The Pennsylvania State University

The Graduate School

College of Engineering

CCHHAARRAACCTTEERRIIZZIINNGG SSAATTUURRAATTEEDD MMAASSSS TTRRAANNSSPPOORRTT IINN FFRRAACCTTUURREEDD CCEEMMEENNTTIITTIIOOUUSS MMAATTEERRIIAALLSS

A Dissertation in

Civil Engineering

by

Alireza Akhavan

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

August 2012

The dissertation of Alireza Akhavan was reviewed and approved* by the following: Farshad Rajabipour Assistant Professor of Civil and Environmental Engineering Dissertation Adviser Chair of Committee John Earl Watson Professor of Crop and Soil Science Maria Lopez de Murphy Associate Professor of Civil and Environmental Engineering Tong Qiu Assistant Professor of Civil and Environmental Engineering William Burgos Professor of Civil Engineering Chair of Graduate Program of the Department of Civil and Environmental Engineering *Signatures are on file in the Graduate School.

iii

ABSTRACT

Concrete, when designed and constructed properly, is a durable material. However in aggressive

environments concrete is prone to gradual deterioration which is due to penetration of water and

aggressive agents (e.g., chloride ions) into concrete. As such, the rate of mass transport is the

primary factor, controlling the durability of cementitious materials. Some level of cracking is

inevitable in concrete due to brittle nature of the material. While mass transport can occur

through concrete’s porous matrix, cracks can significantly accelerate the rate of mass transport

and effectively influence the service life of concrete structures. To allow concrete service life

prediction models to correctly account for the effect of cracks on concrete durability, mass

transport thru cracks must be characterized. In this study, transport properties of cracks are

measured to quantify the saturated hydraulic permeability and diffusion coefficient of cracks as a

function of crack geometry (i.e.; crack width, crack tortuosity and crack wall roughness).

Saturated permeability and diffusion coefficient of cracks are measured by constant head

permeability test, electrical migration test, and electrical impedance spectroscopy. Plain and fiber

reinforced cement paste and mortar as well as simulated crack samples are tested. The results of

permeability test showed that the permeability of a crack is a function of crack width squared and

can be predicted using Louis formula when crack tortuosity and surface roughness of the crack

walls are accounted for. The results of the migration and impedance tests showed that the

diffusion coefficient of the crack is not dependent on the crack width, but is primarily a function

of volume fraction of cracks. The only parameter that is changing with the crack width is the

crack connectivity. Crack connectivity was found to be linearly dependent on crack width for

small crack and constant for large cracks (i.e.; approximately larger than 80 μm). The results of

this study can be used to predict diffusion and permeability coefficients of fractured concrete.

iv

TABLE OF CONTENTS

List of Figures ............................................................................................................................. viii

List of Tables .............................................................................................................................. xiii

Chapter 1: Introduction ................................................................................................................1

1-1 Introduction .................................................................................................................................. 1

1-2 Research objectives ..................................................................................................................... 2

1-3 Organization of contents ............................................................................................................ 3

1-4 References .................................................................................................................................... 4

Chapter 2: Mechanisms of Deterioration and Mass Transport in concrete ............................... 6

2-1 Concrete durability problems..................................................................................................... 7

2-1-1 Corrosion of steel reinforcement ...................................................................................... 7

2-1-1-1 Carbonation ....................................................................................................... 11

2-1-1-2 Chloride attack .................................................................................................. 12

2-1-2 Freeze/thaw damage ......................................................................................................... 14

2-1-3 Alkali silica reaction (ASR) ............................................................................................ 17

2-1-4 Sulfate attack ..................................................................................................................... 20

2-2 Mechanisms of mass transport in concrete ........................................................................... 22

2-2-1 Saturated permeation ....................................................................................................... 23

v

2-2-2 Unsaturated permeation ................................................................................................... 26

2-2-3 Diffusion ............................................................................................................................ 30

2-2-4 Other transport mechanisms ............................................................................................ 34

2-3 Service-life prediction models ................................................................................................. 34

2-3-1 Life-365 Service Life Prediction Model ........................................................................ 34

2-3-2 STADIUM ......................................................................................................................... 37

2-3-3 4SIGHT .............................................................................................................................. 38

2-4 Summary ..................................................................................................................................... 39

2-5 References .................................................................................................................................. 40

Chapter 3: Quantifying the Effects of Crack Width, Tortuosity, and Roughness on Water

Permeability of Cracked Mortars ..................................................................................................... 44

3-1 Introduction ................................................................................................................................ 44

3-2 Quantifying the geometric properties of cracks .................................................................... 48

3-2-1 Effective crack width ....................................................................................................... 48

3-2-2 Crack tortuosity and surface roughness ......................................................................... 53

3-3 Materials and experiments ...................................................................................................... 56

3-3-1 Sample preparation ........................................................................................................... 56

3-3-2 Permeability measurement .............................................................................................. 57

3-3-3 Measuring crack dimensions ........................................................................................... 59

3-4 Results and discussion .............................................................................................................. 60

vi

3-4-1 Comparison between average, effective, and LVDT crack measurements............... 60

3-4-2 Saturated permeability as a function of crack width .................................................... 62

3-4-3 Crack tortuosity and surface roughness ......................................................................... 63

3-4-4 Effect of tortuosity and roughness on crack permeability ........................................... 67

3-5 Conclusions ................................................................................................................................ 69

3-6 References .................................................................................................................................. 70

Chapter 4: Evaluating Ion Diffusivity of Cracked Cement Paste Using Electrical

Impedance Spectroscopy ............................................................................................................75

4-1 Introduction ................................................................................................................................ 75

4-2 Methods for Measuring the Diffusion Coefficient of Concrete .......................................... 78

4-3 Theory ......................................................................................................................................... 84

4-4 Materials and Experiments ....................................................................................................... 94

4-5 Results and Discussion ............................................................................................................. 99

4-6 Conclusion ................................................................................................................................ 103

4-7 References ................................................................................................................................ 103

Chapter 5: Permeability, Electrical Conductivity, and Diffusion Coefficient of Simulated

Cracks .........................................................................................................................................110

5-1 Introduction .............................................................................................................................. 110

5-2 Methods .................................................................................................................................... 112

5-3 Theory ....................................................................................................................................... 112

vii

5-3-1 Hydraulic Permeability of Cracks ................................................................................ 112

5-3-2 Ion Diffusivity of Cracks ............................................................................................... 114

5-4 Experimental Methods ............................................................................................................ 115

5-5 Results and Discussion ........................................................................................................... 125

5-5-1 Hydraulic Permeability .................................................................................................. 125

5-5-2 Ion Diffusivity ................................................................................................................. 127

5-6 Conclusion ................................................................................................................................ 130

5-7 References ................................................................................................................................ 131

Chapter 6: Summary and Conclusion .....................................................................................134

6-1 Summary of Research Approach ........................................................................................... 134

6-2 Conclusion ................................................................................................................................ 135

6-3 Suggested Future Research .................................................................................................... 136

Appendix A ................................................................................................................................137

Appendix B ................................................................................................................................157

viii

LIST OF FIGURES

Figure 1-1: Rapid corrosion of steel due to cracking .......................................................................2

Figure 2-1: Deterioration processes in reinforced concrete .............................................................6

Figure 2-2: The corrosion of steel begins with the rust expanding on the surface of the bar and

causing cracking near the steel/concrete interface. As the corrosion products build up, more

extensive cracking develops until the concrete breaks away from the bar, eventually causing

spalling ......................................................................................................................................................... 8

Figure 2-3: Cracking and spalling due to corrosion of steel reinforcement in a concrete beam ..... 8

Figure 2-4: Corrosion of steel reinforcement ......................................................................................... 9

Figure 2-5: Relative volume of iron and its oxides ............................................................................. 10

Figure 2-6: Bryant Patton Bridges in Florida displays a reinforced concrete pile with significant

corrosion induced damage ....................................................................................................................... 12

Figure 2-7: Typical example of concrete deteriorated from freeze thaw actions. Non-air-entrained

concrete railing ......................................................................................................................................... 15

Figure 2-8: Saturated area adjacent to crack ......................................................................................... 16

Figure 2-9: Map cracking due to ASR................................................................................................... 17

Figure 2-10: Effect of reactive silica content on concrete expansion due to ASR .......................... 18

Figure 2-11: Pipeline support chair damaged after 19 years due to external sulfate attack ........... 21

Figure 2-12: Illustration of fluid flow under pressure gradient .......................................................... 23

Figure: 2-13: Influence of w/c ratio on the permeability of (a) cement paste and (b) concrete .... 25

Figure 2-14: Unidirectional unsaturated flow ...................................................................................... 26

Figure 2-15: Typical water retention curves for a sand and a clay loam .......................................... 28

Figure 2-16: Unsaturated hydraulic conductivity K θ versus volumetric water content θ ........... 29

ix

Figure 2-17: Illustration of solute transport due to concentration gradient ...................................... 31

Figure 3-1: Schematic illustration of the splitting tension setup used to fracture mortar disk

specimens (after modification of the setup used by Wang et al.) ..................................................... 46

Figure 3-2: A thru-thickness crack in a mortar disk specimen showing: (a) crack width variability

and crack tortuosity, (b) crack wall roughness ..................................................................................... 48

Figure 3-3: Cumulative distribution function showing the variability of crack profile along the

surface of a disk specimen ...................................................................................................................... 49

Figure 3-4: Method for calculation of the effective crack width (adopted from Dietrich et al.) .. 50

Figure 3-5: Correlation between the effective surface and thru crack widths .................................. 52

Figure 3-6: (a) Digitized profile of an actual thru crack; (b) Schematics of a crack profile to

illustrate surface metrology procedures ................................................................................................ 53

Figure 3-7: Permeability test ................................................................................................................... 58

Figure 3-8: Correlation between (a) average and effective crack widths, (b) average crack width

and LVDT readings .................................................................................................................................. 61

Figure 3-9: Theoretical and experimental values of crack permeability as a function of effective

crack width ................................................................................................................................................ 63

Figure 3-10: Effective crack length as a function of sampling length scale: (a) Fiber-reinforced

crack fitted by a fractal power function; (b) Comparison between plain and fiber-reinforced

cracks ......................................................................................................................................................... 65

Figure 3-11: Crack surface roughness as a function of sampling length scale ................................ 67

Figure 3-12: Estimation of crack permeability based on Eq. 3-19; data points show experimental

results ......................................................................................................................................................... 68

Figure 4-1: Steady-state diffusion test ................................................................................................... 79

x

Figure 4-2: Salt ponding test ................................................................................................................... 79

Figure 4-3: Bulk diffusion test ................................................................................................................ 80

Figure 4-4: Electrical migration tests .................................................................................................... 81

Figure 4-5: Rapid migration test ............................................................................................................ 81

Figure 4-6: rapid chloride permeability test (RCPT) ........................................................................... 82

Figure 4-7: Parallel law for ion diffusion in cracked concrete ........................................................... 88

Figure 4-8: Schematics of (a) smooth, and (b) constricted crack ...................................................... 90

Figure 4-9: Resistance vs. reactance for a cracked fiber reinforced cement paste sample ............. 93

Figure 4-10: Splitting tension setup used to fracture cement paste disks ......................................... 96

Figure 4-11: Crack patterns for dual and single cracked samples ..................................................... 96

Figure 4-12: EIS test setup ...................................................................................................................... 98

Figure 4-13: Variation of the electrical conductivity of cracked cement paste samples (σComposite)

versus crack volume fraction (Cr) ...................................................................................................... 100

Figure 4-14: Estimated diffusion coefficient of cracked samples (DComposite) as a function of crack

volume fraction (Cr) ............................................................................................................................. 101

Figure 4-15: Variation of the electrical conductivity of cracked samples (σComposite) versus the

average crack width (wCr) .................................................................................................................... 102

Figure 4-16: The calculated crack connectivity (Cr) as a function of average crack width (wCr)

.................................................................................................................................................................. 102

Figure 5-1: Plexiglas test sample used to simulate cracks in concrete ........................................115

Figure 5-2: Noncontact optical profilometer ..............................................................................116

Figure 5-3: Topography map of the test samples surfaces, (a): Rough (b): Smooth ...................117

Figure 5-4: Test samples installed between two test cells ...........................................................118

xi

Figure 5-5: Permeability test setup ...................................................................................................... 119

Figure 5-6: Migration test configuration ............................................................................................. 120

Figure 5-7: Migration test setup ........................................................................................................... 122

Figure 5-8: Variation of chloride concentration over time in downstream cell (migration test) . 123

Figure 5-9: Electrical impedance test setup ........................................................................................ 124

Figure 5-10: Typical result of electrical impedance test ................................................................... 125

Figure 5-11: Measured and predicted Permeability coefficient ....................................................... 126

Figure 5-12: Permeability test results (data point for mortar samples was obtained from) ........126

Figure 5-13: Diffusion coefficient of crack vs. crack width ........................................................128

Figure 5-14: Normalized conductivity vs. crack width ...............................................................128

Figure 5-15: Crack connectivity coefficient, obtain from EIS ....................................................129

Figure 5-16: Diffusion coefficient of crack normalized by crack connectivity obtained from EIS

.................................................................................................................................................................. 129

Figure A-1: Vacuum impregnation of disk samples with epoxy .................................................137

Figure A-2: A polished epoxy impregnated sample ....................................................................138

Figure A-3: A vertically sectioned specimen at the mid-point perpendicular to the surface crack

......................................................................................................................................................138

Figure A-4: A thru crack detected and segmented to measure crack width ................................139

Figure A-5: Crack width distribution of the surface crack ..........................................................140

Figure A-6: The portion of surface crack between 0.375 and 0.625 points that was assumed to

correspond with the middle thru section is establishing the correlation between effective surface

and thru crack widths ...................................................................................................................142

Figure A-7: Correlation between the effective surface and thru crack widths ............................143

Figure A-8: (a) A detected thru crack. (b) The thru crack, sectioned every 1 mm ......................144

xii

Figure A-9: Roughness is calculated by averaging the crack variation within the sampling length

......................................................................................................................................................145

Figure B-1: Splitting tension setup used to fracture cement paste disks ....................................158

Figure B-2: Schematic illustration of the splitting tension setup used to fracture mortar disk

specimens .....................................................................................................................................158

Figure B-3: Variation of applied vertical load and lateral deflection of the sample during splitting

tension test ...................................................................................................................................159

xiii

LIST OF TABLES

Table 3-1: Mixture proportions for mortar specimens ...................................................................56

Table 3-2: Average tortuosity and roughness measured using different values of λ .....................68

Table 4-1: Mixture proportions ......................................................................................................95

Table 4-2: Pore solution composition ............................................................................................95

Table 4-3: Parameters used in eqs. 4-13 and 4-14 .........................................................................99

Table A-1: Summary for the surface crack ..................................................................................140

Table A-2: Summary for the thru crack .......................................................................................141

Table A-3: Summary for the surface crack in the mid quarter ....................................................142

Table A-4: Crack width measurement for the surface crack .......................................................146

Table A-5: Crack width measurement for the thru crack ............................................................150

Table A-6: Crack width measurement for the surface crack in the mid quarter ..........................153

xiv

Acknowledgements

First, I would like to thank my advisor Dr. Farshad Rajabipour for his guidance, suggestions, and support. I would also like to thank my parents for unconditionally loving and supporting me.

1

CHAPTER 1: INTRODUCTION

1-1 Introduction

Concrete is the most widely used man made material in the world. The United States uses about

400 million cubic yards of ready mixed concrete each year [1]. Worldwide, 12 billion tones (≈6.5

billion cubic yards) of concrete are manufactured annually [2]. Most of the transportation

infrastructure is made of concrete with a design service life of 50 to 100 years. Long lasting

materials play a major role in building durable and cost effective structures. Durability is a

problem especially when concrete is exposed to aggressive environment such as deicing salts,

marine structures, or severe freezing and thawing environment. The need to design long lasting

concrete structures requires knowledge of parameters affecting the durability and service life of

concrete and steel reinforcement. Some of the most common durability problems of concrete are

freeze/thaw damage, alkali-silica reaction (ASR), sulfate attack and corrosion of reinforcing steel

[3]. The primarily factor governing the durability of concrete is mass transport. Deterioration of

concrete due to the previously mentioned mechanisms is significantly influenced by the rate of

moisture, ion, and gas/vapor transport in concrete[4]. This is further discussed in chapter 2.

A number of durability models have been developed that can predict service life of concrete

structures by considering the physical and chemical phenomena that influence concrete’s long-

term performance and service life expectancy. Most of the existing service life models (e.g.,

STADIUM, Life-365) consider concrete as a continuum porous media and do not account for the

presence of localized or distributed cracks. Cracking on the other hand, is inevitable in concrete.

Humidity and temperature changes and the resulting volume changes can cause tensile stress

2

development and cracking if concrete is restrained against such movements [4]. Load induced

cracking also occurs when tensile stress (e.g., at negative moment regions in a bridge deck)

exceeds the tensile strength of concrete[5]. Such cracks can widen over time due to creep and

further cracks could develop by fatigue (e.g., due to repeated traffic load). Cracking can increase

the deterioration rate of concrete significantly by accelerating transport of moisture and

aggressive agents into concrete and to the level of reinforcement. Figure 1-1 shows a submarine

pile that was cracked during driving. Signs of rust are visible on the surface of concrete only 6

months after installation.

1-2 Research objectives

The goal of the presented study is to characterize mass transport in saturated fractured concrete.

The results will provide the much needed material/crack transport property inputs that can be

incorporated into service-life prediction models to allow simulation of the effect of cracks on

Figure 1-1: Rapid corrosion of steel due to cracking

3

durability of concrete. This is especially significant for prediction of the remaining life of

structures in service and selection of the best maintenance strategies for concretes that have

experienced some level of cracking (e.g., early age shrinkage cracking). The results will quantify

saturated transport properties (permeability, diffusivity) as a function of crack geometry (width,

length, tortuosity, surface roughness). This will allow one to determine if there is a safe crack

width that has negligible impact on durability of concrete. Safe crack width can be prescribed as

the maximum allowable crack width in codes and specifications such as ACI-318 or AASHTO

Bridge Design Manual. This will further enable weighing the benefits of crack mitigation

strategies (e.g., use of fiber reinforcement or shrinkage reducing admixtures) against their costs.

1-3 Organization of contents

The following provides a brief description of the contents of this thesis. Chapter 2 addresses the

most common durability problems of concrete. The mechanism of each problem is explained and

the theory behind it is briefly discusses. Various modes of mass transport in concrete are

reviewed with focus on fluid permeation and ion diffusion. Finally, some of the existing service

life prediction models are introduced.

In chapter 3, water permeability of cracked mortars in saturated conditions is studied. Effect of

cracking on permeation rate of water into concrete is experimentally determined. Geometry of

cracks is characterized with the use of digital image analysis and relationships between crack

geometry parameters (e.g., width, roughness, tortuosity) and permeability are established. These

relationships are evaluated against the theory of laminar flow inside parallel-plate gaps.

4

Chapter 4 uses electrical impedance spectroscopy to measure electrical conductivity and

saturated diffusion coefficient of cracked cement paste samples. The relation between diffusion

coefficient and crack geometry is studied. Crack connectivity (e.g., inverse tortuosity) is also

measured by electrical impedance spectroscopy.

Chapter 5 introduces a Plexiglas setup that was designed to simulate cracks in concrete.

Saturated permeability, diffusion coefficient (using electrical migration test) and electrical

connectivity (using electrical impedance spectroscopy) are measured on sample cracks with a

broader range of crack widths. Using this setup allows simulation of parallel-plate cracks with

desired width and surface roughness. The results are used to evaluate four hypotheses regarding

permeability, diffusivity, connectivity and surface effects of cracks in concrete.

Finally, chapter 6 provides a summary of the findings in this study and discusses the main

conclusions. Suggestions for future work are also provided.

1-4 References

[1] Portland Cement Association., Design and control of concrete mixtures. Engineering

bulletin, Skokie, Ill. etc.: Portland Cement Association, 1988.

[2] J.P. Broomfield, Corrosion of steel in concrete : understanding, investigation and repair.

2nd ed., London ; New York: Taylor & Francis. xvi, 277 p., 2007.

[3] M.G. Richardson, Fundamentals of durable reinforced concrete. Modern concrete

technology., London ; New York: Spon Press. xii, 260 p., 2002.

[4] S. Mindess, J.F. Young, D. Darwin, Concrete, 2nd Ed., Prentice Hall, Upper Saddle

River, New Jersey, 2003.

5

[5] M.N. Hassoun, A.A. Al-Manaseer, Structural concrete : theory and design. 4th ed.,

Hoboken, NJ: J. Wiley, 2008.

6

CHAPTER 2: MECHANISMS OF DETERIORATION AND MASS

TRANSPORT IN CONCRETE

Concrete is a durable material if exposure conditions are properly predicted and considered

during the design phase and the structure is subsequently constructed according to quality

standards and specifications. Concrete is exposed to various environment conditions and may

deteriorate due to physical and chemical causes. Designing durable concrete that exhibit

satisfactory performance over its designed service life requires knowledge of the mechanisms

that deteriorate concrete [1][2]. Figure 2-1 shows the most common deterioration processes in

concrete.

Figure 2-1: Deterioration processes in reinforced concrete, adopted from [3]

7

In this chapter, some of the most common concrete durability problems are discussed and the

process of deterioration is explained for each problem. Afterwards, mass transport as the primary

factor controlling durability of concrete is explained. Mechanisms of mass transport in concrete

and their effect on different deterioration processes are also discussed in this chapter. Finally

some of the existing service-life prediction models are briefly explained and their assumptions

are discussed.

2-1 Concrete durability problems

2-1-1 Corrosion of steel reinforcement

Corrosion of reinforcing steel is one of the primary causes of deterioration in concrete. In 2002

the cost of corrosion on US highway bridges was estimated as $8.3 billion [4]. The loss of cross

section of rebar and bond between concrete and rebar result in reduction in load bearing capacity

of reinforced concrete elements and may lead to collapse or at least serviceability problems (e.g.,

cracking). However, the loss of rebar cross section is not the only problem caused by corrosion

of steel in concrete. The volume of resulting rust is greater than the volume of steel by a factor of

up to 7. The resulting expansion applies tensile stresses to the concrete, which can eventually

cause cracking and spalling [5]. This is illustrated in figures 2-2 and 2-3.

The process of corrosion of steel reinforcement is shown in figure 2-4. This can be divided into

anodic and cathodic reactions. At the anode, iron oxidizes which results in release of two

electrons:

The anodic reaction: 2 2 1

8

Figure 2-2: The corrosion of steel begins with the rust expanding on the surface of the bar and causing cracking near the steel/concrete interface. As the corrosion products build up, more extensive cracking develops until the concrete breaks away from the bar, eventually causing

spalling [6].

Figure 2-3: Cracking and spalling due to corrosion of steel reinforcement in a concrete beam.

9

The released electrons must be consumed elsewhere; otherwise large amount of electrical charge

will build up at one place on the steel. At the cathode, the electrons reduce water and oxygen and

generate hydroxyl ions:

The cathodic reaction: 2 2 2 2

The generated hydroxyl ions must travel within the pore network of concrete and react with the

ferrous ions ( ) and form ferrous hydroxide ( :

2 2 3

Ferrous hydroxide in presence of water and oxygen forms ferric hydroxide ( which

spontaneously changes to hydrated ferric oxide (rust).

Figure 2-4: Corrosion of steel reinforcement [5]

10

2 2 2 4

2 . rust 2 5

Unhydrated ferric oxide ( ) is about twice the volume of steel. As it hydrates, it swells even

more. This is illustrated in figure 2-5. The resulting expansion is a primarily factor in corrosion

damage in concrete [7].

Figure 2-5: Relative volume of iron and its oxides [8]

After initiation of corrosion, the process of corrosion rapidly decelerates inside concrete to a

negligible rate. In the alkaline environment of concrete (pH commonly greater than 12.5), a thin

but dense oxide layer (known as passive layer) forms on the surface of steel that prevents further

corrosion by limiting access of oxygen and water to the metal [1]. The passive layer will

preserve and repair itself if damaged in the presence of an alkaline environment [7]. However, if

0 1 2 3 4 5 6 7

Fe

FeO

Fe3O4

Fe2O3

Fe(OH)2

Fe(OH)3

Fe(OH)3.3H2O

11

the pH drops below 11.5, the passive layer is destroyed [1]. Two mechanisms can break down

the protective passive layer in concrete, carbonation and chloride attack [7].

2-1-1-1 Carbonation

If penetrated into concrete, carbon dioxide gas ( ) interact with calcium hydroxide ( )

in the concrete. Carbon dioxide dissolves in water and forms carbonic acid ( ) which

neutralizes the alkalies in the concrete pore solution and generates calcium carbonate ( ):

2 6

2 7

The pH drop due to consumption of calcium hydroxide destroys the passive layer and allows the

corrosion to restart. However, the volume of solid calcium hydroxide in concrete is a lot more

than the amount dissolvable in pore solution. When the dissolved calcium hydroxide is

consumed by carbonic acid in the neutralization reaction, the solid calcium hydroxide starts to

dissolve in the pore solution which keeps the pH at its normal level (i.e., >12.5). As the

carbonation reaction proceeds, eventually all the solid calcium hydroxide is consumed and

eventually the pH drops and corrosion initiates [7]. Carbonation damage occurs more rapidly

when concrete has high permeability and diffusivity. The rate of ingress controls the rate of

corrosion due to carbonation. Cracks in concrete (by increasing permeability and diffusivity)

enhance the transport of and increase the rate of deterioration. This is especially significant

in the vicinity of cracks.

12

2-1-1-2 Chloride attack

Chloride penetration is generally known as the most significant threat to reinforced concrete

structures. The source of chlorides can be deicing salts, seawater and admixtures (e.g., CaCl2

accelerating admixture). Bridges, pavements, and near shore structures are exposed to chloride

through deicing salt and seawater. Due to lack of oxygen, Concrete submerged deep inside

seawater may not experience corrosion [2]. Splash zones on the other hand are recognized as

high corrosion risk areas (figure 2-6).

Figure 2-6: Bryant Patton Bridges in Florida displays a reinforced concrete pile with significant corrosion induced damage [9]

Chlorides ions are capable of destroying the protective layer even at high alkalinities. When iron

ions react with chloride ions, the reaction product serves to carry Fe2+ away from the metal

surface resulting in an unstable and porous passive layer [1]. The process starts with oxidation of

iron:

13

2 2 8

Then the iron ions combine with chloride ions to form ferrous chloride (and FeOCl):

2 2 9

Ferrous hydroxide and ferric hydroxide are subsequently formed in presence of water. Chloride

ions are recycled and the process continues.

2 2 2 2 10

2 2 11

Since the chloride ions are recycled, the attack continues even in low chloride contents. But there

is a chloride threshold for corrosion since the passive layer can effectively re-establish itself

when damaged at high pH values. This threshold is suggested to be 0.6 [10] in terms of

chloride/hydroxyl ion ratio. Buenfield [11] suggested the range of 0.2 to 0.4 percent (total

chloride as a percentage of the mass of concrete) for different exposure climates.

The time to the onset of corrosion is commonly called the initiation period. In other words, the

initiation period is the time it takes for chlorides to penetrate the concrete cover and reach a

certain threshold at the level of reinforcements, sufficient to initiate the corrosion. Propagation

period is the time for corrosion to reach an unacceptable level, in which the corrosion products

build up on the surface of the steel reinforcement and cause damage to concrete.

14

Permeability and ion diffusivity of concrete significantly affect its durability in chloride rich

environments. In a dry condition, sorptivity and permeability of concrete control the rate of

chloride ingress; the penetration rate is initially dominated by convectional flow of the moisture

containing chlorides in concrete. Transport inside the concrete will also be by diffusion. Chloride

ions can diffuse through concrete porosity or reach the steel through cracks [2]. The diffusion

mechanism is dominant at high saturation degrees.

In the presence of oxygen and water, the intrusion of chloride ions into reinforced concrete is the

major cause of corrosion. Corrosion accelerates in concrete with higher water permeability and

ion diffusivity [5]. Cracking accelerate corrosion rate by increasing permeability and diffusion

coefficient of concrete.

2-1-2 Freeze/thaw damage

Freeze/thaw damage is due to expansion of water (≈ 9%) in concrete pores when the temperature

drops below freezing point of pore solution. This expansion applies tensile stresses inside the

concrete matrix resulting in cracking if the stresses developed exceed the tensile strength of

concrete. In saturated concrete, most of the water in cement paste will not freeze at 0⁰ C.

Depending on the pore diameter, water only freezes when the temperature drops well below 0⁰

C. For example water in pores of 10-nm diameter will not freeze until -5⁰ C (23⁰ F). Also, the

presence of ions further depresses the freezing point [1]. Dilated pores and developed

microcracks resulting from frost attack may increase water content of concrete and lead to more

severe expansions. Therefore the rate of deterioration increases and can eventually cause failure

15

or serviceability problems. [2]. Figure 2-7 shows an example of concrete deterioration due frost

attack.

Figure 2-7: Typical example of concrete deteriorated from freeze thaw actions. Non-air-entrained

concrete railing [12]

Powers [13] explained the mechanism of frost attack. He explained that formation of ice and

consequent expansion apply pressure to residual water and water tends to move out and escape

from capillary pores to a free space to relieve the pressure. Water needs to move through

unfrozen pores to reach an escape boundary. If the distance to free space is too far or enough

unfrozen pores are not available due to low temperature, the hydraulic pressure causes

microcracking and pores enlargement [1].

16

Generation of hydraulic pressure by ice formation was believed to be the major contributor of

dilation for many years, but this change is insufficient to account for all of the dilation observed

in concrete during freeze-thaw cycles. Later, Powers [13] found that expansion of ice and the

accompanying hydraulic pressure could not be the major cause of damage. He observed

expansion even in partially dry pastes which have enough empty pores to accommodate the 9%

expansion. Also damage was observed in concrete saturated with liquids that do not expand upon

freezing. Powers observed that when paste starts to freeze, it first shrinks and then expands.

One explanation of this behavior is based on osmotic pressure. Freezing results in an increase of

solute concentration in the unfrozen liquid adjacent to the freezing sites. Because of this

concentration difference and through the process of osmosis, water is drawn from surrounding

pore solution toward freezing sites which causes the paste away from the freezing sites to shrink

and crack.

