting a Styrofoam layer during the casting process. The effect of PCC maturity was

studied by evaluating the dielectric properties at different curing times.

Chapter 2 sets out the physical and chemical properties of PCC, mechanisms of

common forms of deterioration, and basic dielectric theory. Chapter 3 describes the

parallel-plate capacitor measurement system and the theoretical equations governing

its operation. Chapter 4 presents the newly developed capacitor probe measurement

system and the theoretical equations regarding its usage. Chapter 5 yields the

5

experimental program involved in this research experiment. Chapter 6 presents and

discusses the results of the experimentation. Chapter 7 offers the summary, findings,

and conclusions, and Chapter 8 makes recommendations for further studies.

6

CHAPTER 2 BACKGROUND

Current NDE methods typically use EM waves as a vehicle to gather information

about the material under examination. One of the earliest adaptations of EM

technology to civil engineering involves EM pulse radar. Although originally used for

geological exploration (Lundien, 1971; Hipp, 1971; Ellerbruch, 1974; Feng and

Delaney, 1974; Moffat and Puskar, 1976; Lord et al., 1979; McNeill, 1980; Shih and

Doolittle, 1994; Feng and Sen, 1985; and Shih and Myhre, 1994), this technique has

been used for highway and bridge applications (Steinway et al., 1981; Clemena, 1983;

Carter et al., 1986; Clemena et al., 1986; Chung and Carter, 1989; Eckrose, 1989;

Bungey and Millard, 1993; and Maser, 1996). Pavement condition studies have been

conducted in which subsurface voids were detected (Steinway et al., 1981; Clemena et

al., 1987) and layer thickness and subsurface moisture measurements were performed

(Bell et al., 1963; Maser et al., 1989; Al-Qadi et al., 1989).

Additionally, dielectric properties have been measured to determine the

moisture content of soils (Topp et al., 1984; Dobson and Ulaby, 1986; Jackson, 1990;

Campbell, 1990; Scott and Smith, 1992; Brisco et al., 1992; and Straub, 1994).

Electromagnetic waves have been used for agricultural applications (Nelson, 1985) and

for measuring the dielectric properties of food items (Bodakian and Hart, 1994). Liu et

al. (1994) and Steeman et al. (1994) measured dielectric properties of various materials

for characterization in the electronics industry.

Before PCC can be characterized successfully, the electromagnetic properties

of the constituents of this composite material must be understood. In this regard,

McCarter and Curran (1984) have demonstrated that characteristics of the electrical

response of cement paste could be used as an effective means for studying the

progress of hydration and structural changes occurring within cement paste. Taylor

and Arulanandan (1974) have also investigated the relationship of mechanical and

electrical properties (conductivity and capacitance) of cement pastes measured at early

ages over a frequency range of 1 to 100 MHz. Whittington and Wilson (1986) have

7

researched the effect of curing time on the conductivity of PCC and its relationship with

compressive strength. A detailed discussion of the hydration of Portland and non-

Portland cements within the first 24 hours with respect to conductivity has been

presented by Tamas et al. (1987) and Perez-Pena et al. (1989). They discussed the

influence on conductivity due to accelerators and retarders (from 2 Hz to 2 MHz) and

the effect of inorganic admixtures (chlorides and hydroxides at 1, 10, 100, and 1000

kHz). Wilson and Whittington (1990) have presented the relationships between

conductivity of PCC and frequency during early stages of curing.

The electrical resistivity of PCC has also been investigated. Whittington,

McCarter, and Forde (1981) have compared the measured resistivity values for PCC of

varying composition with a theoretical model. A new technique for observing the time

dependent resistivity measurements of PCC with varying compositions has been

developed by Hansson and Hansson (1983) and compared with a theoretical model.

Wilson and Whittington (1990) have discussed the validity of a developed theoretical

model which describes the frequency based (1 to 100 MHz) dependence of the

resistivity of PCC.

Similarly, De Loor (1962), Wittmann and Schlude (1975), Perez-Pena et al.

(1989), and Moukwa et al. (1991) have studied the dielectric properties of PCP over the

RF and microwave frequencies. Whittington et al. (1981), McCarter and Whittington

(1981), Hansson and Hansson (1983), McCarter and Curran (1984), McCarter et al.

(1985), and Wilson and Whittington (1990) have performed measurements of dielectric

properties of PCC over RF. Hasted and Shah (1964) and Shah et al. (1965) have

measured the dielectric properties of bricks, Portland cement, and PCC at different w/c

ratios. Results are compared to theoretically obtained values.

Dielectric properties of PCC have been measured in an effort to gain a better

understanding of its mechanical properties. However, the basic relationships between

electromagnetic and mechanical properties of PCC structures are not always well

understood. These properties have been measured using three different systems over

a wideband frequency: a parallel-plate capacitor, a coaxial transmission line, and TEM

Horn antenna. Al-Qadi et al. (1994b, 1995, and 1997), Al-Qadi and Riad (1996), and

Haddad (1996) have presented the development and use of a parallel-plate capacitor

8

operating in the low radio frequency range (0.1 to 40.1 MHz). Al-Qadi et al. (1994a and

1995) and Al-Qadi and Riad (1996) have developed a coaxial transmission line fixture

that operates over a frequency range of 0.1 to 1 GHz. Ghodgaonkar et al. (1989) have

developed a microwave measurement fixture employing an antenna to determine the

dielectric constant at a frequency range of 14.5 to 17.5 GHz. While Al-Qadi et al.

(1991) have implemented a new setup to measure the dielectric constant of hot-mix

asphalt at 8.9-12.4 GHz. Al-Qadi et al. (1996) and Al-Qadi and Riad (1996) describe

another antenna fixture developed to measure the influences of induced deterioration

on the dielectric properties of PCC slabs from 1 to 10 GHz.

Tewary et al. (1991) presents theory regarding a non-contact system to

measure the capacitance of materials. This capacitance probe was modeled to operate

in a manner similar to a parallel-plate capacitor, except that the plates lie within the

same horizontal plane. A similar but expanded method was developed (Diefenderfer et

al., 1997; Yoho, 1998) creating a surface probe to measure in-situ dielectric properties

of PCC. An overview of PCC and dielectric measurements follows.

2.1 Portland Cement Concrete

Portland cement concrete is a composite material consisting of cement, water,

and coarse and fine aggregate. While anhydrous Portland cement does not posses

any bonding properties, its union with water allows it to act as an adhesive to unite

these materials into a cementitious composite. Upon inception of this hydration

reaction, PCC begins to harden and hydration products are formed. Unlike most other

construction materials, PCC is a dynamic system. Some components of PCC continue

to gain strength with time; in fact, the word concrete is derived from the Latin term

“concresure” meaning to grow together (Lewis and Short, 1907).

The hydration process of cement determines the internal structure of PCC. The

type of cement, stage of hydration, curing and temperature conditions, and the

proportions of the mixture ingredients define PCC's final internal structure. Although

the aggregate is often considered filler in ordinary strength PCC, it plays an important

9

role in determining the mixture’s durability. For the purpose of examination, PCC can

be broken down into three distinctly different parts: hydrated cement paste, aggregate,

and transition zone which is located between the cement paste and the aggregate.

2.1.1 Hydration of Portland Cement

The main ingredients used to produce Portland cement are lime, silica, alumina,

and iron oxide. These materials react in a kiln during the production of Portland cement

to form more complex compounds, the main components are abbreviated by civil

engineers as C3S (Tricalcium silicate), C2S (Dicalcium silicate), C3A (Tricalcium

aluminate), and C4AF (Tetracalcium aluminoferrite) where C = CaO, S = SiO2, A =

Al2O3, and F = Fe2O3. Minor constituents include MgO, TiO2, Mn2O3, K2O, and Na2O.

Their listing as minor describes only their relative quantity (a small percent of the weight

of the Portland cement) and not their importance in the PCC mixture. Of particular

interest to civil engineers are sodium and potassium oxides, which have been found to

react with certain types of aggregates. The products of this reaction have been shown

to cause disintegration in PCC (Neville, 1981).

The processes by which Portland cement and water form a bonding substance

take place in a water-cement paste. That is, in the presence of water, the silicates and

aluminates listed above react to form products of hydration. The principal cementing

agent (comprising approximately 50-60% of the total solid volume of hydration

products) is calcium silicate hydrate (C-S-H). A material of poor crystalline structure, C-

S-H is made up of an extremely fine (less than 1 µm) conglomeration of calcium silicate

hydrate and other crystallites formed as a result of the hydration of Portland cement.

The other main hydration product (comprising approximately 20-25% of the total solid

volume of hydration products) is calcium hydroxide. Calcium hydroxide, thought to be

much less cementitious than C-S-H, probably adds little to the cementitious properties

of the final mixture. With time, these products of hydration become the hardened

cement paste. This hydration process begins at a rapid rate that then decreases with

time. If maintained at 100% relative humidity, approximately 75% of the cement

hydrates within the first 28 days. However, the process has been noted to continue for

10

up to 50 years and is believed to never completely cease should water be present

(Taylor and Arulanandan, 1974).

The equations denoting the chemical reactions involved in the hydration process

were developed assuming that each reaction is independent of the others. While this is

not entirely true, it does provide an accurate assessment of the reaction process. The

following equations give a simplified view of the reactions involved in the hydration

process (Mindess and Young, 1981):

2C3S + 6H à C3S2H3 + 3CH (2.1)

2C2S + 4H à C3S2H3 + CH (2.2)

C3A + 3CSH2 + 26H à C6AS3H32 (2.3a)

2C3A + C6AS3H32 + 4H à 3C4ASH12 (2.3b)

C4AF + 3CSH2 + 21H à C6(A,F)S3H32 + (A, F)H3 (2.4a)

C4AF + C6(A,F)S3H32 + 7H à 3C4(A,F)SH12 + (A,F)H3 (2.4b)

where

H = Water (H2O);

C3S2H3 = Calcium hydrate silicate (C-S-H);

CH = Calcium hydroxide;

CSH2 = Gypsum;

C6AS3H32 = 6-calcium aluminate trisulfate-32-hydrate (Ettringite);

3C4ASH12 = Tetracalcium aluminate monosulfate-12-hydrate

(monosulfoaluinate); and

3C4ASH12 = tetracalcium aluminate monosulfate-12-hydrate.

11

Calcium SIlicates

The first of five reaction stages describing the hydration of calcium silicates in

Portland cement is defined by a rapid evolution of heat; it lasts for only a few minutes

after mixing water with Portland cement. The hydrolysis of C3S (Equation 1) begins

quickly and releases both calcium and hydroxide ions into solution. The pH of the

mixture rises above 12, indicating high alkalinity. The first product formed in the

hydration reaction, calcium hydrate silicate (C-S-H) gel, has a CaO:SiO2 ratio of nearly

3. This is identical to the molar ratio in the anhydrous C3S compound. Dicalcium

silicate (C2S) will hydrate in a simillar manner to tricalcium silicate (C3S); however, C2S

is much less reactive and, therefore, less heat is evolved during this process (Equation

2).

Stage 2 begins when calcium silicate hydrate begins to coat the remaining C3S

and retards further hydration. This action also marks a dormant period of little

hydration activity, which temporarily keeps PCC in a plastic state. This temporary halt

to hydration is needed to achieve a certain concentration of ions in solution before the

next hydration products can form from crystal nuclei. The initial products of hydration,

however, are unstable and begin to crystallize from solution when calcium and

hydroxide concentrations reach a critical value. This results in an accelerated reaction

involving C3S, marking the onset of stage three.

During the third stage of the hydration reaction, another hydration product is

formed: C-S-H (I) gel with a CaO:SiO2 ratio of 1.5 or less. This is followed immediately

by C-S-H (II) gel with a CaO:SiO2 ratio of 1.5 to 2.0. During stage three, the rate of

heat evolution increases to a peak at approximately 6 to 11 hrs after the onset of

hydration. Calcium silicate hydrate continues to coat the C3S grains in an ever-

thickening barrier. Therefore, water is only able to penetrate the anhydrous C3S grains

through diffusion. Stage four is marked by both chemical- and diffusion-controlled

rates of hydration involving the coated C3S. Eventually, this process is totally controlled

by the rate of diffusion, thus marking the onset of the diffusion-controlled stage five.

Hydration in this manner is quite slow and approaches 100% hydration asymptotically.

12

Tricalcium Aluminate

The hydration of C3A involves reactions with sulfate ions supplied by gypsum

(CSH2). Gypsum is added to the vitrified cement (also called clinker) during production

in the kiln to prevent flash setting, which is an immediate stiffening of cement paste due

to the reaction of C3A and water. The hydration of C3A, described in Equation 2.3a,

produces a material known as ettringite. The formation of ettringite slows the hydration

of C3A by forming a diffusion barrier around the unhydrated grains, much as C-S-H

slows the hydration of calcium silicates. Ettringite is a stable product so long as

sufficient sulfate is available (supplied in the form of gypsum). Once all available

sulfate is consumed, ettringite transforms into monosulfoaluminate (Equation 2.3b),

another calcium sulfoaluminte hydrate which contains less sulfate. This transformation

again allows C3A to rapidly react with water and typically occurs within 12 to 36 hrs after

all gypsum has been used to form ettringite.

The initial heat release observed within approximately five minutes of adding

water to cement occurs because the hydration retardation properties of gypsum have

yet to begin. Tricalcium aluminate is undesirable in PCC, because when hardened

cement paste is attacked by sulphates, formation of calcium sulphoaluminate from C3A

causes expansion in the hardened paste. Adding little or nothing to the strength of

cement except at early ages, C3A acts as a flux to reduce the temperature required to

burn the clinker during the manufacture of Portland cement and aids in the combination

of lime and silica.

Ferrite Phase

Tetracalcium alumino-ferrite (C4AF) and tricalcium aluminate (C3A) form similar

sequences of hydration products. However, C4AF can form these with or without the

presence of gypsum. Additionally, the reactions involving C4AF (Equations 2.4a and

2.4b) are much slower and produces less heat than the hydration reactions of C3A.

Iron oxide which modifies the rate of hydration, can be substituted for alumina (as seen

from the compound C6(A,F)S3H32) with little change in the hydration reaction.

13

2.1.2 Hydrated Cement Paste

In addition to the solid phase described above (including unhydrated clinker),

hydrated cement paste (HCP) is also comprised of void spaces that may contain water

in various forms. These voids are neither uniform in size nor uniformly distributed

throughout the paste.

Voids in Hydrated Cement Paste

On average, the bulk density of the products of hydration is less than the bulk

density of the anhydrous Portland cement. It has been estimated that one cm3 of

Portland cement occupies approximately two cm3 of space after complete hydration

(Mehta and Monteiro, 1993). Various types of voids, which account for this differing

bulk density, are present in hydrated cement paste (HCP), interlayer space in C-S-H,

capillary voids, and air voids.

The interlayer space in C-S-H is considered to be approximately 5-25 Å in size.

While this void space is too small to have any adverse effect on strength, it may

contain enough water by hydrogen bonding that its release (by breaking the hydrogen

bond) into the capillary void structure may contribute to drying shrinkage and creep.

The volume and size of the capillary voids is determined by the cast w/c ratio

and the degree of hydration. The total volume of the capillary voids is calculated by

determining the porosity of the mixture. Capillary voids may vary in size from 10-50 nm

for well-hydrated pastes with a low w/c ratio to 3-5 µm for high w/c ratio pastes at early

ages. Macropores, capillary voids larger than 50 nm, are thought to play a role in

determining strength and permeability. Micropores, capillary voids smaller than 50 nm,

are thought to affect drying shrinkage and creep.

It is assumed that the capillary pores form an interconnected network that can

be assessed by fluids and gases that penetrate and permeate the concrete. The main

mechanism of fluid transport in PCC is due to capillary forces and hydrostatic pressure.

Gaseous flow is attributed to partial pressure gradients and external pressures. The

ease with which fluids and gases can pass through PCC increases with increasing

porosity of the PCC. The w/c ratio is an important factor in determining the porosity of

14

PCC. At the same degree of hydration, a low w/c ratio mixture produces fewer pores of

smaller size than a high w/c ratio mixture.

Typically spherical in shape, air voids are the largest voids in the HCP. Air voids

can result from air entrainment or air which is entrapped during the mixing process.

Entrapped air voids are approximately up to 3 mm in diameter, while entrained air voids

range from 50 to 200 µm in diameter. Entrapped and entrained air, being larger than

capillary voids, can affect the strength and permeability of the concrete mixture.

2.1.3 Aggregate Phase

Although usually considered an inert filler, aggregate (including both fine and

coarse) makes up nearly 60 to 80%, by volume, of PCC. The aggregate is

predominately responsible for the unit weight, elastic modulus, and dimensional stability

of the concrete mixture (Mehta and Monteiro, 1993). These properties are determined

not by their chemical composition but by their physical attributes, such as volume, size,

pore distribution within the aggregate, shape, and texture. These attributes are derived

from the parent rock, exposure conditions, and processes used to manufacture the

aggregate.

Aggregate can be divided into two classes by size and two classes by weight.

Coarse aggregate is typically larger than 4.75 mm, while fine aggregate is generally

between 4.75 mm and 75 µm in size. Normal weight concrete (approximately 2400

kg/m3) can be made using aggregate with a bulk density of 1520-1680 kg/m3.

Lightweight and heavyweight concrete can be made using aggregate with a bulk

density less than 1120 kg/m3, and from aggregate with a bulk density greater than 2080

kg/m3, respectively.

Many factors can influence the effect of aggregate on PCC, including the

maximum size, coarse/fine aggregate ratio, shape, texture, and material composition.

Concrete with a larger maximum aggregate size requires less mixing water than

concrete with a smaller maximum aggregate size. The former generally leads to

stronger concrete; however, larger aggregate tends to have weaker transition zones.

15

The net effect of these two tendancies is a function of the w/c ratio of the PCC and the

applied stress. If the maximum aggregate size and the w/c ratio are kept constant and

the coarse/fine aggregate ratio is increased, the strength usually decreases.

Crushed aggregate is usually stronger in tension than naturally weathered

gravel of the same mineralology. Also, it is assumed that a stronger mechanical bond

between the aggregate and the cement paste exists. This bond preference is more

pronounced at early ages. Although crushed aggregate may be stronger than

smoother gravel, more mixing water is required to achieve the same workability when

using more roughly textured aggregate. This may offset any advantages gained by

aggregate texture.