If the osmotic and hydraulic pressures are to be

relieved, water needs to travel to reach free spaces.

This distance must not be too large. 200 μm is

recommended as the maximum distance [2]. Air

entrained concrete provides free spaces for water to

expand and can mitigate frost attack. Partially dry

concrete is less vulnerable to freeze-thaw damage

since the empty capillaries provide free space for water

[1]. Concrete in a saturated condition is highly

susceptible to frost attack. In addition to total air

Figure 2-8: Saturated area adjacent to crack

17

content and air void spacing, the degree of saturation and permeability are the major controlling

factors in freeze-thaw damage.

Cracks are larger in size than capillary pores and if filled with water, will greatly contribute to

deterioration due frost attack. The resulting expansion causes further propagation of cracks and

the process accelerates as the volume fraction of cracks increases. In cold and wet climates,

cracks are often water saturated, and stresses generated by freezing can deteriorate the

surrounding concrete. Figure 2-8 shows how cracks can keep the surrounding area saturated

which further enhances the freeze/thaw damage in surrounding concrete.

2-1-3 Alkali silica reaction (ASR)

ASR is due to the presence of reactive silicious aggregate in the alkaline environment of

concrete. The amorphous silica in aggregates can react with hydroxyl ions in concrete and form

an alkali-silica gel that expands as it adsorbs

water. Similar to the freeze/thaw process, the

expansion of gel causes tensile stresses in

concrete and induces distributed cracks (figure 2-

9) which reduce strength and elasticity modulus

and ultimately destroys concrete.

Several factors control the alkali-silica expansion.

The nature of reactive silica (degree of

amorphousness), amount of reactive silica and available alkali, particle size of reactive material,

Figure 2-9: Map cracking due to ASR (photograph, courtesy of the Federal

Highway Administration)

18

and amount of moisture are the major affecting factors. Smaller aggregates and porous particles

are more reactive due to their increased surface area [1]. The effect of amount of reactive silica

and available alkali on ASR expansion is interdependent. Following is the further explanation of

this effect.

The products of alkali silica reaction are divided into two components: calcium-alkali-silicate-

hydrate (C-N-S-H) gels and alkali-silicate-hydrate (N-S-H) gels. Only the second component is a

swelling gel and the first component which has calcium is a nonswelling gel and harmless to

concrete [1]. The source of calcium ions in pore solution is calcium hydroxide which is a

byproduct of cement hydration. Since the solubility of calcium hydroxide decreases with an

increase in alkali concentration, in a high pH environment, fewer calcium ions are available to

form calcium-alkali-silicate-hydrate gels. Consequently the high pH results in the formation of

swelling products. The swelling gel (N-S-H) absorbs water and expands which applies local

tensile stresses in concrete and can cause cracking.

Figure 2-10: Effect of reactive silica content on concrete expansion due to ASR

0

0.5

1

1.5

2

0 10 20 30 40

Exp

ansi

on (

%)

Silica content (%)

19

In a high alkaline environment, as the reactive silica content increases, the amount of swelling

product (N-S-H) increases which result in greater expansion. After a certain point, further

increase in silica content reduces the pH of the environment and consequently the solubility of

calcium hydroxide increases which means more available calcium ions (Ca2+). Availability of

calcium ions leads to the formation of nonswelling C-N-S-H instead of N-S-H gel. Figure 2-10

shows expansion in concrete due to alkali silica reaction as a function of silica content.

Expansion increase with increases in silica content and at a certain percentage of reactive silica

(known as the pessimum content), maximum expansion occurs. After the peak, increase in silica

content results in decrease in expansion. The percentage at peak which causes maximum

deleterious expansion depends on the water to cement ratio, nature of reactive silica, and the

degree of alkalinity [1].

Besides a high pH environment and the presence of amorphous silica, alkali silica reaction

requires water to proceed. Water serves as the carrier of alkali and hydroxyl ions which attack

the silica structure in aggregates. Also, the expansion of the resulting ASR gel is due to water

which is absorbed by the gel and causes swelling of the gel. The developed pressures due to the

expansion will eventually cause cracking in concrete. ASR accelerates in concrete with higher

water permeability. Cracks in concrete enhance the penetration of water and can increase

deterioration due to ASR. In addition, when the source of alkalis is external (e.g., deicing salts)

cracking accelerates and enhances the availability of alkali ions.

Supplementary cementitious materials have been used to mitigate ASR. If cement is replaced, in

proper proportions, with silica fume, fly ash, or slag, expansion due to alkali-silica reactivity

20

reduces considerably [1][14][15]. Supplementary cementitious materials decrease the

permeability and diffusion coefficient of concrete and can control ASR by limiting the supply of

water required to cause expansion of the ASR gel. In addition, partial replacement of cement

reduces the pH of the pore solution through alkali dilution and binding which mitigates attack on

silicious aggregates and promotes formation of nonswelling gel. Using low alkali cement,

avoiding highly reactive aggregates, and using low water to cement ratio concrete are some other

ways to control ASR [1].

2-1-4 Sulfate attack

Sulfate ions are present in sea water and often in groundwater when high proportion of clay are

present in the soil. Also groundwater in the vicinity of industrial wastes and municipal

wastewater may contain sulfates. Aggregates can be a source of sulfates as well. Sulfate is found

in the form of a variety of salts such as sodium sulfate, calcium sulfate, magnesium sulfate and

potassium sulfate. Reaction of sulfates with hydration products of concrete (mainly with calcium

aluminates) generates expansive products. Similar to the other mentioned deterioration

processes, the resulting expansion can destroy concrete (figure 2-11).

Sulfate ions react with calcium hydroxide (Ca(OH)2) and calcium aluminate hydrates (e.g.,

3CaO.Al2O3.CaSO4.12H2O also known as monosulfate) which are the products of cement

hydration in concrete [2]. Gypsum (calcium sulfate CaSO4.2H2O) is the product of reaction of

sulfate with calcium hydroxide. The reaction is accompanied with solid volume expansion of

120% [1]. The reaction of sulfate with monosulfate and other calcium aluminates forms ettringite

(calcium tri-sulfoaluminate hydrate: 3CaO.Al2O3.3CaSO4.32H2O). If sulfate is totally consumed

21

by hydration of tricalcium aluminate (C3A), the remaining C3A reacts with Ettringite and form

monosulfate:

3 . . 3 . 32 2 3 . 3 3 . . . 12 2 12

If sulfate is reintroduced after setting of concrete (e.g., due to penetration of external sulfates),

ettringite forms again [2]. Conversion of monosulfoaluminate to ettringite is accompanied by

55% increase in solid volume [1].

Figure 2-11: Pipeline support chair damaged after 19 years due to external sulfate attack [16]

In the processes described so far the source of sulfate was external (e.g., seawater). Sulfate may

also be supplied internally. The process is known as internal sulfate attack or delayed ettringite

formation (DEF). Ettringite is unstable at high temperatures. During early hydration of Portland

22

cement, if temperature goes above 70⁰ C, ettringite will not form. High temperature may occur

because of heat of hydration of cement especially in mass concrete; i.e., large concrete members

such as concrete dams or drilled shafts. It may also be experienced in accelerated curing when

concrete is kept in a warm environment or heated by steam. Accelerated curing is used when

concrete strength gain is desired at early ages. In such conditions, reaction of sulfate with

calcium aluminates (C3A) forms monosulfoaluminate instead of ettringite. When concrete

subsequently cools down, ettringite crystals start to form if the source of sulfate (gypsum

interground with Portland cement) is not depleted, which causes expansion and cracking.

Formation of etrringite is harmless when concrete is in a plastic state and can accommodate

volume increases. But after the concrete sets, the expansion due to DEF cause internal stresses

and may cause cracking if these stresses exceed the tensile strength of concrete [2].

Transport of sulfate ions into the pores of concrete is controlled by diffusion and permeability

coefficients. Cracking considerably increases both permeability and diffusion coefficient and can

enhance sulfate attack [1].

2-2 Mechanisms of mass transport in concrete

The majority of concrete durability problems, such as those discussed in section 2-1, are due to

penetration of moisture and aggressive agents into concrete. The rate of this transport is one of

the primary controlling factors of concrete deterioration rate. Water permeation in saturated and

unsaturated condition as well as ion diffusion, as two major transport mechanisms, are discussed

in this section.

23

2-2-1 Saturated permeation

Permeation is the convectional mode of transport. In presence of a pressure difference, fluid

(e.g., water containing solutes) moves from higher to lower pressure regions. The pressure

difference in concrete is generally due to capillary suction (for unsaturated concrete) or gravity

(for saturated concrete). Under certain assumptions (Newtonian fluid, laminar flow, inert non-

swelling media), fluid flux in porous media is proportional to the pressure gradient according to

Darcy’s law.

Figure 2-12 shows a sample with different water heads at two sides which generates a pressure

gradient and causes water to flow from the high pressure region to the low pressure region.

Darcy’s law is the fundamental convection transport equation which relates fluid flux (may be

referred as flux density in other fields) J (m/s) in a porous media to the pressure gradient that

drives the flow ( / ), permeability coefficient (m2), and fluid viscosity (Pa.s) [17].

2 13

Figure 2-12: Illustration of fluid flow under pressure gradient

Δh

J

24

Where Q (m3/s) is discharge rate and A (m2) is the cross section of the specimen perpendicular to

direction of flow. Darcy’s law is more commonly stated in terms of pressure head (m) where

, (kg/m3) is fluid density and (m/s2) is gravitational acceleration:

2 14

The coefficient K (m/s) in eq. 2-14 is known as the hydraulic conductivity and is related to the

permeability coefficient [17].

The saturated permeability coefficient of concrete can be measured by forcing flow through a

specimen of uniform cross-sectional area with the lateral surface of the specimen sealed to

ensure unidirectional flow. The quantity of the fluid flowing through the specimen is measured

and Darcy’s law (eq. 2-13) is used to obtain the permeability coefficient. Both the US Army

standard [18] and ASTM standard [19] can be used to measure the permeability of concrete.

The saturated permeability coefficient of concrete is strongly dependent on the porosity and pore

size distribution of cement paste which are primarily controlled by water to cement ratio (w/c).

Higher w/c reflects a higher porosity and larger pore sizes which result in a higher permeability

(figure 2-13). Hagen-Poiseuille law describes flux in a cylindrical tube with length of L (m) and

radius of r (m) due to pressure difference Δ (Pa) [20].

8Δ

2 15

25

Figure: 2-13: Influence of w/c ratio on the permeability of (a) cement paste and (b) concrete [1]

By combining Hagen-Poiseuille law and Darcy’s law one can show that permeability is a linear

function of porosity but a square function of pore size.

18

2 16

Cracking can increase the permeability of concrete by several orders of magnetite depending on

crack width (i.e., aperture). This is because crack apertures are much wider than size of typical

pores in concrete. A detailed analysis of the saturated permeability of cracks is presented in

chapter 3.

26

2-2-2 Unsaturated permeation

In unsaturated condition, the permeability coefficient is a non-linear function of the moisture

content (κ κ θ where θ (-) is volumetric water content). The continuity equation for a

representative volume element of the unsaturated zone states that the change in total volumetric

water content with time is equal to the sum of any change in the flux of water into and out of the

representative volume element (figure 2-14) [20].

. 2 17

Where (-) is volumetric moisture content, t (s) is time and J (m/s) is water flux. By combining

Darcy’s law and the continuity equation, a partial differential equation known as the Richards

equation is obtained which governs moisture transport in unsaturated media. In case of one

dimensional flow, Richards’ equation would be simplified as [20]:

2 18

Figure 2-14: Unidirectional unsaturated flow

dx

J(x+dx)J(x)

27

Where is the pressure (i.e., capillary suction) gradient which is a function of moisture

content. In order to solve Richards’ equation, both permeability as a function of moisture

content κ θ and capillary pressure as function of moisture content must be known.

The later is known as the water retention function of porous material [20]. A number of

equations have been developed to describe unsaturated hydraulic conductivity (which is more

commonly used than unsaturated permeability). In most of these equations unsaturated hydraulic

conductivity is related to saturated hydraulic conductivity. Eq. 2-19, developed by Mualem [21],

is one of the most widely used in soil physics:

2 19

Where (m/s) is hydraulic conductivity as a function of reduced water content, (-) is the

reduced or normalized water content which is defined as: θ / with (-)

and (-) being practical saturated and dry moisture contents. (m/s) is the saturated hydraulic

conductivity, (-) is a fitting parameter and (m) is the capillary head as a function of water

content .

The relation between capillary head and water content is known as the water retention curve. A

typical water retention curve is shown in figure 2-15. An example of the variation of unsaturated

hydraulic conductivity K θ versus volumetric water content θ for sand, clay and loam is shown

in figure 2-16.

28

Figure 2-15: Typical water retention curves for a sand and a clay loam [20].

Similar to unsaturated hydraulic conductivity, a number of equations have been developed for

water retention curve in soil physics. One of the most widely used water retention functions is

that developed by van Genuchten (1980) [22]:

11

1

2 20

where (1/m), (-) and (-) are fitting parameters. With the assumption of 1 ,

Mualem (eq. 2-19) and van Genuchten (eq. 2-20) equations are coupled to give eq. 2-21 [20]:

1 1 / 2 21

29

Eq. 2-21 describes the unsaturated hydraulic conductivity as a function of normalized moisture

content and can be used to numerically solve Richards’ equation (eq. 2-18).

Figure 2-16: Unsaturated hydraulic conductivity K θ versus volumetric water content θ [20].

The measurement of unsaturated flow properties of concrete is complex and not common.

Instead, concrete professionals have adopted a simplified sorptivity test [23]. Sorptivity is a

parameter that describes the rate of penetration of water into unsaturated concrete. To measure

sorptivity concrete is exposed to water from one end and the weight gain due to water absorption

is monitored over time. The depth of penetration of water into unsaturated concrete is measured

as a function of time (m). Sorptivity √

is calculated according to eq. 2-22 [24]:

√ 2 22

30

Sorptivity of concrete is dependent on both the characteristics of concrete (e.g., porosity,

permeability) and the liquid (e.g., viscosity) being absorbed. In addition, the degree of saturation

of concrete prior to the test has a large impact on its sorptivity. As such, sorptivity, although easy

to measure, is not a material property and cannot be directly used to model unsaturated flow

inside concrete.

Using a sharp front model (assuming that the penetrating water front in concrete is sharp), the

saturated permeability coefficient k (m2) of concrete can be obtained from sorptivity

measurements if porosity (-), viscosity of water (Pa.s) and capillary suction (Pa) are

known [24].

2 2 23

can be determined from the equilibrium internal relative humidity of concrete based on

Kelvin’s equation [25][26].

2-2-3 Diffusion

Solute transport occurs through diffusion and convection. Diffusion takes place due to a

concentration gradient. Ions and other solutes travel within the pore solution of concrete from

higher to lower concentration regions (figure 2-17). Diffusion occurs through interconnected

moisture-filled pores and fractures. Cracks, when saturated, can enhance the process of diffusion

by providing wide pathways filled with a large volume of pore fluid. Fick’s first law [27] relates

31

the diffusion flux J (mol/m2.s) to the concentration gradient and a material property known

as the diffusion coefficient D (m2/s).

2 24

By combining Fick’s first law and a mass balance equation, Fick’s second law can be derived.

The change in concentration over time inside a representative volume element is equal to the

difference between the flux entering and exiting the element in that period of time. The mass

balance equation in one dimensional form (z) is written as:

2 25

where C is concentration (mol/m3). Fick’s 2nd law predicts how diffusion causes the

concentration to change with time.

2 26

Figure 2-17: Illustration of solute transport due to concentration gradient

J

C1 C2

32

It can be shown that [1]:

2 27

Where (-) is porosity of the concrete, D0 (m2/s) is diffusion coefficient of the ion of interest

inside the concrete’s pore solution and β (-) is pore connectivity which is a measure of tortuosity

and constrictions of the pore network [28]. The inverse of parameter β is known as the

material’s formation factor (-) and accounts for the physical resistance of the pore network

[1][27].

1 2 28

In the presence of a convective flow, the total ionic flux (J) is the summation of ionic diffusion

flux (Jd) and flux due capillary suction (Jc) [7].

2 29

Concrete pore solution has a relatively high ionic strength (approximately 0.5 mol/kg). At this

strength, idealized transport, which considers that each ionic species behaves independently from

others, is a poor assumption for modeling concrete pore solution. The interaction between

different ionic species is related to (a) the chemical activity of the species which accounts for a

reduction in ion mobility due to high ion concentrations (i.e., crowdedness) of pore solution, and

33

(b) the charge imbalances stemming from differences in self-diffusion coefficients of various

ions. In other words, in a multi-ion solution, diffusion of positive and negative ions creates an

electrical field which influences ion transport. The complete flux equation which considers

interaction between ions and also accounts for diffusion, conduction (i.e., ion diffusion due to an

electrical field), and permeation is known as the electro-diffusion or Nernst-Plank equation [27]:

1 2 30

Where (m2/s) is self diffusion coefficient of ith ionic species, (-) is the formation factor,

(-) is the ion activity coefficient which varies between 0 and 1, (mol/m3) is concentration of ith

ionic species, is the valency of ith ion, F is Faraday constants (=96485 J/V.mol), R is gas

constant (=8.31446 J/mol.K), T (K) is absolute temperature, (V) is electrical voltage created

by charge imbalance, (m2) is the bulk permeability coefficient and (Pa.s) is the fluid

viscosity [27].

Similar to the permeability coefficient, the diffusion coefficient in concrete is dependent on

porosity. However, eq. 2-27 suggests that is independent of pore size, at least when pore

surface interactions are not dominant. It would be interesting to investigate whether the diffusion

coefficient of cracked concrete is primarily dependent on volume fraction and tortuosity of

cracks or if the effects aperture and surface roughness are also significant. A research study that

addresses this question is provided in chapter 4.

34

2-2-4 Other transport mechanisms

There are other transport mechanisms that have effect on service life of concrete. Gas/vapor

transport are important especially in corrosion of steel reinforcement in concrete where carbon

dioxide and oxygen penetrate into concrete. Gas/vapor transport is mostly through diffusion.

The effects of chemical reactions on the mechanisms of ionic transport in concrete should also be

studied. Chemical reaction, in which ions are attracted to the solid surface of the pores under the

influence of electrostatic forces, dissolution and precipitation effect ion transport in concrete.

2-3 Service-life prediction models for concrete

Despite advances in service-life prediction of concrete structures (e.g., Life-365 and STADIUM

software), most of the existing models do not account for the effect of cracks in accelerating

transport and deterioration of concrete. Some service life models are briefly described below.

2-3-1 Life-365 Service Life Prediction Model

Life-365TM software was funded by American Concrete Institute (ACI) Strategic Development

Council (SDC) and the first version was released in 2001 to be used to evaluate corrosion

protection strategies in order to increase service life of reinforced concrete. In Life-365, it is

assumed that corrosion of steel reinforcement due to chloride attack is the primary mode of

deterioration [29].

In Life-365, service life is defined as “the sum of time to initiate the corrosion and the

propagation time required for corroding steel to cause sufficient damage to require repair.”

Initiation time represents the time required for the critical threshold concentration of chlorides to

35

reach the depth of reinforcing steel. Life-365 uses an approach based on Fick’s second law (eq.

2-26) to model diffusion and predict initiation time. The chloride age-dependent diffusion

coefficient is calculated by the software from eq. 2-31 [29]:

2 31

Where (m2/s) is diffusion coefficient at age (s) and is diffusion coefficient at

reference age which is 28 days in Life-365, and is a constant depending on mixture

proportions. Considering the information on mix design inputted by the user and based on an

incorporated experimental data obtained from bulk diffusion tests, the software selects and

and calculates up to 25 years. After 25 years, the diffusion coefficient is assumed to be

constant and equal to D(25years). Eq. 2-32, suggested by Stanish [30], shows the relationship

between and water to cement ratio (w/c) for concrete exposed to chloride at early age (28

days or less)

10 . . 2 32

The software also accounts for temperature-dependent changes in diffusion coefficient. Eq. 2-33

is used to calculate diffusion coefficient as a function of temperature [29]:

1 1 2 33

36

Where U is activation energy of diffusion process (35000 J/mol), R is gas constant (8.31446

J/mol.K), Tref is 293 k (20⁰ C), and T is absolute temperature.

The user inputs required to predict initiation period are geographic location, type of structure,

nature of exposure, thickness of concrete cover, water to cement ratio, type and quantity of

mineral admixtures, and type of steel reinforcement and coatings.

Supplementary cementitious materials (such as silica fume, fly ash and slag) reduce permeability

and diffusivity of concrete. Their subsequent effect on corrosion initiation period is considered in

Life-365. The software applies a reduction factor to concrete diffusion coefficient to account for

the effect of silica fume [29]:

. 0.165 2 34

Where DSF is reduced diffusion coefficient due to use silica fume and SF (%) is the level of silica

fume replacement in term of cement weight. Eq. 2-34 is only valid up to replacement level of

15% and for the higher percentages, the software assume diffusion coefficient equal to D15%. The

effect of fly ash and slag on early age diffusion coefficient (D28) is assumed to be negligible but

their effect on long-term reduction in diffusivity is considered. The parameter in eq. 2-31 is

modified by eq. 2-35 [29]:

0.2 0.450 70

2 35

37

Where FA and SG are level of fly ash and slag replacement respectively in term of cement

weight. The relationship is only valid for FA up to 50% and SG up to 70% and thus the

maximum is 0.6 [29].

In Life-365, the propagation period is assumed to be fixed and equal to 6 years. This time is

extended to 20 years if epoxy-coated steel is used. As a result, the time to repair predicted by the

software is simply equal to initiation period plus 6 (or 20) years [29]. Concrete in Life-365 is

modeled as saturated and uncracked.

2-3-2 STADIUM

STADIUMTM, developed by SIMCO Technologies is able to model unsaturated multi-ionic

transport in concrete [31]. Information on two sets of data is used as input parameters for the

software: material properties and environmental conditions. Based on parameters such as the

concrete cover and the type of rebar, the software can estimate the service life of the structure.

Information on geometry of the concrete element, mixture proportion (such as type, quantities

and densities of cement, supplementary cementitious materials, and aggregate), transport

property (such as porosity, diffusivity, and conductivity) and exposure condition can be inputted

by the users. Material properties can be measured experimentally and inputted. An example is

measurement of diffusion coefficient using a migration test [32]. Alternatively, database on

material properties from 24 different mixture proportions as well as different exposure conditions

are available in the software. The environmental conditions are composed of the temperature,

relative humidity, and exposure level. Eight ionic species are considered: OH-, Na+, K+, SO42-,

Ca2+, Al(OH)4-, Mg2+, and Cl- [31].

38

Richards’ equation (eq. 2-18) is used to simulate water flow in unsaturated condition. The

extended Nernst-Planck equation is used to describe ionic transport in unsaturated media [33].

2-3-3 4SIGHT

The computer model 4SIGHT, developed by the U.S. National institute of standards and

technology (NIST), allows durability assessment of buried concrete structure [27]. The program

simulates multi-species ion transport and chemical reaction in unsaturated concrete (similar to

STADIUM). 4SIGHT has a simplified module to account for moisture flow inside cracks and its

impact on service life prediction. Crack spacing, crack width, and crack depth can be inputted by

the user. Alternatively the software has a module to predict flexural and drying shrinkage cracks

based on simple structural analysis. Porosity, permeability, w/c, formation factor, cement

properties, hydraulic pressure, and exposure condition (OH-, Na+, K+, SO42-, Mg2+, and Cl-) are

some of the other inputs of the software. 4SIGHT provides concentration at any depth over

specified period of time as output [27].

Diffusion coefficient and porosity can be estimated by the software if not entered by user.

Knowing water to cement ratio and degree of hydration (α , 4SIGHT uses the following

equations to estimate diffusion coefficient (m2/s) of chloride ion and porosity of concrete [27]:

log DC 6.0 w/c 13.84 2 36

11 1.16α

1 3.2 w/c 2 37

39

Formation factor is defined as ratio of pore solution conductivity ( ) to bulk conductivity ( )

for a nonconductive porous solid saturated with conductive solution [27]:

1 2 38

This is similar to eq. 2-27 described previously.

Cracks in 4SIGHT are approximated by smooth parallel walls with a gap equal to the observed

crack width. This assumption is conservative in case of flexural crack which are “V” shape and

the observed width is the maximum width. Also, neglecting tortuosity and roughness of cracks

results in overestimating of permeability. The permeability of a crack is assumed to be a function

of crack width square [27]:

12 2 38

This is the upper limit of permeability for crack with width of b and is further explained in

chapter 3.

2-4 Summary

This chapter provided a review of the concrete durability problems and the transport mechanisms

associated with them. Chapter 3 focuses on saturated permeability as one of the transport

mechanisms.

40

2-5 References

[1] S. Mindess, J.F. Young, D. Darwin, Concrete, 2nd Ed., Prentice Hall, Upper Saddle

River, New Jersey, 2003.

[2] M.G. Richardson, Fundamentals of durable reinforced concrete. Modern concrete

technology, London ; New York: Spon Press. xii, 260 p., 2002.

[3] P.K. Mehta, P.J.M. Monteiro, Concrete: Structure, Properties, and Materials. , Prentice-

Hall, 1993.

[4] G.H. Koch, P.H. Brogers, N. Thompson, Y.P. Virmani, J.H. Payer, Corrosion Cost and

Preventive Strategies in the United States, FHWA Report; FHWA-RD-01-156, Federal

Highway Administration, Washington, DC, 2002.

[5] Corrosion of Embedded Metals. Portland Cement Association [cited 2011 June];

Available from: http://www.cement.org/tech/cct_dur_corrosion.asp.

[6] Corrosion Cycle of Steel Rebar. [cited 2011 June]; Available from:

http://www.frpdistributors.com/?page_id=284.

[7] J.P. Broomfield, Corrosion of steel in concrete : understanding, investigation and repair.

2nd ed., London ; New York: Taylor & Francis. xvi, 277 p., 2007.

[8] F.Mansfield, Recording and Analysis of AC Impedance Data for Corrosion Studies,

Corrosion, 37 (1981) 301-307.

[9] A. Sohanghpurwala, W.T. Scannell, Repair and Protection of Concrete Exposed to

Seawater, Concrete Repair Bulletin, Merritt Island, FL, 1994.

[10] D.A. Hausmann, Steel Corrosion in concrete: How Does it Occur? Materials Protection,

6 (1967) 19-23.

41

[11] G.K. Glass, N.R. Buenfeld, Chloride threshold levels for corrosion induced deterioration

of steel in concrete, Chloride Penetration into Concrete, (Ed. L.-O. Nilsson and J.

Ollivier), 1995, pp. 429-440.

[12] Freeze - Thaw Deterioration of Concrete. [cited 2011 June]; Available from:

http://www.concrete-experts.com/pages/ft.htm.

[13] T. C. Powers, Freezing Effects In Concrete, American Concrete Institute SP 47, Detroit,

MI, 1975, pp. 1-12.

[14] R.N. Swamy, The Alkali-silica reaction in concrete, Glasgow, New York: Blackie ;Van

Nostrand Reinhold. xv, 336 p., 1992.

[15] B. Lothenbach, K. Scrivener, R.D. Hooton, Supplementary cementitious materials,

Cement and Concrete Research (2011) 10.1016/j.cemconres.2010.12.001.

[16] CEMENTAID Company Profile. [cited 2011 June]; Available from:

http://www.cementaid.ie/about.html.

[17] H.W. Reinhardt, RILEM Technical Committee 146-TCF., Penetration and permeability

of concrete : barriers to organic and contaminating liquids : state-of-the-art report

prepared by members of the RILEM Technical Committee 146-TCF. 1st ed. RILEM

report 16, London, New York, E & FN Spon. x, 331 p., 1997.

[18] CRD-C48-92, Standard Test Method for Water Permeability of Concrete, Handbook of

Cement and Concrete, US Army Corps of Engineers, 1992.

[19] ASTM D 5084 – 03, Standard Test Methods for Measurement of Hydraulic Conductivity

of Saturated Porous Materials Using a Flexible Wall Permeameter.

[20] D.E. Radcliffe, J. Simunek, Soil physics with HYDRUS: modeling and applications,

Boca Raton, FL: CRC Press/Taylor & Francis. xiii, 373 p., 2010.

42

[21] Y. Mualem, A new model for predicting the hydraulic conductivity of unsaturated porous

media, Water Resources Research, 12 (1976) 513-522.

[22] M.T. van Genuchten, A closed-form equation for predicting the hydraulic conductivity of

unsaturated soils. Soil Science Society of America, 44 (1980) 892-898.

[23] ASTM C1585 - 04e1 Standard Test Method for Measurement of Rate of Absorption of

Water by Hydraulic-Cement Concretes

[24] S. Kelham, A water absorption test for concrete, Magazine of Concrete Research, 40

(1988) 106-110.

[25] C. Hall, W.D. Hoff, Water transport in brick, stone and concrete. 2nd. ed., New York:

Taylor & Francis, 2011.

[26] F. Rajabipour, J. Weiss, Electrical conductivity of drying cement paste. Materials and

Structures, 40 (2007) 1143-1160.

[27] K.A. Snyder, Validation and Modification of the 4SIGHT Computer Program, NIST-IR

6747, National Institute of Standards and Technology, Department of Commerce, 2001.

[28] F.A.L. Dullien, Porous Media: Fluid Transport and Pore Structure, Academic Press, New

York, 1992.

[29] Life-365 Service Life Prediction Model, Computer Program for Predicting the Service

Life and Life-Cycle Costs of Reinforced Concrete Exposed to Chlorides, Silica Fume

Association, 2001.

[30] K. Stanish, Predicting the Diffusion Coefficient of Concrete from Mix Parameters,

University of Toronto Report, 2000.

[31] J. Marchand, Modeling the behavior of unsaturated cement systems exposed to

aggressive chemical environments. Materials and Structures, 34 (2001) 195-200.

43

[32] E. Samson, J. Marchand, K. A. Snyder, Calculation of Ionic Diffusion Coefficients on the

Basis of Migration Test Results. Materials and Structures, 35 (2003) 156-165.

[33] E. Samson, J. Marchand, Numerical Solution of the Extended Nernst-Planck Model.

Journal of Colloid and Interface Science, 215 (1999) 1-8.

44

CHAPTER 3: QUANTIFYING THE EFFECTS OF CRACK WIDTH,

TORTUOSITY, AND ROUGHNESS ON WATER PERMEABILITY OF

CRACKED MORTARS

The existing service-life prediction models rarely account for the effect of cracks on mass

transport and durability of concrete. To correct this deficiency, transport in fractured porous

media must be studied. The objective of this chapter is to quantify the water permeability of

localized cracks as a function of crack geometry (i.e., width, tortuosity, and surface roughness).

Plain and fiber-reinforced mortar disk specimens were cracked by splitting tension; and the crack

profile was digitized by image analysis and translated into crack geometric properties. Crack

permeability was measured using a Darcian flow-thru cell. The results show that permeability is

a function of the square of the crack width. Crack tortuosity and roughness reduce the

permeability by a factor of 4 to 6 below what is predicted by the theory for smooth parallel plate

cracks. Although tortuosity and roughness exhibit fractal behavior, their proper measurement is

possible and results in correct estimation of crack permeability.

3-1 Introduction

The permeability of concrete has an important impact on its durability since permeability

controls the rate of penetration of moisture that may contain aggressive solutes and also controls

moisture movement during heating and cooling or freezing and thawing [1]. While permeability

of concrete is commonly measured using uncracked laboratory specimens [2,3], in real

structures, the existence of cracks (induced by restrained shrinkage or mechanical loading) can

45

significantly increase the penetration of moisture and salts into concrete. This can especially be

significant for high strength concretes which are known to have a higher tendency for cracking

due to a larger autogenous and thermal shrinkage and a lower capacity for stress relaxation

[4,5,6]. As such, for service-life predictions, it is important to account for the effect of cracks on

accelerating the transport of moisture and aggressive agents inside concrete. Unfortunately, the

present generation of service-life models largely overlooks the effect of cracks on durability.

Research on the water permeability of crack-free concrete has been extensive [7,8,9,10,11,12]

and has led to a general understanding that the saturated water permeability of concrete is a

function of its porosity, pore connectivity, and the square of a threshold pore diameter

[10,11,12]. In addition to the classical flow-thru permeability measurements [2,3], new methods

(e.g., thermal expansion kinetics [13], beam bending [14], and dynamic pressurization [15]) have

been offered that allow a more rapid and repeatable measurement of the saturated permeability.

In comparison, research on the permeability of cracked concrete has been limited. The

pioneering works of Kermani [16], Tsukamoto and Wörner [17], and Gérard et al. [18] explored

changes in permeability of concrete caused by the application of compressive or tensile stress.

Wang et al. [19] measured the permeability of concrete disks fractured using a splitting tensile

test, and correlated the crack opening displacement (COD) with the permeability coefficient of a

crack. Their results suggested that for COD smaller than 25μm, there is no significant increase

in permeability beyond the matrix permeability. For larger cracks, permeability increases

exponentially. It should be noted that in this study (as well as some future studies [20,21,22]),

crack width was not directly measured; but assumed to be equal to the lateral displacement of the

46

disk specimen which was measured using an LVDT setup (figure 3-1). This assumption could

result in inaccuracies due to crack branching, variability of crack width along its length, and

inelastic deformation of the matrix; as discussed later in this chapter.

For use in service-life prediction models, it is important to establish a quantitative correlation

between crack geometry and its permeability. Using the theory of laminar flow of

incompressible Newtonian fluids in a smooth parallel-plate gap, equation 3-1, often referred to as

the Poiseuille law, can be derived showing that the cumulative water flow through a crack, Q

(m3/s), is related to the cube of crack width, b (m) [23]:

12 3 1

LVDT LVDT

Frame holding LVDTs

Disk specimen

Diametric crack

Figure 3-1: Schematic illustration of the splitting tension setup used to fracture mortar disk

specimens (after modification of the setup used by Wang et al. [19])

Y

Z

47

where Lb (m2) is the crack cross sectional area perpendicular to the direction of flow, η (Pa.s) is

dynamic viscosity of fluid, and (Pa/m) is the pressure gradient that drives the flow. This

equation can be combined with Darcy’s law:

3 2

and alternatively presented in terms of the permeability coefficient of a crack (m2), as a

function of the square of the crack width [24]:

12

3 3

Equations 3-1 and 3-3 are strictly valid for a smooth, straight, and parallel plate crack. Real

cracks in concrete never have such characteristics. As shown in figure 3-2, the crack width often

varies along the length of a crack; cracks are tortuous meaning their actual length is larger than

their nominal length; and crack wall surfaces are rough. These features reduce the permeability

of a crack, sometimes significantly. To account for this reduction in permeability, in equations

3-1 and 3-3, an empirical reduction factor ξ has been included; the values of ξ = 0.001 to 0.1

have been reported for plain and fiber reinforced concrete [21,25]. Unfortunately, these values

are uncertain (vary several orders of magnitude), purely empirical, and have not been correlated

to the geometric properties of cracks. For implementation in service-life models, it is important

to improve the estimation of crack permeability (and other transport properties) as a function of

48

crack geometric parameters; i.e., average or effective width, tortuosity, and roughness. This

chapter pursues this objective.

3-2 Quantifying the Geometric Properties of Cracks

3-2-1 Effective crack width

In a fractured disk specimen (figure 3-1), the actual crack profile is highly variable in both

parallel and perpendicular dimensions with respect to the direction of the flow. In other words,

the crack widths are variable both on the surface and through the thickness of the disk. For

example, figure 3-3 shows the cumulative distribution function of crack widths on the surface of

a mortar disk specimen. For comparison, the horizontal permanent displacement (after

(a)

(b)

Figure 3-2: A thru-thickness crack in a mortar disk specimen showing:

(a) crack width variability and crack tortuosity, (b) crack wall roughness

10mm

0.5mm

49

unloading), measured by LVDTs (figure 3-1), is also shown. It is clear that the LVDT reading is

not a good measure of the actual crack profile or even the average crack width.

Using the digitized crack profile, an effective thru crack width, beff-thru, can be calculated that

results in the same permeability coefficient as the actual variable crack. This is done by

extension of a technique originally suggested by Dietrich et al. [26] for fractured rocks. The

crack profile is discretized into a series of local parallel plates, which are further combined into a

global parallel plate (figure 3-4). In figure 3-4 (b), dimensions X, Y, and Z represent

respectively the direction of the flow (e.g., thru thickness), diametric direction parallel to crack,

and diametric direction perpendicular to crack (also see figure 3-1). If bij represent the crack

width for the ith element in direction X and jth element in direction Y, the first row of elements

can be represented by b1j. To calculate an effective thru crack width, beff-thru, first, the effective

0%

20%

40%

60%

80%

100%

0 50 100 150 200 250 300

Cum

ulat

ive

dist

ribu

tion

fun

ctio

n of

cra

ck w

idth

s

Crack width (µm)

Avg

. cra

ck w

idth

= 8

4.8μ

m

LV

DT

read

ing

= 2

04μm

Figure 3-3: Cumulative distribution function showing the variability of crack profile

along the surface of a disk specimen

50

crack for each row of elements is obtained (b1,eff, b2,eff, etc.). According to Darcy’s law, for the

first row of elements, the volumetric discharge rate (Q1,T) is described as:

,1 ΔP

3 4

where n is the number of elements in each row, and and ΔP1j represent the permeability

and pressure loss for each element. Assuming that the elements’ length and thickness are chosen

constant: Lij=L and dij=d, and that the flow is 1-dimensional (ΔP11 = ΔP12 = … = ΔP1):

beff

Actual crack profile Set of local parallel plates Global parallel plate

(a)

X

Y

Z

(direction of flow)

L14=L

d11=d

(b)

Figure 3-4: Method for calculation of the effective crack width (adopted from Dietrich et al.)

51

,1

12ΔP 3 5

Combining Eq. 3-5 and Darcy’s law results in:

,1

12ΔP b , 3 6

,1

3 7

Eq. 3-7 can be used to determine the effective surface crack width at the top and bottom faces of

each disk specimen (shown as beff-surf in figure 3-5). To determine the effective thru crack width,

beff-thru, a similar summation procedure is performed in the X direction. For a column of m crack

elements with length, width, and thickness nL, bi,eff, and d:

, , , 3 8

112

ΔPb1

12ΔP b ,

112

ΔP b , 3 9

Where QT is the total discharge rate, ΔP = ΔP1 + … + ΔPm is the total pressure loss across the

specimen, and m is the number of rows. Simplification of Eq. 3-9 results in:

52

ΔP ΔPb ,

b ,

3 10

ΔP ΔP ΔP b ,1

b ,ΔP b ,

1b

3 11

And ultimately:

∑ 1b ,

3 12

Figure 3-5: Correlation between the effective surface and thru crack widths

An example of calculation steps to obtain effective crack width is given in Appendix A.

y = 0.7238xR² = 0.9786

0

50

100

150

200

250

0 50 100 150 200 250

b eff

-thr

u(μ

m)

beff-surf (μm)

Fiber-reinforced Plain

53

3-2-2 Crack tortuosity and surface roughness

Figure 3-6 (a) and (b) show an actual thru-thickness crack profile and a schematic sketch of a

crack to illustrate surface metrology procedures. The crack profile is wavy (i.e., not straight)

resulting in an effective crack length (Le) larger than the nominal crack length Xmax. The ratio:

3 13

(a)

Figure 3-6: (a) Digitized profile of an actual thru crack;

(b) Schematics of a crack profile to illustrate surface metrology procedures

X

Xmax

Z

λ

xo xo+λ

reference lineSlope=α

(b)

1mm

54

is known as the tortuosity factor. It has been shown [27] that permeability is reduced

proportionally with (Xmax/Le)2 and not with (Xmax/Le) since the larger effective length affects both

pressure gradient and fluid velocity. In addition to tortuosity, the crack surfaces are rough which

creates additional friction against the flow. Louis [28][29] suggested the following equation to

estimate the permeability of a parallel-plate crack with rough walls in laminar flow:

12 1 8.8 . 3 14

where /2 is the relative surface roughness, and Ra (m) is the absolute roughness

defined as the mean height of the surface asperities.

To quantify tortuosity and roughness, surface metrology techniques [30] can be employed. First,

the surface profile is digitized and the x and z coordinates of all pixels on the crack surface are

identified. The profile is then divided into brackets of length λ. Within each bracket, a reference

line is drawn connecting the beginning and end points where the bracket intersects the crack

profile. The entire nominal length (Xmax) is covered by n brackets (note that n does not have to

be integer) and the lengths of the reference lines are determined. By summation of the

lengths, the effective length (Le) is obtained and used for calculation of tortuosity. Note that Le

depends on the sampling length λ; smaller λ results in a longer Le (more on this in section 4.3).

55

Roughness is determined in two steps. First the bracket x=0 to x=λ is selected and its roughness

is determined by calculating the average height of surface asperities with respect to its reference

line:

,1

| | 3 15

where Ra,l (m) is the local roughness over this bracket, and the quantity in front of Σ is the

absolute value of the difference between crack profile and the reference line in the direction

perpendicular to the reference line. Next, the bracket is shifted one pixel to the right (x=1 to

x=λ+1) and the local roughness is recalculated. The bracket is swept over the entire assessment

length (x=0 to x=Xmax) and the corresponding Ra,l values calculated. A total of (Xmax-λ) number

of Ra,l values are averaged to determine the global surface roughness:

, Avg.(Ra,g, over entire assessment length) 3 16

In addition, Ra,l values obtained can be used to construct a probability density function for the

surface roughness of the crack. The roughness can be measured using the top, bottom or both

crack surfaces. Note that Ra,l and Ra,g will depend on the sampling length λ (more on this in

section 4.3). In this study, the procedures for measurement of tortuosity and roughness, as

described above, were executed automatically through a MATLAB programming code.

An example of the procedure used to obtain tortuosity and roughness is given in Appendix A.

56

3-3 Materials and Experiments

3-3-1 Sample preparation

Disk-shape plain and fiber-reinforced mortar specimens were prepared, diametrically fractured,

and tested for permeability. The mortar mixture proportions are provided in Table 1. Type I/II

portland cement (per ASTM C150-

07), natural glacier sand (meeting the

gradation requirements of ASTM

C33-07), and polypropylene fibers

(8mm length, 39μm diameter, vol.

fraction 1%) were used. Disks (8.9cm

diameter × 2.5cm thickness) were cut

from 17.8cm tall mortar cylinders

after 28 days of moist curing. The disks were fractured using a deformation controlled splitting

tensile test (figure 3-1). Vertical load was applied using a Universal Testing Machine by

maintaining a constant rate of vertical deformation at 1 µm/s. The horizontal displacement was

continuously monitored using two LVDTs positioned at the opposite sides of the specimen. As

each specimen approached its peak load, a localized vertical crack formed starting from the

middle section of the disk and growing outwards. After reaching a desired horizontal

displacement, each specimen was unloaded at a vertical displacement rate of 5 µm/s. Various

average crack widths in the range 10 to 200µm were generated using this procedure. More

details on the fracture inducing method is given in Appendix B. After fracturing, specimens

were wrapped in plastic covers and kept in a moist room until they were due for permeability

Table 3-1: Mixture proportions for mortar specimens

Component Proportions (kg/m3)

Plain Fiber-Reinforced Cement 600 600

Sand 1375 1375 Water 270 270 Fiber --- 7.5

Stabilizing Admixture

--- 0.9

Water Reducing Admixture

3.25 3.25

57

test. Each disk was vacuum saturated inside saturated Ca(OH)2 solution for 24 hours prior to the

permeability test.

3-3-2 Permeability measurement

The saturated permeability was measured using a Darcian flow-thru cell (figure 3-7) and

according to the procedure of CRD-C48-92. Inside a stainless steel cell, a disk specimen was

securely seated on a retainer ring bonded to the specimen using a layer of high strength plaster.

The circumferential surface of the specimen was sealed using a 70/30 mixture of paraffin and

rosin. A layer of silicone sealant was applied on the top to seal the steel-wax interface. The

silicon was allowed to cure for 4 hours while the top surface of the specimen was kept wet to

prevent drying of the mortar. The permeability test was performed using a pressure gradient of

68.9 kPa (10psi). This resulted in a laminar flow with Reynolds numbers smaller than 118. The

input water was pressurized by air inside a bladder, and this pressure was constantly monitored

during the test. The output water was at atmospheric pressure. The outflow was collected inside

a volumetric flask placed on top of a digital balance with accuracy 0.01g. Weight measurements

were performed automatically by a computer at 10sec intervals. To prevent evaporation of

outflow water, the mouth of the volumetric flask was sealed with adhesive plastic with a small

puncture to allow pressure equilibrium. Further, the water inside the flask was covered with a

thin layer of oil.

Past research has shown that due to a self-healing phenomenon, permeability of cracks

continuously decreases during the test [31,32,33]. The crack healing during the permeability test

has been attributed to carbonation of concrete and formation of calcite (CaCO3), renewed

58

hydration of cement, and/or dissolution and re-deposition of portlandite (Ca(OH)2). The results

of the current study show up to 85% reduction in crack permeability during the first 24 hours of

the experiment, with narrower cracks showing a higher reduction than wider cracks. To maintain

consistency, it was decided to use the outflow rate at 15 minutes to determine the permeability of

cracks. The 15-min water flux inside cracks of various sizes was measured as 3 to 53 cm/sec.

Considering the specimens’ thickness (2.5cm), the measured flux values suggest that cracks are

fully saturated within the first few seconds of the test. In addition, the entire specimen had been

vacuum saturated in Ca(OH)2 solution before the test was initiated.

Figure 3-7: Permeability test

Outflow collected and weighted

Flow thru cell

Concrete disk

Pressure Control board

59

3-3-3 Measuring crack dimensions

Immediately after permeability measurement, the specimen was removed from the cell, cleaned

and air dried for 24 hours (23oC, 50%RH). It should be noted that some changes in the crack

width may be inevitable due to drying shrinkage. The crack dimensions were measured using

digital image analysis. To reach higher contrast between the crack and the matrix, specimens

were vacuum impregnated with a low viscosity black epoxy for 15 minutes. After the epoxy

hardened, the specimen’s top and bottom faces were polished to remove the surface layer of

epoxy and obtain flat surfaces (see Appendix A for more details). Next, the crack profile on the

top and bottom faces was scanned using a digital scanner with resolution 9600dpi (i.e., pixel size

≈ 2.65μm). This resulted in a crack detection limit of approximately 5.3μm (i.e, 2 pixels wide).

The surface crack width was measured every 200μm along the diametric crack, and the results

were used to obtain the effective surface crack width beff-surf (Eq. 3-7).

In addition to crack width measurements along the top and bottom surfaces of each disk, three

plain and five fiber-reinforced specimens were vertically sectioned at the mid-point along a

diameter perpendicular to the surface crack and the crack profile through the specimen’s

thickness was scanned (figure 3-5). The thru crack widths were measured every 50μm, and the

results were used to obtain the effective thru crack width beff-thru using Eq. 3-12. To be able to

calculate the effective thru crack width for the entire specimen, the possibility of establishing a

correlation between the effective surface and the effective thru crack widths was explored. For

the eight specimens vertically sectioned, the effective thru crack width was calculated along each

section. Also, the effective surface crack width corresponding to each section was calculated.

The portion of surface crack between 0.375 and 0.625 points was assumed to correspond with

60

the middle thru section (figure 3-5). Figure 3-5 shows a linear correlation between the effective

surface and thru crack widths obtained for both plain and fiber-reinforced specimens. Using this

correlation, for all specimens, the effective surface crack width was calculated by scanning the

crack at top and bottom surfaces and this value was translated into an effective thru crack width.

It should be noted that alternatively, 3D tomography techniques (e.g., X-ray CAT) can be used to

obtain the three dimensional crack profile. However, the resolution of such measurements can

be a limiting factor. For commonly available X-ray tomography instruments, the resolution is on

the order of 1/1000 of the sample dimension (e.g., 89μm for 89mm diameter specimens).

3-4 Results and Discussion

3-4-1 Comparison between average, effective, and LVDT crack measurements

A total of 20 plain and fiber-reinforced disk specimens were fractured and tested in this study.

Figure 3-8 shows comparisons among the average and effective crack widths and LVDT

measurements. The average and effective crack widths are closely correlated with the effective

thru crack widths approximately 13% larger than the average surface crack widths. This may

suggest that when the average crack width is properly determined from the specimens’ surfaces,

the effective crack width can be estimated with a reasonable accuracy without the need to slice

the specimens or perform calculations described by equations 3-7 and 3-12.

In comparison, the LVDT measurements show a significant scatter while they are consistently

over-estimating the crack widths, approximately by a factor 2.5. This again suggests that

horizontal LVDT measurements must not be used to estimate crack widths in a splitting tensile

test.

61

Figure 3-8: Correlation between (a) average and effective crack widths, (b) average crack width

and LVDT readings

y = 1.1322xR² = 0.9023

0

40

80

120

160

200

0 40 80 120 160 200

b eff

-thr

u(μ

m)

bavg (μm)

y = 2.5418xR² = 0.3747

0

80

160

240

320

400

0 40 80 120 160 200

b LV

DT

(μm

)

bavg (μm)

(b)

Line of equality

62

3-4-2 Saturated permeability as a function of crack width

The results of experimental measurements of crack permeability for plain and fiber-reinforced

mortars are presented in figure 3-9. For comparison, the values predicted by the parallel plate

theory (κ = b2/12) are also included. The curves present the best fit of Eq. 3-3 to the

experimental and theoretical data. For the experimental data, the best ξ corresponding to the

least error was determined. Several important observations can be made. (1) The permeability

of cracks is more than 6 orders of magnitude larger than the matrix permeability. (2) The

experimental results agree with the trend predicted by the theory. In other words, crack

permeability is a function of square of crack width. (3) However, the experimental values of

permeability are smaller than the theory by a factor of 4 to 6. The best fit for the plain specimens

results in ξ = 0.229 and for the fiber-reinforced specimens ξ = 0.163. This could be due to crack

tortuosity, and the friction caused by the crack’s surface roughness and the presence of fibers.

(4) The experimental results exhibit considerable scatter. While a coefficient of variation of 65%

has been reported for single-operator permeability measurement of uncracked concrete [34], the

existence of cracks can further contribute to scattering of results due to crack branching and

variability of crack profile in three dimensions. Future research can explore the precision in

permeability measurement of less variable cracks (e.g., manufactured gaps with certain thickness

and surface roughness).

Measurement of the crack permeability for very narrow crack is relatively difficult since the low-

speed water flux through the narrow crack is hard to accurately measure. Also crack healing

during the permeability test may significantly change the crack geometry in small cracks. In

addition, measurement of crack profile for very narrow cracks is difficult due to resolution

63

limitation of image capturing devices. Therefore the results shown in figure 3-9 for small cracks

(less than 30 μm) may contain errors both in the measured permeability coefficient and effective

crack width. To address these difficulties, artificial cracked samples were used in this study.

More details are provided in chapter 5.

Figure 3-9: Theoretical and experimental values of crack permeability as a function of

effective crack width

3-4-3 Crack tortuosity and surface roughness

It is known that fracture surfaces exhibit fractal behavior [35]. This means that crack profile

looks similarly tortuous and jagged at different scales of magnification (a property called self-

similarity). Examples of fractal functions are numerous in nature including mountains,

coastlines, clouds, plants, and natural and manufactured surfaces. The fractal nature of cracks in

concrete materials has been recognized by earlier researchers [36,37,38,39] who attempted to

1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

0 20 40 60 80 100 120 140 160 180 200

Cra

ck p

erm

eabi

lity

, κ(m

2 )

beff-thru (μm)

TheoryExperiment: PlainExperiment: Fiber-reinforced

Matrix permeability

64

link the surface area and roughness of cracks to the fracture toughness of the material. Lange et

al [37] found a correlation between roughness and fracture toughness, but no correlation to

compressive strength, total porosity, and effective pore diameter (derived from mercury

porosimetry). Ficker et al [38] found roughness to be closely related to water-to-cement ratio

and, as a consequence, to compressive strength. Issa et al [39] suggested an exponential equation

to quantify fracture toughness as a function of fractal dimension and stress intensity factor.

A similar approach can be adopted to relate the tortuosity and roughness of cracks to their

transport properties. Crandall et al [40] tried to find a quantitative relationship between the

roughness of rock fracture and how this wall roughness affect the fluid flow through the

fractures. They used Computational tomography scanning to obtain a three dimensional mesh

from Rock fractures. They characterized the tortuosity and wall roughnesses of the obtained

meshes and used Navier-stokes numerical model to relate roughness to the effective flow

through the fractures. They calculated tortuosity (τ) for differenct fracture with different wall

roughness. The Permeability coefficient from their numerical model showed close relationship

to the rock fracture roughness

In this study, tortuosity and roughness are measured for different sampling length with the

procedure explained in section 3-2-2. Figure 3-10(a) shows the effective length (Le) of a thru-

thickness crack, in a fiber-reinforced specimen, measured using significantly different values of

sampling length scale (λ) per section 3-2-2.

65

Figure 3-10: Effective crack length as a function of sampling length scale: (a) Fiber-reinforced

crack fitted by a fractal power function; (b) Comparison between plain and fiber-reinforced

cracks

y = 58.816x-0.095

R² = 0.9729

10

100

1 100 10000

Eff

ecti

ve le

ngth

, Le

(mm

)

Sampling length, λ (μm)

10

100

1 100 10000

Eff

ecti

ve le

ngth

, Le

(mm

)

Sampling length, λ (μm)

Fiber-reinforced Plain

(b)

66

The crack had a nominal length Xmax= 20.66mm. It is observed that the measured values of Le

depend strongly on λ and increase from 22.40mm at λ=12,755μm to 49.19mm at λ=3.8μm. This

represents a change in the tortuosity factor from τ = 0.85 to 0.18 (i.e., becoming considerably

more tortuous at smaller λ’s). Despite its significant dependence on λ, Le can be considered a

statistically self-similar fractal only if it follows the power function [35]:

3 17

where D (-) is the fractal dimension and F (m) is a constant. This power function shows as a

straight line on a log-log scale which fits well to the data reported in figure 3-10(a), and results in

a fractal dimension D = 1.095. A comparison between the measured Le values from two cracks

in a plain and a fiber-reinforced specimen is provided in figure 3-10(b). The plain crack shows

similar or slightly smaller Le values (i.e., less tortuous crack) depending on the measurement’s

length scale (λ). The fractal dimension of the plain crack was determined as D = 1.096. Similar

results were obtained by analyzing other thru-thickness cracks in plain and fiber-reinforced

specimens.

In addition, the global roughness of the plain and fiber-reinforced thru cracks was measured

based on the procedure of section 2.2. The results are presented in figure 3-11. Unlike the

effective length (Le), which increases for smaller λ’s, the crack roughness decreases

monotonically as λ decreases. This is anticipated since at smaller sampling length scales, crack

shows smaller surface features. Except for very large values of λ, the crack roughness shows a

strong self-similar fractal behavior that can be represented by the power function [41]:

67

, 3 18

Figure 3-11: Crack surface roughness as a function of sampling length scale

The fractal dimensions of D = 1.085 and D = 1.052 were obtained for the plain and fiber-

reinforced cracks. Further, the presence of fibers does not show a measurable impact on the

roughness of cracks.

3-4-4 Effect of tortuosity and roughness on crack permeability

Table 2 shows the average values (between plain and fiber-reinforced specimens) of crack

tortuosity factor and surface roughness measured using different values λ. These values can be

used, along with the effective or average crack width, to estimate crack permeability using Louis

Eq. 3-14 that has been modified by adding the tortuosity factor:

1

10

100

1000

10000

100000

1 100 10000

Cra

ck r

ough

ness

, Ra,

g(μ

m)

Sampling length, λ (μm)

Fiber-reinforced Plain

68

12 1 8.8 . 3 19

Figure 3-12: Estimation of crack permeability based on Eq. 3-19

The results are presented in figure 3-12 which compares the estimated permeability from Eq. 3-

19 with values measured by experiment. Among the three estimate curves, the one

corresponding to λ = 10μm (τ =0.21, Ra,g =8.9μm) matches the best to experimental data. This

underlines the significance of choosing a proper sampling length for estimation of crack

tortuosity and roughness. The observations from figure 3-12 suggest that the sampling length

1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

0 20 40 60 80 100 120 140 160 180 200

Per

mea

bil

ity

(m2 )

b eff-thru (μm)

Plain MortarFiber Reinforced MortarSmooth Parallel Plates TheoryRoughnes= 8.9 μm, Tortuosity=0.21Roughnes= 70 μm, Tortuosity=0.27Roughnes= 637 μm, Tortuosity=0.51

Table 3-2: Average tortuosity and roughness measured using different values of λ

λ (μm) τ (-) Ra,g (μm) 1000 0.51 637 100 0.27 70 10 0.21 8.9

Matrix Permeability

69

must be several times smaller than the width of the examined crack. Further, Eq. 3-19 can

provide a good quantitative estimate of crack permeability, at least for the effective crack widths

in the range 35 to 100μm. Future research should examine the applicability of this equation for

cracks of different size and in concrete materials other than the specific mortars studied in this

work.

3-5 Conclusions

Based on the results of this research, the following conclusions can be drawn:

Using a digitized crack profile, an effective crack width can be calculated that results in

the same permeability as the actual crack whose width is variable along its length. The

effective crack width shows a reasonably good correlation with the arithmetic average of

crack widths. On the other hand, horizontal displacement of disk specimen during the

splitting tensile test (i.e., LVDT reading) does not correlate well with average or effective

crack width and should not be used to estimate crack dimensions.

Experimental measurements show that crack permeability coefficient is a function of

crack width squared. While this trend agrees with the theory of laminar flow in smooth

parallel plate gaps, the measured permeability values are smaller than the theory by a

factor 4 to 6 likely due to tortuosity and surface roughness of cracks.

Tortuosity and surface roughness of cracks exhibit fractal behavior. In other words, the

numerical values of these parameters depend significantly on the magnification of length

70

scale. In this work, plain and fiber-reinforced cracks were examined at several different

length scales from μm to mm. Both tortuosity and roughness show a statistically self-

similar fractal behavior across these length scales, with fractal dimensions measured in

the range 1.052 to 1.096.

Towards the main objective of this work, a modification of the Louis equation by adding

a tortuosity factor was found to be capable of quantifying crack permeability as a

function of crack geometry (i.e., width, tortuosity, and surface roughness). Tortuosity

and roughness of crack must be measured using a sampling length scale that is several

times smaller than crack width.

3-6 References

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River, New Jersey, 2003.

[2] CRD-C48-92, Standard Test Method for Water Permeability of Concrete, Handbook of

Cement and Concrete, US Army Corps of Engineers, 1992.

[3] ASTM D 5084 – 03: Standard Test Methods for Measurement of Hydraulic Conductivity

of Saturated Porous Materials Using a Flexible Wall Permeameter, American Society for

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[4] P.D. Krauss, E.A. Rogalla, Transverse Cracking in Newly Constructed Bridge Decks,

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[6] ACI 231R-10 Report on Early-Age Cracking: Causes, Measurement and Mitigation,

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concrete using a high-pressure triaxial cell, Cement and Concrete Research, 25(1995)

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[8] D. Ludirdja, R.L. Berger, J.F. Young, Simple method for measuring water permeability

of concrete, ACI Materials Journal, 86(1989) 433-439.

[9] T.C. Powers, L.E. Copeland, J.C. Hayes, H.M. Mann, Permeability of portland cement

paste, Journal of the American Concrete Institute, 51 (1954), 285-298.

[10] A.J. Katz, A.H. Thompson, Quantitative prediction of permeability in porous rock,

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[11] P. Halamickova, R.J. Detwiler, D.P. Bentz, E.J. Garboczi, Water permeability and

chloride ion diffusion in portland cement mortars: Relationship to sand content and

critical pore diameter, Cement and Concrete Research, 25 (1995) 790-802.

[12] M.R. Nokken, R.D. Hooton, Using pore parameters to estimate permeability or

conductivity of concrete, Materials and Structures, 41(2008) 1-16.