2.1.4 Transition Zone

As the weakest link of the chain, the transition zone is considered the strength-

limiting phase of PCC. The transition zone exists between large particles of aggregate

and the HCP. Even though it is composed of the same components that exist in the

HCP, the properties of the transition zone differ from the HCP. This difference is seen

as the transition zone fails at a much lower stress level than either of the two main

components of PCC. In fact, 40-70% of the ultimate strength is a large enough

quantity to extend cracks already present in the transition zone. At 70% of the ultimate

strength, stress levels are sufficiently high to initiate cracking in large voids in the HCP.

As stresses increase beyond this level, the cracks will begin to extend from the HCP to

the transition zone. This makes the crack continuous and, thus, ruptures the material.

While it is difficult to extend cracks in PCC under compressive loading, it is relatively

easy to extend cracks under tensile loading. This, in part, explains why PCC is much

weaker in tension than in compression.

Adhesion between the hydration products and aggregate particles is due to Van

der Waals forces of attraction. Therefore, the strength of the transition zone is

dependent upon the size and volume of voids present. At early stages, the size and

volume of voids in the transition zone are larger than in the bulk HCP. Consequently,

the strength of the transition zone is lower than the bulk HCP. However, with time, the

16

transition zone becomes nearly as strong as the bulk HCP. It is assumed that this

occurs due to the formation of new products in the void spaces by slow reactions

between the constituents of the cement paste and the aggregate. These reactions also

reduce the amount of the less-adhesive calcium hydroxide. Additionally, microcracks

help to weaken the transition zone. The number of microcracks is a function of the

aggregate size and grading, cement content, w/c ratio, degree of consolidation, curing

conditions, environmental humidity, thermal history of the concrete mixture, impact

loads, drying shrinkage, and sustained loads at high stress levels (Mehta and Monteiro,

1993). However, some microcracks are present even before the finished structure is

loaded.

2.2 Deterioration of PCC

Generally, deterioration of PCC takes place involving one or more of the

constituents of PCC and aggressive reactants from the external environment. Among

these forms of deterioration are the electrochemical corrosion of embedded steel due

to chloride intrusion into PCC, carbonation, alkali-silica reaction (ASR), and freeze-thaw

damage. Deterioration often begins as a chemical reaction but results in physical

defects such as increased porosity and permeability, decreased strength, and/or

cracking and spalling. In-situ PCC structures may experience several chemical and

physical deterioration processes simultaneously; in fact, some may accelerate the

effects of others. A brief description of three forms of deterioration follows.

2.2.1 Corrosion of Reinforcing Steel in PCC

Bradford (1992) states that the direct cost of structural deterioration due to

corrosion of reinforcing steel in an industrialized nation consumes approximately 4.9%

of the gross national product of that nation. Metallic reinforcing is used in PCC

structures for several reasons, one of which is because the failure of metallic reinforced

PCC is less brittle than the failure of unreinforced PCC. Metallic reinforcement placed

in PCC structures is usually concentrated in areas of greatest tensile forces. If the

17

structure were to fail due to these tensile forces, the metallic reinforcement would

stretch to a certain degree due to its high ductility. However, an unreinforced PCC

structure would undergo catastrophic brittle failure. Steel is most often used as metallic

reinforcement in PCC since the coefficients of thermal expansion for steel and PCC are

similar.

Properly mixed and placed PCC (having a sufficient cover depth) usually

provides adequate protection for internal reinforcing. In addition, the high pH of PCC

(typically 12.5-13.5) provides an environment in which the oxides of iron are

thermodynamically stable. A passive protective film of iron oxide is created around the

steel reinforcement in the presence of water, oxygen, and water-soluble alkaline

products (predominately calcium hydroxide) from the hydration of cement. This film of

corrosion products slows the rate at which further corrosion can occur and protects the

remaining metal from further corrosion. In this passive state, steel corrodes at a rate

approximately equal to 10 x 10-6 cm/yr (Hansson and Sorensen, 1990). However, if this

film becomes soluble, the passivity of the steel is eliminated and corrosion continues at

an increased rate.

Two ways, in which the passive film layer is destroyed, are a reduction in the

alkalinity of the concrete and an electrochemical reaction involving chloride ions in the

presence of oxygen. The alkalinity can be reduced by the leaching of alkaline

substances with water or by a neutralization effect involving carbon dioxide. Chlorides

are often present due to use of salts as a deicer on roads, spray from seawater, and

inclusion during mixing. However, reinforcing steel is usually covered by approximately

25 mm of PCC (at least when properly constructed). Therefore, these deleterious

results only occur when the corrosion-causing agents reach the steel after penetrating

the PCC.

The electrochemical process describing the corrosion of reinforcing steel in PCC

involves an anode (site of electrochemical reduction), a cathode (site of oxidation), an

electrolyte (in PCC, the paste-pore solution), and an electrically continuous connection.

The removal of any one of these four components will halt the corrosion reaction. The

anode and cathode sites develop as corrosion cells of differing electrochemical

potential, where the reaction occurring at the cathode consumes electrons produced by

18

a reaction at the anode. Electrochemical potentials can form from the presence of

dissimilar metals (e.g., steel reinforcing and aluminum conduit) and differences in

concentrations of dissolved ions (alkalis, chlorides, and oxygen) near the reinforcing

steel.

One of the most common causes of corrosion of reinforcing steel in PCC is the

presence of chlorides (Rosenberg et al., 1989). The proper amounts of oxygen and

moisture in close proximity to the internal reinforcing steel, combined with chlorides,

can lead to deterioration (ultimately by delamination and spalling) of the PCC structure.

According to Al-Qadi et al. (1993) reinforcing steel will begin to corrode when the

concentration of chloride ions in the pore solution reaches a threshold level of 0.6 kg/m3

of PCC. Chlorides, in the form of salt-contaminated aggregate, deicing salts, or

seawater can penetrate PCC structures through cracks or diffusion through the PCC’s

pore water.

Free chloride ions (Cl-) moving through the PCC pore system react with Fe2+ in

areas where the passive coating (γ-Fe2O3) surrounding the embedded steel has been

destroyed. This passive layer is reported to be stable when the pH of the pore solution

remains above 11.5 (Mehta and Monteiro, 1993). Additional Cl- and H+ ions are

released and iron hydroxide is formed when FeCl2 undergoes further reactions in the

presence of moisture. The newly-formed iron hydroxide reacts with oxygen to form

Fe2O3 (rust). This transformation of metallic iron to rust is also accompanied by an

increase in volume, potentially occupying up to six times the original metallic volume.

This process results in a reduction of the effective area of the reinforcing steel and

creation of tensile forces in the PCC structure; ultimately, this processs can lead to

cracking, delamination (between the reinforcing steel and the surrounding PCC), and

spalling. Cracks that extend to the surface of the PCC allow more chlorides to intrude

into the PCC and thus perpetuate the reaction.

There are many factors that will influence and control the rate at which the

corrosion of reinforcing bars occurs. Higher temperatures will increase the rate of

corrosion by up to two times for every 10°C increase in temperature. A higher moisture

content in the concrete will also increase the rate of corrosion by providing an

electrolyte for the transfer of electrons from the anode to the cathode. However,

19

oxygen can diffuse more easily into dry concrete than wet concrete, because diffusion

through water is much slower than diffusion through air.

2.2.2 Alkali-Silica Reaction

Alkali-silica reaction (ASR) is an expansive chemical reaction involving alkali

ions present in the PCC paste and certain siliceous materials present in the aggregate.

The high pH level present in the PCC pore solution results in a highly alkaline solution

in which aggregates formed from silica and siliceous materials do not remain stable

after long periods of exposure. Ultimately, this expansive reaction can lead to pop-outs

and exudation of an alkali-silicate fluid. Alkali-silica reaction was first recognized as a

problem in the United States in the New River Valley area of Virginia in the 1930s

(Hobbs, 1988).

In order for this expansive reaction to occur, both hydroxyl ions and alkali-metal

ions are necessary. Hydroxyl ions are present in hydrated Portland cement due to the

existance of calcium hydroxide; therefore, the amount of alkali-metal ions will control

the degree of ASR reaction. These alkali-metal ions are introduced into PCC through

alkali-containing admixtures, salt-contaminated aggregates or penetration of seawater

or deicing solutions containing sodium chloride.

Alkaline hydroxides, derived from alkalis (Na2O and K2O), attack siliceous

material in the aggregate. This process results in the formation of an alkali-silicate gel

that swells in size due to the osmosis of water. Since this gel is confined within the

surrounding cement paste, destructive tensile forces develop within the PCC. Two

theories exist that may explain the mechanism of expansion caused by ASR (Hobbs,

1988). One theory attributes the stresses generated within the PCC to expansion of

the ASR gel by absorption of the pore fluid. The other theory attributes the induced

stresses to an osmotic pressure generated across impermeable memebranes.

According to the absorption theory, expansion depends on the volume

concentration, growth rate, and physical properties of the alkali-cement gel.

Additionally, the amount of damage is proportional to the rate of gel growth. At a high

20

growth rate, the PCC cannot absorb any tensile stresses by particle movement. As the

tensile stresses increase and exceed the tensile strength of PCC, cracking occurs. The

osmotic cell pressure theory suggests that the cement paste acts as an impermeable

memebrane for the silicate ions. This membrane allows water, hydroxyl ions, and alkali

metal ions to diffuse through it, but does not permit the diffusion of silicate ions.

Therefore, a site undergoing ASR exerts a pressure against the restraining paste.

2.2.3 Freeze-Thaw Damage

Environmental conditions profoundly influence the performance of PCC.

Constantly changing external temperatures and thermal gradients within a PCC

structure create cyclic stresses. Temperature extremes that include freezing and

thawing cycles can be destructive to PCC, especially if the mix contains low durability

aggregate and/or high water content. Partially saturated PCC (approximately 70% of

the pores initially saturated with water at 91%) can experience damage from freezing

conditions. The amount of damage depends on the number of applied freezing and

thawing cycles, the internal structure of PCC (pore size distribution and total porosity)

for both the Portland cement and the aggregate, and the presence of an air-entraining

agent. The damage to PCC caused by freezing and thawing is created by two

mechanisms: hydraulic (Powers, 1945) and osmotic pressures (Powers, 1956).

However, whatever the prevailing mechanism, the movement of water during freezing

develops an internal pressure that creates damage in the PCC pore system. Cracks

are induced in the PCC surface and eventually the repeated stresses cause failure

from fatigue.

The hydraulic pressure theory (Powers, 1945) suggests that deterioration by

freeze and thaw is caused by hydraulic pressures created by the expansion of water

upon freezing. This hypothesis suggests that PCC is a closed system where stresses

are generated by the flow of unfrozen water out of large pores. Since the resistance to

flow is proportional to length of the pathway, there is a critical flow path length beyond

which hydraulic pressures exceed the stress necessary to crack the PCC after repeated

freeze-thaw cycles.

21

The osmotic pressure theory (Powers, 1956) suggests that an osmotic pressure

is created by a difference in ion concentration in the capillary water between the pore

barriers. Freezing water that has accumulated in the larger pores creates the

difference. This results in a higher ion concentration in the remaining unfrozen water,

which attempts to create a concentration equilibrium by moving to adjacent pores of

lower ion concentration. This movement creates the same effect as water movement

due to hydraulic pressure.

Air entrainment is added to PCC mixes to induce air bubbles (approximately 10

to 1000 µm in diameter) to reduce the flow path of the pressurized water (Kosmatka

and Panarese, 1988). Entrained air also affects the total air content, the spacing

factor, and the specific surface of the voids. Additionally, the coarse aggregate

physical properties and critical size contribute to the freeze-thaw behavior of PCC.

High resistance to freeze-thaw is found when coarse aggregate with low porosity and

large pore sizes is used in PCC. Each specific aggregate has a critical aggregate size.

This critical size marks the largest size that still provides resistance to freeze-thaw

regardless of the number of cycles applied.

2.3 Dielectric Materials

Materials that are electrically characterized as dielectrics are insulators (non-

conductors) and consist of atoms with an electric dipole structure. This structure

means that there is a physical separation between positively and negatively charged

entities on an atomic level. These charges are bound by atomic forces and are not free

to travel. Ideal dielectrics, as shown in Figure 2.1a, do not contain any free charges (as

do conductors) and are neutrally charged on a molecular level. However, when an

external field (e.g., an electric field) is applied, as shown in Figure 2.1b, the bound

positive and negative entities are able to slightly shift their positions, opposing the

atomic forces. This shift allows dielectric materials to store energy, like a stretched

spring, as potential energy.

22

Figure 2.2 illustrates the conceptual model describing a dielectric material in an

external field (e.g., between charged plates of a parallel-plate capacitor). When a

vacuum exists between the two plates, equal but opposite free surface charge densities

(+ρs and -ρs C.m-2) accumulate at the two plates (Figure 2.2a). The electric intensity at

the plates, oE (V.m-1), is given as:

o

soE

ερ

= (2.5)

where

oε = permittivity of free space, 8.85 x 10-12 [F/m].

However, when a material is placed between the two plates, a bound system of

dipole charges is formed in the material; this phenomenon is called dielectric

polarization (Figure 2.2b). The net charges within the material remain equal to zero

since this polarization is assumed to be uniform (Tomboulian, 1965). Thus, the bound

charges can be represented by an electric field, iE , given as:

o

siiE

ερ

= (2.6)

Figure 2.1 Typical atom in (a) the absence of and (b) under an applied field (afterBalanis, 1989).

lE E

(a) (b)

23

where

siρ = induced surface charge density [C.m-2].

The strength of the total electric field, E , can be written as the sum of the

electric field due to free charges (Eo) and the electric field due to induced charges (Ei).

A polarization vector, P [C.m-2], is also present and is equal to the sum of the induced

surface charge density. From these relationships and from Equation 2.5, the electric

flux density, D [C.m-2], can be expressed as:

PED o +ε= (2.7)

Two independent electromagnetic properties describe the interaction of a

material with electric and magnetic fields: the complex permittivity, ε*, and the complex

(magnetic) permeability, µ*. These two characterizing properties of materials are

defined as the electromagnetic constitutive relations and are given as follows:

E*D ×ε= (2.8)

H*B ×µ= (2.9)

where

Figure 2.2 Parallel-plate capacitor in the presence of (a) a vacuum and (b) dielectricmaterial (after Callister, 1994).

V VP & E

Dielectrica) b)

+ + + + + + + ++ + + + + + + +

+ + + + + + + +

+ + + + + + + ++ + + + + + + +

+ + + + + + + +

_ _ _ _ _ _ _ _+ + + + + +

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _P & EVacuum

24

D = electric flux density [C.m-2];

E = electric field strength [V.m-2];

B = magnetic flux density [W.m-2]; and

H = magnetic field strength [A.m-1].

However, most dielectric materials, including PCC, can be described by ε* alone as

they are nonmagnetic (therefore, µ* ≈ µo = 4π x 10-7 [H.m-1]). The complex permittivity

of a material, ε*, is defined as:

ε ′′−ε′=ε j* (2.10)

where

ε′ = real part of the complex permittivity;

ε ′′ = imaginary part of the complex permittivity; and

1j −= .

By dividing Equation 2.10 by the permittivity of free space, εo, a relation of

dimensionless quantity results and is given as:

oooj

*

εε ′′

−εε′

=εε

rrr j* ε ′′−ε′=ε (2.11)

where

*rε = relative complex permittivity or dielectric constant;

′rε = real part of the relative complex permittivity; and

25

″rε = imaginary part of the relative complex permittivity.

The real part of the relative complex permittivity indicates a material’s abililty to

store an electric charge, while the imaginary part depicts the loss due to conduction

and molecular friction. The imaginary part is always greater than zero and is usually

much smaller than the real part for low loss dielectric materials (Buyukozturk, 1997).

2.3.1 Polarization Concepts

Common to all dielectric materials is their ability to store energy when an

external field is applied; this phenomenon is called polarization. There are four ways in

which PCC at low radio frequencies can be electrically polarized (i.e., polarization due

to an electric field): ionic, electronic, dipole, or heterogeneous. Ionic (or molecular)

polarization, shown in Figure 2.3a, occurs in materials that posses positive and

negative ions which tend to displace themselves when an external field is applied.

Ionic polarization also contributes to the formation of induced dipoles. Ionic polarization

is less detectable at microwave frequencies. This is due to a phenomenon known as

anomalous dispersion (discussed in section 2.3.1.1) and to ionic bonds that are very

strong. Thus, the bonds strongly resist rotational forces induced by an electric field.

Sodium chloride (NaCl) is an example of a material that undergoes ionic polarization.

Electronic polarization, shown in Figure 2.3b, occurs in materials in which the

electron cloud center surrounding the nucleus of the atom is displaced relative to the

center of the nucleus when an external field is applied. The magnitude of this type of

polarization is dependent upon the strength of the applied field and the attraction forces

imposed on the electrons by the nucleus. Additionally, electronic polarization

contributes to the formation of induced dipoles.

Dipole (or orientation) polarization, shown in Figure 2.3c, occurs in substances

composed of polar molecules (e.g., water), which posses permanent dipoles where the

molecules are randomly oriented when no external field is applied. However, when an

external field is applied, the dipoles align themselves with the applied field. This type of

polarization is strongly temperature dependent, because the randomization of the polar

26

molecules is supported by thermal agitation. Rotation of the polar molecules is also

affected by the substance's phase. Lattice forces restrict this type of polarization in

solid substances. Thus, the dielectric constant for water is approximately eight times

higher than the dielectric constant of ice. Dipole polarization is easy to detect at both

radio and microwave frequencies. This is due to the fact that the forces that hold

dipoles together are relatively weak.

Heterogeneous polarization (Figure 2.3d) occurs in dielectric materials in which

conducting volumes are distributed. A relaxation effect takes place at a critical

frequency. Charge carriers can redistribute themselves within the conductive particles,

if the applied frequency is less than the critical frequency. This yields an artificially high

Figure 2.3 Representation of dielectric polarization: (a) ionic, (b) electronic, (c)dipole, (d) heterogeneous (after Jastrzebski, 1977).

-+

-

+

-+

-+

-+-+

-+

-+

+

+

+

+

+

+

+

+

+-

--

---

++

++ +

+-

-

-

E

Direction of AppliedElectromagnetic Field

a)

b)

c)

d)

27

dielectric constant and low electrical loss associated with a low value of conductivity.

However, if the applied frequency of the field is greater than the critical frequency, the

charge carriers cannot redistribute fully. This leads to a reduction in dielectric constant

and an increase in conductivity.

The dielectric constant of many liquids and solids usually depends on the

frequency of the measurement. The dependence generally decreases from a static

value, εs, at low frequencies to a smaller limiting value, ε∞, at high frequencies.

Between which lies a transition region of anomalous dispersion, in which "absorption

conductivity" occurs yielding a complex dielectric constant, ε*r.