[13] H. Ai, J.F. Young, G.W. Scherer, Thermal expansion kinetics: Method to measure

permeability of cementitious materials: II, Application to hardened cement pastes,

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[14] G.W. Scherer, Measuring permeability of rigid materials by a beam-bending method: I,

Theory, Journal of the American Ceramic Society, 83 (2000) 2231-2239.

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[15] Z.C. Grasley, G.W. Scherer, D.A. Lange, J.J. Valenza, Dynamic pressurization method

for measuring permeability and modulus: II. Cementitious materials, Materials and

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[16] A. Kermani, Permeability of stressed concrete, Building Research and Information, 19

(1991) 360-366.

[17] M. Tsukamoto, J.-D. Wörner, Permeability of cracked fibre-reinforced concrete,

Darmstadt Concrete: Annual Journal on Concrete and Concrete Structures, 6 (1991),

123–135.

[18] B. Gérard, D. Breysse, A. Ammouche, O. Houdusse, O. Didry, ‘Cracking and

permeability of concrete under tension’ Materials and Structures, 29 (1996) 141-151.

[19] K. Wang, D.C. Jansen, S.P. Shah, Permeability study of cracked concrete, Cement and

Concrete Research, 27 (1997) 381-393.

[20] C-M Aldea, S.P. Shah, A. Karr, Effect of cracking on water and chloride permeability of

concrete, ASCE Journal of Materials in Civil Engineering, 11 (1999) 181-187.

[21] V. Picandet, A. Khelidj, H. Bellegou, Crack effect on gas and water permeability of

concrete, Cement and Concrete Research, 39 (2009) 537-547.

[22] S.Y. Janga, B.S. Kimb, B.H. Oh, Effect of crack width on chloride diffusion coefficients

of concrete by steady-state migration tests, Cement and Concrete Research, 41 (2011), 9-

19 .

[23] B. Massey, J. Ward-Smith, Mechanics of Fluids, 8th Ed., Taylor & Francis, London,

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[24] D. Snow, Anisotropic permeability of fractured media, Water Resources Research, 5

(1969) 1273-1289.

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[25] J-P Charron, E. Denarié, E. Brühwiler, Transport properties of water and glycol in an

ultra high performance fiber reinforced concrete (UHPFRC) under high tensile

deformation, Cement and Concrete Research, 38 (2008) 689-698.

[26] P. Dietrich, R. Helming, M. Sauter, H. Hötzl, J. Köngeter, G. Teutsch, Flow and

Transport in Fractured Porous Media, Springer, Berlin, 2005.

[27] J. Bear, Dynamics of Fluids in Porous Media, Dover Publications, New York, 1988.

[28] G. de Marsily, Quantitative Hydrogeology, Academic Press, San Diego, 1986.

[29] C. Louis, Section III, Introduction à l'hydraulique des roches, Bull BRGM Série 2, vol. 4,

1974, pp. 283–356, (in French).

[30] D. Whitehouse, Surfaces and Their Measurement, Taylor and Francis, New York, 2002.

[31] N. Hearn, Self-sealing, autogenous healing, and continuous hydration: What is the

difference?, Materials and Structures, 31 (1998) 563-567.

[32] C. Edvartsen, Water permeability and autogenous healing of cracks in concrete, ACI

Materials Journal, 96 (1999) 448-454.

[33] H-W Reinhardt, M. Jooss, Permeability and self-healing of cracked concrete as a function

of temperature and crack width, Cement and Concrete Research, 33 (2003) 981-985.

[34] A. Bhargava, N. Banthia, Permeability of concrete with fiber reinforcement and service-

life predictions, Materials and Structures, 41 (2007) 363-372.

[35] B.B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and Company, New

York, 1983.

[36] V.E. Saouma, C.C. Barton, N.A. Gamaleldin, Fractal characterization of fracture surfaces

in concrete, Engineering Fracture Mechanics, 35 (1/2/3) (1990) 47-53.

74

[37] D.A. Lange, H.M. Jennings, S.P. Shah, Relationship between fracture surface roughness

and fracture behavior of cement paste and mortar, Journal of the American Ceramic

Society, 76(3) (1993) 589-597.

[38] T. Ficker, D. Martišek, H.M. Jennings, Roughness of fracture surfaces and compressive

strength of hydrated cement pastes, Cement and Concrete Research, 40 (2010) 947-955.

[39] M.A. Issa, A.M. Hammad, A. Chudnovsky, Correlation between crack tortuosity and

fracture toughness in cementitious materials, International Journal of Fracture, 60 (1993)

97-105.

[40] Dustin Crandall, Grant Bromhal, Zuleima T. Karpyn, Numerical simulations examining

the relationship between wall-roughness and fluid flow in rock fractures, International

Journal of Rock Mechanics and Mining Sciences, 47 (2010) 784-796.

[41] J.C. Russ, Fractal Surfaces, Plenum Press, New York, 1994.

75

CHAPTER 4: EVALUATING ION DIFFUSIVITY OF CRACKED

CEMENT PASTE USING ELECTRICAL IMPEDANCE SPECTROSCOPY

Cracking can significantly accelerate mass transport in concrete and as such, impact its

durability. This chapter is aimed at quantifying the effect of saturated cracks on ion diffusion.

Electrical conductivity, measured by electrical impedance spectroscopy (EIS), was used to

characterize the diffusion coefficient of fiber-reinforced cement paste disks that contained one or

two through-thickness cracks. Crack widths in the range 20 to 100μm were generated by a

controlled indirect tension test. Crack profiles were digitized and quantified by image analysis to

determine crack volume fraction and average crack width. Crack connectivity (e.g., inverse

tortuosity) was also measured by EIS. The results suggest that the diffusion coefficient of

cracked samples is strongly and linearly related to the crack volume fraction; but is not directly

dependent on crack width. Crack tortuosity does reduce the ion diffusion through cracks, but its

impact is not very significant. Overall, the most important parameter governing ion diffusion in

saturated cracked concrete is the volume fraction of cracks. Theoretical justifications of these

observations are also provided.

4-1 Introduction

Corrosion of steel is a major durability problem in reinforced concrete structures. Penetration of

chloride ions is known to be the primary cause of steel corrosion in concrete exposed to deicing

salts and in marine environments [1]. In saturated concrete, the major chloride transport

mechanism is ionic diffusion. The rate of chloride penetration is primarily a function of

diffusion coefficient of concrete, which is known to be dependent on the porosity and

76

connectivity of the pores in the concrete matrix [2][3]. While literature on the measurement

techniques for the diffusion coefficient of undamaged concrete is extensive [2][4][5][6][7][8][9],

cracked concrete has received much less attention [10][11][12]. In practice, concrete is often

cracked due to restrained shrinkage and/or mechanical loading. Cracking can significantly

accelerate mass (e.g., moisture, ion) transport in concrete and can reduce the service life of

concrete structures in aggressive environments.

In the present work, ion diffusion in cracked cement paste is studied using electrical impedance

spectroscopy. The main objective is to quantify how cracking affects ion transport in saturated

concrete and how diffusion in a crack is related to crack geometry.

A number of past researchers attempted to quantify diffusion in cracked concrete simply as a

function of the level of stress that the concrete had experienced. For example, Locogne et al [13]

found that microcracks caused by hydrostatic pressure up to 200 MPa have no influence on the

effective diffusion coefficient of concrete; while Konin et al. [14] reported a linear correlation

between apparent diffusion coefficient of concrete and the applied load. This approach, although

simple, may not be accurate since it makes an implicit assumption that cracking density (e.g.

volume fraction) and crack geometry (e.g., crack width, length, and tortuosity) is only a function

of the applied stress level. It is now well known that geometry of cracks is not solely dependent

on the stress level, but also on loading patterns and material properties (e.g., fracture toughness,

aggregate content, presence of fibers and other reinforcement, etc.). As such, a more

77

fundamental approach is needed to quantify the transport properties of cracks based on their

geometry.

Other researchers studied the effect of cracks on the ion diffusion coefficient in concrete.

Jacobsen et al. [10], Aldea et al. [15], and Gerard and Marchand [16] reported a linear correlation

between crack width and the ion diffusion coefficient in cracked concrete. Meanwhile, Gagne et

al. [17] and Jang et al. [18] reported that below a threshold crack width (e.g., 80µm), the ion

diffusion coefficient in concrete is not affected by cracking; while above this threshold, the ion

diffusion coefficient increases linearly with crack width.

A number of researchers tried to relate the ion diffusion coefficient in crack, Dcr, to its geometry.

Rodriguez and Hooton [19] suggested that Dcr should be independent of both crack width and

crack wall roughness and is equal to the diffusivity of ions in bulk pore solution (Do). Others

[11][20][21], suggested a threshold crack width of 53 to 80 μm, in which cracks wider than the

threshold have Dcrack=Do; while for smaller cracks, Dcrack is related to the crack width. Ismail et

al. [11] attributed this crack width dependence to mechanical interaction between the closely

spaced fracture surfaces, as well as self-healing and deposition of hydration products in the crack

path. It should be noted that these researchers did not account for the connectivity (e.g.,

tortuosity and constrictedness) of cracks. As will be discussed in this chapter, crack connectivity

could be affected by crack width, resulting in a reduction in the apparent diffusivity of the crack;

while the actual diffusion coefficient of ions in the solution saturating the crack is not affected by

the crack width (i.e., = Do independent of the crack width).

78

To address contradictions in the existing literature and improve the understanding of ion

diffusion in cracked concrete, this research measures the diffusivity of cement paste disks that

contain one or two through-thickness cracks. The measured diffusivity is related to the crack

volume fraction, width, and tortuosity. Specifically, the following hypothesis is evaluated: “The

diffusion coefficient of a cracked cementitious matrix (Dcomposite) can be properly described based

on the modified parallel law, which relates Dcomposite to the diffusion coefficient (Dcr), volume

fraction (cr), and connectivity (βcr) of cracks. Among these parameters, only βcr is directly

influenced by crack width, while Dcr is independent of crack width and is equal to the ion

diffusivity of pore solution, Do.”

4-2 Methods for Measuring the Diffusion Coefficient of Concrete

Before describing the theory and experimental procedures, a review of common methods for

measuring the ion diffusion coefficient in concrete is helpful to justify the validity of using

impedance spectroscopy for diffusivity measurements. These include the steady-state diffusion

test [22], salt ponding test [23], the bulk diffusion test [24][25], the steady-state migration test

[5][26], the rapid migration test [27], the rapid chloride permeability [28] and other DC

resistivity tests, and the AC electrical impedance spectroscopy [29][30].

In the steady-state diffusion test (figure 4-1), a concrete disk is placed between two

compartments; one filled with saturated Ca(OH)2, and the other with saturated Ca(OH)2 and 1M

79

NaCl. The time dependent changes in the concentration of Cl- in the two solutions (due to

chloride ion diffusion from high to low concentrations) are determined by titration or using ion-

selective electrodes. This data is used to calculate the diffusion coefficient of Cl- through

concrete.

Figure 4-1: Steady-state diffusion test

This test can nicely duplicate ion diffusion in saturated concrete. However, similar to other

diffusion tests, it is time consuming as it may take a few weeks (depending on concrete porosity)

before the test reaches the steady-state condition. An alternative is the salt ponding test [23],

which attempts to duplicate the non-steady-state diffusion. Figure 4-2 shows the test setup.

Figure 4-2: Salt ponding test

Concrete Sample

Ca(OH)2 Ca(OH)2

1M NaCl

80

Three duplicate concrete slabs are prepared, moist cured for 14 days, and then allowed to dry at

50% relative humidity for 28 day. The slabs are then exposed to 3% NaCl solution, ponded on

their top surface. Each slab’s sides are sealed and the bottom is exposed to drying in ambient air.

After 90 days of continuous ponding, the solution is removed, the slabs are milled, and Cl

concentration is determined in 12.5mm increments from the exposed surface to calculate the

concrete’s effective diffusion coefficient. This too is a long-term test, as it takes 132 days to

complete. In addition, slab samples are never saturated; as such, chloride transport due to a

combination of ion diffusion and moisture flow is measured. To address this drawback, the bulk

diffusion test [24][25] has been offered. In this test, a concrete sample is saturated with Ca(OH)2

solution and then exposed to 16.5% NaCl solution from one surface (other surfaces are sealed).

After 35 days exposure, the sample is removed and milled in thin layers. The Cl profile is

determined and used to calculate the apparent diffusion coefficient of concrete. Figure 4-3 shows

the test setup.

Figure 4-3: Bulk diffusion test

81

To shorten the test duration, migration tests (figure 4-4) accelerate Cl transport by application of

a constant DC voltage. The steady-state migration test [5][26] is performed in a two-chamber

cell with the pre-saturated concrete sample in between (similar to the cell used for the steady-

state diffusion test). The upstream chamber is filled with 5% NaCl solution and the downstream

chamber is filled with 0.3N NaOH solution [31]. A DC voltage in the range 10~12V is applied

and the chloride concentration change in the downstream chamber is monitored over time. After

establishing the steady-state condition, the results are used to calculate concrete diffusivity.

Figure 4-4: Electrical migration tests

Figure 4-5: Rapid migration test

ΔE

Upstream 5% NaCl

Downstream

0.3N NaOHCathode Anode

- +

Concrete sample

82

An alternative and faster test is the rapid migration test [27][32], which is based on non-steady

state ion migration. The test setup is shown in figure 4-5. Here, the applied voltage is higher (up

to 60V) and there is no need for monitoring the Cl concentration in the chambers’ solutions.

Instead, after the test (6 to 96 hours depending on concrete electrical resistivity), the concrete

sample is split and sprayed with AgNO3 solution to determine the chloride penetration depth.

This result is used in a formula derived from non-steady-state migration theory to back calculate

the diffusion coefficient [33]. In comparison with direct diffusion methods, migration tests are

faster and easier to perform.

Figure4-6: Rapid chloride permeability test (RCPT)

An even faster and easier method of assessing ion transport in concrete is based on electrical

conductivity (i.e., inverse of resistivity) measurements. Since the solid skeleton of concrete is

electrically insulating [34], the electrical current passes exclusively via ionic conduction through

the liquid filled pores. In parallel, ionic diffusion is also limited to the liquid phase. As such,

electrical conductivity measurements can quantify the resistance of microstructure against the

83

movement of ions. The most common conductivity-based test is the rapid chloride permeability

test (RCPT) [28]. The test setup is shown in figure 4-6.

In this test, a 60V DC voltage is applied to a concrete sample that is sandwiched between two

electrolyte cells. The electric charge passed through concrete is measured over 6 hours and

correlated to concrete’s diffusion coefficient [1]. An even faster version of this test has been

recently adopted by ASTM [35] in which the electrical current passing 1 minute after the

application of 60V voltage is measured and used for calculation of concrete’s electrical

conductivity. These are rapid and commonly used tests but are prone to a number of problems.

Mainly, the tests do not account for the electrical conductivity of pore solution and its effect on

concrete conductivity. As such, the magnitude of charge passed may not truly reflect the

microstructural diffusion coefficient. This problem can be especially acute when concrete

contains some mineral or chemical admixtures (e.g., fly ash, or ionic accelerators) that

significantly alter the ionic strength of pore solution. A second drawback of RCPT is that the

high voltage can cause considerable temperature rise, which would result in erroneously high

currents. In addition, the direct current (DC) results in developing electric polarization, which

causes the actual voltage to be reduced [33]. Other DC resistivity measurements, such as the 4-

point surface resistivity test [36], are prone to similar problems. In addition, it is critical to

account for the significant effect of the concrete’s moisture content on its conductivity [37][38].

An alternative method for measuring electrical conductivity is electrical impedance spectroscopy

(EIS). EIS is a powerful tool for measuring the dielectric properties of materials and interfaces.

84

EIS is very fast (e.g., <1min depending on the voltage frequency) and allows insitu, non-

destructive, and continuous measurements. EIS avoids heating of the specimen since the

potential difference is low (<1V) and polarization is not a concern as an alternating voltage (AC)

is applied [30]. In addition, measurements are obtained over a wide range of frequencies, which

allows frequency-dependent responses to be properly characterized. The history of EIS goes

back to late 19th century through the work of Oliver Heaviside who defined the terms

“impedance” and “reactance” that are still being used. However the application of EIS to

cementitious materials was developed mostly in the last 30 years [30][39][40][41][42]. By

coupling EIS with the measurement or estimation of pore solution conductivity, the

microstructural formation factor and diffusion coefficient can be determined [37][43][44]. In

this chapter, EIS is used to measure the diffusion coefficient of Cl- through cracked cement

paste.

4-3 Theory

Solute transport in concrete occurs through a combination of diffusion and convection. In

saturated concrete and in the absence of a pressure gradient, diffusion is the sole transport

mechanism. Diffusion takes place as a result of a concentration gradient. Ions and other solutes

travel within the pore solution of concrete from higher to lower concentration regions. Diffusion

occurs through interconnected moisture-filled pores and fractures. Cracks, when saturated, can

enhance the process of diffusion by providing wide pathways filled with large volume of pore

fluid. The complete ionic flux equation through bulk aqueous solutions, which considers the

interaction between multiple ions and also accounts for diffusion and migration (i.e., ion

85

movement due to an electrical field) is known as the electro-diffusion or Nernst-Plank equation

[44][45]:

, 1 4 1

Where subscript i represents the ith ionic specie, (mol/m3.s) is the ionic flux in bulk solution,

(m2/s) is the self diffusion coefficient of ion in bulk solution, (-) is the ion activity coefficient

0 1 , (mol/m3) is the ion concentration in pore solution, is the ion valency, F is

Faraday constants (=96485 J/V.mol), R is universal gas constant (=8.31446 J/mol.K), T (K) is

absolute temperature, and (V) is the electrical voltage (imposed externally or created by

charge imbalance). The term 1 accounts for the non-ideality of high ionic strength

solutions where ion-ion interactions are not negligible [44]. The convective transport due to a

pressure gradient is not considered in eq. 4-1 but can be simply added as a separate term.

For a composite material containing parallel solid and liquid phases:

, , . , . 4 2

where subscripts S and L represent solid and liquid phases, respectively; and (-) is the volume

fraction of each phase. For porous materials where ion transport occurs only in the liquid phase,

86

the first term on the right hand side of eq. 4-2 is eliminated. In a more general case where the

liquid phase is tortuous:

, , . , 4 3

where βL (-) is the pore connectivity that is a measure of tortuosity and constrictions of the pore

network, and is the microstructural formation factor which represent the resistance of

microstructure to movement of ions [46]. Combining eqs. 4-3 and 4-1 results in:

,, 4 4

Similarly, the electrical conductivity of composite, (S/m), can be related to the electrical

conductivity of pore solution, (S/m):

4 5

87

Eqs. 4-4 and 4-5 provide a theoretical basis to use electrical conductivity measurement for

calculation of ion diffusivity for porous materials with insulating solid skeleton. Combining eqs.

4-4 and 4-5 results in eq. 4-6, which is known as the Nernst-Einstein equation [43]:

,

,

1 4 6

Electrical conductivity measurements have been used by a number of researchers to estimate the

diffusion coefficient of rocks and concrete [29][47]. Their results showed a good agreement

with other diffusion measurement techniques.

It should be noted that eq. 4-6 accounts for the geometric restriction effect of pore structure on

ion motion and neglects the interaction between ions and the pore walls [2]. In most solid-liquid

interfaces, an electrical double layer forms inside the solution adjacent to the solid surface due to

the surface being electrically charged [48]. As such, hydrated ions with opposite charge are

attracted to pore walls. This electrical double layer interferes with ionic movement and reduces

the velocity of ions near the walls [49]. Within the double layer near the surface, in a so-called

Stern layer, the ions are immobile. To account for such surface effects, one should consider the

change in the electrical field near pore surfaces. The electrical potential is maximum at the

surface, (V), and decreases as one proceeds out into the bulk solution. The electrical

potential ( at distance (m) from the surface is given by eq. 4-7 [50]:

88

4 7

The effective thickness of the double layer is defined as m , which is also known as Debye

length. The Debye length is controlled by the type of electrolyte, ionic strength of the solution,

and ion valences [49]. For pore solution in concrete, the Debye length is in the range of a few

nanometers. Similarly, Rajabipour and Weiss [37] showed that surface conduction in cement

paste is only significant within approximately 15 nm of pore surfaces. As such, when studying

ion transport through cracked concrete, for cracks that are at least few tens of μm wide, the

electrical effect of cracks walls can be ignored. This means that cracks only have a geometric

effect on ion transport that can be properly characterized by eq. 4-6.

Diffusion through a cracked concrete occurs as diffusion through the concrete matrix plus

diffusion through the cracks. A concrete specimen containing through-thickness cracks can be

defined as a composite containing the concrete matrix in parallel with one or more cracks (figure

4-7). A modified parallel law (eq. 4-2), which also include phase connectivity terms) can be

used to quantify the diffusion coefficient of this composite as:

Figure 4-7: Parallel law for ion diffusion in cracked concrete

= +

DComposite DMatrix DCr

89

4 8

Similarly, the electrical conductivity of the composite can be described as:

4 9

Here, and are the volume fractions of the matrix and crack ( 1 .

An important question is how crack density and crack geometry affect eqs. 4-8 and 4-9; more

specifically, the parameters , , and . As discussed above, for μm-wide cracks,

electrical interactions with crack walls can be neglected and as such, and .

The crack density can be simply represented by the crack volume fraction, . The impact of

crack aperture on is only through changing the volume occupied by cracks. The

connectivity factor (β) is defined as the reciprocal of tortuosity ( ) multiplied by the

constrictedness factor ( ) [46]:

1 4 10

Tortuosity is the square of the effective length (Le) divided by the nominal length (L) of a crack,

while constrictedness represents the effect of change in the crack aperture over its length (figure

4-8):

90

Figure 4-8: Schematics of (a) smooth, and (b) constricted crack

4 11

14

4 12

The parameter S should be calculated for every single sharp change in the crack aperture and

averaged over the length of the crack to determine an effective constrictedness Seff = Avg(S1, …,

Sn). Eq. 4-12 suggests S to be dependent on crack width for a similar crack surface profile. For

example, a 20μm change in crack aperture from w1=50μm to w2=30μm results in S=1.284; while

the same 20μm change in aperture but from w1=220μm to w2=200μm results in a much less

significant S=1.009. The impact of crack aperture on tortuosity factor T might be less

pronounced.

L

Le > L

w1 w2

L/2 L/2

(a)

(b)

91

Eqs. 4-8 and 4-9 can be further simplified by combining with the Nernst-Einstein equation for

the matrix phase :

4 13

4 14

Where σo and Do are the electrical conductivity and ion diffusion coefficient of the solution

saturating the crack and the matrix phase. It should be noticed here that is the

connectivity of the matrix phase in the cracked sample, which is different than the connectivity

of the liquid-filled pores inside the matrix, . In a two-phase composite specimen of cracked

concrete, the cracks are considered as one phase, and the concrete matrix (together with its pores,

air voids, and other constituents) is considered as a continuum second phase. For specimens

containing through-thickness cracks (as those studied here), it is reasonable to assume ≈

1. Also, in eqs. 4-13 and 4-14, .

Eqs. 4-13 and 4-14 suggest that the diffusion coefficient of cracked concrete ( ) can be

determined simply be measuring σComposite and σo, and making a justified approximation of Do

based on the type of ionic species and the ionic strength of pore solution. Further, the only

parameter in eq. 4-13 that is directly affected by crack aperture is 1/ . Where

92

changes in with respect to crack width are insignificant, eq. 4-13 suggests a linear

relationship between diffusion coefficient of cracked concrete and the volume fraction of cracks,

. The validity of these conclusions will be examined in this study.

In this study electrical impedance spectroscopy was use to measure σComposite. The theoretical

basis of this method is further explained here. Electrical Impedance spectroscopy consists of

multi-frequency alternating (AC) measurement of concrete’s impedance. A sinusoidal voltage is

applied over a broad range of frequencies and the generated current is measured. The current has

the same frequency of the corresponding voltage but with a phase shift of θ (rad). Electrical

impedance Z (Ω) can be calculated as follows:

cos cos

4 15

Where is voltage (V) at time t (s), 2 is the angular frequency (rad/s), is frequency

(Hz), is current (A) as a function of time and (V) and (A) are the amplitude of voltage

and current respectively. Alternatively, current and voltage can be described in polar coordinates

and electrical impedance can be written as:

exp exp

exp 4 16

93

Where impedance amplitude Z0 (Ω) is V0/I0 and √ 1 (unitless). Electrical impedance (Z) in

equation 4-16 is composed of real and imaginary components. The real term is known as

resistance ( and the imaginary term is known as reactance ( . The

typical experimental result of resistance vs. reactance for a cracked fiber reinforced cement paste

sample is shown in figure 4-9 which is known as Nyquist plot. As it is shown in figure 4-3 at a

particular frequency, the imaginary component of electrical impedance becomes zero and the

total impedance (Z) becomes equal to real impedance (Z’). This value is called bulk resistance

which is used in eq. 4-17 to calculate electrical conductivity.

Figure 4-9: Resistance vs. reactance for a cracked fiber reinforced cement paste sample

In this study bulk resistance R (Ω) was measured for all samples and used to calculate electrical

conductivity. Then electrical conductivity of the samples was used in combination with image

analysis results of the crack profile to calculate pore connectivity (β) and finally the diffusion

coefficient of cracked samples was calculated using equation 4-13.

-8

-7

-6

-5

-4

-3

-2

-1

036 38 40 42 44 46

Z"

(Ω

)

Z' (Ω)

Bulk resistance (R)

94

4-4 Materials and Experiments

Fiber reinforced cement paste samples were tested in this study. Table 1 shows the mixture

proportions. PVA fibers were used (at 5.8 % volume fraction) to increase the ductility of the

samples and to prevent their sudden fracture and ensure stable formation of cracks during

splitting tensile test. Water reducing admixture was added to improve the workability. ASTM

C150 type I portland cement was used. The paste was mixed according to ASTM C305 and cast

in 10 20cm cylindrical molds in three layers and consolidated on a shaker table. After 3 days

moist curing at 22⁰C, one sample was demolded for measurement of the pore solution

composition. This sample was broken into pieces and its pore solution was extracted using a

pore fluid expression die with capacity of 550 MPa [51]. The pore solution chemical

composition was determined using inductively coupled plasma atomic emission spectroscopy

(ICP-AES). The results are provided in Table 4-2. The knowledge of pore solution composition

was needed for saturating cracks with a similar synthetic pore solution with known Do and σo, as

discussed later. Pore solution conductivity was measured using a commercially available

conductivity meter. After one week moist curing, the remaining cylinders were demolded and

disks of 100×25mm (diameter×thickness) were cut from the cylinders using a diamond blade

saw. The disks were then submerged in synthetic pore solution at 60⁰C for one more week to

reach an equivalent age (maturity) of 26 days at ambient temperature (22⁰C) (assuming an

approximate datum temperature 0⁰C). The disk samples were then cracked in a deformation-

controlled indirect tension test. Figure 4-10 shows the indirect tension test setup. Two LVDTs

were used to control the lateral displacement of the sample during loading. This lateral

displacement was used as a rough estimate of average crack width during the test. Actual crack

widths were later quantified using digital image analysis, as discussed below. The fracture tests

95

were conducted using displacement-control method with the actuator displacement rate of 1μm/s

and 5 μm/s for the loading and unloading phases, respectively. Cracks in the approximate range

of 20 to 100μm were induced, by unloading the test at desired values of lateral displacements.

Figure 4-11 shows typical crack patterns induced. Samples with both single crack and dual

cracks were created. The dual cracked samples were produced by reloading the single cracked

samples in a direction perpendicular to the first crack. After cracking, the circumferential

surface of the samples was sealed using an epoxy-based paint. Samples were then re-saturated

(under vacuum) in the synthetic pore solution before diffusion testing.

Table 4-1: Mixture proportions

Component Proportions (/m3 paste)

Cement (Kg) 1480 Water (Kg) 547.6 Fiber (Kg) 5.3

Water Reducing Admixture (Lit) 11.84

Table 4-2: Pore solution composition

Element Concentration (ppm)

Al 7.1 Ca 43.8 K 27500 Na 6900 S 2800 Fe 0.59 Si 43.8

96

Figure 4-10: Splitting tension setup used to fracture cement paste disks

Figure 4-11: Crack patterns for dual and single cracked samples

LVDTs

Direction of load

97

The setup for measurement of the diffusion coefficient using electrical impedance spectroscopy

(EIS) is shown in figure 4-12. A cracked disk sample was installed between two fluid

compartments using a test cell similar to those used in the rapid chloride permeability test [28] .

The joint between the sample and the fluid compartments was sealed with silicone sealant. Care

was taken to prevent drying. The synthetic pore solution was introduced in the two

compartments 3 hours prior to the test and was renewed immediately before the test time to

minimize the potential carbonation effect. Two stainless steel electrodes (8×155mm

diameter×length) were immersed into solutions to establish the electrical connectivity. The bulk

resistance (Rb) of the test cell containing the sample was measured by applying a 500mV AC

voltage in the sweep frequency range of 40 Hz to 10 MHz. Frequency sweep were performed in

a logarithmic mode with 150 measurements recorded per frequency decade. A nice review of

EIS measurements and data interpretation for cement-based materials is provided by [30]. Here,

the electrical conductivity of a cracked sample (σComposite) was determined based on its bulk

resistance:

4 17

where the geometry factor, k (1/m), was determined experimentally according to the method of

[34].

98

After EIS measurements, the sample was taken out of the cell, air dried, and vacuum

impregnated with a low viscosity black epoxy to fill the cracks and increase the optical contrast

between cracks and the cement paste matrix. After the epoxy had set, samples were surface

polished (grit #220), and scanned using a digital scanner at the resolution of 4800 dpi (pixel size

= 5.3μm). Crack width was measured by image analysis on the two surfaces of each disk sample

at 0.85mm intervals along the length of each crack. The results were arithmetically averaged to

obtain the mean crack width (wCr). For dual cracked samples, the second crack was induced to

be approximately the same size as of the first crack. The width of both cracks were quantified by

image analysis and averaged to determine wCr. The length of cracks was measured as well. The

volume fraction of cracks in each sample ( ) was obtained by multiplying the mean crack

width by the crack length.

Figure 4-12: EIS test setup

Cement paste

sample

Synthetic pore

solution

99

4-5 Results and Discussion

The results of EIS electrical conductivity measurements (σComposite , ) were used in

combination with the image analysis results (wCr, ) in eqs. 4-13 and 4-14 to calculate the

values for crack connectivity ( ) and the diffusion coefficient of the cracked sample

(DComposite). The constant parameters used in eqs. 4-13 and 4-14 are listed in Table 3. For Do, the

self diffusion coefficient of NaCl in water is used [52]; however, this value can be determined

more accurately by accounting for the activity and ionic strength of the solution.

Table 4-3: Parameters used in eqs. 4-13 and 4-14

Solution electrical conductivity σo (S/m) 20.28

Solution diffusivity Do (m2/s) 2.032 10-9

Matrix electrical conductivity σMatrix (S/m) 0.061

Matrix formation factor μMatrix (-) 332.5

Matrix connectivity factor βMatrix (-) 1.0

Figure 4-13 shows the measured electrical conductivity of cracked samples as a function of

volume fraction of cracks. σComposite exhibits an approximately linear relationship with the crack

volume fraction, in agreement with the theoretical prediction (eq. 4-14). The vertical intercept

corresponds to the conductivity of the crack-free cement matrix; σMatrix=0.061 S/m. The slope of

this line equals (note that 1), which suggests approximately

0.619. The conductivity measurements can be further translated into the diffusion

coefficient of the cracked samples (DComposite), which is presented in figure 4-14. Again,

100

DComposite shows a linear relationship with (in agreement with eq. 4-13); having a slope of

and a vertical intercept DMatrix = 6.22 10-12(m2/s).

Figure 4-13: Variation of the electrical conductivity of cracked cement paste samples (σComposite)

versus crack volume fraction (Cr)

Figures 4-13 and 4-14 also show that single- and dual-cracked samples with similar but

significantly different mean crack width (wCr) show similar σComposite and DComposite. For example,

a single-cracked sample with wCr =64.8μm and a dual-cracked sample with wCr =38.2μm have

= 0.0010 and 0.0011, respectively. These samples show σComposite = 0.0744 and 0.0714 S/m,

respectively, and DComposite = 7.16 10-12 and 7.45 10-12 m2/s, respectively. This suggests that

conductivity and ion diffusivity of cracked cementitious materials are dictated by the volume

fraction of cracks and not by crack widths. When the results are graphed as a function of crack

width (figure 4-15), the (or ) correlation is weak and

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

σ com

posi

te(S

/m)

Crack volume fraction ( Cr)

Double Cracked

Single Cracked

wCr= 64.8 μm

wCr= 38.2 μm

R2=0.91

101

primarily due to the fact that wCr indirectly impacts . These observations may suggest that,

strictly speaking, for fully saturated systems, crack width has minor impact on the diffusivity of

cracked cementitious materials. This might further suggest that methods such as fiber

reinforcement, which are designed to control and reduce crack width, may have less than

anticipated benefits for saturated cracks if they do not reduce the volume fraction of cracks.

Figure 4-14: Estimated diffusion coefficient of cracked samples (DComposite) as a function of crack

volume fraction (Cr)

The connectivity of crack path ( ) is the only term in eqs. 4-13 and 4-14 that could be

dependent on crack width. Using eq. 4-14 and the EIS measurements, at each data point was

calculated (figure 4-16). The results show considerable scatter in agreement with the nature of

cracks in cementitious materials. The average is 0.547, which is slightly less than the 0.619,

obtained from the line slope in figure 4-13. A weak correlation between wCr and is observed;

with modestly increasing for wider cracks. This could be due to an increase in the

0.0E+00

2.0E-12

4.0E-12

6.0E-12

8.0E-12

1.0E-11

1.2E-11

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035

DC

ompo

site

(m2 /

s)

Crack volume fraction ( Cr)

Double Cracked

Single Cracked

R2=0.91

102

constrictedness factor SCr for smaller cracks as suggested by eq. 4-12. Meanwhile, Cr is

primarily dictated by its tortuosity factor (TCr) which is largely dependent on concrete properties

R² = 0.3465

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 20 40 60 80 100

σ Com

posi

te(S

/m)

Avg. crack width; wCr (μm)

Double Cracked

Single Cracked

Figure 4-15: Variation of the electrical conductivity of cracked samples (σComposite) versus the

average crack width (wCr)

R² = 0.2425

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Cra

ck c

onne

ctiv

ity;β C

r(-

)

Ave. crack width; wCr (μm)

Figure 4-16: The calculated crack connectivity (Cr) as a function of average crack width (wCr)

103

(such as aggregate size, type, and volume fraction; presence of fibers or other reinforcement) as

well as loading patterns. The effect of crack width (wCr) on TCr could be small. Most

importantly, crack connectivity is relatively large; meaning that it does not significantly reduce

the ion diffusion in saturated cracks.

4-6 Conclusions

Based on testing of fiber-reinforced cement paste disk samples that contained one or two

through-thickness cracks, it was found that:

Ion diffusion coefficient and electrical conductivity of cracked samples are strongly (and

approximately linearly) related to the volume fraction of cracks. This is in agreement with

the modified parallel law.

Diffusivity and conductivity are not significantly influenced by crack width.

Crack connectivity (Cr) in the range of 0.37 to 0.69 was measured, suggesting that Cr does

not significantly reduce ion diffusion in cracks (i.e., beyond a factor 0.37-1=2.70). Cr

decreases modestly by reducing crack width.

4-7 References

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110

CHAPTER 5: PERMEABILITY, ELECTRICAL CONDUCTIVITY, AND

DIFFUSION COEFFICIENT OF SIMULATED CRACKS

In this chapter, transport properties of simulated cracks are measured to quantify the permeability

and diffusion coefficient of cracks based on crack geometry (crack width, and crack wall

roughness). Saturated permeability and diffusion coefficient of cracks are measured using

constant head permeability test, electrical migration test, and electrical impedance spectroscopy.

A Plexiglas rough parallel plate is used to simulate cracks in concrete. The results of

permeability test showed that permeability of a crack can be predicted using Louis equation;

which determines permeability based on crack width and surface roughness of the crack walls.

The result of migration and impedance tests proved that the diffusion coefficient of cracked

samples is linearly related to the crack volume fraction. When crack connectivity is correctly

accounted for, diffusion coefficient of cracks is independent of crack width and is equal to the

diffusion coefficient of the solution contained in the cracks. Crack connectivity increases with

increase in crack width up to a threshold value (~ 80 μm) where the connectivity value reaches

its theoretical maximum (β=1). Cracks larger than the threshold width can be assumed to be fully

connected.

5-1 Introduction

As discussed in chapter 1, the main objective of this dissertation is qualifying the transport

properties of cracked cementitious materials (more specifically, saturated permeability, and ion

111

diffusivity). In the two previous chapters, permeability and diffusion coefficient of cracked

mortar and cement paste samples were studied. One of the major difficulties that exists in the

study of transport properties of fractured concrete is measurement of the crack geometry. Crack

profile of natural cracks in concrete varies both in the surface and through the depth of the

fracture. Precise measurement of the crack characteristics is very important and failing to do so

will result in unreliable and inaccurate conclusions. In addition to this problem, it is often not

easy to obtain and measure very narrow and very wide cracks with real concrete samples due to

equipment limitations and brittleness of concrete. To address these difficulties, in this chapter a

test which setup is designed and built to simulate straight cracks in concrete is introduced. The

setup is used to quantify transport properties (saturated diffusion and saturated permeability

coefficients) of crack as a function of crack geometry (crack width and surface roughness). The

advantages of using an artificial cracked sample are 1- measuring crack geometry more

accurately, and 2- achieving wider range of crack width.

In this research a setup was designed and built from Plexiglas to simulate cracks in concrete.

Using a simulated crack sample, crack width and connectivity were accurately measured.

Permeability and diffusion coefficient of simulated cracks were measured using constant head

permeability test, electrical impedance spectroscopy and electrical migration test. Since Plexiglas

materials are non-porous and inert, the measured values only reflect the crack properties.

Permeability and diffusivity of cracks in concrete was studied in Chapter 3 and 4. In this chapter

theses properties are further studied to fully address the research questions in two previous

chapters. The result of this study was used to evaluate the following hypotheses:

112

I. Permeability of cracks can be qualitatively predicted based on crack width, tortuosity and

crack wall roughness.

II. Diffusion coefficient of crack is independent from crack width and is equal to the

diffusivity of the solution saturating the crack.

III. The surface effect on diffusion coefficient of cracks is insignificant and can be ignored.

IV. Crack connectivity is dependent on crack width for small cracks and constant for large

cracks.

5-2 Methods

There are several developed method that are used to measure coefficients of permeability [1][2]

and diffusion [3][4][5][6][7][8][9][10]. In this study constant head permeability test was used to

measure permeability coefficient. Migration test [7][9] and electrical impedance test [10] was

used to measure diffusion coefficient. More details on these methods are provided in section 5-4.

Description of various methods for measurement of ion diffusivity of concrete is provided in

chapter 4.

5-3 Theory

5-3-1 Hydraulic Permeability of Cracks

As discussed in chapter 3, using the theory of laminar flow for incompressible Newtonian fluids

inside a smooth parallel-plate gap, the permeability coefficient of a crack (m2), can be written

as a function of crack width square [11]:

113

12

5 1

Where b (m) is crack width. Eq. 5-1 is valid for straight thru cracks with parallel and smooth

wall surfaces. Such “perfect” cracks are rarely observed in concerete whose cracks are tortuous,

have rough surfaces, and are continuously narrowing and widening along the crack path (see

figure 4-8). Crack tortuosity and roughness reduce permeability by introducing friction and

energy loss. Chapter 3 discussed an empirical equation to account for the reduction in crack

permeability due to crack tortuosity and surface roughness (Eq. 5-2):

1 8.8 . 12 5 2

Where is the tortuosity factor which is defined and square of nominal crack length to

effective crack length. /2 is the relative surface roughness and (m) is the absolute

roughness defined as the mean height of the surface asperities. In this chapter, the measured

values of permeability are compared to estimated values obtained from eq. 5-2 for wider range of

crack widths using the simulated crack sample. The simulated crack sample models straight

cracks with rough surfaces. Therefore the tortousity factor is assumed to be one in this

chapter.

114

5-3-2 Ion Diffusivity of Cracks

Ions can travel through cracks filled with pore fluid. This occurs through a combination of

convection, diffusion, and migration (i.e., ion movement due to an electrical field or voltage

gradient). The electro-diffusion or Nernst-Plank equation [12][13] gives the complete ionic flux

through bulk aqueous solutions:

1 , , 5 3

Where subscript i represents ith ionic species, (mol/m3.s) is the ionic flux in bulk solution,

(m2/s) is the self diffusion coefficient of ion in bulk solution, (-) is the ion activity coefficient

0 1 , (mol/m3) is the ion concentration in pore solution, is the ion valency, F is

Faraday constants (=96485 J/V.mol), R is gas constant (=8.31446 J/mol.K), T (K) is absolute

temperature, (V) is the electrical voltage (imposed externally or created by charge imbalance),

and (m/s) is the convective velocity. The term 1 accounts for the non-ideality of

high ionic strength solutions. The ion-ion interactions are accounted for by the change rate of

the logarithm of chemical activity per unit change in ion concentration [12]. The convective

transport term in eq. 5-3 is equal to zero if there is no pressure gradient.

Diffusion coefficient of cracked fiber reinforced cement paste samples were studied in chapter 4,

using electrical impedance spectroscopy (EIS). The relationship between diffusion coefficient of

115

crack and crack width was not fully covered in chapter 4. In this chapter diffusion coefficient of

crack is measured for the simulated crack samples with wider range of crack widths. In addition

to EIS, electrical migration test was conducted on the samples to measure ionic flux. Crack

diffusion coefficient was calculated and its relation with crack width is studied.

5-4 Experimental Methods

The test setup shown in figure 5-1 is designed to simulate a cracked concrete sample. The setup

is made of Plexiglas with adjustable crack width. The test setup is composed of two half

cylinders which can move towards or away from each other by means of two adjustment rods

and provide a broad range of gaps in between. Two LVDTs is mounted in two sides of the setup

to measure and monitor the gap between to cylinders. Cracks width in the range of 10 to 220 μm

were produced and tested with this method.

Figure 5-1: Plexiglas test sample used to simulate cracks in concrete

Adjustment rods & nuts

LVDTs

Plexiglas half cylinders

116

Duplicates of this setup were built with exactly the same dimensions. The only difference was

surface roughness of gap walls which were treated with machining with different grit sizes. The

surface roughness of the setups was measured using noncontact optical profilometry. Figure 5-2

shows the profilometer. Noncontact optical profilometry is a surface metrology technique in

which light from a lamp is split into two paths by a beam splitter. One path directs the light onto

the surface under the test, the other path directs the light to a reference mirror. Reflections are

recombined to generate an interface which contains information about the surface contours of the

test surface. Vertical resolution can be on the order of several angstroms.

Figure 5-2: Noncontact optical profilometer

Figure 5-3 shows the topography map of the surface of both setups measured using noncontact

optical profilometry. For each test sample (smooth and rough), three rectangles of 280 4000 µm

was scanned. Within each rectangle, five linear sections (with the length of 4000 µm) were

117

analyzed to measure roughness. Each section was divided into five segments and the height of

highest peak and the lowest valley was averaged for each segment. The total absolute roughness

was calculated by averaging the values obtained from all 75 segments (total of 150 peaks and

valleys). The absolute roughness obtained with this method for the rough Plexiglas test sample

with rough and smooth gap wall were 10.34 µm and 1.70 µm respectively.

+15 μm

-15 μm

+4 μm

-4 μm (b)

(a)

Figure 5-3: Topography map of the test samples surfaces, (a): Rough (b): Smooth

118

The test setup was installed between two compartments as shown in figure 5-4. These

compartments can contain water or other aqueous solution and facilitates the measurements of

hydraulic permeability and ion diffusivity coefficients. The interface of the Plexiglas cylinders

with the compartments was sealed using epoxy sealants. Each compartment is equipped with an

stainless steel mesh which is used to apply an electrical potential. Two water values are attached

to each compartment which are used to apply pressurized water and collect outflow in

permeability test (as shown in figure 5-5). Two cylindrical holes were provided near the sample

surfaces which were used as electrodes point of contact with the solutions. The electrodes are

used to measure chloride concentration and voltage across the sample. These holes were blocked

by brass caps when permeability test (figure 5-5) was conducted.

Figure 5-4: Test samples installed between two test cells

Water valve Brass cap

Stainless steel mesh and rod

Plexiglas test sample

Cylindrical compartment

(725 mL)

119

The saturated permeability was measured using a constant head method. A layer of silicone

sealant was applied on the compartments-sample interface. The silicon was allowed to cure for

24 h. After silicon was cured, the two compartments were filled with water under -30 psi vacuum

pressure to remove entrapped air. The permeability test was performed using a constant pressure

gradient ranging from 2 to 10 psi (varying depending on the gap width) which resulted in a

laminar flow with Reynolds number smaller than 186. The inflow water was pressurized by air

inside a bladder, and this pressure was constantly monitored during the test. The outflow water

was at atmospheric pressure. The outflow was collected inside a volumetric flask placed on top

of a digital balance with accuracy 0.01 g. Weight measurements were performed automatically

by a computer at 10 s intervals. To prevent evaporation of the outflow water, the mouth of the

volumetric flask was sealed with adhesive plastic with a small puncture to allow pressure

equilibrium. Further, the water inside the flask was covered with a thin layer of oil.

Figure 5-5: Permeability test setup

Water pressure gauges

Balance & flask

Pressure tank

Inflow compartment

Outflow compartment

Test sample

120

The steady-state migration test was adopted in this study to measure diffusion coefficient of

cracks. Figure 5-6 shows the migration cell configuration. The two compartments were filled

with different concentrations of sodium chloride solution (20000 ppm chloride in upstream and

100 to 300 ppm in downstream, the concentration variation in downstream solution is due to

filling procedure. The gap was also initially filled with low concentration solution). A vacuum

pressure of -30 psi was applied to the setup during filling of the solutions to remove the

entrapped air. An electrical potential difference (i.e., voltage) was applied to accelerate ion

transport. The driving forces in this case are both concentration gradient and potential difference.

Two Ag-AgCl reference electrodes were used to monitor electrical potential during the test.

Chloride concentration in both cells was measured periodically during the test using a chloride

ion selective electrode. Chloride concentration variation was used to calculate ionic flux (J).

Figure 5-6: Migration test configuration

For the test setup shown in figure 5-6, the diffusion coefficient D (m2/s) within the Plexiglas

sample can be determined from eq. 5-4 (assuming dilute solution, i.e. 1) [14].

ΔE

Upstream NaCl

20000 ppm

DownstreamNaCl

100 ppm Cathode Anode

- +

Plexiglas sample

121

5 4

Where J(x) is the flux of chloride ions (mol/m2s), is ions valency ( =1 for chloride ions), F is

Faraday constant (F=96485 (J/V.mol)), (Volts) is the potential drop measured (ΔE in figure

5-6), R is gas constant (R=8.31446 (J/mol.K)), T is the absolute temperature (K), C is the average

chloride concentration in upstream compartment during the test, and is the concentration

gradient across the sample. The term is electrical potential gradient across the sample which

assumed to be linear and equal to where L is sample thickness (m).

The applied electrical potential (E) in this test was 13 volts. Because of the electrode solution

interaction, when an external voltage is applied, the solution experiences a lower potential.

Reference electrodes were used to determine the exact voltage that is applied to the solution. The

value of 12.3 volts was measured adjacent to the sample surface. The later value was used in the

calculation of the diffusion coefficient. At this electrical potential difference, the effect of

concentration gradient on ionic flux (J) is very small compared with migration flux due to

electrical potential gradient . The ratio of the two is about 0.0002. Therefore it is reasonable

to assume that 0. With this assumption eq. 5-4 may be written as:

5 5

The ionic flux (J) can be determined by eq. 5-6:

122

∆∆

5 6

Where V (m3) is volume of the cell, A (m2) is the cross section area of the ionic flux (gap area in

this test), and ∆

∆ is the rate of chloride concentration change which is obtained by monitoring

chloride concentration in downstream cell over time. Combining eq. 5-5 and 5-6, the diffusion

coefficient can be calculated by eq. 5-7:

∆∆ 5 7

Figure 5-7: Migration test setup

Power Source

Ion Meter Volt Meter

Ion Selective Electrode Magnetic Stirrers

Reference Electrodes Plexiglas Sample

Power Source

Ion Meter Volt Meter

Ion Selective Electrode Magnetic Stirrers

Reference Electrodes Plexiglas Sample

123

The test setup used in this study to perform migration test is shown in figure 5-7. Figure 5-8

shows typical results of migration test. For the sample with crack width of 60 μm, there was no

significant change in the concentration of downstream cell in the first couple of hours. This is the

time required for the chloride ions to travel through the sample thickness and establish a steady-

state condition. After this initial unsteady-state period, the rate of increase in chloride

concentration of downstream compartment becomes constant. The steady state diffusion

coefficients D (m2/s) can be calculated from eq. 5-7, knowing the rate of chloride concentration

change ∆

∆ in the downstream cell.

Figure 5-8: Variation of chloride concentration over time in downstream cell (migration test)

Electrical conductivity of all test samples was also measure using electrical impedance

spectroscopy. After migration test, both cells were filled with 20000 ppm chloride solution under

-30 psi vacuum pressure. Bulk resistance of the test cells containing the sample were measured

(figure 5-9) by applying 500 mV alternating voltage with frequency ranging from 40 Hz to 10

y = 1.056x + 98.69R² = 0.9992

100

110

120

130

140

150

160

0 10 20 30 40 50

Con

cen

trat

ion

(p

pm

)

Time (hr)

Gap width=60 μm

124

MHz. For each frequency decade, about 150 measurements were recorded. A typical result of

electrical impedance test is shown in figure 5-10. In this curve the intersection between the half

circle and the horizontal axis is considered the bulk resistance. Other data in this figure is used to

determine the capacitance of the composites which is not covered in this dissertation. More

details on this are given in [15].

Figure 5-9: Electrical impedance test setup

125

Figure 5-10: Typical result of electrical impedance test

5-5 Results and Discussion

5-5-1 Hydraulic Permeability

The result of permeability test is shown in figure 5-11. Permeability coefficients obtained from

smooth setup (average roughness of 0.43 µm) closely match the theoretical values from theory of

smooth parallel plate. There is a reduction in permeability coefficient for the rough setup

(average roughness of 5.43 µm). This reduction is due to friction caused by the features on crack

wall surface. The result of this test is compared to the equation suggested by Louis (eq. 5-2) to

estimate the permeability of a parallel-plate crack with rough walls in laminar flow. The dashed

line shows the predicted values from Louis equation (both lines intersect vertical axis at zero).

The predicted values are fairly close to measured values. This indicates that the Louis equation is

able to properly predict the permeability coefficient of cracks with rough surfaces and proves the

first hypothesis of this chapter.

-15000

-12000

-9000

-6000

-3000

00 10000 20000 30000

Rea

ctan

ce (Ω

)

Resistance (Ω)

Bulk resistance (R)

Angular frequency

(ω)

126

Figure 5-11: Measured and predicted Permeability coefficient

Figure 5-12: Permeability test results (data point for mortar samples was obtained from [16])

A modified version of Louis equation which account for tortuosity (and roughness) was used to

predict permeability of cracked fiber reinforced and plain mortars in chapter 3 [16]. The

experimental result of that study is shown in figure 5-12 together with the result of simulated

crack for comparison. The reduction in permeability coefficient is higher for mortar samples

comparing to Plexiglas samples and that is because of tortuosity of natural cracks (as opposed to

1E-14

1E-13

1E-12

1E-11

1E-10

1E-09

1E-08

0 50 100 150 200 250

Per

mea

bil

ity

(m2)

Gap width (μm)

Smooth

Smooth parallel plate theory

Rough

Louis Eq.(Ra=10.86 μm)

(eq. 5-1)

(Ra=10.34 μm) (eq. 5-2)

1E-14

1E-13

1E-12

1E-11

1E-10

1E-09

1E-08

0 50 100 150 200 250

Per

mea

bil

ity

(m2)

Gap width (μm)

SmoothRoughPlain MortarFR MortarLouis Eq.(Ra=8.9 μm, τ= 0.21)

127

straight simulated cracks). Tortuosity further reduces the flow rate and while the effect of

roughness is only significant in small cracks, reductions due to tortuosity are significant for all

cracks.

5-5-2 Ion Diffusivity

Chloride diffusion coefficient of the crack (Dcr) was calculated from the result of migration test

using eq. 5-7. Figure 5-13 shows the variation of Dcr versus crack width. Diffusion coefficient of

the crack increases linearly with increase of crack width up to a threshold (60- 80 μm) and then

remains constant. The value of Dcr for cracks larger than the threshold is equal to diffusion

coefficient of chloride in free solution (2.032 10-9 m2/s). This indicates that the effect of crack

width on diffusion coefficient of the crack is insignificant for large cracks (e.g. >100 μm). This

result is in agreement with the result of Djebri et al. [17], Ismail et al. [18], and Kato et al. [19]

although the threshold value in some cases is slightly different (80, 53, and 75 respectively).

From the results shown in figure 5-13 the question arises as to why there is a drop from diffusion

coefficient in free solution for small cracks. Electrical conductivity of the samples, measured

using electrical impedance spectroscopy, was used to answer this question. Figure 5-14 shows

the variation of electrical conductivity of the samples normalized by the volume fraction of the

crack with crack width. Using eq. 4-5 crack connectivity βcrack was calculated from this data. The

results are shown in figure 5-15. Crack connectivity is almost constant and equal to 1 (maximum

connectivity) for cracks larger than the threshold (60-80 μm) and drops as the crack width

decreases. This supports the hypothesis IV of this chapter. The results indicate that the

128

dependency of crack diffusion coefficient on crack width for small cracks can be due to variation

of crack connectivity. To test this hypothesis, the values of crack diffusion coefficient from

migration test ware normalized by values of crack connectivity obtained from impedance test.

The results are shown in figure 5-16.

Figure 5-13: Diffusion coefficient of crack vs. crack width

Figure 5-14: Normalized conductivity vs. crack width

1.E-10

1.E-09

1.E-08

0 20 40 60 80 100 120 140

D c

rack

(m

2/s)

Gap width (μm)

SmoothRoughFree Solution

1.E-01

1.E+00

1.E+01

0 20 40 60 80 100 120 140

σ/φ

(S/m

)

Gap width (μm)

Smooth

Rough

Solution

129

Figure 5-15: Crack connectivity coefficient, obtain from EIS

Figure 5-16: Diffusion coefficient of crack normalized by crack connectivity obtained from EIS

An interesting observation from figure 5-16 is that all the data points lie on a line that

corresponds to chloride diffusion coefficient in free solution. This indicates that if the crack

connectivity is accounted for, diffusion coefficient of crack is independent of crack width and is

0

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60 80 100 120 140

Cra

ck c

onn

ecti

vity

β

Gap width (μm)

Smooth

Rough

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

0 20 40 60 80 100 120 140

D/β

crac

k (

m2 /

s)

Gap width (μm)

Free Solution

130

equal to diffusion coefficient in free solution. This supports the hypotheses II and III of this

chapter.

5-6 Conclusions

The following conclusions can be drawn from the results presented in this study:

If roughness is accounted for, permeability of cracks can be quantified based on crack width.

The Louis equation showed a good ability to predict permeability coefficient for the range of

cracks tested in this study.

If crack connectivity is accounted for, diffusion coefficient of cracks is independent of crack

width and is equal to the diffusion coefficient in the solution that the crack is saturated with.

Crack connectivity increases with increase in crack width up to a threshold value (60-80 μm

in this study) where the connectivity value reaches maximum value (β=1). Cracks larger than

the threshold can be assumed to be fully connected.

It should be noted that the discussion given in this chapter is only valid for straight cracks where

the tortousity factor is assumed to be one. The effect of tortuosity can be considered by replacing

nominal crack depth (or sample thickness) with effective length where it appears in calculation

of permeability and diffusion coefficient (e.g.: pressure gradient, concentration gradient,

electrical potential gradient, water flux, and ion flux).

131

5-7 References

[1] CRD-C48-92, Standard test method for water permeability of concrete, Handbook of

Cement and Concrete, US Army Corps of Engineers, 1992.

[2] ASTM D 5084-03, Standard Test Methods for Measurement of Hydraulic Conductivity

of Saturated Porous Materials Using a Flexible Wall Permeameter, American Society for

Testing and Materials, West Conshohocken, Pennsylvania, 2003.

[3] CL. Page, NR. Short, AEl. Tarras, Diffusion of chloride ions in hardened cement pastes,

Cement and Concrete Research, 11 (1981) 395-406.

[4] AASHTO T259, Standard method of test for resistance of concrete to chloride ion

penetration, Washington D.C., USA, 1980.

[5] ASTM C1202-10, Standard test method for electrical indication of concrete’s ability to

resist chloride ion penetration, American Society for Testing and Materials, West

Conshohocken, Pennsylvania, USA, 2010.

[6] ASTM C1556-11, Standard test method for determining the apparent chloride diffusion

coefficient of cementitious mixtures by bulk diffusion, American Society for Testing and

Materials, West Conshohocken, Pennsylvania, USA, 2011.

[7] NT BUILD 355, Chloride diffusion coefficient from migration cell experiments,

Nordtest, Tekniikantie 12, FIN-02150 Espoo, Finland, 1997.

[8] NT BUILD 443, Concrete, hardened: Accelerated chloride penetration, Nordtest, Esbo,

Finland, 1995.

[9] C. Andrade, Calculation of chloride diffusion coefficients in concrete from ionic

migration measurements. Cement and Concrete Research, 23 (1993) 724–742.

132

[10] A. Atkinson, AK. Nickerson, The diffusion of ions through water-saturated cement,

Journal of Materials Science, 19 (1984) 3068-3078.

[11] D. Snow, Anisotropic permeability of fractured media, Water Resources Research, 5

(1969) 1273-1289.

[12] KA. Snyder, Validation and Modification of the 4SIGHT Computer Program, NIST-IR

6747, National Institute of Standards and Technology (NIST), Gaithersburg, Maryland,

USA, 2001.

[13] L. Dresner, Some remarks on the integration of the extended Nernst-Planck equations in

the hyperfiltration of multicomponent solutions, Desalin., 10 (1972) 27-46.

[14] S.Y. Jang, B.S. Kim, B.H. Oh, Effect of crack width on chloride diffusion coefficients of

concrete by steady-state migration tests, Cement and Concrete Research, 41 (2011) 9–19.

[15] BJ. Christensen, T. Coverdale, RA. Olson, SJ. Ford, EJ. Garboczi, HM. Jennings, TO.

Mason, Impedance spectroscopy of hydrating cement-based materials: Measurement,

interpretation, and application, Journal of the American Ceramic Society, 77 (1994)

2789-2804.

[16] A. Akhavan, SMH. Shafaatian, F. Rajabipour, Quantifying the effects of crack width,

tortuosity, and roughness on water permeability of cracked mortars, Cement and Concrete

Research, 42 (2012) 313–320.

[17] A. Djerbi, S. Bonnet, A. Khelidj, V. Baroghel-bouny, Influence of traversing crack on

chloride diffusion into concrete. Cement and Concrete Research, 38 (2008) 877-883.

[18] M. Ismail, A. Toumi, R. François, R. Gagné, Effect of crack opening on the local

diffusion of chloride in inert materials, Cement and Concrete Research, 34 (2004) 711-

716.

133

[19] E. Kato, Y. Kato, T. Uomoto, Development of simulation model of chloride ion

transportation in cracked concrete. Journal of the Advanced Concrete Technology, 3

(2005) 85-94.