In an alternating electric field, the orientation of polar molecules is opposed by

the effect of the thermal agitation and molecular interaction (Cole and Cole, 1941).

Debye (1929) models the second effect by viscous damping, where the molecules are

regarded as spheres in a continuous medium with the macroscopic viscosity shown in

Figure 2.4. Theoretical analysis of this behavior is presented in the following:

( )20

s

1 ωτ+

ε−ε+ε=ε′ ∞

∞ (2.12)

( )( )20

0s

1 ωτ+

ωτε−ε=ε ′′ ∞ (2.13)

where

ω = angular frequency, 2πf;

ε∞ = dielectric constant at infinite frequency;

εs = static dielectric constant;

τ0 = relaxation time [sec]; and

f = frequency.

28

For a static field, τ0 ranges from 10-6 to 10-13 sec. The relaxation time depends on

temperature, chemical composition, and structure of the dielectric. In heterogeneous

materials, consisting of two or more components having a discrepancy n the

conductivity potentials, a dispersion known as the Maxwell-Wagner effect arises. This

dispersion can be modeled using Debye's equations after modifying εs and ε∞ values.

Historical Development of Polarization Concepts

Electricity has been known as a natural phenomenon since ancient times.

However, experimental studies were not performed until the 18th century. In 1745,

Caneus and Musschenbroek constructed a condenser consisting of two conducting

plates separated by an insulating material. When it was found that this condenser

could store large quantities of charge, it became popular for experimental studies under

the name of Leyden jar.

Little attention was paid to the insulating material until 1837 when Faraday

published the first numerical analysis of the insulating material that he called a

dielectric. His experiments showed that the capacity of a condenser was dependent on

the properties of the insulating material between the two conducting surfaces. Faraday

also introduced the term specific inductive capacity, defined as the ratio between the

capacity of a condenser filled with a dielectric and the capacity of the same condenser

when empty. This is the same quantity now called the permittivity or dielectric constant.

ε∞ ε0 - ε∞

∞ε−ετ

0

Figure 2.4 A model representation the molecular interaction effect (after Debye,1929).

29

Summarizing the investigations of electric and magnetic phenomena, Maxwell

published his unified theory of electromagnetic phenomena. In this theory, the

permittivity is given as the ratio of the electric field intensity and the dielectric

displacement. Maxwell also thought that light was a form of electromagnetic radiation.

He, therefore, saw that for most dielectrics, the dielectric constant should be equal to

the square of the refractive index, n. The relation, ε = n2, is known as the Maxwell

relation (Böttcher, 1973).

In the later part of the nineteenth century and the early part of the twentieth

century, the dielectric constant was determined for a number of materials, especially to

evaluate the validity of the Maxwell relation. The experimental results agreed well with

the theoretically obtained values for most solids and even some liquids and gases.

However, for many substances, called “associating,” the dielectric constant was

measured to be higher than the square of the refractive index over frequencies in the

visible region. These same experiments revealed that some substances absorbed

energy at frequencies in the visible region and that an anomalous dispersion (or a

decrease in the refractive index with an increase in frequency) always accompanied

this energy absorption. Thus, it was possible to extend the validity of Maxwell’s relation

by determining the dielectric constant using a complex frequency-dependent relation

(where the imaginary part measures the absorption of energy) and the refractive index.

It was theorized that the discrepancy between actual measurements and

theoretically obtained results was attributable to a permanent electric dipole moment

associated with the molecules. However, this theory remained vague and largely

qualitative until Debye published his quantitative theory (Debye, 1922). Debye

developed an expression for the dielectric constant that depended not only on the

molecular polarizability but also the permanent dipole moment of the molecule.

Debye later explained the anomalous dispersion of the dielectric constant by

pointing out that the orientation process of the permanent dipole moments associated

with changes in an applied electric field required a time interval due to the rotational

process involved in orienting the molecule. From Debye’s assumptions, it was stated

that after the removal of an externally applied field, the average dipole orientation

decays exponentially with time; this was defined as the relaxation time. Debye

30

concluded that the time lag between the average orientation of the molecules and a

change in the electric field became noticeable when the frequency of the field

approached the same order as the inverse of the relaxation time. The molecular

relaxation time led to the anomalous dispersion of the dielectric constant and

subsequent absorption of electromagnetic energy; this process is defined as dielectric

relaxation.

Several modifications and additions have been proposed to Debye’s theory for

the dielectric relaxation time. These have led to the general replacement of a single

relaxation time by a set of relaxation times dependent on the description of the

macroscopic relaxation process. As an example, the Cole-Cole plot represents a

graphical interpretation to distinguish cases of continuous distribution of relaxation time

from those of single relaxation times (Cole and Cole, 1941).

31

CHAPTER 3

PARALLEL-PLATE MEASUREMENT SYSTEM

The parallel-plate capacitor was originally designed at Virginia Tech (Al-Qadi et

al., 1994a) to characterize materials based on their dielectric properties and is relatively

easy to use because of its simplicity, suitability for low RF frequency range

measurements, and the convenience of casting or cutting parallel-faced PCC

specimens. The parallel-plate capacitor induces a uniform electric field over a fairly

large volume of space. Therefore, large specimens can be measured with acceptable

accuracy. The custom made fixture allows measurement of different specimen sizes

due an adjustable separation between its plates. An HP-4195A Network/Spectrum

Analyzer (Hewlett-Packard Co., Santa Clara, Calif.) was connected to the fixture to

measure the capacitor impedance. Rectangular-shaped specimens, used for this

setup, simplified both the design and the casting mold required.

3.1 System Design and Setup

Figure 3.1 shows the experimental setup of the parallel-plate capacitor. The

capacitor plates are mounted in a horizontal direction. Each stress-relieved plate is

approximately 460 x 460 x 13 mm and is made of steel. A supporting rod at each

corner fixes the upper plate. The lower plate is mounted on a threaded rod located at

its center, allowing the lower plate to move vertically. Fifty-mm-long sleeves on the

supporting rods maintain the lower plate in a horizontal position, allowing a range of 50

to 130 mm displacement between the two plates. The PCC is placed at the center of

the parallel-plate capacitor. Carefully cast rectangular PCC blocks allow for complete

surface contact with the plates.

32

The impedance of the capacitor is measured using an HP-4195A

Network/Spectrum Analyzer. A change in the impedance of the capacitor results from

the lossy and dielectric nature of PCC. Through an internal mathematical process, the

HP-4195A analyzer transforms the received signal into the complex impedance (real

and imaginary parts) in the frequency domain.

3.2 Theoretical Background of the Parallel-Plate Capacitor

The measurement techniques are based on planar transmission line principles.

The measuring device assumes a plane transmission line in the form of a parallel-plate

capacitor configuration. The specimen under test forms the dielectric media between

the plates. To ensure a uniform electric field in the middle of the plates where the

specimen is placed (see Figure 3.2), the length of each plate should be at least three

times the largest dimension of the tested specimen to minimize edge diffraction effects

(Al-Qadi, 1992). Thus, the uniform electric field equation can be used (see Equation

2.8).

Figure 3.1 Schematic setup for the parallel-plate capacitor.

HP-4195A Network/SpectrumAnalyzer PCC

SpecimenCapacitor

Plates

33

ED *ε= (3.1)

∫ ερ=−=

0

d*so

dEdLV (3.2)

oCV = Q (3.3)

where

oV = potential [V];

d = thickness of the dielectric specimen in the direction of EM wave

propagation [m];

L = length of parallel-plate capacitor plate [m];

sρ = surface charge density [C/m2];

Q = total charge [C]; and

C = capacitance [F].

+ + +++ ++

- - --- --

E

46 cm

Figure 3.2 Electric field distribution between the two plates of the parallel-platecapacitor.

460 mm

34

From equations 3.1 through 3.3, the following results:

dS

C *ε= (3.4)

where S is the surface area of the specimen in contact with one plate and is

perpendicular to the direction of wave propagation [m2]. Equation 3.4 is valid for an

infinitely large parallel-plate capacitor that guarantees low edge disturbance.

3.3 Parallel-Plate Capacitor Model

The calibrated impedance is assumed to be due to the complex capacitance,

C*, given by:

YL = LZ

1 = j2π f (C* - C0) = GL + jBL (3.5)

where

YL = complex load admittance;

GL and BL = load conductance and susceptance, respectively;

f = frequency; and

j = −1.

C0 is the capacitance due to an equivalent sample of air (air capacitance), as illustrated

in Figure 3.3. In equation 3.5, the difference (C* - C0) is used since C0 is included as

part of the open circuit calibration.

Assuming a uniform electric field distribution at the center of the capacitor and a

homogeneous specimen, the complex capacitance is given by:

C* = dS*

r0εε = dS

j rr0

″ε−′εε (3.6)

35

Where ε0 is the free space permittivity (ε0 = 8.854 x 10-12 F/m); ε r* is the complex

relative permittivity of the specimen; ε r′ and ε r

″ are the real and imaginary part of the

dielectric constant, respectively; and S and d are the cross-sectional area and the

thickness of the specimen being measured, respectively.

The capacitance of the air-filled capacitor is given as follows:

C0 = dS

0ε (3.7)

Hence, the complex permittivity is given in terms of the calibrated load as follows:

′εr = 1 + fS2

Bdπ

(3.8)

″εr = fS2

Gdπ

(3.9)

For simplicity, the loss tangent can be defined as follows:

tan δ = ′ε

″ε

r

r (3.10)

The designed capacitor fixture can be treated as a waveguiding system

consisting of two parallel-plates of large extent confining a dielectric region between

S

d

C* Co

Zm Z0

Figure 3.3 Parallel-plate capacitor with and without specimen under test.

36

them. The mode of propagation is the principle mode or the transverse

electromagnetic (TEM) field mode. The electric field lies vertically between the plates,

while the magnetic field lies along a horizontal plane parallel to the plates. The wave

propagates between the conducting planes with a phase velocity equal to the free

space velocity of light (air dielectric). Assuming a width of b′ and a thickness of a′ at

the center (of the PCC specimen), the following parameters can be defined for such a

transmission line:

Capacitance, C: Capacitance per unit length of a parallel-plate transmission line may

be expressed as follows:

C = ab

′ε

(3.11)

Phase velocity, pv : The phase velocity is found using the following expression:

pv = µε1

(3.12)

Resistance, R: The resistance per unit length may be expressed as follows:

R = b

R2 s

′(3.13)

where Rs is the surface resistivity in ohms.

Characteristic Impedance, Z0: The characteristic impedance has the following

expression:

Z0 = Cv

1

p

(3.14)

Although the dimensions of the fixture can vary, the ones used in this study are as

follows:

Length, l = 460 mm;

37

Width, w = 460 mm;

Height, a′ = 76 mm;

Rs (for steel) = 188 x 10-6 f ; and

Width (of PCC specimen), b′ = 102 mm.

From the values given above, the electrical parameters of interest can be

evaluated for an air-filled transmission line as:

C = 2 x (8.854 x 10-12) F/m;

pv = 3 x 108 m/s;

R = 25 x 10-6 f ; and

Z0 = 188.38 Ω.

Higher order models can also exist in a parallel-plate transmission line. The

higher order waves or the complementary waves can exist for a nonzero incidence

angle on the conducting plates. The following expression gives the cut-off frequency

( f c ) for higher order modes for both transverse electric (TE) field mode and transverse

magnetic field (TM) mode:

a2

nvf pc ′

= (3.15)

where n = 1, 2,… any integer value denoting the order of the modes.

With a ′ = 76 mm, the value for cut-off frequency ( cf ) for an air-dielectric line is given

by cf = (2 x 109) n = 2 n GHz.

38

3.4 Parallel-Plate Calibration Standards

The calibration measurements include open, load (matched impedance), and

short standards.

3.4.1 Open Calibration Standard

The open calibration standard is simply an air dielectric between the plates of

the parallel-plate system. It is known, however, that using air as an open calibration

standard introduces a small amount of error due to the capacitance that is present

between the plates. This error is taken into consideration with simulation performed to

find the average value of this capacitance over different values of spacing between the

parallel capacitor plates. It would be very difficult to make a high quality open

calibration standard for this system due to the system’s physical attributes. Therefore,

an air dielectric is used for this calibration measurement. Since the capacitance

measurement is dependant on the distance between the plates, the distance for each

of the calibration standards must be the same as the distance between the plates when

measuring the material with unknown dielectric constant.

3.4.2 Load Calibration Standard

The load standard is a 50Ω resistor. This calibration standard needs to have

the ability to adjust for different distances between the plates for the same reason

mentioned in section 3.4.1 Open Calibration Standard. Shown in Figure 3.4 are the

designed load calibration standard and the standard’s dimensions. The standard is

constructed of two solid brass pieces (similar to a piston) with six low tolerance three

hundred ohm (300Ω) resistors in series with a dielectric medium separating the plates

where the resistors are connected. A brass spring is used to allow adjustment for

different plate separations.

The narrow end of the load calibration standard containing the spring is inserted

into a base. Two bases have been constructed with different heights to allow for a

39

wide range (approximately 73 mm to 111.2 mm) of parallel-plate measurement

distances. Having multiple bases will allow for flexibility in measuring different sized

specimens. The base diagrams are shown in Figures 3.5 and 3.6.

3.4.3 Short Calibration Standard

The short calibration standard is shown in Figure 3.7. This calibration standard

is a solid piece of brass with a cylinder removed from the underside for placement of a

spring. This standard is also used with the two calibration bases shown in Figures 3.5

and 3.6. Making a perfect short calibration standard is easier than making an open

calibration standard, because the effects of a parasitic capacitance and/or other noise

Figure 3.5 Large height calibration standard base.

24.2 mm φ 30.2 mm φ

57.5 mm

24.5 mm

Figure 3.4 Parallel-plate load calibration standard.

52.1 mm

10.0 mm φ

37.8 mm φ30.4 mm φ 24.0 mm φ

18.6 mm

40

contributions do not exist. Since the quality of this type of short standard is very high,

it, therefore, is assumed a perfect short standard.

3.5 Equations Governing the Parallel-Plate System

A scattering parameter matrix is a valuable representation of a multiport network

and is helpful in developing the equations governing the parallel-plate system. The

scattering matrix of any n port device is unique to that device and is independent of the

loads at the n ports. In the case of the parallel-plate test fixture, there are a total of two

ports (n=2), one at the measurement plane and one at the reference plane, as

illustrated in Figure 3.8. A network analyzer is connected to the reference port and

various loads (open, short, matched, known dielectric material, or unknown dielectric,

24.2 mm φ 30.2 mm φ

43.5 mm

Figure 3.6 Small height calibration standard base.

24.5 mm

50.8 mm

3.02 mm φ 24.0 mm φ

Figure 3.7 Short calibration standard.

27.0 mm

19.6 mm 10.0 mm φ

41

material such as PCC) are connected to the measurement port. The open, short, and

matched loads are employed in order to determine the scattering parameters of the

matrix. Once these parameters are defined at a given frequency, the test fixture is

defined and a unique relationship is established between the unknown loads and the

reflection coefficient measured by the network analyzer. Figure 3.8 is a schematic of

the measurement system with the two port scattering parameters where

a1 = voltage wave input by network analyzer;

b1 = voltage wave reflected by the entire measurement system to the network

analyzer;

a2 = voltage wave reflected by load between parallel-plates;

Network Analyzer Interface (cables and connectors) Parallel-plate Structure

Reference

Plane

MeasurementPlane

(Port 2)

Γm

S21

S22

S12

S11 ΓL

a1

b1

b2

a2

Figure 3.8 Schematic of parallel-plate measurement system and model.

42

b2 = voltage wave incident to load between parallel-plates;

ΓM = reflection coefficient measured by network analyzer at the reference plane

(= b1/a1); and

ΓL = reflection coefficient of the load between the parallel-plates at the

measurement plane (= a2/b2), ΓL is what is desired to be determined from

the measured ΓM.

For the 2 port, parallel-plate capacitor fixture, the scattering matrix is as follows:

=

2

1

2221

1211

2

1

a

a

SS

SS

b

b(3.16)

Evaluating the scattering matrix results in the following equations:

2121111 aSaSb += (3.17)

2221212 aSaSb += (3.18)

Recalling that the point of the parallel-plate capacitor calibration scheme is devised to

define the four scattering parameters (S11, S21, S12, and S22), dividing equation 3.17 by

a1 yields the following equation for Γm:

+==Γ

1

21211

1

1m a

aSS

ab

(3.19)

Dividing equation 3.18 by a2 yields the following equation for ΓL-1:

+==

Γ 2

12122

2

2

L aa

SSab1

(3.20a)

Rearranging equation 3.20a results in the following relation between a2 and a1:

22L

21L

1

2

S1

S

a

a

Γ−Γ

= (3.20b)

43

Substituting equation 3.20b into equation 3.19 yields the following equation for the

reflection coefficient at the reference plane in terms of the reflection coefficient at the

measurement plane and the scattering parameters:

L22

L211211M S1

SSS

Γ−Γ

+=Γ (3.21)

The four scattering parameters are a property of the test fixture and are independent of

the load or the network analyzer. The following sections will describe each of the three

calibration measurements in detail and how they are used for error compensation. The

calibration coefficients, consisting of the scattering parameters, will then be applied to

generate an expression to determine the complex permittivity of a material under test.

3.5.1 Parallel-Plate Measurement System Calibration

The parallel-plate measurement system, as seen in Figure 3.9, is calibrated

using a one port calibration method. This method uses three calibration standards for

error compensation. These three calibration measurements consist of an open circuit

(Ya), a short circuit (Ys = ∞), and a 50Ω load (YL) between the conducting plates of the

b)

ReferencePlane

MeasurementPlane

Γm

S21

S22

S12

S11 S Y measurement

a)

Γm

Ymeasurement

a2

a1 b2

b1

Figure 3.9 (a) General parallel-plate system model and (b) general S-parameter model.

44

system; where Y is an admittance. These three calibration measurements are used to

solve a three-unknown calibration model. The unknowns generated by the model are

the scattering parameters of the model, S11, S21S12, and S22; where S11 and S21

represent the reflection and transmission, respectively, at the plane of reference and

S22 and S12 represent the same parameters at the plane of measurement. Since the

plates are assumed large enough that the fields are vertical between the plates in the

area that the measurement is taken, the measurements are assumed to be

independent of fringing effects.