134

CHAPTER 6: SUMMARY AND CONCLUSIONS

6-1 Summary of Research Approach

Concrete is the most widely used man made material in the world. Most of the transportation

infrastructure is made of concrete with a design service life of 50 to 100 years. Long lasting

materials play a major role in building durable and cost effective structures. The primary factor

governing the durability of concrete is mass transport. Deterioration of concrete is significantly

influenced by the rate of moisture, ion, and gas/vapor transport in concrete. A number of

concrete service life prediction models currently exist that are based on simulating mass

(moisture, ion, vapor/gas) transport in concrete. Despite usefulness of these models, they do not

consider the presence of cracks in concrete. Since some level of cracking in concrete is

inevitable, and since cracks are known to accelerate mass transport, neglecting the effect of

cracks in existing models may result in inaccurate prediction of deterioration rate and expected

service life. Therefore, the focus of the present study was on fractured concrete and quantifying

the role of cracks in saturated mass transport in concrete. More specifically, the role of crack

density (i.e. volume fraction) and crack geometry (length, width, tortuosity, surface roughness)

on saturated permeability and ion diffusion coefficient of concrete was investigated.

Plain mortar, fiber-reinforced mortar, and fiber-reinforced cement paste disk specimens were

cracked by splitting tension; and the crack profile was digitized by image analysis and translated

into crack geometric properties. A simulated crack specimen with impervious matrix (Plexiglas)

135

was also built and tested. Constant head permeability test, electrical migration test, and electrical

impedance spectroscopy test were conducted on cracked and uncracked samples to measure

saturated coefficients of permeability and diffusion.

6-2 Conclusions

Based on findings of this research, the following conclusions are drawn:

An effective crack width can be found from crack digitized profile that results in the same

permeability as the actual crack with variable width along its length.

The crack permeability coefficient is a function of the crack width square. Tortuosity and

roughness of cracks reduce permeability.

Tortuosity and roughness of cracks exhibit fractal behavior. In other words, the numerical

values of these parameters depend significantly on the magnification of length scale chosen

for measurement.

A modified form of the Louis equation was found to be capable of quantifying crack

permeability as a function of crack geometry (i.e., width, tortuosity, and surface roughness).

Ion diffusion coefficient and electrical conductivity of cracked samples are strongly (and

approximately linearly) related to the volume fraction of cracks. This is in agreement with the

modified parallel law.

Diffusivity and conductivity are not significantly influenced by crack width.

Crack connectivity increases with increase in crack width up to a threshold value (60-80 μm

in this study) where the connectivity value reaches maximum value (β=1). Cracks larger than

the threshold can be assumed fully connected.

136

If crack connectivity is accounted for, diffusion coefficient of cracks is independent of crack

width and is equal to diffusion coefficient of ions in the solution that the crack is saturated

with.

6-3 Suggested Future Research

An interesting area that can be investigated in future studies is transport in unsaturated fractured

concrete. This will add an additional parameter (degree of saturation) to the problem and

represent a more general realistic condition. Unsaturated permeability coefficient is a function of

moisture content. The theoretical basis of unsaturated flow is discussed on sec 2-2-2 of this

dissertation. A number of equations have been suggested in the literature to calculate unsaturated

permeability. Most of these equations relate the unsaturated permeability coefficient to saturated

permeability by means of some fitting parameters. If the fitting parameters are determined,

unsaturated flow can be modeled. A finite element model can be developed to calculate the

moisture content of each element and use that to predict the unsaturated permeability coefficient

as the moisture content changes due to the flow within concrete. Sorptivity is another parameter

that is needed to be determined if existence of cracks is to be considered. X-ray tomography is a

powerful tool to measure and monitor variation of moisture content and ion transport in concrete.

137

APPENDIX A: IMAGE CAPTURING AND ANALYSIS PROCEDURE

In this study, the crack profile of the cracked sample was measured using digital image analysis

methods. After tested (permeability and impedance test), samples were allowed to dry for at least

24 hours in ambient temperature. Samples were centered in plastic cylindrical molds with a

dimension slightly larger than the sample dimension. Low viscosity black epoxy was introduced

to the molds to fully cover the samples. A vacuum pressure of -30 psi was applied to the samples

(for 15 minutes inside a dessicator) to remove entrapped air and increase the depth of penetration

of the epoxy (figure A-1).

Figure A-1: Vacuum impregnation of disk samples with epoxy

After the epoxy hardened, the specimen were polished to remove the surface layer of epoxy and

obtain flat surfaces. A polished cracked sample is shown in figure A-2. The crack profile was

138

scanned using a high resolution digital scanner with resolution of 9600 dpi. In addition to crack

profile on the surface of the specimens, three plain and five fiber-reinforced specimens were

vertically sectioned at the mid-point along a diameter perpendicular to the surface crack and the

crack profile through the specimen’s thickness was scanned (figure A-3).

Figure A-2: A polished epoxy impregnated sample

Figure A-3: A vertically sectioned specimen at the mid-point perpendicular to the surface crack

Y

Z

Y

Z

X

139

An image analysis software package was used to detect the cracks and measure the crack width.

First a curve was fitted to the crack path and then the crack was segmented perpendicular to the

fitted curve every 200 μm for the surface crack and every 50 μm for the thru cracks. Figure A-4

shows a detected thru crack and the segments. For each section the width of the crack was

measured. The effective crack width was calculated from the results of image analysis.

Figure A-4: A thru crack detected and segmented to measure crack width

The following is an example of how effective crack width is calculated for a cracked sample:

Z

X

Z

X

X

Y

Z

140

The measured values on the surface of the sample for a cracked sample are given in Table A-4.

Figure A-5 shows the crack width distribution on the surface of the sample. The measured values

of the crack width through the thickness of the same cracked sample are shown in Table A-5. The

summary of the data for surface and thru crack is given in tables A-1 and A-2. The effective

surface crack width and the effective thru crack width are measured by equations A-1 and A-2:

Figure A-5: Crack width distribution of the surface crack

Table A-1: Summary for the surface crack Statistics

Largest 132.64 132.44 7.36 Item Sec 499 Sec 499 Sec 102 Smallest 7.36 7.36 0.00 Item Sec 12 Sec 12 Sec 1 Average 39.67 39.64 0.55 Median 29.43 29.43 0.00 Std Dev 24.32 24.30 1.94 COV 0.61 0.61 3.52

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90 100 110 120 130 140

Fre

qu

ency

Crack Width (μm)

141

Table A-2: Summary for the thru crack Statistics

Largest 131.77 131.63 6.12 Item Sec 291 Sec 291 Sec 285 Smallest 9.18 9.18 0.00 Item Sec 1 Sec 1 Sec 1 Average 54.15 54.11 1.52 Median 48.98 48.98 0.00 Std Dev 22.36 22.35 1.59 COV 0.41 0.41 1.04

,1

A 1

,1

682987091911.92 52.50

∑ 1b ,

A 2

4360.008665

36.92

The effective surface crack width was calculated with this method for all the samples. The

effective thru crack with was only calculated for the eight specimens vertically sectioned. To

obtain the effective thru crack width for the entire specimen, a correlation between the effective

surface and the effective thru crack widths was established. The portion of surface crack between

0.375 and 0.625 points was assumed to correspond with the middle thru section (figure A-6).

Table A-6 shows the measured values of crack width in the mid quarter (between 0.375 and

0.625 points) of the cracked sample of this example. The summary of the measurements are

142

given in table A-3. Equation A-1 is used to calculate the effective surface crack width for the mid

quarter of the sample:

Figure A-6: The portion of surface crack between 0.375 and 0.625 points that was assumed to

correspond with the middle thru section is establishing the correlation between effective surface

and thru crack widths

Table A-3: Summary for the surface crack in the mid quarter Statistics

Largest 125.15 125.15 3.58 Item Sec 38 Sec 38 Sec 3 Smallest 7.15 7.15 0.00 Item Sec 194 Sec 194 Sec 1 Average 42.65 42.61 1.07 Median 35.76 35.76 0.00 Std Dev 25.56 25.55 1.64 COV 0.60 0.60 1.53

,1

622106653822.87 55.56

143

Same procedure was repeated for other sample vertically sectioned and effective surface crack

width in the mid quarter was calculated for all eight samples. the results are shown in figure A-7.

The following correlation was found:

0.7238

Figure A-7: Correlation between the effective surface and thru crack widths

And finally the effective thru crack width for the sample in this example can be calculated as

shown below:

0.7238 52.50 38.00

This procedure was used to calculate the effective thru crack width for all the samples.

y = 0.7238xR² = 0.9786

0

50

100

150

200

250

0 50 100 150 200 250

b eff

-thr

u(μ

m)

beff-surf (μm)

Fiber-reinforced Plain

beff-thru =36.92 μm beff-surf =55.65 μm

144

Image analysis was also used to measure tortuosity and roughness. As it is explained in chapter 3,

tortousity and roughness are fractal parameters meaning that the values of these parameters are a

function of sampling length. In this study a MATLAA code was used to measure tortuosity and

roughness with sampling length varying in the range of 3 μm to 50 mm. The following example

shows how totruosity and roughness were measured for sampling length of 1 mm.

(a)

In the example shown in figure A-8, the actual length of the crack can be calculated by counting

the circles and adding the length of portion left at the end of the crack

Actual length = (number of circles) X (sampling length) + length of remaining portion at the end

of crack

Sample thickness or nominal length of the crack = 21.4985 mm

Actual Length = 22.3356 mm

0.3356 mm 21.4985 mm

(b)

Figure A-8: (a) A detected thru crack. (b) The thru crack, sectioned every 1 mm

Circle Radius = 1 mm

145

22 1 0.3356 22.3356

The tortuosity factor is defined as square of nominal length to actual length:

21.498522.3356

0.93

Figure A-9: Roughness is calculated by averaging the crack variation within the sampling length

Within each sampling length, the variation of crack profile against a reference line (connecting

the start and end of the section) were averaged to measure roughness. Figure A-9 illustrates how

roughness is measured for a single section

146

Table A-4: Crack width measurement for the surface crack Line

D value (µm)

X value (µm)

Y value (µm)

Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 1 14.72 14.72 0.00 Sec 63 29.43 29.43 0.00 Sec 125 51.50 51.50 0.00 Sec 2 14.72 14.72 0.00 Sec 64 29.43 29.43 0.00 Sec 126 73.58 73.58 0.00 Sec 3 22.07 22.07 0.00 Sec 65 36.79 36.79 0.00 Sec 127 51.50 51.50 0.00 Sec 4 14.72 14.72 0.00 Sec 66 44.15 44.15 0.00 Sec 128 73.58 73.58 0.00 Sec 5 14.72 14.72 0.00 Sec 67 29.43 29.43 0.00 Sec 129 81.27 80.93 7.36 Sec 6 14.72 14.72 0.00 Sec 68 44.15 44.15 0.00 Sec 130 88.60 88.29 7.36 Sec 7 29.43 29.43 0.00 Sec 69 66.22 66.22 0.00 Sec 131 73.94 73.58 7.36 Sec 8 14.72 14.72 0.00 Sec 70 22.07 22.07 0.00 Sec 132 95.65 95.65 0.00 Sec 9 14.72 14.72 0.00 Sec 71 36.79 36.79 0.00 Sec 133 88.29 88.29 0.00 Sec 10 29.43 29.43 0.00 Sec 72 22.07 22.07 0.00 Sec 134 58.86 58.86 0.00 Sec 11 22.07 22.07 0.00 Sec 73 29.43 29.43 0.00 Sec 135 73.58 73.58 0.00 Sec 12 7.36 7.36 0.00 Sec 74 36.79 36.79 0.00 Sec 136 88.60 88.29 7.36 Sec 13 29.43 29.43 0.00 Sec 75 36.79 36.79 0.00 Sec 137 44.15 44.15 0.00 Sec 14 14.72 14.72 0.00 Sec 76 58.86 58.86 0.00 Sec 138 95.65 95.65 0.00 Sec 15 7.36 7.36 0.00 Sec 77 36.79 36.79 0.00 Sec 139 58.86 58.86 0.00 Sec 16 14.72 14.72 0.00 Sec 78 44.15 44.15 0.00 Sec 140 66.22 66.22 0.00 Sec 17 14.72 14.72 0.00 Sec 79 51.50 51.50 0.00 Sec 141 58.86 58.86 0.00 Sec 18 14.72 14.72 0.00 Sec 80 110.36 110.36 0.00 Sec 142 58.86 58.86 0.00 Sec 19 14.72 14.72 0.00 Sec 81 88.29 88.29 0.00 Sec 143 80.93 80.93 0.00 Sec 20 22.07 22.07 0.00 Sec 82 58.86 58.86 0.00 Sec 144 66.22 66.22 0.00 Sec 21 7.36 7.36 0.00 Sec 83 44.15 44.15 0.00 Sec 145 81.27 80.93 7.36 Sec 22 14.72 14.72 0.00 Sec 84 22.07 22.07 0.00 Sec 146 73.94 73.58 7.36 Sec 23 7.36 7.36 0.00 Sec 85 73.58 73.58 0.00 Sec 147 73.94 73.58 7.36 Sec 24 7.36 7.36 0.00 Sec 86 36.79 36.79 0.00 Sec 148 73.94 73.58 7.36 Sec 25 7.36 7.36 0.00 Sec 87 14.72 14.72 0.00 Sec 149 22.07 22.07 0.00 Sec 26 14.72 14.72 0.00 Sec 88 44.15 44.15 0.00 Sec 150 7.36 7.36 0.00 Sec 27 7.36 7.36 0.00 Sec 89 29.43 29.43 0.00 Sec 151 51.50 51.50 0.00 Sec 28 7.36 7.36 0.00 Sec 90 36.79 36.79 0.00 Sec 152 73.94 73.58 7.36 Sec 29 22.07 22.07 0.00 Sec 91 22.07 22.07 0.00 Sec 153 81.27 80.93 7.36 Sec 30 14.72 14.72 0.00 Sec 92 29.43 29.43 0.00 Sec 154 88.60 88.29 7.36 Sec 31 14.72 14.72 0.00 Sec 93 36.79 36.79 0.00 Sec 155 73.58 73.58 0.00 Sec 32 7.36 7.36 0.00 Sec 94 22.07 22.07 0.00 Sec 156 73.58 73.58 0.00 Sec 33 22.07 22.07 0.00 Sec 95 29.43 29.43 0.00 Sec 157 58.86 58.86 0.00 Sec 34 29.43 29.43 0.00 Sec 96 58.86 58.86 0.00 Sec 158 52.03 51.50 7.36 Sec 35 14.72 14.72 0.00 Sec 97 36.79 36.79 0.00 Sec 159 44.15 44.15 0.00 Sec 36 29.43 29.43 0.00 Sec 98 29.43 29.43 0.00 Sec 160 44.15 44.15 0.00 Sec 37 22.07 22.07 0.00 Sec 99 36.79 36.79 0.00 Sec 161 14.72 14.72 0.00 Sec 38 29.43 29.43 0.00 Sec 100 22.07 22.07 0.00 Sec 162 36.79 36.79 0.00 Sec 39 14.72 14.72 0.00 Sec 101 29.43 29.43 0.00 Sec 163 59.32 58.86 7.36 Sec 40 14.72 14.72 0.00 Sec 102 30.34 29.43 7.36 Sec 164 66.63 66.22 7.36 Sec 41 22.07 22.07 0.00 Sec 103 22.07 22.07 0.00 Sec 165 95.93 95.65 7.36 Sec 42 29.43 29.43 0.00 Sec 104 44.15 44.15 0.00 Sec 166 14.72 14.72 0.00 Sec 43 22.07 22.07 0.00 Sec 105 36.79 36.79 0.00 Sec 167 14.72 14.72 0.00 Sec 44 22.07 22.07 0.00 Sec 106 51.50 51.50 0.00 Sec 168 7.36 7.36 0.00 Sec 45 14.72 14.72 0.00 Sec 107 66.22 66.22 0.00 Sec 169 29.43 29.43 0.00 Sec 46 22.07 22.07 0.00 Sec 108 22.07 22.07 0.00 Sec 170 22.07 22.07 0.00 Sec 47 44.15 44.15 0.00 Sec 109 58.86 58.86 0.00 Sec 171 22.07 22.07 0.00 Sec 48 29.43 29.43 0.00 Sec 110 36.79 36.79 0.00 Sec 172 29.43 29.43 0.00 Sec 49 29.43 29.43 0.00 Sec 111 22.07 22.07 0.00 Sec 173 29.43 29.43 0.00 Sec 50 58.86 58.86 0.00 Sec 112 44.15 44.15 0.00 Sec 174 36.79 36.79 0.00 Sec 51 22.07 22.07 0.00 Sec 113 29.43 29.43 0.00 Sec 175 29.43 29.43 0.00 Sec 52 29.43 29.43 0.00 Sec 114 59.32 58.86 7.36 Sec 176 14.72 14.72 0.00 Sec 53 29.43 29.43 0.00 Sec 115 95.93 95.65 7.36 Sec 177 14.72 14.72 0.00 Sec 54 36.79 36.79 0.00 Sec 116 29.43 29.43 0.00 Sec 178 14.72 14.72 0.00 Sec 55 36.79 36.79 0.00 Sec 117 14.72 14.72 0.00 Sec 179 22.07 22.07 0.00 Sec 56 51.50 51.50 0.00 Sec 118 22.07 22.07 0.00 Sec 180 14.72 14.72 0.00 Sec 57 44.15 44.15 0.00 Sec 119 14.72 14.72 0.00 Sec 181 14.72 14.72 0.00 Sec 58 44.15 44.15 0.00 Sec 120 29.43 29.43 0.00 Sec 182 7.36 7.36 0.00 Sec 59 36.79 36.79 0.00 Sec 121 36.79 36.79 0.00 Sec 183 14.72 14.72 0.00 Sec 60 36.79 36.79 0.00 Sec 122 73.94 73.58 7.36 Sec 184 29.43 29.43 0.00 Sec 61 44.15 44.15 0.00 Sec 123 58.86 58.86 0.00 Sec 185 22.07 22.07 0.00 Sec 62 29.43 29.43 0.00 Sec 124 66.22 66.22 0.00 Sec 186 22.07 22.07 0.00

147

Table A-4: Continued Line

D value

X value

Y value Line

D value

X value

Y value Line

D value (µm)

X value

Y value

Data Data Data Sec 187 22.07 22.07 0.00 Sec 249 14.72 14.72 0.00 Sec 311 22.07 22.07 0.00 Sec 188 29.43 29.43 0.00 Sec 250 29.43 29.43 0.00 Sec 312 29.43 29.43 0.00 Sec 189 22.07 22.07 0.00 Sec 251 29.43 29.43 0.00 Sec 313 29.43 29.43 0.00 Sec 190 14.72 14.72 0.00 Sec 252 36.79 36.79 0.00 Sec 314 22.07 22.07 0.00 Sec 191 14.72 14.72 0.00 Sec 253 14.72 14.72 0.00 Sec 315 22.07 22.07 0.00 Sec 192 7.36 7.36 0.00 Sec 254 22.07 22.07 0.00 Sec 316 22.07 22.07 0.00 Sec 193 7.36 7.36 0.00 Sec 255 30.34 29.43 7.36 Sec 317 29.43 29.43 0.00 Sec 194 7.36 7.36 0.00 Sec 256 36.79 36.79 0.00 Sec 318 29.43 29.43 0.00 Sec 195 7.36 7.36 0.00 Sec 257 44.15 44.15 0.00 Sec 319 51.50 51.50 0.00 Sec 196 36.79 36.79 0.00 Sec 258 58.86 58.86 0.00 Sec 320 51.50 51.50 0.00 Sec 197 51.50 51.50 0.00 Sec 259 66.22 66.22 0.00 Sec 321 29.43 29.43 0.00 Sec 198 51.50 51.50 0.00 Sec 260 36.79 36.79 0.00 Sec 322 66.22 66.22 0.00 Sec 199 66.22 66.22 0.00 Sec 261 51.50 51.50 0.00 Sec 323 66.22 66.22 0.00 Sec 200 51.50 51.50 0.00 Sec 262 58.86 58.86 0.00 Sec 324 44.15 44.15 0.00 Sec 201 30.34 29.43 7.36 Sec 263 22.07 22.07 0.00 Sec 325 29.43 29.43 0.00 Sec 202 22.07 22.07 0.00 Sec 264 29.43 29.43 0.00 Sec 326 88.29 88.29 0.00 Sec 203 44.15 44.15 0.00 Sec 265 22.07 22.07 0.00 Sec 327 103.01 103.01 0.00 Sec 204 66.22 66.22 0.00 Sec 266 29.43 29.43 0.00 Sec 328 80.93 80.93 0.00 Sec 205 58.86 58.86 0.00 Sec 267 36.79 36.79 0.00 Sec 329 88.29 88.29 0.00 Sec 206 81.27 80.93 7.36 Sec 268 36.79 36.79 0.00 Sec 330 110.36 110.36 0.00 Sec 207 88.60 88.29 7.36 Sec 269 36.79 36.79 0.00 Sec 331 117.72 117.72 0.00 Sec 208 88.60 88.29 7.36 Sec 270 29.43 29.43 0.00 Sec 332 73.58 73.58 0.00 Sec 209 88.60 88.29 7.36 Sec 271 14.72 14.72 0.00 Sec 333 73.58 73.58 0.00 Sec 210 58.86 58.86 0.00 Sec 272 23.27 22.07 7.36 Sec 334 80.93 80.93 0.00 Sec 211 66.22 66.22 0.00 Sec 273 14.72 14.72 0.00 Sec 335 88.29 88.29 0.00 Sec 212 66.22 66.22 0.00 Sec 274 14.72 14.72 0.00 Sec 336 88.29 88.29 0.00 Sec 213 66.22 66.22 0.00 Sec 275 36.79 36.79 0.00 Sec 337 73.58 73.58 0.00 Sec 214 66.22 66.22 0.00 Sec 276 22.07 22.07 0.00 Sec 338 66.22 66.22 0.00 Sec 215 73.58 73.58 0.00 Sec 277 22.07 22.07 0.00 Sec 339 29.43 29.43 0.00 Sec 216 58.86 58.86 0.00 Sec 278 36.79 36.79 0.00 Sec 340 66.22 66.22 0.00 Sec 217 36.79 36.79 0.00 Sec 279 51.50 51.50 0.00 Sec 341 73.58 73.58 0.00 Sec 218 51.50 51.50 0.00 Sec 280 29.43 29.43 0.00 Sec 342 80.93 80.93 0.00 Sec 219 58.86 58.86 0.00 Sec 281 22.07 22.07 0.00 Sec 343 51.50 51.50 0.00 Sec 220 52.03 51.50 7.36 Sec 282 66.63 66.22 7.36 Sec 344 58.86 58.86 0.00 Sec 221 44.15 44.15 0.00 Sec 283 88.29 88.29 0.00 Sec 345 58.86 58.86 0.00 Sec 222 36.79 36.79 0.00 Sec 284 80.93 80.93 0.00 Sec 346 73.58 73.58 0.00 Sec 223 66.22 66.22 0.00 Sec 285 66.22 66.22 0.00 Sec 347 58.86 58.86 0.00 Sec 224 80.93 80.93 0.00 Sec 286 14.72 14.72 0.00 Sec 348 51.50 51.50 0.00 Sec 225 66.22 66.22 0.00 Sec 287 58.86 58.86 0.00 Sec 349 66.22 66.22 0.00 Sec 226 58.86 58.86 0.00 Sec 288 80.93 80.93 0.00 Sec 350 73.58 73.58 0.00 Sec 227 73.58 73.58 0.00 Sec 289 59.32 58.86 7.36 Sec 351 58.86 58.86 0.00 Sec 228 103.27 103.01 7.36 Sec 290 66.63 66.22 7.36 Sec 352 44.15 44.15 0.00 Sec 229 88.60 88.29 7.36 Sec 291 73.58 73.58 0.00 Sec 353 44.15 44.15 0.00 Sec 230 81.27 80.93 7.36 Sec 292 73.58 73.58 0.00 Sec 354 58.86 58.86 0.00 Sec 231 80.93 80.93 0.00 Sec 293 80.93 80.93 0.00 Sec 355 80.93 80.93 0.00 Sec 232 44.15 44.15 0.00 Sec 294 51.50 51.50 0.00 Sec 356 95.65 95.65 0.00 Sec 233 36.79 36.79 0.00 Sec 295 44.15 44.15 0.00 Sec 357 95.65 95.65 0.00 Sec 234 51.50 51.50 0.00 Sec 296 36.79 36.79 0.00 Sec 358 88.29 88.29 0.00 Sec 235 66.22 66.22 0.00 Sec 297 14.72 14.72 0.00 Sec 359 66.22 66.22 0.00 Sec 236 52.03 51.50 7.36 Sec 298 36.79 36.79 0.00 Sec 360 88.29 88.29 0.00 Sec 237 80.93 80.93 0.00 Sec 299 51.50 51.50 0.00 Sec 361 36.79 36.79 0.00 Sec 238 80.93 80.93 0.00 Sec 300 51.50 51.50 0.00 Sec 362 7.36 7.36 0.00 Sec 239 95.93 95.65 7.36 Sec 301 51.50 51.50 0.00 Sec 363 7.36 7.36 0.00 Sec 240 73.94 73.58 7.36 Sec 302 22.07 22.07 0.00 Sec 364 7.36 7.36 0.00 Sec 241 81.27 80.93 7.36 Sec 303 51.50 51.50 0.00 Sec 365 7.36 7.36 0.00 Sec 242 81.27 80.93 7.36 Sec 304 66.22 66.22 0.00 Sec 366 7.36 7.36 0.00 Sec 243 95.93 95.65 7.36 Sec 305 66.22 66.22 0.00 Sec 367 14.72 14.72 0.00 Sec 244 22.07 22.07 0.00 Sec 306 51.50 51.50 0.00 Sec 368 14.72 14.72 0.00 Sec 245 22.07 22.07 0.00 Sec 307 22.07 22.07 0.00 Sec 369 22.07 22.07 0.00 Sec 246 14.72 14.72 0.00 Sec 308 29.43 29.43 0.00 Sec 370 14.72 14.72 0.00 Sec 247 29.43 29.43 0.00 Sec 309 29.43 29.43 0.00 Sec 371 7.36 7.36 0.00 Sec 248 44.15 44.15 0.00 Sec 310 22.07 22.07 0.00 Sec 372 22.07 22.07 0.00

148

Table A-4: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 373 14.72 14.72 0.00 Sec 435 36.79 36.79 0.00 Sec 497 58.86 58.86 0.00 Sec 374 22.07 22.07 0.00 Sec 436 66.22 66.22 0.00 Sec 498 58.86 58.86 0.00 Sec 375 14.72 14.72 0.00 Sec 437 58.86 58.86 0.00 Sec 499 132.64 132.44 7.36 Sec 376 14.72 14.72 0.00 Sec 438 95.65 95.65 0.00 Sec 500 59.32 58.86 7.36 Sec 377 22.07 22.07 0.00 Sec 439 36.79 36.79 0.00 Sec 501 36.79 36.79 0.00 Sec 378 22.07 22.07 0.00 Sec 440 29.43 29.43 0.00 Sec 502 36.79 36.79 0.00 Sec 379 29.43 29.43 0.00 Sec 441 51.50 51.50 0.00 Sec 503 51.50 51.50 0.00 Sec 380 22.07 22.07 0.00 Sec 442 44.15 44.15 0.00 Sec 504 36.79 36.79 0.00 Sec 381 29.43 29.43 0.00 Sec 443 36.79 36.79 0.00 Sec 505 73.58 73.58 0.00 Sec 382 14.72 14.72 0.00 Sec 444 29.43 29.43 0.00 Sec 506 66.22 66.22 0.00 Sec 383 29.43 29.43 0.00 Sec 445 22.07 22.07 0.00 Sec 507 36.79 36.79 0.00 Sec 384 22.07 22.07 0.00 Sec 446 14.72 14.72 0.00 Sec 508 22.07 22.07 0.00 Sec 385 22.07 22.07 0.00 Sec 447 14.72 14.72 0.00 Sec 509 22.07 22.07 0.00 Sec 386 22.07 22.07 0.00 Sec 448 22.07 22.07 0.00 Sec 510 14.72 14.72 0.00 Sec 387 22.07 22.07 0.00 Sec 449 44.15 44.15 0.00 Sec 511 14.72 14.72 0.00 Sec 388 22.07 22.07 0.00 Sec 450 58.86 58.86 0.00 Sec 512 29.43 29.43 0.00 Sec 389 22.07 22.07 0.00 Sec 451 58.86 58.86 0.00 Sec 513 22.07 22.07 0.00 Sec 390 29.43 29.43 0.00 Sec 452 44.15 44.15 0.00 Sec 514 44.15 44.15 0.00 Sec 391 14.72 14.72 0.00 Sec 453 22.07 22.07 0.00 Sec 515 22.07 22.07 0.00 Sec 392 14.72 14.72 0.00 Sec 454 22.07 22.07 0.00 Sec 516 44.15 44.15 0.00 Sec 393 22.07 22.07 0.00 Sec 455 7.36 7.36 0.00 Sec 517 44.15 44.15 0.00 Sec 394 7.36 7.36 0.00 Sec 456 73.58 73.58 0.00 Sec 518 29.43 29.43 0.00 Sec 395 7.36 7.36 0.00 Sec 457 66.22 66.22 0.00 Sec 519 36.79 36.79 0.00 Sec 396 14.72 14.72 0.00 Sec 458 73.58 73.58 0.00 Sec 520 36.79 36.79 0.00 Sec 397 14.72 14.72 0.00 Sec 459 58.86 58.86 0.00 Sec 521 29.43 29.43 0.00 Sec 398 14.72 14.72 0.00 Sec 460 29.43 29.43 0.00 Sec 522 22.07 22.07 0.00 Sec 399 22.07 22.07 0.00 Sec 461 44.15 44.15 0.00 Sec 523 36.79 36.79 0.00 Sec 400 7.36 7.36 0.00 Sec 462 29.43 29.43 0.00 Sec 524 22.07 22.07 0.00 Sec 401 7.36 7.36 0.00 Sec 463 22.07 22.07 0.00 Sec 525 44.15 44.15 0.00 Sec 402 14.72 14.72 0.00 Sec 464 22.07 22.07 0.00 Sec 526 51.50 51.50 0.00 Sec 403 22.07 22.07 0.00 Sec 465 22.07 22.07 0.00 Sec 527 36.79 36.79 0.00 Sec 404 29.43 29.43 0.00 Sec 466 14.72 14.72 0.00 Sec 528 7.36 7.36 0.00 Sec 405 29.43 29.43 0.00 Sec 467 29.43 29.43 0.00 Sec 529 22.07 22.07 0.00 Sec 406 22.07 22.07 0.00 Sec 468 29.43 29.43 0.00 Sec 530 14.72 14.72 0.00 Sec 407 29.43 29.43 0.00 Sec 469 29.43 29.43 0.00 Sec 531 22.07 22.07 0.00 Sec 408 29.43 29.43 0.00 Sec 470 14.72 14.72 0.00 Sec 532 36.79 36.79 0.00 Sec 409 36.79 36.79 0.00 Sec 471 22.07 22.07 0.00 Sec 533 103.01 103.01 0.00 Sec 410 29.43 29.43 0.00 Sec 472 14.72 14.72 0.00 Sec 534 88.29 88.29 0.00 Sec 411 29.43 29.43 0.00 Sec 473 22.07 22.07 0.00 Sec 535 80.93 80.93 0.00 Sec 412 14.72 14.72 0.00 Sec 474 29.43 29.43 0.00 Sec 536 58.86 58.86 0.00 Sec 413 7.36 7.36 0.00 Sec 475 22.07 22.07 0.00 Sec 537 29.43 29.43 0.00 Sec 414 22.07 22.07 0.00 Sec 476 29.43 29.43 0.00 Sec 538 29.43 29.43 0.00 Sec 415 58.86 58.86 0.00 Sec 477 22.07 22.07 0.00 Sec 539 29.43 29.43 0.00 Sec 416 44.15 44.15 0.00 Sec 478 14.72 14.72 0.00 Sec 540 36.79 36.79 0.00 Sec 417 22.07 22.07 0.00 Sec 479 14.72 14.72 0.00 Sec 541 14.72 14.72 0.00 Sec 418 22.07 22.07 0.00 Sec 480 29.43 29.43 0.00 Sec 542 14.72 14.72 0.00 Sec 419 29.43 29.43 0.00 Sec 481 14.72 14.72 0.00 Sec 543 22.07 22.07 0.00 Sec 420 29.43 29.43 0.00 Sec 482 29.43 29.43 0.00 Sec 544 22.07 22.07 0.00 Sec 421 73.58 73.58 0.00 Sec 483 14.72 14.72 0.00 Sec 545 22.07 22.07 0.00 Sec 422 73.58 73.58 0.00 Sec 484 22.07 22.07 0.00 Sec 546 14.72 14.72 0.00 Sec 423 36.79 36.79 0.00 Sec 485 22.07 22.07 0.00 Sec 547 14.72 14.72 0.00 Sec 424 80.93 80.93 0.00 Sec 486 7.36 7.36 0.00 Sec 548 14.72 14.72 0.00 Sec 425 66.22 66.22 0.00 Sec 487 22.07 22.07 0.00 Sec 549 7.36 7.36 0.00 Sec 426 73.58 73.58 0.00 Sec 488 14.72 14.72 0.00 Sec 550 14.72 14.72 0.00 Sec 427 80.93 80.93 0.00 Sec 489 44.15 44.15 0.00 Sec 551 14.72 14.72 0.00 Sec 428 73.58 73.58 0.00 Sec 490 29.43 29.43 0.00 Sec 552 14.72 14.72 0.00 Sec 429 58.86 58.86 0.00 Sec 491 22.07 22.07 0.00 Sec 553 7.36 7.36 0.00 Sec 430 36.79 36.79 0.00 Sec 492 22.07 22.07 0.00 Sec 554 22.07 22.07 0.00 Sec 431 44.15 44.15 0.00 Sec 493 14.72 14.72 0.00 Sec 555 14.72 14.72 0.00 Sec 432 44.15 44.15 0.00 Sec 494 29.43 29.43 0.00 Sec 556 22.07 22.07 0.00 Sec 433 58.86 58.86 0.00 Sec 495 66.22 66.22 0.00 Sec 557 22.07 22.07 0.00 Sec 434 66.22 66.22 0.00 Sec 496 95.65 95.65 0.00 Sec 558 73.58 73.58 0.00

149

Table A-4: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Data Data

Sec 559 51.50 51.50 0.00 Sec 621 44.15 44.15 0.00 Sec 560 80.93 80.93 0.00 Sec 622 51.50 51.50 0.00 Sec 561 73.94 73.58 7.36 Sec 623 44.15 44.15 0.00 Sec 562 73.58 73.58 0.00 Sec 624 58.86 58.86 0.00 Sec 563 103.01 103.01 0.00 Sec 625 66.22 66.22 0.00 Sec 564 73.58 73.58 0.00 Sec 626 29.43 29.43 0.00 Sec 565 103.01 103.01 0.00 Sec 627 29.43 29.43 0.00 Sec 566 58.86 58.86 0.00 Sec 628 36.79 36.79 0.00 Sec 567 66.22 66.22 0.00 Sec 629 103.01 103.01 0.00 Sec 568 36.79 36.79 0.00 Sec 630 73.58 73.58 0.00 Sec 569 58.86 58.86 0.00 Sec 631 80.93 80.93 0.00 Sec 570 14.72 14.72 0.00 Sec 632 58.86 58.86 0.00 Sec 571 7.36 7.36 0.00 Sec 633 73.58 73.58 0.00 Sec 572 14.72 14.72 0.00 Sec 634 95.65 95.65 0.00 Sec 573 29.43 29.43 0.00 Sec 635 51.50 51.50 0.00 Sec 574 51.50 51.50 0.00 Sec 636 44.15 44.15 0.00 Sec 575 22.07 22.07 0.00 Sec 637 37.52 36.79 7.36 Sec 576 29.43 29.43 0.00 Sec 638 29.43 29.43 0.00 Sec 577 14.72 14.72 0.00 Sec 639 52.03 51.50 7.36 Sec 578 22.07 22.07 0.00 Sec 640 51.50 51.50 0.00 Sec 579 14.72 14.72 0.00 Sec 641 51.50 51.50 0.00 Sec 580 14.72 14.72 0.00 Sec 642 58.86 58.86 0.00 Sec 581 22.07 22.07 0.00 Sec 643 66.22 66.22 0.00 Sec 582 14.72 14.72 0.00 Sec 644 22.07 22.07 0.00 Sec 583 14.72 14.72 0.00 Sec 645 22.07 22.07 0.00 Sec 584 14.72 14.72 0.00 Sec 646 36.79 36.79 0.00 Sec 585 14.72 14.72 0.00 Sec 647 36.79 36.79 0.00 Sec 586 14.72 14.72 0.00 Sec 648 51.50 51.50 0.00 Sec 587 14.72 14.72 0.00 Sec 649 36.79 36.79 0.00 Sec 588 22.07 22.07 0.00 Sec 650 44.15 44.15 0.00 Sec 589 14.72 14.72 0.00 Sec 651 66.22 66.22 0.00 Sec 590 14.72 14.72 0.00 Sec 652 44.75 44.15 7.36 Sec 591 14.72 14.72 0.00 Sec 653 23.27 22.07 7.36 Sec 592 22.07 22.07 0.00 Sec 654 44.15 44.15 0.00 Sec 593 22.07 22.07 0.00 Sec 655 22.07 22.07 0.00 Sec 594 14.72 14.72 0.00 Sec 656 14.72 14.72 0.00 Sec 595 14.72 14.72 0.00 Sec 657 29.43 29.43 0.00 Sec 596 22.07 22.07 0.00 Sec 658 66.22 66.22 0.00 Sec 597 14.72 14.72 0.00 Sec 659 52.03 51.50 7.36 Sec 598 22.07 22.07 0.00 Sec 660 44.15 44.15 0.00 Sec 599 29.43 29.43 0.00 Sec 661 36.79 36.79 0.00 Sec 600 29.43 29.43 0.00 Sec 662 29.43 29.43 0.00 Sec 601 22.07 22.07 0.00 Sec 663 23.27 22.07 7.36 Sec 602 29.43 29.43 0.00 Sec 664 14.72 14.72 0.00 Sec 603 44.15 44.15 0.00 Sec 665 29.43 29.43 0.00 Sec 604 22.07 22.07 0.00 Sec 666 22.07 22.07 0.00 Sec 605 22.07 22.07 0.00 Sec 667 29.43 29.43 0.00 Sec 606 44.15 44.15 0.00 Sec 668 22.07 22.07 0.00 Sec 607 29.43 29.43 0.00 Sec 669 29.43 29.43 0.00 Sec 608 36.79 36.79 0.00 Sec 670 22.07 22.07 0.00 Sec 609 29.43 29.43 0.00 Sec 671 22.07 22.07 0.00 Sec 610 51.50 51.50 0.00 Sec 672 22.07 22.07 0.00 Sec 611 29.43 29.43 0.00 Sec 673 36.79 36.79 0.00 Sec 612 36.79 36.79 0.00 Sec 674 29.43 29.43 0.00 Sec 613 14.72 14.72 0.00 Sec 675 30.34 29.43 7.36 Sec 614 22.07 22.07 0.00 Sec 676 29.43 29.43 0.00 Sec 615 14.72 14.72 0.00 Sec 677 44.15 44.15 0.00 Sec 616 14.72 14.72 0.00 Sec 678 44.15 44.15 0.00 Sec 617 14.72 14.72 0.00 Sec 679 29.43 29.43 0.00 Sec 618 23.27 22.07 7.36 Sec 680 59.32 58.86 7.36 Sec 619 14.72 14.72 0.00 Sec 681 66.22 66.22 0.00 Sec 620 29.43 29.43 0.00 Sec 682 44.15 44.15 0.00

150

Table A-5: Crack width measurement for the thru crack Line

D value (µm)

X value (µm)

Y value (µm)

Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 1 9.18 9.18 0.00 Sec 63 49.07 48.98 3.06 Sec 125 42.96 42.85 3.06 Sec 2 70.47 70.40 3.06 Sec 64 39.91 39.79 3.06 Sec 126 49.07 48.98 3.06 Sec 3 73.47 73.47 0.00 Sec 65 36.86 36.73 3.06 Sec 127 42.96 42.85 3.06 Sec 4 58.16 58.16 0.00 Sec 66 39.91 39.79 3.06 Sec 128 33.81 33.67 3.06 Sec 5 52.13 52.04 3.06 Sec 67 30.61 30.61 0.00 Sec 129 36.86 36.73 3.06 Sec 6 55.10 55.10 0.00 Sec 68 46.02 45.92 3.06 Sec 130 49.07 48.98 3.06 Sec 7 52.04 52.04 0.00 Sec 69 36.86 36.73 3.06 Sec 131 46.02 45.92 3.06 Sec 8 46.02 45.92 3.06 Sec 70 33.67 33.67 0.00 Sec 132 30.76 30.61 3.06 Sec 9 42.85 42.85 0.00 Sec 71 52.13 52.04 3.06 Sec 133 36.86 36.73 3.06 Sec 10 52.04 52.04 0.00 Sec 72 30.61 30.61 0.00 Sec 134 36.86 36.73 3.06 Sec 11 61.30 61.22 3.06 Sec 73 33.67 33.67 0.00 Sec 135 39.79 39.79 0.00 Sec 12 55.10 55.10 0.00 Sec 74 27.55 27.55 0.00 Sec 136 58.24 58.16 3.06 Sec 13 52.13 52.04 3.06 Sec 75 39.79 39.79 0.00 Sec 137 52.04 52.04 0.00 Sec 14 48.98 48.98 0.00 Sec 76 45.92 45.92 0.00 Sec 138 55.10 55.10 0.00 Sec 15 52.13 52.04 3.06 Sec 77 64.36 64.28 3.06 Sec 139 48.98 48.98 0.00 Sec 16 46.02 45.92 3.06 Sec 78 61.30 61.22 3.06 Sec 140 42.96 42.85 3.06 Sec 17 49.07 48.98 3.06 Sec 79 76.59 76.53 3.06 Sec 141 24.49 24.49 0.00 Sec 18 45.92 45.92 0.00 Sec 80 76.59 76.53 3.06 Sec 142 36.73 36.73 0.00 Sec 19 45.92 45.92 0.00 Sec 81 85.76 85.71 3.06 Sec 143 30.61 30.61 0.00 Sec 20 52.04 52.04 0.00 Sec 82 91.88 91.83 3.06 Sec 144 45.92 45.92 0.00 Sec 21 64.28 64.28 0.00 Sec 83 113.30 113.26 3.06 Sec 145 52.04 52.04 0.00 Sec 22 67.34 67.34 0.00 Sec 84 88.82 88.77 3.06 Sec 146 36.73 36.73 0.00 Sec 23 61.22 61.22 0.00 Sec 85 79.65 79.59 3.06 Sec 147 45.92 45.92 0.00 Sec 24 42.96 42.85 3.06 Sec 86 76.59 76.53 3.06 Sec 148 33.67 33.67 0.00 Sec 25 49.07 48.98 3.06 Sec 87 91.88 91.83 3.06 Sec 149 39.79 39.79 0.00 Sec 26 64.36 64.28 3.06 Sec 88 98.00 97.95 3.06 Sec 150 33.67 33.67 0.00 Sec 27 82.71 82.65 3.06 Sec 89 85.76 85.71 3.06 Sec 151 30.61 30.61 0.00 Sec 28 73.53 73.47 3.06 Sec 90 88.82 88.77 3.06 Sec 152 30.61 30.61 0.00 Sec 29 45.92 45.92 0.00 Sec 91 91.88 91.83 3.06 Sec 153 49.07 48.98 3.06 Sec 30 42.85 42.85 0.00 Sec 92 76.59 76.53 3.06 Sec 154 39.79 39.79 0.00 Sec 31 36.86 36.73 3.06 Sec 93 67.34 67.34 0.00 Sec 155 42.85 42.85 0.00 Sec 32 46.02 45.92 3.06 Sec 94 70.40 70.40 0.00 Sec 156 36.73 36.73 0.00 Sec 33 46.02 45.92 3.06 Sec 95 79.65 79.59 3.06 Sec 157 58.16 58.16 0.00 Sec 34 39.91 39.79 3.06 Sec 96 82.71 82.65 3.06 Sec 158 42.85 42.85 0.00 Sec 35 36.86 36.73 3.06 Sec 97 67.34 67.34 0.00 Sec 159 39.79 39.79 0.00 Sec 36 30.76 30.61 3.06 Sec 98 91.88 91.83 3.06 Sec 160 45.92 45.92 0.00 Sec 37 39.79 39.79 0.00 Sec 99 107.18 107.14 3.06 Sec 161 39.79 39.79 0.00 Sec 38 30.76 30.61 3.06 Sec 100 82.71 82.65 3.06 Sec 162 39.79 39.79 0.00 Sec 39 33.67 33.67 0.00 Sec 101 61.30 61.22 3.06 Sec 163 45.92 45.92 0.00 Sec 40 30.61 30.61 0.00 Sec 102 67.41 67.34 3.06 Sec 164 24.49 24.49 0.00 Sec 41 33.67 33.67 0.00 Sec 103 70.47 70.40 3.06 Sec 165 21.43 21.43 0.00 Sec 42 30.76 30.61 3.06 Sec 104 58.24 58.16 3.06 Sec 166 30.61 30.61 0.00 Sec 43 49.07 48.98 3.06 Sec 105 48.98 48.98 0.00 Sec 167 39.79 39.79 0.00 Sec 44 58.16 58.16 0.00 Sec 106 55.10 55.10 0.00 Sec 168 21.43 21.43 0.00 Sec 45 45.92 45.92 0.00 Sec 107 61.22 61.22 0.00 Sec 169 33.81 33.67 3.06 Sec 46 45.92 45.92 0.00 Sec 108 79.65 79.59 3.06 Sec 170 36.73 36.73 0.00 Sec 47 36.86 36.73 3.06 Sec 109 64.28 64.28 0.00 Sec 171 42.85 42.85 0.00 Sec 48 27.55 27.55 0.00 Sec 110 52.04 52.04 0.00 Sec 172 48.98 48.98 0.00 Sec 49 33.67 33.67 0.00 Sec 111 48.98 48.98 0.00 Sec 173 45.92 45.92 0.00 Sec 50 39.79 39.79 0.00 Sec 112 52.04 52.04 0.00 Sec 174 45.92 45.92 0.00 Sec 51 27.55 27.55 0.00 Sec 113 24.49 24.49 0.00 Sec 175 33.67 33.67 0.00 Sec 52 30.61 30.61 0.00 Sec 114 39.79 39.79 0.00 Sec 176 39.79 39.79 0.00 Sec 53 36.86 36.73 3.06 Sec 115 55.10 55.10 0.00 Sec 177 61.22 61.22 0.00 Sec 54 39.79 39.79 0.00 Sec 116 55.18 55.10 3.06 Sec 178 18.37 18.37 0.00 Sec 55 42.96 42.85 3.06 Sec 117 46.02 45.92 3.06 Sec 179 33.67 33.67 0.00 Sec 56 46.02 45.92 3.06 Sec 118 39.79 39.79 0.00 Sec 180 27.55 27.55 0.00 Sec 57 46.02 45.92 3.06 Sec 119 61.22 61.22 0.00 Sec 181 27.55 27.55 0.00 Sec 58 33.81 33.67 3.06 Sec 120 39.79 39.79 0.00 Sec 182 39.79 39.79 0.00 Sec 59 36.73 36.73 0.00 Sec 121 39.91 39.79 3.06 Sec 183 45.92 45.92 0.00 Sec 60 30.61 30.61 0.00 Sec 122 30.61 30.61 0.00 Sec 184 42.85 42.85 0.00 Sec 61 33.67 33.67 0.00 Sec 123 36.73 36.73 0.00 Sec 185 27.55 27.55 0.00 Sec 62 39.91 39.79 3.06 Sec 124 36.73 36.73 0.00 Sec 186 55.10 55.10 0.00

151

Table A-5: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 187 42.85 42.85 0.00 Sec 249 73.53 73.47 3.06 Sec 311 73.53 73.47 3.06 Sec 188 58.16 58.16 0.00 Sec 250 79.65 79.59 3.06 Sec 312 55.18 55.10 3.06 Sec 189 36.73 36.73 0.00 Sec 251 73.53 73.47 3.06 Sec 313 52.13 52.04 3.06 Sec 190 42.85 42.85 0.00 Sec 252 67.34 67.34 0.00 Sec 314 79.65 79.59 3.06 Sec 191 39.79 39.79 0.00 Sec 253 79.65 79.59 3.06 Sec 315 76.59 76.53 3.06 Sec 192 42.85 42.85 0.00 Sec 254 79.65 79.59 3.06 Sec 316 64.36 64.28 3.06 Sec 193 52.04 52.04 0.00 Sec 255 82.71 82.65 3.06 Sec 317 61.30 61.22 3.06 Sec 194 52.04 52.04 0.00 Sec 256 82.65 82.65 0.00 Sec 318 33.81 33.67 3.06 Sec 195 48.98 48.98 0.00 Sec 257 101.06 101.02 3.06 Sec 319 46.02 45.92 3.06 Sec 196 45.92 45.92 0.00 Sec 258 110.24 110.20 3.06 Sec 320 55.18 55.10 3.06 Sec 197 48.98 48.98 0.00 Sec 259 88.82 88.77 3.06 Sec 321 88.98 88.77 6.12 Sec 198 76.53 76.53 0.00 Sec 260 119.42 119.38 3.06 Sec 322 94.94 94.89 3.06 Sec 199 79.59 79.59 0.00 Sec 261 113.30 113.26 3.06 Sec 323 91.88 91.83 3.06 Sec 200 64.28 64.28 0.00 Sec 262 104.12 104.08 3.06 Sec 324 88.82 88.77 3.06 Sec 201 52.04 52.04 0.00 Sec 263 73.53 73.47 3.06 Sec 325 79.65 79.59 3.06 Sec 202 52.04 52.04 0.00 Sec 264 85.76 85.71 3.06 Sec 326 88.82 88.77 3.06 Sec 203 58.16 58.16 0.00 Sec 265 70.40 70.40 0.00 Sec 327 91.88 91.83 3.06 Sec 204 67.34 67.34 0.00 Sec 266 76.59 76.53 3.06 Sec 328 85.76 85.71 3.06 Sec 205 27.55 27.55 0.00 Sec 267 79.65 79.59 3.06 Sec 329 85.76 85.71 3.06 Sec 206 30.61 30.61 0.00 Sec 268 88.82 88.77 3.06 Sec 330 46.02 45.92 3.06 Sec 207 45.92 45.92 0.00 Sec 269 70.47 70.40 3.06 Sec 331 46.02 45.92 3.06 Sec 208 36.73 36.73 0.00 Sec 270 76.59 76.53 3.06 Sec 332 49.07 48.98 3.06 Sec 209 30.61 30.61 0.00 Sec 271 79.65 79.59 3.06 Sec 333 42.96 42.85 3.06 Sec 210 21.43 21.43 0.00 Sec 272 76.59 76.53 3.06 Sec 334 36.86 36.73 3.06 Sec 211 24.68 24.49 3.06 Sec 273 82.71 82.65 3.06 Sec 335 33.67 33.67 0.00 Sec 212 33.67 33.67 0.00 Sec 274 82.71 82.65 3.06 Sec 336 36.86 36.73 3.06 Sec 213 27.72 27.55 3.06 Sec 275 79.65 79.59 3.06 Sec 337 46.02 45.92 3.06 Sec 214 30.61 30.61 0.00 Sec 276 94.94 94.89 3.06 Sec 338 58.24 58.16 3.06 Sec 215 21.43 21.43 0.00 Sec 277 61.30 61.22 3.06 Sec 339 58.24 58.16 3.06 Sec 216 18.37 18.37 0.00 Sec 278 39.91 39.79 3.06 Sec 340 46.02 45.92 3.06 Sec 217 30.61 30.61 0.00 Sec 279 67.34 67.34 0.00 Sec 341 46.02 45.92 3.06 Sec 218 24.49 24.49 0.00 Sec 280 79.59 79.59 0.00 Sec 342 36.73 36.73 0.00 Sec 219 27.55 27.55 0.00 Sec 281 94.94 94.89 3.06 Sec 343 52.13 52.04 3.06 Sec 220 24.49 24.49 0.00 Sec 282 98.00 97.95 3.06 Sec 344 58.24 58.16 3.06 Sec 221 33.67 33.67 0.00 Sec 283 82.71 82.65 3.06 Sec 345 58.24 58.16 3.06 Sec 222 67.34 67.34 0.00 Sec 284 91.88 91.83 3.06 Sec 346 58.16 58.16 0.00 Sec 223 76.53 76.53 0.00 Sec 285 101.20 101.02 6.12 Sec 347 64.36 64.28 3.06 Sec 224 61.22 61.22 0.00 Sec 286 82.71 82.65 3.06 Sec 348 39.79 39.79 0.00 Sec 225 91.88 91.83 3.06 Sec 287 98.00 97.95 3.06 Sec 349 45.92 45.92 0.00 Sec 226 98.00 97.95 3.06 Sec 288 113.30 113.26 3.06 Sec 350 27.72 27.55 3.06 Sec 227 79.65 79.59 3.06 Sec 289 125.54 125.50 3.06 Sec 351 27.72 27.55 3.06 Sec 228 52.13 52.04 3.06 Sec 290 125.54 125.50 3.06 Sec 352 30.76 30.61 3.06 Sec 229 61.30 61.22 3.06 Sec 291 131.77 131.63 6.12 Sec 353 33.67 33.67 0.00 Sec 230 61.22 61.22 0.00 Sec 292 128.71 128.56 6.12 Sec 354 67.34 67.34 0.00 Sec 231 61.22 61.22 0.00 Sec 293 98.00 97.95 3.06 Sec 355 64.28 64.28 0.00 Sec 232 39.79 39.79 0.00 Sec 294 48.98 48.98 0.00 Sec 356 55.10 55.10 0.00 Sec 233 52.04 52.04 0.00 Sec 295 52.04 52.04 0.00 Sec 357 61.22 61.22 0.00 Sec 234 48.98 48.98 0.00 Sec 296 67.41 67.34 3.06 Sec 358 70.47 70.40 3.06 Sec 235 48.98 48.98 0.00 Sec 297 67.41 67.34 3.06 Sec 359 64.36 64.28 3.06 Sec 236 36.73 36.73 0.00 Sec 298 85.76 85.71 3.06 Sec 360 70.47 70.40 3.06 Sec 237 30.61 30.61 0.00 Sec 299 85.76 85.71 3.06 Sec 361 58.24 58.16 3.06 Sec 238 33.67 33.67 0.00 Sec 300 73.53 73.47 3.06 Sec 362 55.10 55.10 0.00 Sec 239 27.55 27.55 0.00 Sec 301 73.53 73.47 3.06 Sec 363 67.41 67.34 3.06 Sec 240 30.61 30.61 0.00 Sec 302 85.76 85.71 3.06 Sec 364 52.13 52.04 3.06 Sec 241 36.73 36.73 0.00 Sec 303 107.18 107.14 3.06 Sec 365 55.18 55.10 3.06 Sec 242 27.55 27.55 0.00 Sec 304 85.76 85.71 3.06 Sec 366 55.18 55.10 3.06 Sec 243 27.55 27.55 0.00 Sec 305 64.36 64.28 3.06 Sec 367 36.73 36.73 0.00 Sec 244 42.85 42.85 0.00 Sec 306 61.22 61.22 0.00 Sec 368 33.81 33.67 3.06 Sec 245 55.10 55.10 0.00 Sec 307 48.98 48.98 0.00 Sec 369 33.67 33.67 0.00 Sec 246 42.85 42.85 0.00 Sec 308 48.98 48.98 0.00 Sec 370 33.81 33.67 3.06 Sec 247 61.30 61.22 3.06 Sec 309 64.36 64.28 3.06 Sec 371 30.76 30.61 3.06 Sec 248 58.24 58.16 3.06 Sec 310 61.30 61.22 3.06 Sec 372 42.96 42.85 3.06

152

Table A-5: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Data Data

Sec 373 39.91 39.79 3.06 Sec 435 21.43 21.43 0.00 Sec 374 55.18 55.10 3.06 Sec 436 36.86 36.73 3.06 Sec 375 73.53 73.47 3.06 Sec 376 67.41 67.34 3.06 Sec 377 67.41 67.34 3.06 Sec 378 70.47 70.40 3.06 Sec 379 67.41 67.34 3.06 Sec 380 67.41 67.34 3.06 Sec 381 76.59 76.53 3.06 Sec 382 91.88 91.83 3.06 Sec 383 82.65 82.65 0.00 Sec 384 82.71 82.65 3.06 Sec 385 82.65 82.65 0.00 Sec 386 82.71 82.65 3.06 Sec 387 79.65 79.59 3.06 Sec 388 76.53 76.53 0.00 Sec 389 79.59 79.59 0.00 Sec 390 70.47 70.40 3.06 Sec 391 61.22 61.22 0.00 Sec 392 64.28 64.28 0.00 Sec 393 52.04 52.04 0.00 Sec 394 46.02 45.92 3.06 Sec 395 46.02 45.92 3.06 Sec 396 61.30 61.22 3.06 Sec 397 58.24 58.16 3.06 Sec 398 52.04 52.04 0.00 Sec 399 55.18 55.10 3.06 Sec 400 33.81 33.67 3.06 Sec 401 33.67 33.67 0.00 Sec 402 27.55 27.55 0.00 Sec 403 42.85 42.85 0.00 Sec 404 27.55 27.55 0.00 Sec 405 39.79 39.79 0.00 Sec 406 42.85 42.85 0.00 Sec 407 42.85 42.85 0.00 Sec 408 27.55 27.55 0.00 Sec 409 36.73 36.73 0.00 Sec 410 30.61 30.61 0.00 Sec 411 30.61 30.61 0.00 Sec 412 24.49 24.49 0.00 Sec 413 42.85 42.85 0.00 Sec 414 36.73 36.73 0.00 Sec 415 39.79 39.79 0.00 Sec 416 39.79 39.79 0.00 Sec 417 24.49 24.49 0.00 Sec 418 33.67 33.67 0.00 Sec 419 33.67 33.67 0.00 Sec 420 18.37 18.37 0.00 Sec 421 12.24 12.24 0.00 Sec 422 30.61 30.61 0.00 Sec 423 21.43 21.43 0.00 Sec 424 27.55 27.55 0.00 Sec 425 45.92 45.92 0.00 Sec 426 52.04 52.04 0.00 Sec 427 39.79 39.79 0.00 Sec 428 33.67 33.67 0.00 Sec 429 36.86 36.73 3.06 Sec 430 30.76 30.61 3.06 Sec 431 24.68 24.49 3.06 Sec 432 27.55 27.55 0.00 Sec 433 30.61 30.61 0.00 Sec 434 30.61 30.61 0.00

153

Table A-6: Crack width measurement for the surface crack in the mid quarter Line

D value

X value

Y value Line

D value

X value

Y value Line

D value (µm)