Load Calibration

The load calibration model, shown in Figure 3.10, also includes the admittance

of the load calibration standard, YL, and the admittance compensation for the load

standard, Yerr (which can also be written as YL-YO, where YO is the admittance of the

50Ω line). The resistance and capacitance values of the load standard were found to

be RL=50.7Ω and CL=3.4pF, respectively. This initial step in the load calibration

description corrects the measured value of the 50Ω load calibration standard by

compensating for the admittance of the 50Ω line (YO). Next, the quantity YL-YO is

introduced into the S-parameter model, leaving YO as the only value not included in the

S-parameter model. By including the admittance compensation for the load (Yerr) in the

Γml S Yerr=YL – YO YO

a)

b)

YL

Γml

Figure 3.10 (a) Load parallel-plate system model and (b) load S-parameter model.

45

S-parameter model, the reflection coefficient at the measurement plane generated from

the load standard (Γml) is simplified. Thus, the complexity of the entire equation set can

be reduced and Yerr can be written as follows:

OLerr YYY −= (3.22a)

LOLerr Cj)GG(Y ω+−= (3.22b)

where

j = 1− ;

ω = 2πf;

f = frequency;

GL = conductance of the load standard (1/RL);

G0 = conductance of a 50Ω load; and

CL = capacitance of the load standard.

The reflection coefficient at the reference plane of the load measurement is as follows:

0YY

YY

oo

ooL =

+−

=Γ (3.23)

The reflection coefficient, ΓL, reduces to zero by leaving only the YO term outside the S-

parameter load model. After obtaining the value for ΓL, Γm can be found, as shown in

Figure 3.9. Using the S-parameter model, the reflection coefficient of the parallel-plate

system with a 50Ω load calibration standard, Γml, is equal to S11:

11ml S=Γ (3.24)

46

Open Calibration

The admittance compensation for the load, Yerr, must be accounted for in all of

the calibration measurements. Therefore, it can be included in the open S-parameter

model, shown in Figure 3.11, as in the load calibration measurement. To accomplish

this, the admittance of the air calibration standard, Ya, is corrected to account for the

admittance compensation. The positive value of the admittance compensation, Yerr, is

then included in the S-parameter model, leaving the corrected admittance of the open

calibration standard (Yop) separated from the S-parameter model. Thus, the actual

value for Yop is as follows:

erraop YYY −= (3.25a)

)CC(j)GG(Y LaLoop −ω+−= (3.25b)

The admittance of the open calibration standard, Ya, was determined when the parallel-

plate measurement system was simulated using (Zeland Software's IE3D Microwave

Structure Simulator) and the value of Ca, the capacitance of the air between the plates,

was found to be 0.37pF. The equation for Ya is developed from the simulated value of

Ca as follows:

aa CjY ω= (3.26)

ShortΓms S Yerr=YL – YO

a)

b)

Ys

Γms

Figure 3.12 (a) Short parallel-plate system model and (b) short S-parameter model.

47

where Ca ≈ simulated capacitance of the air between the parallel conducting plates.

The reflection coefficient of the open calibration measurement, Γop, is as follows:

opo

opoop YY

YY

+

−=Γ (3.27)

After obtaining the value for Γop, Γm can be found as shown in Figure 3.9. Using the S-

parameter model, the reflection coefficient of the parallel-plate measurement system

using an open calibration standard, Γmop, may be obtained as the following:

op22

op211211mop S1

SSS

Γ−

Γ+=Γ (3.28)

Short Calibration

The short calibration measurement is assumed to be a perfect short. Thus, the

short S-parameter model, shown in Figure 3.12, decreases in complexity since the

admittance compensation (Yerr) is not included in the model. The admittance for any

short is defined as infinite. Therefore, the admittance for the measured short, Ys, is as

follows:

∞=sY (3.29)

Γmop S Yerr=YL – YO Yop

a)

b)

Ya

Γmop

Figure 3.11 (a) Open parallel-plate system model and (b) open S-parameter model.

48

The reflection coefficient of the short measurement, Γs, is given as:

1Y

Y

o

os −=

∞+∞−

=Γ (3.30)

After obtaining the value for Γs, Γm can be found as shown in Figure 3.9. Using the S-

parameter model, the reflection coefficient of the parallel-plate system using a short

calibration standard, Γms, is given as:

22

211211ms S1

SSS

+−=Γ (3.31)

Solving for the scattering parameters, the product of S21S12 can be written as Sp:

1221p SSS = (3.32)

The equations developed above are summarized in Table 3.1. These equations

represent the reflection coefficients at the input side of the system, denoted as Γml,

Γmop, and Γms in Figures 3.10 through 3.12, respectively.

3.5.2 Determination of Remaining Unknowns

Determining the remaining unknowns begins by developing a new equation from

those shown in Table 3.1. One of the unknowns, S11, has already been determined,

since it was found to be equal to the reflection coefficient of the parallel-plate system

with a 50Ω load calibration standard, Γml. This is a main reason for including the load

compensation admittance in the S-parameter model. Subtracting the load reflection

coefficient from the short reflection coefficient yields:

22

pmlms S1

S

+

−=Γ−Γ (3.33)

49

Table 3.1 Reflection coefficients from the measured calibration standards.

Calibration Reflection Coefficient ( Γm )

Load 11ml S=Γ

Openop22

op211211mop S1

SSS

Γ−

Γ+=Γ

Short22

211211ms S1

SSS

+−=Γ

Subtracting the load reflection coefficient from the open reflection coefficient yields:

op22

oppmlmop S1

S

Γ−

Γ=Γ−Γ (3.34)

Equations 3.33, and 3.34 can be reduced to obtain an equation that is defined as the

variable, Q. Equation 3.35 was obtained by dividing the expression found in Equation

3.33 by the expression found in Equation 3.34.

Q)S1(

S1

22op

op22

mlmo

mlms =+Γ

Γ−−=

Γ−ΓΓ−Γ

(3.35)

Equation 3.35, referred to as Q, can now be solved for S22:

)1Q(

Q1S

op

op22 −Γ

Γ+−= (3.36)

Using the results from Equation 3.24 and Equation 3.31, Sp can be written as follows:

)S1)((S 22msmlp +Γ−Γ= (3.37)

50

The equations developed for determining the dielectric constant of a material

under test (MUT) can now be addressed. As with the calibration measurements, the

admittance compensation for the load (Yerr) is common to all of the measurements and

is included in the S-parameter model, shown in Figure 3.13. Also, the admittance of

the MUT, Ym, must be corrected using the admittance compensation, Yerr. By including

the positive value of the admittance compensation in the S-parameter model, the

corrected admittance value of the MUT, Ymut, is given as:

errmmut YYY −= (3.38)

The reflection coefficient of the MUT measurement (Γmut), developed from the equation

given above for Ymut, is given as follows:

muto

mutomut YY

YY

+−

=Γ (3.39)

After obtaining the value for Γmut, Γm can be determined as shown in Figure 3.9. Using

the S-parameter model, the reflection coefficient of the MUT (Γmm) can be determined:

mut22

mutp11mm S1

SS

Γ−

Γ+=Γ (3.40)

Γmm S Yerr=YL – YO Ymut

a)

b)

Ym

Γmm

Figure 3.13 (a) MUT parallel-plate system model and (b) MUT S-parameter model.

51

The expression for Γmm from Equation 3.40 can be rewritten in terms of Γmut as:

)(SS mlmm22p

mlmmmut Γ−Γ+

Γ−Γ=Γ (3.41)

From Equation 3.40, a numerical value for the reflection coefficient of the MUT in

Equation 3.41 can be obtained using known parameters determined by calibration. In

order to solve for the complex dielectric constant of the MUT, ε*mut, Equation 3.39

needs to be written in terms of Zmut:

Z1

Y = (3.42a)

)1(

)1(ZZ

mut

mutOmut Γ−

Γ+= (3.42b)

Equation 3.42b can be written in terms of an admittance as follows:

mutmut Z

1Y = (3.43)

From Equation 3.38, the admittance of the MUT, Ym, is known and can be expressed

as follows:

errmutm YYY += (3.44a)

mmm CjGY ω+= (3.44b)

Substituting the classical equations for a parallel-plate capacitor and conductivity

(Equations 3.45 and 3.46 respectively), the new form of the admittance of the MUT can

be expressed in Equation 3.47.

d

AC roεε

= (3.45)

dA

Gσ

= (3.46)

52

d

Aj

dA

Y rom

εεω+

σ= (3.47)

By dividing both sides of Equation 3.47 by the following expression:

dA

j oεω (3.48)

The resulting form of Equation 3.47 is as follows:

or

o

m j

dA

j

Yωε

σ−ε=

εω

(3.49)

The final two identities needed to complete the solution are given as follows:

εω

−=εε=

ωεσ=ε

d

Aj

YIm

"

o

m

oo

"r (3.50)

εω

=ε=ε

d

Aj

YRe

o

mr

'r (3.51)

Equations 3.50 and 3.51 are the real and imaginary portions of the complex dielectric

constant (ε’ and ε”, respectively) extracted from Equation 3.49.

3.6 Calibration Schemes

When the developed calibration standards were used as the sole standards in

the calibration process, the output was excessively noisy. This noise could be a result

of the estimation of the true value of the standards. Two methods were developed to

optimize the calibration scheme. These two methods involve calibrating the system up

to a certain point using HP calibration standards, and then completing the calibration

with the developed standards. The first scheme used the HP standards to calibrate the

53

vector network analyzer directly at the device. This scheme was found to decrease the

noise, but the imaginary portion of the dielectric constant appears to be negative,

Figures 3.14 and 3.15. The second method was to calibrate the vector network

analyzer at the end of the cable that connects the analyzer to the parallel-plate test

fixture. This calibration scheme developed the best measurement results and was

used as the calibration scheme for future measurements.

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35 40

Frequency (MHz)

Rea

l Par

t o

f th

e D

iele

ctri

c C

on

stan

t

Calibration Method 2


Figure 3.14 Real part of dielectric constant of nylon using different calibrations.

54

-2

-1.5

-1

-0.5

0

0.5

1

0 5 10 15 20 25 30 35 40

Frequency (MHz)

Imag

inar

y P

art

of

the

Die

lect

ric

Co

nst

ant



Figure 3.15 Imaginary part of dielectric constant of nylon using different calibrations.

55

CHAPTER 4

CAPACITOR PROBE MEASUREMENT SYSTEM

The capacitor probe, in design, resembles a parallel-plate capacitor in the sense

that it consists of two conducting plates with a known separation. However, a parallel-

plate capacitor does not allow for nondestructive in-situ measurements, whereas the

capacitor probe does, because its plates are placed on the surface of the tested

specimen or structural element. The capacitor probe, shown in Figure 4.1, was

designed as a surface probe to measure the capacitance properties of materials. From

these capacitance measurements, the dielectric constant of the material under test can

be found. The capacitor probe can be implemented as a field-ready measurement tool

to characterize the physical properties of PCC based on the materials dielectric

constant. The capacitor probe, therefore, was designed to be small, lightweight, and

durable.

The plates are manufactured of “flexible” metal sheet (e.g., copper or brass) that

allows complete contact when placed on the PCC structural element. Rubber backing

is used for mechanical strength, handling, and protection purposes. The probe is

Flexible Backing Cable to Instrument

Figure 4.1 The capacitor probe.

Capacitor Probe Plates

56

flexible so that it can conform to different geometric shapes, such as the curved surface

of a column or pile. Different overall sizes were considered for measurement purposes;

however, typically the total length is approximately 50 to 100 mm to ensure adequate

bulk averaging of the properties of the structures constituents.

As shown in Figure 4.2, EM fields will emanate from the capacitor plates and

excite the test medium. The distribution of EM fields will govern the impedance of the

probe. Impedance measurements of this probe will result in information related to the

average dielectric performance of the bulk media in the EM field. Internal flaws and

chloride presence will alter the field distribution and dielectric properties, thus affecting

a change in the impedance of the probe. In addition, by changing the frequency of the

EM excitation and/or adjusting the distance between the plates, it is possible to reveal

different information at different depths in the PCC structure.

The capacitor probe NDE system will include a portable frequency-domain

measurement instrument and a portable personal computer for on-site data acquisition

and processing. The system is calibrated using known standards to ensure accurate

determination of the electrical properties of the structure being tested.

a)

b)

Figure 4.2 A schematic of EM field distribution at (a) high frequency and (b) low frequency.

57

The capacitor probe is designed to maximize the interaction of the EM fields and

the PCC material. In addition, the frequency used should be in the range where

specific polarization (such as the ionic polarization in the case of chloride presence or

alkali-silica reaction) is dominant over other effects. Based on the size, shape, and the

location of the probe, in addition to the excitation frequency of the EM waves, the

degree of interaction and the depth of penetration of EM waves in the PCC structural

element can be controlled.

4.1 Physical Construction of the Capacitor Probe

Several probes were constructed during this study with each new design more

adaptive to a field environment. The four types of capacitor probes that have been

designed and tested will be discussed in this section.

4.1.1 Capacitor Probe Design

Plexiglas Probe

An initial capacitor probe was made using two square brass conducting plates

(75 x 75 x 5 mm with a 50 mm separation) mounted on a 12-mm-thick sheet of

Plexiglas approximately 600 x 600 mm in size. These plates were mounted to the

Plexiglas with brass screws that were inserted into holes in the Plexiglas and fastened

with wing nuts. This capacitor probe was used with the existing Hewlett-Packard

Spectrum/Network Analyzer (Model 4195A). The outer conductor of the coaxial-type

connecting cable connected to one of the plates while the inner conductor connected to

the other plate.

A 600 x 600 x 300 mm wooden box was constructed (using no metallic

connectors) and filled with Ottawa sand. This measurement box was used to

determine if the preliminary capacitor probe design could detect changes in the

dielectric properties of sand due to insertion and relative placement of inhomogeneities.

No attempts were made to measure the actual dielectric constant of the sand or any

58

inserted inhomogeneities, because a calibration system had not been completed.

However, it was determined that changes in the dielectric properties of the sand could

be detected.

Rubber-Backed Capacitor Probe

A second capacitor probe was built using two 75 mm square brass sheets (0.04

mm thick with a 50 mm separation) as electrodes and a sheet (250 x 125 x 3 mm) of

natural rubber sheet as a backing material. Initially, computer jumper stands and pins

were to be used as connectors to attach the capacitor probe to a cable. However, after

unsuccessful attempts to locate a commercial source, DC power adapter plugs and

jacks were used as interface connectors. Later, it was decided that the DC adapter

would not be used in a final design because of questions about its suitability: therefore,

a change in the connector was made. The question of the connectors' suitability came

from the fact that the DC adapter was not designed as a connector for a coaxial fixture.

The brass electrodes were affixed to the backing material by means of 1.6 mm

thick double-sided tape. This design was very well suited for field use due to the

rubber backing’s high durability and flexibility. The rubber backing and the double-

sided tape on this design, as well as the Plexiglas in the initial design, were found to

have a minimal effect on the measurements. The minimal error effect was achieved

using an error parameter inserted into the calibration model to compensate for the

space above the probe.

Tape-Backed Capacitor Probe

A third capacitor probe, resembling the rubber-backed capacitor probe in

appearance, was built using masking tape as a backing material and similar conducting

plates (without the double-sided tape) in the same geometric configuration. By using

the masking tape, intentions were to reduce the effects (if any) of the backing material

on the measurements and to have a means of fastening the probe to the material

under test. A RCA connector was used to connect the capacitor probe to a cable since

the RCA connector is specifically designed to work with a coaxial-type fixture. The

outer conductor of the RCA plug makes solid contact around the entire connector

(which was connected to the network analyzer).

59

Final Capacitor Probe Design

The final capacitor probe design consisted of the rubber backing also 250 x 125

mm in size, but only 0.6 mm thick. Along with the natural rubber sheet as a backing,

copper tape with a conductive adhesive was used as the conducting plates. The

copper tape was also 75 mm wide; however, it could be cut to any desired length to

conform to the previous designs. Using the tape allows easy change of the electrical

conducting plates in the field. The RCA connectors will also be used in any future

designs.

4.2 Capacitor Probe Plate Configurations

Several capacitor probes were constructed with varying plate size and plate

separations to determine whether a change in plate configuration would yield data

indicating a change due to the depth of measurement. In future experimentation, the

spacing between the plates will be used to control the depth of the measurement into a

specimen. The dimensions of the different capacitor probes are described in Table 4.1.

Illustrations of the different capacitor probes are located in Appendix A: Figures A1

through A6. The data associated with these measurements will be presented in

Chapter 5.

Table 4.1 Plate size and spacing of the different capacitor probes.

Capacitor probe Plate Size Plate Spacing

a 75 mm x 75 mm 50 mm

b 75 mm x 75 mm 75 mm

c 75 mm x 75 mm 100 mm

d 50 mm x 50 mm 50 mm

e 50 mm x 125 mm 50 mm

f 75 mm x 75 mm 150 mm

60

4.3 Capacitor Probe Calibration Standards

Three calibration standards are used for the capacitor probe and are presented

in the following subsections.

4.3.1 Open Calibration Standard

The open calibration standard is simply an air dielectric between the plates of

the capacitor probe system. It is known that using air as an open calibration standard

introduces a small amount of error due to the capacitance present between the plates.

However, this error is taken into consideration with the fourth calibration measurement,

explained in Section 4.3.4. It would be very difficult to make a high quality open

calibration standard for this system due to its physical attributes; therefore, an air

dielectric is used for this calibration measurement.

4.3.2 Load Calibration Standard

The load standard is a 50Ω equivalent resistance. Shown in Figure 4.3, the

standard is constructed of two solid brass plates with six low tolerance 300Ω resistors

Figure 4.3 Capacitor probe load calibration standard.

310 mm

150 mm

61

in series mounted on two long pieces of thin Plexiglas. The plates were attached to the

Plexiglas using standard epoxy. This standard was measured in the laboratory over

the frequency range of interest and the resistance was found to be 50.5Ω and the

capacitance 71.0pF.

4.3.3 Short Calibration Standard

The short calibration standard is shown in Figure 4.4. This calibration standard

is a solid sheet of brass. A short calibration standard is easier to construct than an

open calibration standard because the effects of parasitic capacitance and/or other

noise contributions are minimal. Since this short standard is of very high quality, it is

assumed that this calibration standard acts as a perfect short circuit.

4.3.4 Known Dielectric Material Calibration Standard

Materials used for this calibration consist of a PCC slab (450 x 300 x 100 mm)

and ultra high molecular weight (UHMW) polyethylene slab (450 x 300 x 100 mm). The

dielectric constant is obtained from the parallel-plate capacitor measurement system

300 mm

150 mm

Figure 4.4 Capacitor probe short calibration standard.

62

and set as a reference value. This reference dielectric constant of the known material

is used in the calibration equations of the capacitor probe measurement system as

ε*rm1.

4.4 Equations Governing the Capacitor Probe System

The impedance of the capacitor probe is measured using a network analyzer is

connected to the capacitor probe through an interface network that consists of a cable

and an adapter. The analyzer is used to measure the reflection coefficient, Γ, at its

reference plane. This reflection coefficient is a function of the S-parameters of the

interface network (Sint) as well as the impedance of the capacitor probe when applied to

the PCC material. The measured Γ is used to evaluate the complex impedance (real

and imaginary parts) of the PCC material as a function of frequency.

To ensure proper evaluation of the dielectric properties of a material under test,

four calibration measurements are taken. Three calibration measurements are taken

with the capacitor probe open-circuited, short-circuited, and terminated in a nominal

50Ω load at the terminals of the capacitor. The fourth calibration measurement is taken

using a material of known dielectric properties (ε*m1) at the frequencies desired. The

admittance of the four calibration standards are Ya, Ys = ∞, YL, and YM for the open

(air), short, load, and material terminations, respectively.

The general calibration model, shown in Figure 4.5, can be simplified by

including the admittance of the backside of the capacitor probe, Yb, in the S-parameter

model of the combined network (lumping the unknowns). The error YL–YO,

representing the deviation of YL from its nominal value (1/50Ω), is also included in the

S-parameters of the combined network. These four calibration measurements are used

to solve a four-unknown calibration model. The unknowns generated by the model are

the admittance of air (Ya) and S11, the product S21S12, and S22.

63

4.4.1 Load Calibration

The load calibration model also includes the admittance of the load calibration

standard, YL, and the admittance compensation for the load standard, Yerr (which can

also be written as YL-YO, where YO is the admittance of the 50Ω line). The resistance

and capacitance values of the load standard were found to be RL=50.5Ω and

CL=71.0pF, respectively. This initial step in the load calibration description corrects the

measured value of the 50Ω load calibration standard by compensating for the

admittance of the 50Ω line (YO). The load calibration model is shown in Figure 4.6

Figure 4.5 (a) General capacitor probe model, (b) general S-parameter model of theinterface network, and (c) general S-parameter model of the combinednetwork.

NetworkAnalyzer

Material Under TestYst = YO, S, L, M

Yb = admittanceof background

Interface Network

a)

Yb

ReferencePlane

MeasurementPlane

SintS11

S21

S22

S12

Yst

Interface Network

b) ΓmYb+Yerr

SintS11

S21

S22

S12

Yst–Yerr

Combined Network

S = SCombined Network

Γm c)

64

Next, the admittance value Yb and the quantity YL-YO are included in the S-

parameter model, leaving YO as the only value not included in the S-parameter model.

By including the admittance compensation for the load, Yerr, in the S-parameter model,

the reflection coefficient at the measurement plane generated from the load standard

(Γml) is simplified. By including these two values within the model, the complexity of the

entire equation set can be reduced. The reflection coefficient at the reference plane of

the load measurement is as follows:

0YY

YY

oo

ooL =

+−

=Γ (4.1)

The reflection coefficient, ΓL, reduces to zero by not including the YO term in the

S-parameter load model. After obtaining the value for ΓL, Γm can be found, as shown in

Figure 4.5. Using the S-parameter model, the reflection coefficient of the capacitor

probe system with a 50Ω load calibration standard, Γml, is equal to S11 as follows:

11ml S=Γ (4.2)

Yst = YL

a)

b) Γml S YO

Figure 4.6 (a) Load capacitor probe model and (b) load S-parameter model.

Γml

Yb

65

4.4.2 Open Calibration

The admittance value of air above the capacitor probe, Yb, is common to all the

calibration measurements. Therefore, it can be introduced into the open S-parameter

model, shown in Figure 4.7, as in the load calibration measurement. The admittance

compensation for the load, Yerr, must also be included in the open S-parameter model.

To accomplish this, the admittance of the air calibration standard, Ya, is corrected to

account for the admittance compensation. The positive value of the admittance

compensation, Yerr, is then included in the S-parameter model, leaving the corrected

admittance of the open calibration standard (Yop) and the negative value of the load

admittance compensation outside the S-parameter model. Thus, the actual value for

the unknown Ya is as follows:

erraop YYY −= (4.3)

The admittance of the open calibration standard, Ya, can be described in terms

of a capacitance-containing variable F. Replacing Ya as one of four unknowns that will

be determined through the four calibration measurements, the value of F is as follows:

FjY oa ϖε= (4.4)

Figure 4.7 (a) Open capacitor probe model and (b) open S-parameter model.

Γmo

Yb

Yst = Ya

a)

b) Γmo S Ya - Yerr

66

where F ≈ C/εO results from the general admittance equation, Y=jωC.

The reflection coefficient of the open calibration measurement, Γop, is as follows:

opo

opoop YY

YY

+

−=Γ (4.5)

After obtaining the value for Γop, Γm can be found, as shown in Figure 4.5. Using the S-

parameter model, the reflection coefficient of the capacitor probe system using an open

calibration standard, Γmo, may be obtained as the following:

op22

op211211mo S1

SSS

Γ−

Γ+=Γ (4.6)

4.4.3 Calibration Using Material of Known Dielectric Constant

As mentioned previously, the admittance value of air behind the capacitor probe

(Yb) is common to all the calibration measurements. This background admittance is

included in the S-parameter model, shown in Figure 4.8, as with the load and open

calibration measurements. Also, the admittance compensation for the load, Yerr, must

be included in the material S-parameter model. As with the load and open calibration

measurements, the admittance of the material calibration measurement, Ym1, must be

corrected using the admittance compensation, Yerr. Thus the corrected admittance of

the material calibration measurement, Ym1e, is as follows:

err1me1m YYY −= (4.7)

The admittance of the material calibration standard, Ym1, can also be described in terms

of the unknown variable, F. Equation 4.8 yields Ym1, where εm1* is the known dielectric

constant of the calibration material:

FjY *1m 1m

ϖε= (4.8)

where F ≈ C/ε*m1 results from the general admittance equation, Y=jωC.

67

The reflection coefficient of the material measurement, Γm1, can be given as follows:

e1mo

e1mo1m YY

YY+−

=Γ (4.9)

After obtaining the value for Γm1, Γm can be found, as shown in Figure 4.5. Using the

S-parameter model, the reflection coefficient of the capacitor probe system using the

known material calibration standard, Γmm1, can be determined as:

1m22

1m2112111mm S1

SSS

Γ−Γ

+=Γ (4.10)

4.4.4 Short Calibration

Since the short calibration is assumed a perfect short, the short calibration S-

parameter model (shown in Figure 4.9) decreases in complexity, since no correction

parameters (i.e., Yb and Yerr) are needed to complete the model. As for any short

a)

b)

Figure 4.8 (a) Material capacitor probe model and (b) material S-parameter model.

Γmm1 S Ym1 - Yerr

Γmm1

Yb

Yst = Ym1

68

standard, the admittance is equal to infinity. Thus, the admittance for the measured

short measurement, Ys, is as follows:

∞=sY (4.11)

The reflection coefficient of the short measurement, Γs, is given as:

1Y

Y

o

os −=

∞+∞−

=Γ (4.12)

After obtaining the value for Γs, Γm can be found, as shown in Figure 4.5. Using the S-

parameter model, the reflection coefficient of the capacitor probe system using a short

calibration standard, Γms, is given as:

22

211211ms S1

SSS

+−=Γ (4.13)

Solving for the scattering parameters, the product of S21S12 can be written as Sp:

1221p SSS = (4.14)

Γms

Yb

Yst = Ys

ΓmsShortS

a)

b)

Figure 4.9 (a) Short capacitor probe model and (b) short S-parameter model.

69

The equations developed above are summarized in Table 4.2. These equations

represent the reflection coefficients at the input side of the system, denoted as Γml, Γmo,

Γmm1, and Γms, in Figures 4.6 through 4.9, respectively.

Table 4.2 Reflection coefficients from the measured calibration standards.

Calibration Reflection Coefficient ( Γm )

Load 11ml S=Γ

Openop22

op211211mo S1

SSS

Γ−

Γ+=Γ

Material1m22

1m2112111mm S1

SSS

Γ−Γ

+=Γ

Short22

211211ms S1

SSS

+−=Γ

4.4.5 Determination of Remaining Unknowns

Determining the remaining unknowns begins by developing three new equations

from those shown in Table 4.2. One of the unknowns, S11, has already been

determined, since it was found equal to the reflection coefficient of the capacitor probe

system with a 50Ω load calibration standard, Γml. This is a main reason for including

the load compensation admittance in the S-parameter model. Subtracting the load

reflection coefficient from the short reflection coefficient yields:

22

pmlms S1

S

+

−=Γ−Γ (4.15)

Subtracting the load reflection coefficient from the open reflection coefficient yields:

70

)F(S1

)F(S

op22

oppmlmo Γ−

Γ=Γ−Γ (4.16)

where Γop is a function of F.

Subtracting the load reflection coefficient from the material reflection coefficient yields:

)F(S1

)F(S

1m22

1mpml1mm Γ−

Γ=Γ−Γ (4.17)

where Γm1 is also a function of F.

Equations 4.15 through 4.17 can be reduced to obtain two equations with two

unknowns. Equation 4.18 was obtained by dividing the expression found in Equation

4.15 by the expression found in Equation 4.16. Equation 4.19 was formulated by

dividing the expression found in Equation 4.15 by the expression found in Equation

4.17. The two unknowns remaining in these equations are the values of F and S22.

The values Γm1 and Γop are functions of the variable F.

A)S1(

S1

22op

op22

mlmo

mlms =+Γ

Γ−−=

Γ−ΓΓ−Γ

(4.18)

B)S1(

S1

221m

1m22

ml1mm

mlms =+Γ

Γ−−=

Γ−ΓΓ−Γ

(4.19)

Equations 4.18 and 4.19, referred to as A and B, need to be solved simultaneously to

yield the two unknowns. The values of A and B are known quantities since all of the

variables on the left of the first equality sign are measured values.

Equations 4.18 and 4.19 can be written in terms of the reflection coefficients,

Γm1 and Γop, respectively. The resulting equations are as follows:

A)A1(S1

22op −−

=Γ (4.20)

71

B)B1(S1

221m −−

=Γ (4.21)

Equations 4.5 and 4.9 need to be written in terms of Yop and Ym1e as follows:

op

opoop 1

1YY

Γ+

Γ−= (4.22)

1m

1moe1m 1

1YY

Γ+Γ−

= (4.23)

Substituting equations 4.20 and 4.21 into equations 4.22 and 4.23, respectively, the

following can be written:

1A)A1(S1A)A1(S

YY22

22oop +−−

−−−= (4.24)

1B)B1(S1B)B1(S

YY22

22oe1m +−−

−−−= (4.25)

Using the relation found in equation 4.4, an equation can be written for Ya using the

expression for Yop found in equation 4.24. Equation 4.5 relates Ya to the unknown

variable F.

FjY1A)A1(S1A)A1(S

YY oerr22

22oa ωε=+

+−−−−−

= (4.26)

Similarly, using the relation found in equation 4.7, an equation for Ym1 can be presented

using the expression for Ym1e found in equation 4.28. Equation 4.8 relates Ym1e to the

unknown variable F.

FjY1B)B1(S1B)B1(S

YY *1rmoerr

22

22o1m εωε=+

+−−−−−

= (4.27)

72

The result shown in equation 4.27 uses the relation for the dielectric constant in terms

of the relative complex dielectric constant of the material, ε*rm1, multiplied by the

dielectric constant of air, εo, as shown in equation 4.28.

*1rmo

*1m εε=ε (4.28)

An expression can be obtained for the relative dielectric constant, ε*rm1, by dividing the

expression found in equation 4.27 by the expression found in equation 4.26. The

resulting equation is shown as follows:

err22

22o

err22

22o

*1rm

Y)A1()A1(S)A1()A1(S

Y

Y)B1()B1(S)B1()B1(S

Y

+−+−+−−

+−+−+−−

=ε (4.29)

Using the relations given in equations 4.30a and 4.30b, equation 4.29 can be reduced

to the expression found in 4.31.

A1A1

C−+

= (4.30a)

B1B1

D−+

= (4.30b)

)1S(Y)CS(Y

)1S(Y)DS(Y

22err22o

22err22o*1rm ++−

++−=ε (4.31)

Separating the unknown variable S22 from the expressions found in the numerator and

denominator of equation 4.31 results in an equation for ε*rm1 as follows:

erroerro22

erroerro22*1rm YCY)YY(S

YDY)YY(S+−++−+

=ε (4.32)

The numerator and denominator of equation 4.32 can be divided by Yo+Yerr to isolate

S22 and the following expressions are defined:

73

erro

erro

YY

YDY'D

++−

= (4.33a)

erro

erro

YY

YCY'C

++−

= (4.33b)

Using the identities found in equations 4.33a and 4.33b, equation 4.32 can be reduced

to the expression found in equation 4.34.

'CS'DS

22

22*1rm +

+=ε (4.34)

Solving equation 4.34 in terms of S22 will produce the following expression:

1

'C'DS

*1rm

*1rm

22−ε

ε−= (4.35)

Using the expression found in equation 4.15, Sp can be written as follows:

)S1)((S 22msmlp +Γ−Γ=

The final unknown variable, F, can be obtained using the expression found in equation

4.4. The value of Ya is obtained from substituting the expression for S22 found in

equation 4.35 into equation 4.26.

o

a

j

YF

ωε= (4.36)

The equations that are developed for determining the dielectric constant of a

material under test (MUT) are similar to the equations for the material of known

dielectric constant for calibration purposes. As mentioned previously for the material

calibration measurements, the admittance value of air above the capacitor probe (Yb) is

common to all of the measurements and is included in the S-parameter model, shown

in Figure 4.10. The admittance compensation for the load, Yerr, must again be included

in the material S-parameter model. As before, the admittance of the MUT, Ym2, is

74

corrected using the admittance compensation, Yerr. By including the positive value of

the admittance compensation in the S-parameter model, the corrected admittance

value of the MUT, Ym2e, is given as:

err2me2m YYY −= (4.37)

The admittance of the MUT, Ym2, in terms of the known variable F is given as follows:

FjY *2m2m ϖε= (4.38)

where εm2* is the dielectric constant of the MUT.

The reflection coefficient of the MUT measurement (Γm2), developed from the equations

given above for Ym2e and Ym2, is given as follows:

e2mo

e2mo2m YY

YY+−

=Γ (4.39)

Γmm

Yb

Yst = Ym2

a)

b)

Figure 4.10 (a) MUT capacitor probe model and (b) MUT S-parameter.

Γmm S Ym2 - Yerr

75

After obtaining the value for Γm2, Γm can be determined, as shown in Figure 4.5. Using

the S-parameter model, the reflection coefficient of the MUT (Γmm) is given as follows:

2m22

2mp11mm S1

SS

Γ−

Γ+=Γ (4.40)

The expression for Γmm from equation 4.40 can be rewritten in terms of Γm2:

mm222211p

11mm2m SSSS

SΓ+−

−Γ=Γ (4.41)

From equation 4.41, a numerical value for the reflection coefficient of the MUT can be

obtained using known parameters determined by calibration. In order to solve for the

complex dielectric constant of the MUT, ε*2m, equation 4.39 needs to be written in terms

of Ym2e:

2m

2moe2m 1

1YY

Γ+Γ−

= (4.42)

Using equations 4.37 and 4.38, the relative complex dielectric constant can be

expressed as:

Fj

YY

o

erre2m*2rm ωε

+=ε (4.43)

4.4.6 Correction Function

A correction function was devised to account for undesirable systematic

effects/errors (e.g., penetration of EM waves beyond the dimensions of the specimen

and effects due to influence of the operator). The correction function is defined as a

scaling function to be applied to the values of the dielectric constant of the material

used as a calibration standard. This scaling function is applied so that the calculated

dielectric constant of the material under test will be identical to values obtained using

the parallel-plate capacitor measurement system.

76

The correction function was developed using an iterative approach where the

dielectric constant of the material under test is determined using a reference material

for calibration with a dielectric constant in the range of the MUT. Using the known

dielectric constant of the material standard (e.g. UHMW and nylon), the dielectric

constant of the MUT is evaluated. The ratio between the dielectric constant values

obtained from the capacitor probe and that obtained from the parallel plate capacitor is

used to scale the dielectric constant of the material used for calibration. Equations 4.44

and 4.45 express the calculation performed to accomplish this scaling:

)'('

'' wncalmat_kno

MUT_cp

MUT_ppdcalmat_use ε

ε

ε=ε (4.44)

)"("

"" wncalmat_kno

MUT_cp

MUT_ppdcalmat_use ε

ε

ε=ε (4.45)

where

εmut = the reference (parallel plate) and the generated (capacitor probe)

dielectric constant data in the range of the dielectric constant of the MUT;

and

εcalmat = the scaled and known values of the dielectric constant of the calibration

material.

This iterative process was applied until the dielectric constant obtained from the

capacitor probe system converged to the results obtained from the parallel plate. The

final ratio of the scaled values of the calibration material with the known values is called

the correction function:

*wncalmat_kno

*dcalmat_use

Function Correctionε

ε= (4.46)

where

77

εused = the dielectric constant of the calibration material after the iterative

process; and

εmeasured = the known dielectric constant of the calibration material.

It is important to state that the correction function was consistent throughout different

sample and material measurements. Therefore, one correction function worked

acceptably for measurements of different PCC samples using different calibration

materials (UHMW and extruded nylon).

78

CHAPTER 5 TESTING PROGRAM

The effects of different mix properties and induced deterioration on the dielectric

properties of PCC slab specimens have been studied. The PCC mixes were prepared

using type I Portland cement and limestone aggregate. Prism-shaped specimens were

prepared for testing using the parallel-plate capacitor. Two specimens were prepared

for each mix parameter. The physical and chemical properties of the coarse and fine

aggregate are shown in Tables B.1 and B.2 (Appendix B), respectively. The chemical

analysis of the cement can be found in Table B.3 (Appendix B). Two air contents, two

internal void thicknesses, and two internal void depths were evaluated. In addition, six

different capacitor probe configurations (including plate size and separation) were

studied to determine their influence on measurements of a PCC slab with an induced

void.

5.1 Specimen Preparation

The proportioning procedure recommended by ACI committee 211, absolute

volume method for selecting proportions for normal weight PCC, was followed. The w/c

ratio was kept constant for all specimens to ensure that the changes in PCC dielectric

properties were attributable to the desired condition and not a change in water content.

The mix proportions are found in Table B.4 (Appendix B).