X value

Y value

Data Data Data Sec 1 10.73 10.73 0.00 Sec 63 28.61 28.61 0.00 Sec 125 25.03 25.03 0.00 Sec 2 100.12 100.12 0.00 Sec 64 39.33 39.33 0.00 Sec 126 39.33 39.33 0.00 Sec 3 107.33 107.27 3.58 Sec 65 28.61 28.61 0.00 Sec 127 28.61 28.61 0.00 Sec 4 103.76 103.70 3.58 Sec 66 14.30 14.30 0.00 Sec 128 17.88 17.88 0.00 Sec 5 89.46 89.39 3.58 Sec 67 21.45 21.45 0.00 Sec 129 17.88 17.88 0.00 Sec 6 85.82 85.82 0.00 Sec 68 21.45 21.45 0.00 Sec 130 10.73 10.73 0.00 Sec 7 64.36 64.36 0.00 Sec 69 25.03 25.03 0.00 Sec 131 10.73 10.73 0.00 Sec 8 60.79 60.79 0.00 Sec 70 21.45 21.45 0.00 Sec 132 14.30 14.30 0.00 Sec 9 68.03 67.94 3.58 Sec 71 25.03 25.03 0.00 Sec 133 21.45 21.45 0.00 Sec 10 96.61 96.54 3.58 Sec 72 32.18 32.18 0.00 Sec 134 10.73 10.73 0.00 Sec 11 100.18 100.12 3.58 Sec 73 35.76 35.76 0.00 Sec 135 14.30 14.30 0.00 Sec 12 82.24 82.24 0.00 Sec 74 21.45 21.45 0.00 Sec 136 14.30 14.30 0.00 Sec 13 78.67 78.67 0.00 Sec 75 14.30 14.30 0.00 Sec 137 10.73 10.73 0.00 Sec 14 78.67 78.67 0.00 Sec 76 21.45 21.45 0.00 Sec 138 10.73 10.73 0.00 Sec 15 75.09 75.09 0.00 Sec 77 25.03 25.03 0.00 Sec 139 10.73 10.73 0.00 Sec 16 64.36 64.36 0.00 Sec 78 17.88 17.88 0.00 Sec 140 10.73 10.73 0.00 Sec 17 71.60 71.51 3.58 Sec 79 17.88 17.88 0.00 Sec 141 10.73 10.73 0.00 Sec 18 60.89 60.79 3.58 Sec 80 14.30 14.30 0.00 Sec 142 14.30 14.30 0.00 Sec 19 71.60 71.51 3.58 Sec 81 14.30 14.30 0.00 Sec 143 14.30 14.30 0.00 Sec 20 57.32 57.21 3.58 Sec 82 14.74 14.30 3.58 Sec 144 21.45 21.45 0.00 Sec 21 53.76 53.64 3.58 Sec 83 14.30 14.30 0.00 Sec 145 14.30 14.30 0.00 Sec 22 60.89 60.79 3.58 Sec 84 14.30 14.30 0.00 Sec 146 14.30 14.30 0.00 Sec 23 57.21 57.21 0.00 Sec 85 14.30 14.30 0.00 Sec 147 21.45 21.45 0.00 Sec 24 50.06 50.06 0.00 Sec 86 14.30 14.30 0.00 Sec 148 21.45 21.45 0.00 Sec 25 46.48 46.48 0.00 Sec 87 14.30 14.30 0.00 Sec 149 28.61 28.61 0.00 Sec 26 50.19 50.06 3.58 Sec 88 17.88 17.88 0.00 Sec 150 21.75 21.45 3.58 Sec 27 50.19 50.06 3.58 Sec 89 17.88 17.88 0.00 Sec 151 25.03 25.03 0.00 Sec 28 64.46 64.36 3.58 Sec 90 14.30 14.30 0.00 Sec 152 21.45 21.45 0.00 Sec 29 64.36 64.36 0.00 Sec 91 21.45 21.45 0.00 Sec 153 42.91 42.91 0.00 Sec 30 53.64 53.64 0.00 Sec 92 17.88 17.88 0.00 Sec 154 32.18 32.18 0.00 Sec 31 100.18 100.12 3.58 Sec 93 17.88 17.88 0.00 Sec 155 21.45 21.45 0.00 Sec 32 78.67 78.67 0.00 Sec 94 21.45 21.45 0.00 Sec 156 21.45 21.45 0.00 Sec 33 89.39 89.39 0.00 Sec 95 14.30 14.30 0.00 Sec 157 21.45 21.45 0.00 Sec 34 107.33 107.27 3.58 Sec 96 21.45 21.45 0.00 Sec 158 14.30 14.30 0.00 Sec 35 85.82 85.82 0.00 Sec 97 28.61 28.61 0.00 Sec 159 21.45 21.45 0.00 Sec 36 92.97 92.97 0.00 Sec 98 42.91 42.91 0.00 Sec 160 28.61 28.61 0.00 Sec 37 107.27 107.27 0.00 Sec 99 14.30 14.30 0.00 Sec 161 28.61 28.61 0.00 Sec 38 125.15 125.15 0.00 Sec 100 17.88 17.88 0.00 Sec 162 25.03 25.03 0.00 Sec 39 42.91 42.91 0.00 Sec 101 17.88 17.88 0.00 Sec 163 25.03 25.03 0.00 Sec 40 60.79 60.79 0.00 Sec 102 28.61 28.61 0.00 Sec 164 28.61 28.61 0.00 Sec 41 67.94 67.94 0.00 Sec 103 25.03 25.03 0.00 Sec 165 39.33 39.33 0.00 Sec 42 57.21 57.21 0.00 Sec 104 32.18 32.18 0.00 Sec 166 25.28 25.03 3.58 Sec 43 75.09 75.09 0.00 Sec 105 32.18 32.18 0.00 Sec 167 17.88 17.88 0.00 Sec 44 92.97 92.97 0.00 Sec 106 46.48 46.48 0.00 Sec 168 17.88 17.88 0.00 Sec 45 67.94 67.94 0.00 Sec 107 42.91 42.91 0.00 Sec 169 28.61 28.61 0.00 Sec 46 67.94 67.94 0.00 Sec 108 25.03 25.03 0.00 Sec 170 21.45 21.45 0.00 Sec 47 53.64 53.64 0.00 Sec 109 21.45 21.45 0.00 Sec 171 14.30 14.30 0.00 Sec 48 53.64 53.64 0.00 Sec 110 21.45 21.45 0.00 Sec 172 35.76 35.76 0.00 Sec 49 39.33 39.33 0.00 Sec 111 25.03 25.03 0.00 Sec 173 25.28 25.03 3.58 Sec 50 57.21 57.21 0.00 Sec 112 25.03 25.03 0.00 Sec 174 14.74 14.30 3.58 Sec 51 50.06 50.06 0.00 Sec 113 21.45 21.45 0.00 Sec 175 21.75 21.45 3.58 Sec 52 67.94 67.94 0.00 Sec 114 32.18 32.18 0.00 Sec 176 17.88 17.88 0.00 Sec 53 78.67 78.67 0.00 Sec 115 35.76 35.76 0.00 Sec 177 25.28 25.03 3.58 Sec 54 68.03 67.94 3.58 Sec 116 28.61 28.61 0.00 Sec 178 21.75 21.45 3.58 Sec 55 57.21 57.21 0.00 Sec 117 28.61 28.61 0.00 Sec 179 10.73 10.73 0.00 Sec 56 46.48 46.48 0.00 Sec 118 21.45 21.45 0.00 Sec 180 11.31 10.73 3.58 Sec 57 50.06 50.06 0.00 Sec 119 17.88 17.88 0.00 Sec 181 21.45 21.45 0.00 Sec 58 46.48 46.48 0.00 Sec 120 21.45 21.45 0.00 Sec 182 25.03 25.03 0.00 Sec 59 39.33 39.33 0.00 Sec 121 17.88 17.88 0.00 Sec 183 25.03 25.03 0.00 Sec 60 28.61 28.61 0.00 Sec 122 10.73 10.73 0.00 Sec 184 17.88 17.88 0.00 Sec 61 32.18 32.18 0.00 Sec 123 25.03 25.03 0.00 Sec 185 17.88 17.88 0.00 Sec 62 32.18 32.18 0.00 Sec 124 17.88 17.88 0.00 Sec 186 14.30 14.30 0.00

154

Table A-6: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 187 17.88 17.88 0.00 Sec 249 64.46 64.36 3.58 Sec 311 21.45 21.45 0.00 Sec 188 17.88 17.88 0.00 Sec 250 75.18 75.09 3.58 Sec 312 32.18 32.18 0.00 Sec 189 10.73 10.73 0.00 Sec 251 75.18 75.09 3.58 Sec 313 35.76 35.76 0.00 Sec 190 17.88 17.88 0.00 Sec 252 78.75 78.67 3.58 Sec 314 39.33 39.33 0.00 Sec 191 17.88 17.88 0.00 Sec 253 85.89 85.82 3.58 Sec 315 39.33 39.33 0.00 Sec 192 14.74 14.30 3.58 Sec 254 75.18 75.09 3.58 Sec 316 42.91 42.91 0.00 Sec 193 17.88 17.88 0.00 Sec 255 93.04 92.97 3.58 Sec 317 32.18 32.18 0.00 Sec 194 7.15 7.15 0.00 Sec 256 82.32 82.24 3.58 Sec 318 35.76 35.76 0.00 Sec 195 14.30 14.30 0.00 Sec 257 32.18 32.18 0.00 Sec 319 42.91 42.91 0.00 Sec 196 10.73 10.73 0.00 Sec 258 21.45 21.45 0.00 Sec 320 35.94 35.76 3.58 Sec 197 14.30 14.30 0.00 Sec 259 14.30 14.30 0.00 Sec 321 14.30 14.30 0.00 Sec 198 14.30 14.30 0.00 Sec 260 42.91 42.91 0.00 Sec 322 28.61 28.61 0.00 Sec 199 10.73 10.73 0.00 Sec 261 35.76 35.76 0.00 Sec 323 25.03 25.03 0.00 Sec 200 28.61 28.61 0.00 Sec 262 35.76 35.76 0.00 Sec 324 32.18 32.18 0.00 Sec 201 21.45 21.45 0.00 Sec 263 25.03 25.03 0.00 Sec 325 17.88 17.88 0.00 Sec 202 17.88 17.88 0.00 Sec 264 21.45 21.45 0.00 Sec 326 21.45 21.45 0.00 Sec 203 28.61 28.61 0.00 Sec 265 39.33 39.33 0.00 Sec 327 28.61 28.61 0.00 Sec 204 28.61 28.61 0.00 Sec 266 28.61 28.61 0.00 Sec 328 28.61 28.61 0.00 Sec 205 17.88 17.88 0.00 Sec 267 28.61 28.61 0.00 Sec 329 32.18 32.18 0.00 Sec 206 10.73 10.73 0.00 Sec 268 17.88 17.88 0.00 Sec 330 46.48 46.48 0.00 Sec 207 10.73 10.73 0.00 Sec 269 21.45 21.45 0.00 Sec 331 53.64 53.64 0.00 Sec 208 14.30 14.30 0.00 Sec 270 21.45 21.45 0.00 Sec 332 42.91 42.91 0.00 Sec 209 10.73 10.73 0.00 Sec 271 21.45 21.45 0.00 Sec 333 35.76 35.76 0.00 Sec 210 10.73 10.73 0.00 Sec 272 32.18 32.18 0.00 Sec 334 35.94 35.76 3.58 Sec 211 10.73 10.73 0.00 Sec 273 21.45 21.45 0.00 Sec 335 25.28 25.03 3.58 Sec 212 17.88 17.88 0.00 Sec 274 21.45 21.45 0.00 Sec 336 39.50 39.33 3.58 Sec 213 25.03 25.03 0.00 Sec 275 21.75 21.45 3.58 Sec 337 46.48 46.48 0.00 Sec 214 25.03 25.03 0.00 Sec 276 21.45 21.45 0.00 Sec 338 57.21 57.21 0.00 Sec 215 10.73 10.73 0.00 Sec 277 25.28 25.03 3.58 Sec 339 57.21 57.21 0.00 Sec 216 25.03 25.03 0.00 Sec 278 28.83 28.61 3.58 Sec 340 53.64 53.64 0.00 Sec 217 25.03 25.03 0.00 Sec 279 25.03 25.03 0.00 Sec 341 50.06 50.06 0.00 Sec 218 28.61 28.61 0.00 Sec 280 28.61 28.61 0.00 Sec 342 21.45 21.45 0.00 Sec 219 10.73 10.73 0.00 Sec 281 17.88 17.88 0.00 Sec 343 17.88 17.88 0.00 Sec 220 10.73 10.73 0.00 Sec 282 25.03 25.03 0.00 Sec 344 53.64 53.64 0.00 Sec 221 18.23 17.88 3.58 Sec 283 14.30 14.30 0.00 Sec 345 68.03 67.94 3.58 Sec 222 18.23 17.88 3.58 Sec 284 17.88 17.88 0.00 Sec 346 35.76 35.76 0.00 Sec 223 25.28 25.03 3.58 Sec 285 14.30 14.30 0.00 Sec 347 46.48 46.48 0.00 Sec 224 14.74 14.30 3.58 Sec 286 21.45 21.45 0.00 Sec 348 71.60 71.51 3.58 Sec 225 11.31 10.73 3.58 Sec 287 25.03 25.03 0.00 Sec 349 39.33 39.33 0.00 Sec 226 11.31 10.73 3.58 Sec 288 28.61 28.61 0.00 Sec 350 35.76 35.76 0.00 Sec 227 10.73 10.73 0.00 Sec 289 25.03 25.03 0.00 Sec 351 28.61 28.61 0.00 Sec 228 14.30 14.30 0.00 Sec 290 17.88 17.88 0.00 Sec 352 64.46 64.36 3.58 Sec 229 14.30 14.30 0.00 Sec 291 17.88 17.88 0.00 Sec 353 53.76 53.64 3.58 Sec 230 28.61 28.61 0.00 Sec 292 17.88 17.88 0.00 Sec 354 21.75 21.45 3.58 Sec 231 14.30 14.30 0.00 Sec 293 17.88 17.88 0.00 Sec 355 21.45 21.45 0.00 Sec 232 17.88 17.88 0.00 Sec 294 10.73 10.73 0.00 Sec 356 10.73 10.73 0.00 Sec 233 14.30 14.30 0.00 Sec 295 10.73 10.73 0.00 Sec 357 21.45 21.45 0.00 Sec 234 14.30 14.30 0.00 Sec 296 10.73 10.73 0.00 Sec 358 17.88 17.88 0.00 Sec 235 14.30 14.30 0.00 Sec 297 14.30 14.30 0.00 Sec 359 14.30 14.30 0.00 Sec 236 10.73 10.73 0.00 Sec 298 28.61 28.61 0.00 Sec 360 17.88 17.88 0.00 Sec 237 10.73 10.73 0.00 Sec 299 28.83 28.61 3.58 Sec 361 35.76 35.76 0.00 Sec 238 10.73 10.73 0.00 Sec 300 39.50 39.33 3.58 Sec 362 42.91 42.91 0.00 Sec 239 10.73 10.73 0.00 Sec 301 39.50 39.33 3.58 Sec 363 46.48 46.48 0.00 Sec 240 10.73 10.73 0.00 Sec 302 35.94 35.76 3.58 Sec 364 14.30 14.30 0.00 Sec 241 10.73 10.73 0.00 Sec 303 39.50 39.33 3.58 Sec 365 39.50 39.33 3.58 Sec 242 10.73 10.73 0.00 Sec 304 21.75 21.45 3.58 Sec 366 28.83 28.61 3.58 Sec 243 14.30 14.30 0.00 Sec 305 21.75 21.45 3.58 Sec 367 53.76 53.64 3.58 Sec 244 10.73 10.73 0.00 Sec 306 28.83 28.61 3.58 Sec 368 60.89 60.79 3.58 Sec 245 10.73 10.73 0.00 Sec 307 28.83 28.61 3.58 Sec 369 68.03 67.94 3.58 Sec 246 10.73 10.73 0.00 Sec 308 32.38 32.18 3.58 Sec 370 60.89 60.79 3.58 Sec 247 10.73 10.73 0.00 Sec 309 28.83 28.61 3.58 Sec 371 17.88 17.88 0.00 Sec 248 82.32 82.24 3.58 Sec 310 35.76 35.76 0.00 Sec 372 14.30 14.30 0.00

155

Table A-6: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Line D value

(µm) X

value Y

value Data Data Data

Sec 373 32.38 32.18 3.58 Sec 435 85.82 85.82 0.00 Sec 497 89.46 89.39 3.58 Sec 374 28.61 28.61 0.00 Sec 436 82.24 82.24 0.00 Sec 498 89.39 89.39 0.00 Sec 375 25.03 25.03 0.00 Sec 437 85.82 85.82 0.00 Sec 499 107.33 107.27 3.58 Sec 376 60.79 60.79 0.00 Sec 438 89.46 89.39 3.58 Sec 500 110.91 110.85 3.58 Sec 377 60.89 60.79 3.58 Sec 439 85.89 85.82 3.58 Sec 501 93.04 92.97 3.58 Sec 378 64.46 64.36 3.58 Sec 440 82.32 82.24 3.58 Sec 502 89.46 89.39 3.58 Sec 379 64.46 64.36 3.58 Sec 441 85.89 85.82 3.58 Sec 503 93.04 92.97 3.58 Sec 380 68.03 67.94 3.58 Sec 442 89.46 89.39 3.58 Sec 504 100.18 100.12 3.58 Sec 381 60.89 60.79 3.58 Sec 443 96.61 96.54 3.58 Sec 505 96.61 96.54 3.58 Sec 382 64.46 64.36 3.58 Sec 444 100.18 100.12 3.58 Sec 506 110.91 110.85 3.58 Sec 383 50.06 50.06 0.00 Sec 445 89.39 89.39 0.00 Sec 507 103.76 103.70 3.58 Sec 384 57.21 57.21 0.00 Sec 446 85.89 85.82 3.58 Sec 508 64.46 64.36 3.58 Sec 385 57.21 57.21 0.00 Sec 447 89.46 89.39 3.58 Sec 509 67.94 67.94 0.00 Sec 386 75.18 75.09 3.58 Sec 448 75.18 75.09 3.58 Sec 510 75.09 75.09 0.00 Sec 387 64.46 64.36 3.58 Sec 449 57.21 57.21 0.00 Sec 511 71.51 71.51 0.00 Sec 388 60.79 60.79 0.00 Sec 450 78.75 78.67 3.58 Sec 512 78.67 78.67 0.00 Sec 389 32.18 32.18 0.00 Sec 451 71.60 71.51 3.58 Sec 513 57.21 57.21 0.00 Sec 390 21.75 21.45 3.58 Sec 452 60.89 60.79 3.58 Sec 514 64.36 64.36 0.00 Sec 391 35.94 35.76 3.58 Sec 453 25.03 25.03 0.00 Sec 515 68.03 67.94 3.58 Sec 392 46.62 46.48 3.58 Sec 454 53.64 53.64 0.00 Sec 516 71.51 71.51 0.00 Sec 393 35.76 35.76 0.00 Sec 455 71.60 71.51 3.58 Sec 517 64.36 64.36 0.00 Sec 394 60.89 60.79 3.58 Sec 456 60.79 60.79 0.00 Sec 518 75.09 75.09 0.00 Sec 395 60.89 60.79 3.58 Sec 457 75.18 75.09 3.58 Sec 519 67.94 67.94 0.00 Sec 396 57.32 57.21 3.58 Sec 458 68.03 67.94 3.58 Sec 520 71.51 71.51 0.00 Sec 397 42.91 42.91 0.00 Sec 459 64.36 64.36 0.00 Sec 521 71.51 71.51 0.00 Sec 398 50.06 50.06 0.00 Sec 460 28.61 28.61 0.00 Sec 522 78.75 78.67 3.58 Sec 399 46.48 46.48 0.00 Sec 461 32.18 32.18 0.00 Sec 523 53.76 53.64 3.58 Sec 400 57.32 57.21 3.58 Sec 462 25.03 25.03 0.00 Sec 524 57.21 57.21 0.00 Sec 401 71.60 71.51 3.58 Sec 463 17.88 17.88 0.00 Sec 525 64.36 64.36 0.00 Sec 402 78.75 78.67 3.58 Sec 464 46.48 46.48 0.00 Sec 526 60.79 60.79 0.00 Sec 403 75.18 75.09 3.58 Sec 465 75.09 75.09 0.00 Sec 527 42.91 42.91 0.00 Sec 404 68.03 67.94 3.58 Sec 466 75.09 75.09 0.00 Sec 528 28.61 28.61 0.00 Sec 405 67.94 67.94 0.00 Sec 467 82.32 82.24 3.58 Sec 529 32.18 32.18 0.00 Sec 406 53.64 53.64 0.00 Sec 468 71.51 71.51 0.00 Sec 530 35.76 35.76 0.00 Sec 407 57.21 57.21 0.00 Sec 469 82.32 82.24 3.58 Sec 531 42.91 42.91 0.00 Sec 408 50.19 50.06 3.58 Sec 470 71.51 71.51 0.00 Sec 532 50.06 50.06 0.00 Sec 409 78.75 78.67 3.58 Sec 471 71.51 71.51 0.00 Sec 533 50.06 50.06 0.00 Sec 410 82.32 82.24 3.58 Sec 472 64.36 64.36 0.00 Sec 534 50.06 50.06 0.00 Sec 411 78.75 78.67 3.58 Sec 473 42.91 42.91 0.00 Sec 535 64.46 64.36 3.58 Sec 412 82.32 82.24 3.58 Sec 474 82.24 82.24 0.00 Sec 536 57.32 57.21 3.58 Sec 413 71.60 71.51 3.58 Sec 475 67.94 67.94 0.00 Sec 537 50.19 50.06 3.58 Sec 414 64.46 64.36 3.58 Sec 476 50.19 50.06 3.58 Sec 538 57.32 57.21 3.58 Sec 415 46.48 46.48 0.00 Sec 477 68.03 67.94 3.58 Sec 539 43.06 42.91 3.58 Sec 416 50.06 50.06 0.00 Sec 478 68.03 67.94 3.58 Sec 540 71.60 71.51 3.58 Sec 417 35.76 35.76 0.00 Sec 479 57.32 57.21 3.58 Sec 541 57.32 57.21 3.58 Sec 418 17.88 17.88 0.00 Sec 480 60.79 60.79 0.00 Sec 542 43.06 42.91 3.58 Sec 419 25.03 25.03 0.00 Sec 481 42.91 42.91 0.00 Sec 543 42.91 42.91 0.00 Sec 420 25.03 25.03 0.00 Sec 482 75.18 75.09 3.58 Sec 544 32.18 32.18 0.00 Sec 421 39.33 39.33 0.00 Sec 483 68.03 67.94 3.58 Sec 545 35.76 35.76 0.00 Sec 422 32.18 32.18 0.00 Sec 484 57.32 57.21 3.58 Sec 546 50.06 50.06 0.00 Sec 423 42.91 42.91 0.00 Sec 485 32.18 32.18 0.00 Sec 547 53.64 53.64 0.00 Sec 424 46.48 46.48 0.00 Sec 486 46.48 46.48 0.00 Sec 548 57.21 57.21 0.00 Sec 425 42.91 42.91 0.00 Sec 487 53.76 53.64 3.58 Sec 549 46.48 46.48 0.00 Sec 426 46.48 46.48 0.00 Sec 488 39.33 39.33 0.00 Sec 550 39.33 39.33 0.00 Sec 427 71.51 71.51 0.00 Sec 489 53.64 53.64 0.00 Sec 551 46.48 46.48 0.00 Sec 428 60.89 60.79 3.58 Sec 490 60.79 60.79 0.00 Sec 552 57.21 57.21 0.00 Sec 429 60.79 60.79 0.00 Sec 491 89.39 89.39 0.00 Sec 553 60.79 60.79 0.00 Sec 430 64.36 64.36 0.00 Sec 492 89.46 89.39 3.58 Sec 554 57.21 57.21 0.00 Sec 431 60.79 60.79 0.00 Sec 493 89.46 89.39 3.58 Sec 555 75.18 75.09 3.58 Sec 432 75.18 75.09 3.58 Sec 494 89.46 89.39 3.58 Sec 556 64.46 64.36 3.58 Sec 433 75.09 75.09 0.00 Sec 495 89.46 89.39 3.58 Sec 557 71.60 71.51 3.58 Sec 434 75.09 75.09 0.00 Sec 496 103.76 103.70 3.58 Sec 558 75.18 75.09 3.58

156

Table A-6: Continued

Line D

value X

value Y

value Line D

value X

value Y

value Data Data

Sec 559 89.46 89.39 3.58 Sec 621 21.45 21.45 0.00 Sec 560 78.75 78.67 3.58 Sec 622 17.88 17.88 0.00 Sec 561 96.61 96.54 3.58 Sec 562 89.46 89.39 3.58 Sec 563 64.46 64.36 3.58 Sec 564 53.76 53.64 3.58 Sec 565 57.32 57.21 3.58 Sec 566 68.03 67.94 3.58 Sec 567 57.32 57.21 3.58 Sec 568 53.76 53.64 3.58 Sec 569 57.32 57.21 3.58 Sec 570 60.89 60.79 3.58 Sec 571 53.76 53.64 3.58 Sec 572 57.32 57.21 3.58 Sec 573 57.32 57.21 3.58 Sec 574 68.03 67.94 3.58 Sec 575 53.76 53.64 3.58 Sec 576 60.79 60.79 0.00 Sec 577 53.64 53.64 0.00 Sec 578 64.36 64.36 0.00 Sec 579 53.76 53.64 3.58 Sec 580 57.32 57.21 3.58 Sec 581 64.46 64.36 3.58 Sec 582 68.03 67.94 3.58 Sec 583 68.03 67.94 3.58 Sec 584 60.89 60.79 3.58 Sec 585 64.36 64.36 0.00 Sec 586 50.06 50.06 0.00 Sec 587 39.33 39.33 0.00 Sec 588 25.03 25.03 0.00 Sec 589 17.88 17.88 0.00 Sec 590 25.03 25.03 0.00 Sec 591 17.88 17.88 0.00 Sec 592 25.03 25.03 0.00 Sec 593 21.75 21.45 3.58 Sec 594 21.75 21.45 3.58 Sec 595 32.38 32.18 3.58 Sec 596 32.38 32.18 3.58 Sec 597 35.76 35.76 0.00 Sec 598 28.61 28.61 0.00 Sec 599 21.45 21.45 0.00 Sec 600 35.76 35.76 0.00 Sec 601 32.18 32.18 0.00 Sec 602 14.30 14.30 0.00 Sec 603 10.73 10.73 0.00 Sec 604 17.88 17.88 0.00 Sec 605 14.30 14.30 0.00 Sec 606 21.75 21.45 3.58 Sec 607 25.03 25.03 0.00 Sec 608 21.45 21.45 0.00 Sec 609 28.61 28.61 0.00 Sec 610 21.45 21.45 0.00 Sec 611 21.45 21.45 0.00 Sec 612 17.88 17.88 0.00 Sec 613 25.03 25.03 0.00 Sec 614 21.45 21.45 0.00 Sec 615 32.18 32.18 0.00 Sec 616 35.76 35.76 0.00 Sec 617 42.91 42.91 0.00 Sec 618 39.33 39.33 0.00 Sec 619 17.88 17.88 0.00 Sec 620 17.88 17.88 0.00

157

APPENDIX B: CRACK INDUCING PROCEDURE

Disk specimens were cut from the mortar cylinders. The thickness of the disk specimens was 25

mm. cracks were induced by indirect tension. Figure B-1 and B-2 show the indirect tension

setup. Two LVDTs were used to monitor the deflection of the samples perpendicular to the

direction of loading. Vertical load was applied using a Universal Testing Machine using

displacement control method by a constant rate of vertical deformation of 1 µm/s. Figure B-3

shows the applied load and measured lateral displacement versus time. As the applied load

increases, LVDTs show continuous increase in lateral deflection of the sample up to the point of

cracking. At cracking, the load drops while there is a jump in LVDTs reading. The jump

corresponds to the crack opening at the center of the disk specimen. After cracking the lateral

deflection increases at higher rate. When the desired deflection is reached, samples are unloaded.

The rate of unloading was 5 µm/s. As the sample is unloaded, lateral deflection decreases.

However after the sample is fully unloaded all the deflection does not spring back. The residual

displacement is due to cracking and can be used as a rough estimation of the crack width in the

center of the sample.

In the example shown in figure B-3 sample cracked at the load of 16 KN. The jump in LVDT

reading at cracking was 88 µm (from 42 to 130 µm ) and sample was loaded to reach lateral

deflection of 152 µm. Then sample was unloaded. The lateral deflection after unloading was 44

µm which means that 108 µm (of the maximum deflection of 152 µm) was recovered. This is

mainly due to crack closing upon unloading. In this study, the samples were loaded to reach

maximum deflection in the range of 80 to 600 µm and then unloaded. The residual deflection

obtained with this method was in the range of 40 to 400 µm. After samples were tested, the

158

actual crack width was measured using image analysis (see Appendix A). The measured crack

width varied in the range of 10 to 200 µm.

Figure B-1: Splitting tension setup used to fracture cement paste disks

LVDT LVDT

Frame holding LVDTs

Disk specimen

Diametric crack

Figure B-2: Schematic illustration of the splitting tension setup used to fracture mortar disk specimens

Y

Z

LVDTs

Direction of load

Z

XY

159

Figure B-3: Variation of applied vertical load and lateral deflection of the sample during splitting tension test

0

20

40

60

80

100

120

140

160

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300

Load

lvdtLVDT

Loa

d (

KN

)

LV

DT

(μ

m)

Time (S)

Loading Unloading

Residual Displacement

Time ofCracking

Alireza Akhavan Curriculum Vita

1100 W. Aaron Dr. Apt. C1, State College PA 16803 Tel: (814) 470 150, e‐mail: alireza.eng@psu.edu

EDUCATION

Doctor of Philosophy (PhD), Civil/Materials Engineering The Pennsylvania State University, August 2012 Dissertation title: Characterizing Mass Transport in Fractured Cementitious Materials Master of science (MSc), Civil/Structural Engineering Gilan University, March 2005 Thesis subject: Experimental Evaluation and Numerical Modeling of Column Base Anchorage in Steel Structures Bachelor of Science (BSc), Civil Engineering Gilan University, May 2002

SELECTED PUBLICATIONS Akhavan A., and Rajabipour F., Quantifying the effects of crack width, tortuosity, and roughness on water permeability of cracked mortars, Cement and Concrete Research 42 (2012) 313–320 Akhavan A., and Rajabipour F., Evaluating Diffusivity of Cracked Cement Paste Based on Electrical Impedance Spectroscopy, Materials and Structures, 2012, submitted Akhavan A., Rajabipor F., Permeation, Electrical Conduction and Diffusion through Rough Parallel Plates, Manuscripts in preparation, 2012 Shafaatian S., Akhavan A., Maraghechi H., Rajabipour F., How Does Fly Ash Mitigate Alkali-Silica Reaction (ASR) in Accelerated Mortar Bar Test (ASTM C1567)?, Cement and Concrete Composites, in peer review, May 2012

TEACHING AND RESEARCH EXPERIENCE

2010-Present, Teaching and research assistant, Civil Eng. Dep. PennState University, 2009-2010, Research assistant, Civil Eng. Dep. University of Hawaii, 2008-2009, Research assistant, Mechanical Eng. Dep. South Dakota State University,

PROFESSIONAL DEVELOPMENT AND AFFILIATION

Certified Engineer-in-Training (EIT) in Civil Engineering, MI, 2011 Member of ASCE (American Society of Civil Engineers) Member of ACI (American Concrete Institute)