To begin mixing, aggregate was oven dried for 24 hrs at 105°C. The aggregate

was then allowed to cool to the ambient laboratory temperature before mixing with the

Type I Portland cement and tap water using a 0.04 m3 mixer. The PCC mixes were

prepared at a w/c ratio of 0.45 (Table 5.1). To achieve the 6% air content, Master

Builders Micro-Air entraining mixture was used according to the manufacture's

recommended dosages. A dosage rate of approximately 66 ml/100 kg of cement was

used. To achieve a mixture with approximately 2% air, no air entraining agent was

79

used. Quality control measurements including slump, unit weight, and air content were

taken in accordance with ASTM standards designation C 138-92. In addition, cylinders

(150 mm in diameter and 300 mm long) were cast according to ASTM standards

designation C 39-94. Results of the quality control measurements are listed in Table

B.5 (Appendix B).

Table 5.1 Mix design and specimen characteristics.

SpecimenName

w/cratio

Aggregatetype

Air voidcontent

Void(depth)

VoidThickness

A* 0.45 Limestone 2% None -

C* 0.45 Limestone 6% None -

D* 0.45 Limestone 6% 25 mm 7.5 mm

E 0.45 Limestone 6% 50 mm 7.5 mm

F* 0.45 Limestone 6% 25 mm 15 mm

G 0.45 Limestone 6% 50 mm 15 mm

* prism specimens were prepared for these mixes (without

Styrofoam)

Portland cement slab specimens were cast in plywood molds (approximately

450 x 300 x 100 mm in size) for capacitor probe measurements, and prism specimens

were cast in stainless steel molds (approximately 100 x 75 x 75 mm in size) for

measurement using the parallel-plate capacitor. After mixing, the PCC was placed in

the molds in two lifts. Each lift was compacted using a compacting rod. Styrofoam

slabs were placed in selected slab specimens at the desired depths, as shown in

Figure 5.1. The remaining PCC was carefully placed on top and tamped so as not to

disturb the Styrofoam.

80

The surface of each slab and prism specimen was troweled to a smooth finish.

The slab and prism specimens were then placed in a moist curing room at 25°C for 10

days after which they were demolded and returned to the curing room until 28 days

after casting. After 28 days in the curing room, the specimens were stored in the

laboratory under ambient room temperature and humidity. The slab specimens were

removed for approximately 2 hrs to conduct testing on each of the first 10 days and on

the 14th, 21st, 28th, and 42nd day after casting. Prism specimens were measured on the

first day after mixing and again on the 28th day after mixing.

5.2 Dielectric Constant Measurements

Prior to dielectric constant measurements using the capacitor probe and the

parallel-plate capacitor, all PCC specimens were removed from the moist curing room,

toweled dry, and then allowed to air dry for approximately 45 minutes at ambient

laboratory room temperature. Each capacitor probe specimen was placed on a frame

(constructed using no metallic fasteners) approximately 500 mm above the floor

surface. This ensured that the underlying floor would not affect the measurements.

The capacitor probe was placed on the surface of each slab and a constant pressure

was applied to the back of the probe. A block of Styrofoam approximately 150-mm-

thick allowed the operator to apply pressure without influencing the measurement. An

PCC slabspecimen

Styrofoam slab –Thickness: 7.5 or 15 mm

Depth: 25 or 50 mm

Figure 5.1 Schematic of Styrofoam placement in PCC slabs.

81

additional measurement, shown in Figure 5.2, using an inflatable plastic air bag of

approximately the same thickness was used to ensure that the Styrofoam had little

effect on the measurements.

A calibration process was also performed daily employing an open, load, and

short calibration, and measurement of a material of known dielectric constant. The

complex impedance of the calibration measurements and each specimen was

measured by an HP 4195A Network Analyzer over a frequency range of 2-20 MHz.

The results were then entered into a spreadsheet to determine the complex dielectric

constant of the material under test.

Each prism-shaped specimen was measured using the parallel-plate capacitor.

The prism specimens were centered between the two parallel plates; the complex

impedance between the plates was measured using an HP 4195A Network Analyzer.

0

10

20

30

40

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Die

lect

ric

Co

nst

ant

Styrofoam - real

Styrofoam - imaginary

Air Bag - realAir Bag - imaginary

Figure 5.2 Dielectric properties of PCC measured with capacitor probecomparing Styrofoam and an Air Bag used to apply a systematicand repeatable pressure.

82

A systematic pressure was applied to the prism specimens by the parallel plates. A

calibration process was performed on each day of measurement using an open, load,

and short calibration at each specimen height. The accuracy of the parallel-plate

capacitor was verified through the measurement of a cylindrical Teflon specimen

(Figure 5.3). The Teflon specimen, approximately 140 mm in diameter and 75 mm

thick, was also measured over a frequency range of 2-20 MHz.

0

0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Die

lect

ric

Co

nst

ant

real

imaginary

Figure 5.3 Dielectric properties of Teflon measured with parallel-plate capacitor.

83

CHAPTER 6 DATA PRESENTATION AND ANALYSIS

The results of the dielectric constant measurements using the capacitor probe

(75 mm x 75 mm plates at a 100 mm separation) are presented in Appendices C and E.

Appendix C shows each specimen individually as curing time progresses. Appendix E

shows the dielectric constant of each specimen versus curing time over three

frequencies (5, 10, and 20 MHz). All measurements shown in Appendices C and E

were conducted in duplicate. The average of the measurements is used in the data

analysis as shown in Figures 6.1 and 6.2. Each plot in Appendices C and E is an

average of two specimens. No significant differences were noted between duplicate

measurements.

To study the effect of air content in PCC on its dielectric properties, two air

contents, 2% and 6%, were used to prepare capacitor probe and parallel-plate

0

20

40

60

80

100

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

A1 - 42 days - realA2 - 42 days - realA - 42 days - real avg

Figure 6.1 Average dielectric properties (real part) for type A specimens at 42 daysafter mixing.

84

capacitor specimens. The results of the testing using the capacitor probe are

presented in Tables 6.1 and 6.2. The results of the testing using the parallel-plate

capacitor are presented in Tables 6.3 and 6.4.

0

20

40

60

80

100

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant A1 - 42 days - imag

A2 - 42 days - imagA - 42 days - imag avg

Figure 6.2 Average dielectric properties (imaginary part) for type A specimens at 42 daysafter mixing.

Table 6.1 Dielectric constant for type A specimens (2% air content, w/c = 0.45)measured using capacitor probe a.

Specimen Areal imaginary real imaginary real imaginary

5 hours 88.75 448.56 79.22 216.29 57.64 142.4712 hours 91.98 154.38 66.65 89.10 45.75 66.1121 hours 86.91 98.92 55.49 62.09 32.86 51.71

1 day 67.55 72.05 43.64 46.74 31.16 33.373 days 59.08 63.93 39.81 38.90 30.32 26.187 days 63.19 61.49 38.76 39.48 30.77 25.8714 days 54.78 51.20 38.76 31.93 30.50 22.8728 days 49.28 45.55 35.35 27.80 28.34 19.3142 days 49.41 45.79 35.77 30.39 26.44 21.11

5 MHz 10 MHz 20 MHz

85

The capacitor probe data for type A specimens is presented graphically in

Figures C.1 through C.6 (Appendix C). These figures represent plots of the real and

imaginary parts of the dielectric constant for three ranges of curing time. The first or

early curing time plots (Figures C.1 and C.2) consist of 5, 12, 21 hr, and 1 and 3 day

measurements. The second or middle curing time plots (Figures C.3 and C.4) consist

of 1, 3, 7, and 14 day measurements. The third or overall curing time plots (Figures

C.5 and C.6) consist of 1, 3, 7, 28, and 42 day measurements. The parallel-plate

capacitor data for type A specimens is presented graphically in Figures D.1 through D.4

(Appendix D).

Specimen Creal imaginary real imaginary real imaginary

1 day 47.14 67.53 29.04 42.52 19.79 26.0928 days 24.66 32.27 17.66 19.80 14.43 12.09

5 MHz 10 MHz 20 MHz

Table 6.4 Dielectric constant for type C specimens (6% air content, w/c = 0.45)measured using the parallel-plate capacitor.

Specimen Areal imaginary real imaginary real imaginary

1 day 43.76 75.72 26.57 44.94 18.61 26.5728 days 24.10 38.53 17.58 22.64 14.47 13.33

5 MHz 10 MHz 20 MHz

TTable 6.3 Dielectric constant for type A specimens (2% air content, w/c = 0.45)measured using the parallel-plate capacitor.

Table 6.2 Dielectric constant for type C specimens (6% air content, w/c = 0.45)measured using capacitor probe a.

Specimen Creal imaginary real imaginary real imaginary

10 hours 79.08 175.42 62.61 95.28 45.24 63.6219 hours 83.62 83.78 54.11 55.20 33.36 48.13

1 day 64.81 64.58 42.30 43.05 30.22 30.783 days 52.60 46.11 35.62 29.40 27.13 20.277 days 57.35 46.57 36.27 31.90 28.99 21.83

14 days 49.54 42.14 35.52 26.76 28.14 19.2828 days 48.05 41.83 34.93 26.13 27.93 17.9742 days 45.48 39.16 33.44 26.30 24.97 18.49

5 MHz 10 MHz 20 MHz

86

The capacitor probe data for type C specimens is also presented graphically in

Appendix C. These figures represent plots of the real and imaginary parts of the

dielectric constant for three ranges of curing time. The first or early curing time plots

(Figures C.7 and C.8) consist of 10 and 19 hour, and 1 and 3 day measurements. The

second or middle curing time plots (Figures C.9 and C.10) consist of 1, 3, 7, and 14 day

measurements. The third or overall curing time plots (Figures C.11 and C.12) consist

of 1, 3, 7, 28, and 42 day measurements. The parallel-plate capacitor data for type C

specimens is presented graphically in Figures D.5 through D.8 (Appendix D).

To study the effect of air voids in PCC on its dielectric properties, two void

thicknesses (7.5 mm and 15 mm) and two void depths (25 mm and 50 mm) were used

to make capacitor probe specimens. Styrofoam (300 x 150 x 7.5 mm and 300 x 150 x

15 mm) was used to simulate an air void since it possesses the same dielectric

properties as air. The results of this testing are presented in Tables 6.5 through 6.8.

Table 6.5 Dielectric constant for type D specimens (6% air content, w/c = 0.45, and 7.5mm thick void at 25 mm depth) measured using capacitor probe a.

Specimen Dreal imaginary real imaginary real imaginary

1 day 50.16 47.20 32.70 32.13 24.43 23.633 days 40.91 32.89 28.14 22.04 21.20 14.737 days 41.13 33.94 26.73 22.64 21.52 15.2014 days 36.22 31.64 26.74 19.76 21.40 13.8328 days 34.53 28.72 25.59 17.85 20.82 12.1742 days 34.21 28.71 25.71 19.37 19.54 13.80

5 MHz 10 MHz 20 MHz

Table 6.6 Dielectric constant for type E specimens (6% air content, w/c = 0.45, and7.5 mm thick void at 50 mm depth) measured using capacitor probe a.

Specimen Ereal imaginary real imaginary real imaginary

1 day 66.29 73.06 41.45 46.61 29.57 33.143 days 49.55 50.82 33.33 31.42 25.00 20.347 days 56.95 62.25 35.32 38.80 28.33 25.28

14 days 45.97 47.57 33.19 28.44 26.37 19.4628 days 43.16 42.12 31.57 25.22 25.49 16.9642 days 40.26 39.30 29.86 25.66 22.35 17.19

10 MHz 20 MHz5 MHz

87

Specimens for measurement in the parallel-plate capacitor were also prepared;

however, no Styrofoam was placed in these prism specimens. Therefore, prism type D

and F specimens are identical and were cast for repeatability analysis. The results of

testing the parallel-plate specimens are presented in Tables 6.9 and 6.10.

Specimen Freal imaginary real imaginary real imaginary

5 hours 70.03 387.93 57.32 208.45 40.40 118.651 day 47.91 63.86 34.80 37.29 24.91 26.443 days 41.57 58.56 30.78 34.03 23.13 20.297 days 40.87 47.30 29.81 29.25 21.71 17.6814 days 39.55 45.48 28.44 26.93 22.74 19.0028 days 36.25 39.99 26.20 24.07 21.11 15.8242 days 35.80 37.86 26.46 22.82 21.42 15.14

5 MHz 10 MHz 20 MHz

Table 6.7 Dielectric constant for type F specimens (6% air content, w/c = 0.45, and 15mm thick void at 25 mm depth) measured using capacitor probe a.

Specimen Greal imaginary real imaginary real imaginary

1 day 58.07 63.48 40.35 38.81 29.91 29.243 days 43.48 54.32 31.22 31.92 23.50 19.147 days 46.21 52.47 33.60 32.82 24.66 20.36

14 days 44.62 39.92 31.82 25.87 25.21 19.8528 days 41.70 42.02 29.83 25.40 23.81 16.7142 days 39.63 39.92 28.90 24.20 23.15 15.80

5 MHz 10 MHz 20 MHz

Table 6.8 Dielectric constant for type G specimens (6% air content, w/c = 0.45, and15 mm thick void at 50 mm depth) measured using capacitor probe a.

Specimen Dreal imaginary real imaginary real imaginary

1 day 39.19 74.16 24.83 43.47 17.88 25.6328 days 22.56 29.55 16.35 18.15 13.34 10.93

5 MHz 10 MHz 20 MHz

Table 6.9 Dielectric constant for type D specimens (6% air content, w/c = 0.45)measured using the parallel-plate capacitor.

88

The data for type D, E, and G specimens is presented graphically in Appendix

C. This data is represented by plots of the real part and the imaginary part of the

dielectric constant for two ranges of curing time for each specimen. The first or initial

curing time plots consist of 1, 3, 7, and 14 day measurements (Figures C.13 and C.14,

Figures C.17 and C.18, and Figures C.27 and C.28 for type D, E, and G specimens,

respectively). The second or overall curing time plots consist of 1, 3, 7, 28, and 42 day

measurements (Figures C.15 and C.16, Figures C.19 and C.20, and Figures C.29 and

C.30 for type D, E, and G specimens, respectively). The parallel-plate capacitor data

for type D and E specimens is presented graphically in Figures D.9 through D.12

(Appendix D) and Figures D.13 through D.16 (Appendix D), respectively.

The capacitor probe data for type F specimens is presented graphically in

Appendix C (Figures C.21 through C.26). These figures show plots of the real and

imaginary parts of the dielectric constant for three ranges of curing time. The first or

early curing time plots (Figures C.21 and C.22) consist of 5 hr, 1, and 3 day

measurements. The second or middle curing time plots (Figures C.23 and C.24)

consist of 1, 3, 7, and 14 day measurements. The third or overall curing time plots

(Figures C.25 and C.26) consist of 1, 3, 7, 28, and 42 day measurements. The parallel-

plate capacitor data for type F specimens is presented graphically in Figures D.17

through D.20 (Appendix D).

6.1 Discussion of Data

All specimens were prepared in duplicate and the average measurement is

presented in the appendices. The relationship between the real and imaginary parts of

Table 6.10 Dielectric constant for type F specimens (6% air content, w/c = 0.45)measured using the parallel-plate capacitor.

Specimen Freal imaginary real imaginary real imaginary

1 day 43.79 99.11 28.02 56.02 20.41 32.2428 days 24.14 38.20 18.09 22.41 14.57 13.62

5 MHz 10 MHz 20 MHz

89

the dielectric constant and changes in frequency can be seen in Appendix C. These

figures show that both the real and imaginary parts of the dielectric constant decrease

with increasing frequency. This behavior may be attributed to a reduction in

conductivity and the effects of heterogeneous polarization with the frequency

increases, as described by De Loor (1962).

The effect of curing time on the dielectric properties of PCC can be seen in

Tables 6.11 through 6.15. These tables show that both the real and imaginary parts of

the dielectric constant decrease with increasing curing time over all frequencies. This

phenomenon can be attributed to one or more of the following:

(a) a reduction in the Portland cement paste conductivity may occur when water

becomes adsorbed from its initial bulk form, reducing the effect of dipole

polarization (Hasted, 1973; Whittington and Wilson, 1986);

(b) a decrease in the overall pore diameter of the Portland cement paste pore

system, restricting the movement of ionized water, may lead to reducing the

effects of ionic polarization (De Loor, 1962). Also, a reduction in Portland

cement paste interface conductivity may occur due to further reduction in

the pore sizes and changes in the pore shape from elliptical to spherical (De

Loor, 1962);

(c) a reduction in the ion concentration in the capillary water, due to the

Portland cement hydration process, at early stages of curing will reduce the

effects of ionic conduction (McCarter and Curran, 1984).

The effect of air content on the dielectric properties is clear for all ages, as seen

in Table 6.11, which shows that an increased air content lowers both the real and the

imaginary part of the dielectric constant. This effect is noted over all frequencies. It is

expected that if these voids are air-filled or water-filled, the real and imaginary parts of

the dielectric constant will decrease and increase, respectively.

The effect of void location on the dielectric properties is shown in Tables 6.12

and 6.13 for 7.5 mm and 15 mm void thickness, respectively. Changes in dielectric

properties due to void depth are a function of the depth of penetration of the EM

90

waves. The depth of penetration is dependent upon the plate spacing (see Figure 4.2)

and the frequency of the EM waves. In this study, the plate spacing was held constant

at 50 mm. The depth of penetration of EM waves would increase at lower frequencies.

Thus, more of an effect should be expected on the dielectric properties due to void

depth at 5 MHz than at 20 MHz. This trend can be seen for nearly all curing ages in

Tables 6.12 and 6.13. It is also evident that the voids at a 50 mm depth (for both 7.5

mm and 15 mm void thickness) have less effect on the dielectric constant than voids at

a 25 mm depth. This is seen as higher values for both the real and imaginary parts of

the dielectric constant for PCC specimens with 50 mm void depth as compared to the

25 mm void depth. These results indicate that the capacitor probe penetration at this

plate spacing is limited and did not provide sufficient penetration of the EM energy to

the 50 mm void depth.

Table 6.11 Difference in dielectric constant due to air content as measured usingcapacitor probe a.

Specimen Measured airname and age content, % real imaginary real imaginary real imaginary

A - 1 day 1.6 67.55 72.05 43.64 46.74 31.16 33.37C - 1 day 5.8 64.81 64.58 42.30 43.05 30.22 30.78A - 7 days 1.6 63.19 61.49 38.76 39.48 30.77 25.87C - 7 days 5.8 57.35 46.57 36.27 31.90 28.99 21.83A - 28 days 1.6 49.28 45.55 35.35 27.80 28.34 19.31C - 28 days 5.8 48.05 41.83 34.93 26.13 27.93 17.97A - 42 days 1.6 49.41 45.79 35.77 30.39 26.44 21.11C - 42 days 5.8 45.48 39.16 33.44 26.30 24.97 18.49

20 MHz5 MHz 10 MHz

Table 6.12 Difference in dielectric constant due to void depth (7.5 mm thick void) asmeasured using capacitor probe a.

Specimen Void name and age depth, mm real imaginary real imaginary real imaginary

D - 1 day 25 50.16 47.20 32.70 32.13 24.43 23.63E - 1 day 50 66.29 73.06 41.45 46.61 29.57 33.14D - 7 days 25 41.13 33.94 26.73 22.64 21.52 15.20E - 7 days 50 56.95 62.25 35.32 38.80 28.33 25.28D - 28 days 25 34.53 28.72 25.59 17.85 20.82 12.17E - 28 days 50 43.16 42.12 31.57 25.22 25.49 16.96D - 42 days 25 34.21 28.71 25.71 19.37 19.54 13.80E - 42 days 50 40.26 39.30 29.86 25.66 22.35 17.19

5 MHz 10 MHz 20 MHz

91

The effect of void thickness on the dielectric properties is shown in Tables 6.14

and 6.15 for 25 mm and 50 mm void depth, respectively. Changes in dielectric

properties due to void thickness are a function of the wavelength of the EM wave. As

the frequency of an EM wave increases the wavelength decreases. Thus, a larger

difference in the dielectric properties at 20 MHz than at 5 MHz is expected. However,

at the frequency range stated (2-20 MHz) the wavelength is significantly larger than the

thickness of the void to be detected. Therefore, the data in Table 6.14 cannot be

analyzed with respect to the frequency used in this study. This frequency used is

necessary since, at this larger wavelength, PCC appears to the capacitor probe as a

homogeneous material.

Table 6.14 Change in dielectric constant due to void thickness (25 mm void depth) asmeasured using capacitor probe a.

Specimen Void name and age thickness, mm real imaginary real imaginary real imaginary

D - 1 day 7.5 50.16 47.20 32.70 32.13 24.43 23.63F - 1 day 15 47.91 63.86 34.80 37.29 24.91 26.44

D - 7 days 7.5 41.13 33.94 26.73 22.64 21.52 15.20F - 7 days 15 40.87 47.30 29.81 29.25 21.71 17.68

D - 28 days 7.5 34.53 28.72 25.59 17.85 20.82 12.17F - 28 days 15 36.25 39.99 26.20 24.07 21.11 15.82D - 42 days 7.5 34.21 28.71 25.71 19.37 19.54 13.80F - 42 days 15 35.80 37.86 26.46 22.82 21.42 15.14

5 MHz 10 MHz 20 MHz

Table 6.13 Difference in dielectric constant due to void depth (15 mm thick void) asmeasured using capacitor probe a.

Specimen Void name and age depth, mm real imaginary real imaginary real imaginary

F - 1 day 25 47.91 63.86 34.80 37.29 24.91 26.44G - 1 day 50 58.07 63.48 40.35 38.81 29.91 29.24F - 7 days 25 40.87 47.30 29.81 29.25 21.71 17.68G - 7 days 50 46.21 52.47 33.60 32.82 24.66 20.36F - 28 days 25 36.25 39.99 26.20 24.07 21.11 15.82G - 28 days 50 41.70 42.02 29.83 25.40 23.81 16.71F - 42 days 25 35.80 37.86 26.46 22.82 21.42 15.14G - 42 days 50 39.63 39.92 28.90 24.20 23.15 15.80

5 MHz 10 MHz 20 MHz

92

In an effort to control the depth of penetration of the EM waves in the PCC slab

specimens, six different capacitor probes were constructed (see Table 4.1). These

probes are identical except for the size of the conducting plates and the spacing

between them. Each measurement was performed on the same specimen on the

same day. Therefore, any changes in the dielectric properties are not due to changes

in specimen properties or differences in curing time.

Changes in the dielectric constant, due to different probe geometry, of

specimens with and without air voids can be seen in Tables 6.16 and 6.17,

respectively. As shown in Table 6.17, the dielectric constant of a specimen containing

a void changes in response to differences in plate spacing while the plate size remains

constant (comparing probes a, b, c, and f). In addition, it can be seen that with

increasing plate separation both the real and imaginary parts of the dielectric constant

generally decrease. This can be attributed to an increased depth of penetration by the

EM waves emanating from the capacitor probe. Since the void placed in the specimen

is Styrofoam (having a lower dielectric constant than the surrounding PCC), the

dielectric constant would be lower for a measurement in which more EM waves

penetrate to the depth of the void.

It can also be seen from Table 6.17 that the dielectric constant of a specimen

containing an air void changes slightly in response to differences in plate size when the

plate separation distance is held constant. When comparing probes a and d, it can be

seen that the dielectric constant measured with the larger plates (probe a) is lower than

Table 6.15 Change in dielectric constant due to void thickness (50 mm void depth) asmeasured using capacitor probe a.

Specimen Void name and age thickness, mm real imaginary real imaginary real imaginary

E - 1 day 7.5 66.29 73.06 41.45 46.61 29.57 33.14G - 1 day 15 58.07 63.48 40.35 38.81 29.91 29.24E - 7 days 7.5 56.95 62.25 35.32 38.80 28.33 25.28G - 7 days 15 46.21 52.47 33.60 32.82 24.66 20.36E - 28 days 7.5 43.16 42.12 31.57 25.22 25.49 16.96G - 28 days 15 41.70 42.02 29.83 25.40 23.81 16.71E - 42 days 7.5 40.26 39.30 29.86 25.66 22.35 17.19G - 42 days 15 39.63 39.92 28.90 24.20 23.15 15.80

5 MHz 10 MHz 20 MHz

93

with the smaller plates (at 10 and 20 MHz). This is most likely due to the longer overall

length of the larger plates (having the same separation), which allows the EM waves to

penetrate more deeply. When comparing probes d and e, it can be seen that the real

part of the dielectric constant is slightly lower (at 10 and 20 MHz) for the probe e

(having a larger plate area with the same plate separation distance as probe d).

However, the imaginary part of the dielectric constant is higher for probe e than probe

d.

6.2 Parallel-Plate Capacitor vs. Capacitor Probe

Although the trends are similar, differences were noted in the measured

dielectric constant for type A, C, D, and F specimens when using the parallel-plate

capacitor compared to the capacitor probe over different curing periods and frequency

Table 6.16 Change in dielectric constant of type A specimens (6% air, 0.45 w/c) due todifferent capacitor probes.

Capacitor Plate Size, PlateProbe mm Spacing, mm real imaginary real imaginary real imaginary

a 75 x 75 50 22.63 14.71 18.59 8.87 12.56 6.36b 75 x 75 75 22.25 14.41 18.59 9.55 14.10 7.37c 75 x 75 100 23.21 15.25 18.79 9.68 14.26 6.73d 50 x 50 50 22.21 13.38 18.95 8.81 14.79 6.11e 50 x 125 50 23.98 15.73 19.29 9.81 14.64 6.25f 75 x 75 150 20.05 12.90 16.48 8.28 12.03 6.53

10 MHz 20 MHz5 MHz

Capacitor Plate Size, PlateProbe mm Spacing, mm real imaginary real imaginary real imaginary

a 75 x 75 50 19.23 11.16 16.09 6.85 10.70 4.94b 75 x 75 75 18.16 10.62 15.44 7.12 11.72 5.38c 75 x 75 100 18.75 11.28 15.56 7.28 11.93 5.02d 50 x 50 50 19.13 10.42 16.47 6.97 12.56 4.85e 50 x 125 50 20.00 11.85 16.30 7.38 12.45 4.98f 75 x 75 150 17.23 9.90 14.34 6.51 10.34 5.40

5 MHz 10 MHz 20 MHz

Table 6.17 Change in dielectric constant of type G specimens (6% air, 0.45 w/c, 15 mmthick void at 50 mm depth) due to different capacitor probes.

94

range. The real and imaginary parts of the dielectric constant are generally lower when

obtained by the parallel-plate capacitor. This can be attributed to several factors

including development of air gaps between the specimen and plates (in the parallel-

plate capacitor), specimen size and shape, and system calibration.

6.3 Final Remarks

The capacitor probe represents an initial step in what could be an important

assessment tool for civil constructed facilities. This study has shown that the capacitor

probe can detect dielectric changes in PCC due to its hydration process and the

presence of internal voids. While these are important, the most useful feature of the

capacitor probe may be forthcoming. There are currently no nondestructive methods to

measure the chloride content of in-situ civil engineering structures. Since sodium

chloride is ionic in structure, it is postulated that the capacitor probe will be useful in

detecting its presence and quantifying its amount due to the manifestation of ionic

polarization at low radio frequency.

95

CHAPTER 7 SUMMARY AND CONCLUSIONS

This study was conducted to design and fabricate a capacitor probe to measure

the in-situ dielectric properties of PCC. Once a suitable measurement device was

completed, it was tested to ensure the validity of its results by measuring specimens

with known dielectric properties (Teflon). The system was used to examine its

effectiveness to detect changes in PCC dielectric properties due to different mix

variables. The results of this study show that significant changes in the complex

dielectric constant were measured over the initial curing time of PCC specimens.

Changes in the complex dielectric constant, attributable to a change in air content, air

void presence, and void depth were also measured. However, no appreciable change

could be detected with regards to varying void thickness. In addition, plate separation

distance and plate size were found to have an influence over the type of deterioration

that can be detected.

7.1 Findings

The following findings were noted during this study:

• The complex dielectric constant of PCC specimens decreased as frequency

increased. The rate of change of the complex dielectric constant decreased as the

frequency increased.

• The complex dielectric constant of PCC specimens, in general, decreased slightly

as the air content increased.

• The complex dielectric constant of PCC specimens significantly decreased as

curing time progressed.

• The complex dielectric constant of PCC specimens containing an induced void

(Styrofoam) was lower than specimens of the same mix with no induced void. The

96

complex dielectric constant increased as the void depth from the surface increased

(void thickness remaining constant), however, the effect generally decreased as the

frequency increased.

• The effect of an induced void (Styrofoam) on the complex dielectric constant of

PCC specimens was indeterminable with regard to the void thickness.

• Increasing the capacitor probe plate separation distance would result in deeper

penetration of the electromagnetic energy into the specimen.

7.2 Conclusions

A capacitor probe was developed to allow in-situ dielectric measurements of PCC

structural members and to detect internal flaws.

• The developed system has the capability to detect changes in PCC's basic

properties (e.g., air content, hydration process, and internal voids) based on the

measured complex dielectric constant at low radio frequency.

• The plate size and plate separation distance can change the depth of penetration of

electromagnetic energy from the capacitor probe.

97

CHAPTER 8 RECOMMENDATIONS

• A nondestructive method for detecting the in-situ chloride content in PCC structures

is needed. The developed capacitor probe should be employed in future research

to study the effects of chloride intrusion in PCC specimens.

• Further testing involving PCC specimens made using more than one type of

aggregate and more than one w/c ratio is needed.

• Further testing involving PCC specimens of different sizes is needed to determine

the depth of penetration of the electromagnetic waves. Additionally, when using

capacitor probes with larger plate separation distances, the distance to the edge of

the PCC specimen decreases. Larger specimens should be cast so that a constant

distance from capacitor probe to edge of specimen can be maintained during

testing involving capacitor probes of different sizes.

• The geometric configuration of the capacitor probe conducting plates could be a

source of error when considering the coaxial nature of the cable used for

measurement. The distance between the inside edges of the conducting plates as

compared to the distance between the outside edges of the conducting plates is

significantly different. A capacitor probe consisting of two thin strips or two

concentric circles could possibly alleviate this problem and is currently under

evaluation.

98

REFERENCES

Al-Qadi, I. L. (1992) “Using Microwave Measurements to Detect Moisture in Hot-Mix

Asphalt.” Journal of Testing and Evaluation, Vol. 20, No. 1, 45-50.

Al-Qadi, I. L., D. K. Ghodgaonkar, V. K. Varadan, and V. V. Varadan. (1991) "Effect of

Moisture on Asphaltic Concrete at Microwave Frequencies." IEEE Transactions on

Geoscience and Remote Sensing, Vol. 29, No. 5, 710-717.

Al-Qadi, I. L., D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan. (1989) “Detecting

Water Content of Asphaltic Cement Concrete by Microwave Reflection and

Transmission Measurement.” 91st Annual Meeting of the American Ceramic

Society, Indianapolis, IN, 23-27.

Al-Qadi, I. L., O. A. Hazim, W. Su, N. Al-Akhras, and S. M. Riad. (1994a) "Variation of

Dielectric Properties of Portland Cement Concrete During Curing Time Over Low

RF Frequencies." Paper No. 940479, Transportation Research Board 73rd Annual

Meeting, Jan.

Al-Qadi, I. L., A. Loulizi, R. Haddad, and S. Riad. (1997) “Correlation Between Concrete

Dielectric Properties and its Chloride Content.” Presented at Structural Faults and

Repair – 97, Proceedings of the 7th International Conference on Structural Faults

and Repair, Vol. 2 – Concrete and Composites, Edinburgh, Scotland, 423-429.

Al-Qadi, I. L. and S. M. Riad. (1996) “Characterization of Portland Cement Concrete:

Electromagnetic and Ultrasonic Measurements Techniques.” Report Submitted to

National Science Foundation, Department of Civil Engineering, Virginia Polytechnic

Institute and State University, Blacksburg, VA, 445 p.

Al-Qadi, I. L., S. M. Riad, R. Mostafa, and B. K. Diefenderfer. (1996) “Development of

TEM Horn Antenna to Detect Delamination in Portland Cement Concrete

Structures.” Third Nondestructive Conference, Boulder, CO, Sept, 241-256.

99

Al-Qadi, I. L., S. M. Riad, R. Mostafa, and W. Su. (1995) "Design and Evaluation of a

Coaxial Transmission Line Fixture to Characterize Portland Cement Concrete."

Proceedings of the 6th International Conference on Structural Faults and Repairs,

U. K., 337-347.

Al-Qadi, I. L., W. Su, S. M. Riad, R. Mostafa, and O. A. Hazim. (1994b) "Coaxial Fixture

Development to Characterize Portland Cement Concrete." Proceedings of the

Symposium and Workshop on Time Domain Reflectometry in Environment,

Infrastructure and Mining Applications, Evanston, IL, 443-452.

Al-Qadi, I. L., R. E. Weyers, N. L. Galagedera, and P. D. Cady. (1993) “Condition

Evaluation of Concrete Bridges Relative to Reinforced Corrosion, Vol. 4: Deck

Membrane Effectiveness and Method for Evaluating Membrane Integrity.” Report

No. SHRP-S/FR-92-10V, Strategic Highway Research Program, National Research

Council, Washington, DC, 143 p.

ASCE. (1998) “1998 Report Card for America’s Infrastructure.” American Society of

Civil Engineers, Washington, D. C.

Bell, J. R., G. A. Leonards, and W. A. Doch. (1963) “Determination of Moisture Content

of Hardened Concrete by its Dielectric Properties.” Proceedings of the American

Society for Testing and Materials, Vol. 63.

Bodakian, B. and F. X. Hart. (1994) “The Dielectric Properties of Meat.” IEEE

Transactions on Dielectric and Electrical Insulation, Vol. 1, No. 2, Apr, 181-187.

Böttcher, C. J. F. (1973) Theory of Electric Polarization. Elsevier Publishing Company,

New York, NY.

Bradford, S. A. (1992) Corrosion Control. Van Nostrand Reinhold, New York, NY.

Brisco, B., T. J. Pultz, R. J. Brown, G. C. Topp, M. A. Hares, and W. D. Zebchuk.

(1992) Soil Moisture Measurement Using Portable Dielectric Probes and Time

Domain Reflectometry.” Water Resources Research, Vol. 28, No. 5, May, 1339-

1246.

100

Bungey, J. H., and S. G. Millard. (1993) “Radar Inspection of Structures.” Proceedings

of the Institution of Civil Engineers Structures and Buildings, Vol. 99, 173-186.

Buyukozturk, O. (1997) “Electromagnetic Properties of Concrete and Their Significance

in Nondestructive Testing.” Paper No. 97-0872, Transportation Research Board

76th Annual Meeting, Jan.

Callister, Jr., W. D. (1994) Materials Science and Engineering: An Introduction. Third

Edition, John Wiley and Sons, Inc., New York, NY.

Campbell, J. E. (1990) “Dielectric Properties and Influence of Conductivity in Soils at

One to Fifty Megahertz.” Soil Science Society American Journal, Vol. 54, Mar-Apr,

332-341.

Carter, C. R., T. Chung, F. B. Holt, and D. Manning. (1986) “An Automated Signal

Processing System for the Signature Analysis of Radar Waveforms from Bridge

Decks.” Canadian Electrical Engineering Journal, Vol. 11, No. 3, 128-137.

Chung, T., and C. R. Carter. (1989) “Radar Signal Enhancement for Dart.” MAT-89-05,

Ontario Ministry of Transportation and Communications, Research and

Development Branch, Ontario, Canada.

Clemena, G. (1983) “Nondestructive Inspection of Overlaid Bridge Decks with Ground-

Penetrating Radar.” Transportation Research Record 899, Transportation Research

Board.

Clemena, G., M. Sprinkel, and R. Long, Jr. (1986) “Use of Ground-Penetration Radar

for Detecting Voids Under a Jointed Concrete Pavement.” Final Report, Virginia

Highway and Transportation Research Council, Charlottesville, VA.

Clemena, G., M. Sprinkel, and R. Long, Jr. (1987) “Use of Ground-Penetration Radar

for Detecting Voids Under a Jointed Concrete Pavement.” Transportation Research

Board, No. 1109, Washington, DC, 1-10.

Cole, K. S., and R. H. Cole. (1941) “Dispersion and Absorption in Dielectrics; I.

Alternating Current Characteristics.” Journal of Chemical Physics, Vol. 9, 341-351.

101

Debye, P. (1929) Polar Molecules. Chemical Catalog Co., New York, NY.

Diefenderfer, B. K., I. L. Al-Qadi, J. J. Yoho, S. M. Riad, and A. Loulizi. (1997)

“Development of a Capacitor Probe to Detect Subsurface Deterioration in

Concrete.” Nondestructive Characterization of Materials in Aging Systems.

Proceedings of Materials Research Society Fall 1997 Meeting, Symposium JJ,

Boston, MA, 231-236.

Dobson, M. C. and F. T. Ulaby. (1986) “Active Microwave Soil Moisture Research.”

IEEE Transactions on Geoscience and Remote Sensing, GE-24, Vol. 1, Jan, 23-36.

Eckrose, R. (1989) “Ground Penetrating Radar Supplements Deflection Testing to

Improve Airport Pavement Evaluations.” Non-destructive Testing of Pavements and

Back Calculation of Moduli: ASTM Special Technical Publication 1026, A.J. Bush III

and G.Y. Baladi, eds., Philadelphia, PA.

Ellerbruch, D. A. (1974) “Electromagnetic Attenuation of Clay and Gravel Soils.” Report

NBSIR 74-382, National Bureau of Standards, Boulder, CO, Aug.

Federal Highway Administration. (1993) "The Status of the Nation's Highway, Bridges,

and Transit Conditions and Performance” FHWA, Publication No. FHWA-PL-93-

017, Washington, D. C.

Feng, S. and A. Delaney. (1974) “Dielectric Properties of Soils at UHF and Microwave

Frequencies.” American Geophysical Union.

Feng, S. and P. N. Sen. (1985) “Geometrical Model of Conductive and Dielectric

Properties of Partially Saturated Rocks.” Journal of Applied Physics, Vol. 58, No. 8,

Oct.

Haddad, R. H. (1996) “Characterization and Deterioration Detection of Portland Cement

Concrete Using Electromagnetic Waves Over a Wideband of Frequency.” PhD

Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.

Hansson, C. M. and B. Sorensen. (1990) “The Threshold Concentration of Chloride in

Concrete for the Initiation of Reinforcement Corrosion.” Corrosion Rates of Steel in

102

Concrete, ASTM STP 1065, N. S. Berke, V. Chaker, and D. Whiting, eds., American

Society for Testing and Materials, Philadelphia, PA, 3-16.

Hansson, I. L., and C. M. Hansson. (1983) “Electrical Resistivity Measurements of

Portland Cement Materials.” Cement and Concrete Research, Vol. 13, 675-683.

Hasted, J. B. (1973) Aqueous Dielectrics. Chapman and Hall, Ltd., London, England.

Higazy, A. A. (1995) “Electrical Conductivity and Dielectric Constant of Magnesium

Phosphate Glasses.” Materials Letters, Vol. 22, Mar, 289-296.

Hipp, J. E. (1971) “Soil Electromagnetic Parameters as a Function of Frequency, Soil

Density, Soil Moisture.” Proceedings of the Institute of Electrical and Electronics

Engineers, Vol. 62, No. 1, Jan, 98-103.

Hobbs, D. W. (1988) Alkali-Silica Reaction in Concrete. Thomas Telford, London,

England.

Jackson, T. J. (1990) “Laboratory Evaluation of a Field-Portable Dielectric/Soil-Moisture

Probe.” IEEE Transactions on Geoscience and Remote Sensing, Vol. 28, No. 2,

Mar, 241-245.

Jastrzebski, Z. D. (1977) The Nature and Properties of Engineering Materials. Second

Edition, SI Version, John Wiley and Sons, New York, NY.

Kosmatka, H. S. and W. C. Panarese. (1988) "Design and Control of Concrete

Mixtures." Portland Cement Association, Skokie, IL, 205 p.

Lewis, C. T. and C. Short. (1907) "A New Latin Dictionary." E. A. Andrews, ed.,

American Book Company, New York, NY.

Liu, W. T., S. Cochrane, X. M. Wu, P. K. Singh, X. Zhang, D. B. Knorr, J. F. McDonald,

E. J. Rymaszewski, J. M. Borrego, and T. M. Lu. (1994) “Frequency Domain (1kHz-

40GHz) Characterization of Thin Films for Multichip Module Packaging Technology.”

Electronics Letters, Vol. 30, No. 2, 117-118.

103

Lord, A. E., Jr., R. M. Koerner, and J. S. Reif. (1979) “Determination of Attenuation and

Penetration Depth of Microwaves in Soil.” Geotechnical Testing Journal, Vol. 2, No.

2, June, 77-83.

Lundien, J. R. (1971) “Terrain Analysis by Electromagnetic Means. Report 5:

Laboratory Measurement of Electromagnetic Propagation Constants in the 1.0-1.5

GHz Microwave Spectral Region.” Technical Report 3-693, US Army Waterways

Experiment Station, MI, Feb.

Maser, K. R. (1996) “Condition Assessment of Transportation Infrastructure Using

Ground-Penetrating Radar.” Journal of Infrastructure Systems, Vol. 2, No. 2, Jun,

94-101.

Maser, K. R., R. Littlefield, and B. Brandemeyer. (1989) “Pavement Condition Diagnosis

Based on Multisensor Data.” Transportation Research Record 1196, Transportation

Research Board, 62-72.

McCarter, W. J., and P. N. Curran. (1984) “The Electrical Response Characteristics of

Setting Cement Paste.” Magazine of Concrete Research, Vol. 36, No. 126, 42-49.

McNeill, J. D. (1980) Electrical Conductivity of Soils and Rocks, Technical Note TN-5,

Geonics Ltd., Oct.

Mehta, P. K. and P. J. M. Monteiro. (1993) Concrete: Structure, Properties, and

Materials. 2nd ed., Prentice Hall, Englewood Cliffs, NJ.

Mindess, S. and J. F. Young. (1981) Concrete. Prentice Hall, Inc., Englewood Cliffs,

NJ.

Moffat, D. L., and R. J. Puskar. (1976) “A Subsurface Electromagnetic Pulse Radar.”

Geophysics, Vol. 41, No. 3, June, 605-617.

Nelson, S. (1985) “RF and Microwave Energy for Potential Agricultural Applications.”

Journal of Microwave Power and Electromagnetic Energy, Vol. 24, No. 4, 515-522.

104

Neville, A. M. (1981) Properties of Concrete. Pittman Publishing Limited, Marshfield,

MA.

Perez-Pena, M., D. M. Roy, and F. D. Tamas. (1989) “Influence of Chemical

Composition and Inorganic Admixtures on the Electrical Conductivity of Hydrating

Cement Paste.” Journal of Materials Research, Vol. 4, No. 1, 215-223.

Powers, T. C. (1945) “A Working Hypothesis for Further Studies of Frost Resistance of

Concrete.” Journal of the American Concrete Institute, Proceedings, Vol. 41, No. 3,

245-272.

Powers, T. C. (1956) “Resistance of Concrete to Frost at Early Ages.” Proceedings,

RILEM Symposium on Winter Concreting, Danish National Institute of Building

Research, Copenhagen, Denmark, C1-C47.

Rosenberg, W. R, C. M. Hansson, and C. Andrade. (1989) “Mechanisms of Corrosion

of Steel in Concrete.” Materials Science of Concrete. Vol. 3. Ed. Jan Skalny, The

American Ceramic Society, Inc., Westerville, OH, 285-313.

Scott, W. R. and G. S. Smith. (1992) “Measured Electrical Constitutive Parameters of

Soil as Functions of Frequency and Moisture Content.” IEEE Transactions on

Geoscience and Remote Sensing, Vol. 30, No.3, May, 621-623.

Shih, S. F. and J. A. Doolittle. (1984) “Using Radar to Investigate Organic Soil

Thickness in the Florida Everglades.” Soil Science Society American Journal, Vol.

48, No. 3, 651-656.

Shih, S. F. and D. L. Myhre. (1994) “Ground-Penetrating Radar for Salt-Affected Soil

Assessment.” Journal of Irrigation and Drainage Engineering, Vol. 120, No. 2, Mar-

Apr, 322-333.

Sillars, R. W. (1937) “The Properties of a Dielectric Containing Semi-Conducting

Particles of Various Shapes.” Journal of the Institute of Electrical Engineers, Vol.

80, 378-394.

105

Steeman, P. A. M., F. H. J. Maurer, and J. Van Turnhout. (1994) “Dielectric Properties

of Blends of Polycarbonate and Acrylonitrite-Butadiene-Styrene Copolymer.”

Polymer Engineering and Science, Vol. 34, No. 9, Mid-May, 697-706.

Steinway, W. J., J. D. Echard, and C. M. Luke. (1981) “Locating Voids Beneath

Pavement Using Pulsed Electromagnetic Waves.” National Cooperative Highway

Research Program Project 10-14, National Cooperative Highway Research

Program, National Research Council, Washington, DC.

Straub, A. (1994) “Boundary Element Modeling of a Capacitive Probe for in Situ Soil

Moisture Characterization.” IEEE Transactions on Geoscience and Remote

Sensing, Vol. 32, No. 2, Mar, 261-266.

Tamas, F. D., E. Farkas, M. Voros, and D. M. Roy. (1987) “Low-Frequency Electrical

Conductivity of Cement, Clinker, and Clinker Mineral Pastes.” Cement and

Concrete Research, Vol. 17, No. 2, 340-348.

Taylor, M. A. and K. Arulanandan. (1974) “Relationships Between Electrical and

Physical Properties of Cement Pastes.” Cement and Concrete Research, Vol. 4,

No. 4, 881-897.

Tewary, V. K., P. R. Heyliger, and A. V. Clark. (1991) “Theory of a Capacitive Probe

Method for Noncontact Characterization of Dielectric Properties of Materials.”

Journal of Materials Research, Vol. 6, No. 3, Mar, 629-638.

Tomboulian, D. H. (1965) Electric and Magnetic Fields. Harcourt, Brace, and World,

Inc., New York, NY.

Topp, G. C., J. L. Davis, W. G. Bailey, and W. D. Zebchuk. (1984) “The Measurement

of Soil Water Content Using a Portable TDR Hand Probe.” Canadian Journal of

Soil Science, Vol. 64, Aug, 313-321.

Whittington, H.W., and J. G. Wilson. (1986) "Low-frequency Electrical Characteristics of

Fresh Concrete." IEE Proceedings, Vol. 133, Part A, No. 5, July, 265-271.

106

Whittington, H. W., J. McCarter, and M. C. Forde. (1981) “The Conduction of Electricity

Through Concrete.” Magazine of Concrete Research, Vol. 33, No. 114, 48-60.

Wilson, J. G., and H. W. Whittington. (1990) "Variations in the Electrical Properties of

Concrete with Change in Frequency." IEE Proceedings, Vol. 137, Part A, No. 5,

Sept.

Yoho, J. J. (1998) “Design and Calibration of a RF Capacitance Probe for Non-

Destructive Evaluation of Civil Structures.” Masters Thesis, Virginia Polytechnic

Institute and State University, Blacksburg, VA.

107

APPENDIX A

• This appendix includes illustrations of the different capacitor probes used in this

study.

108

125 mm

250 mm

Figure A.1 Capacitor probe a – 75 x 75 mm plates with 50 mm separation.

125 mm

250 mm

Figure A.2 Capacitor probe b – 75 x 75 mm plates with 75 mm separation.

275 mm

125 mm

Figure A.3 Capacitor probe c – 75 x 75 mm plates with 100 mm separation.

109

125 mm

250 mm

Figure A.5 Capacitor probe d – 50 x 50 mm plates with 50 mm separation.

325 mm

125 mm

Figure A.6 Capacitor probe f – 75 x 75 mm plates with 150 mm separation.

125 mm

250 mm

Figure A.4 Capacitor probe e – 50 x 125 mm plates with 50 mm separation.

110

APPENDIX B

This appendix includes the following:

• Physical and chemical properties of limestone aggregate (coarse and fine); Tables

B.1 and B.2.

• Chemical properties of Type I Portland cement; Table B.3.

• Proportions for different PCC mixes; Table B.4.

• Quality control measurements for PCC mixes; Table B.5.

111

Table B.1 Physical properties of limestone aggregate

Physical Property Fine Coarse

Bulk Specific Gravity

(dry) 2.53 2.80

Apparent Specific

Gravity2.76 2.86

Absorption (%) 3.31 0.68

Fineness Modulus 3.22

Unit Weight (kg/m3) 1490.01

Table B.2 Chemical properties of limestone aggregate.

Aggregate Compound (% by weight)

SiO2 Al2O3 Fe2O3 CaO CaCO3 MgO MgCO3 SO3

Coarse

and Fine 3.05 0.54 0.40 29.93 53.42 20.34 42.53 0.04

112

Table B.3 Chemical properties of Type I Portland cement.

Cement Compound (% by wt)

SiO2 Al2O3 Fe2O3 CaO MgO SO3 Na2O L. I.

Type I 21.01 4.77 2.45 63.97 3.15 2.81 0.75 0.70

Table B.4 Proportions for different PCC mixes.

Mix Water (kg) Cement (kg) CA* (kg) FA** (kg)

A 13.76 30.58 69.25 54.91

C 13.76 30.58 69.25 47.69

D 13.76 30.58 69.25 47.69

E 13.76 30.58 69.25 47.69

F 13.76 30.58 69.25 47.69

G 13.76 30.58 69.25 47.69

*CA: Coarse Aggregate

**FA: Fine Aggregate

113

Table B.5 Results of quality control testing.

Compressive Strength

MixUnit Weight

(kg/m3)

Slump

(mm)

Air Content

(%) 3 days

(MPa)

7 days

(MPa)

28 days

(MPa)

A 2950.60 64 1.6 31.41 35.80 45.13

C 2841.88 83 5.8 20.30 24.97 32.24

D 2809.91 102 7.2 19.75 21.95 30.59

E 2804.79 95 7.0 19.62 21.40 28.94

F 2797.12 108 7.4 19.89 20.58 31.14

G 2817.58 95 6.4 18.93 23.73 32.51

114

APPENDIX C

• This appendix includes the dielectric properties versus frequency for PCC slab

specimens measured using the capacitor probe.

Figure C.1 Dielectric properties vs. frequency for type A specimens measured using the capacitor probe.

115

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 hours - real

12 hours - real

21 hours - real

1 day - real

3 days - real


116

0

50

100

150

200

250

300

350

400

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 hours - imag

12 hours - imag

21 hours - imag

1 day - imag

3 days - imag


117

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


118

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


119

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


120

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

Figure C.7 Dielectric properties vs. frequency for type C specimens measured using the capacitor probe.

121

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

10 hours - real

19 hours - real

1 day - real

3 days - real


122

0

50

100

150

200

250

300

350

400

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

10 hours - imag

19 hours - imag

1 day - imag

3 days - imag


123

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


124

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


125

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


126

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

Figure C.13 Dielectric properties vs. frequency for type D specimens measured using the capacitor probe.

127

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


128

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


129

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


130

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

Figure C.17 Dielectric properties vs. frequency for type E specimens measured using the capacitor probe.

131

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


132

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


133

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


134

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

Figure C.21 Dielectric properties vs. frequency for type F specimens measured using the capacitor probe.

135

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 hours - real

1 day - real

3 days - real


136

0

50

100

150

200

250

300

350

400

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 hours - imag

1 day - imag

3 days - imag


137

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


138

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


139

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


140

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

Figure C.27 Dielectric properties vs. frequency for type G specimens measured using the capacitor probe.

141

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

3 days - real

7 days - real

14 days - real


142

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

3 days - imag

7 days - imag

14 days - imag


143

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

7 days - real

14 days - real

28 days - real

42 days - real


144

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

7 days - imag

14 days - imag

28 days - imag

42 days - imag

145

APPENDIX D

• This appendix includes the dielectric properties versus frequency for PCC prism

specimens measured using the parallel-plate capacitor.

Figure D.1 Dielectric properties vs. frequency for type A specimens measured using the parallel-plate capacitor.

146

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real28 days - real

Figure D.2 Dielectric properties vs. frequency for type A specimens measured using the parallel-plate capacitor.

147

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

28 days - imag

Figure D.3 Dielectric properties vs. frequency for type C specimens measured using the parallel-plate capacitor.

148

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

28 days - real

Figure D.4 Dielectric properties vs. frequency for type C specimens measured using the parallel-plate capacitor.

149

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

28 days - imag

Figure D.5 Dielectric properties vs. frequency for type D specimens measured using the parallel-plate capacitor.

150

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

28 days - real

Figure D.6 Dielectric properties vs. frequency for type D specimens measured using the parallel-plate capacitor.

151

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

28 days - imag

Figure D.7 Dielectric properties vs. frequency for type F specimens measured using the parallel-plate capacitor.

152

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

1 day - real

28 days - real

Figure D.8 Dielectric properties vs. frequency for type F specimens measured using the parallel-plate capacitor.

153

0

30

60

90

120

2 4 6 8 10 12 14 16 18 20

Frequency, MHz

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

1 day - imag

28 days - imag

154

APPENDIX E

• This appendix includes the dielectric properties of PCC slab specimens (measured

using the capacitor probe) versus curing time for three frequencies (5, 10, and 20

MHz).

Figure E.1 Dielectric properties vs. curing time for type A specimens measured using the capacitor probe.

155

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.2 Dielectric properties vs. curing time for type A specimens measured using the capacitor probe.

156

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz10 MHz20 MHz

Figure E.3 Dielectric properties vs. curing time for type C specimens measured using the capacitor probe.

157

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.4 Dielectric properties vs. curing time for type C specimens measured using the capacitor probe.

158

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz

10 MHz

20 MHz

Figure E.5 Dielectric properties vs. curing time for type D specimens measured using the capacitor probe.

159

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.6 Dielectric properties vs. curing time for type D specimens measured using the capacitor probe.

160

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz

10 MHz

20 MHz

Figure E.7 Dielectric properties vs. curing time for type E specimens measured using the capacitor probe.

161

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.8 Dielectric properties vs. curing time for type E specimens measured using the capacitor probe.

162

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz

10 MHz

20 MHz

Figure E.9 Dielectric properties vs. curing time for type F specimens measured using the capacitor probe.

163

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.10 Dielectric properties vs. curing time for type F specimens measured using the capacitor probe.

164

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz

10 MHz

20 MHz

Figure E.11 Dielectric properties vs. curing time for type G specimens measured using the capacitor probe.

165

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Rea

l Par

t o

f D

iele

ctri

c C

on

stan

t

5 MHz

10 MHz

20 MHz

Figure E.12 Dielectric properties vs. curing time for type G specimens measured using the capacitor probe.

166

0

30

60

90

120

0 5 10 15 20 25 30 35 40 45

Curing Time, Days

Imag

inar

y P

art

of

Die

lect

ric

Co

nst

ant

5 MHz

10 MHz

20 MHz

167

VITA

Brian K. Diefenderfer

The author was born on April 10, 1973 in Washington, D. C. He completed his high

school education at North Hagerstown High School, Hagerstown, Maryland in 1991. He

received his Bachelor of Science degree in Civil Engineering from Virginia Polytechnic

Institute and State University in May 1996. He joined the Masters Program at Virginia

Tech in May 1996. During his study, he was a research assistant in the Civil

Engineering Materials Program where he conducted research in nondestructive

evaluation of civil infrastructure.

development and testing of a capacitor probe to detect

Documents