STRAIN-RESPONSE CHARACTERIZATION FOR UNBONDED CONCRETE

The Pennsylvania State University

The Graduate School

College of Engineering

STRAIN-RESPONSE CHARACTERIZATION FOR UNBONDED CONCRETE

OVERLAYS SUBJECTED TO

HEAVY AIRCRAFT GEAR WITH MULTIPLE AXLES

A Thesis in

Civil Engineering

by.

Vishal Kumar Singh

© 2010 Vishal K. Singh

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2010

ii

The thesis of Vishal K. Singh was reviewed and approved* by the following:

Shelley Stoffels

Associate Professor of Civil Engineering

Thesis Adviser

Mansour Solaimanian

Senior Research Associate

Farshad Rajabipour

Assistant Professor of Civil Engineering

Angelica Palomino

Assistant Professor of Civil Engineering

Peggy Johnson

Professor of Civil Engineering

Head of the Department of Civil Engineering

*Signatures are on file in the graduate school

iii

ABSTRACT

Concrete pavement performance, with regard to fatigue life, has previously been studied

using strain gages installed in-situ in the pavement, with the primary focus on peak strain

response. This study focuses on identifying and characterizing additional components of

strain responses from unbonded concrete overlays for concrete pavement on airfields, and

relating those strain responses to observed performance. Strain data collected through a

series of full-scale tests at the Federal Aviation Administration (FAA) National Airfield

Pavement Test Facility (NAPTF) are analyzed to observe effects of repeated loading with

heavy aircraft gear with multiple axles on three different structural cross-sections of

unbonded concrete overlays. Components of strain response, such as peak strain,

cumulative area, percent recovery, pre-stress area, post-stress area and duration are

defined; these additional strain response components are analyzed and correlated to peak

strain response. The peak strain is found to be strongly correlated to the cumulative strain

area component of the strain response, but not to other components of the strain response.

Preliminary regression relationships with performance, defined in terms of structural

condition index (SCI), could be established only with peak strain, percent recovery and

number of axles for the top of unbonded overlay, or alternately with area components.

This study provides the foundation for future study of airfield concrete pavement overlay

performance, especially for the subsequent experiment, performed at the same location

with same pavement cross-section but with weakened support conditions.

iv

List of Acronyms

ASTM American Society for Testing and Materials

FAA Federal Aviation Administration

IPRF Innovative Pavement Research Foundation

LPT Linear Position Transducer

NAPTF National Airfield Pavement Test Facility

PCI Pavement Condition Index

QES Quality Engineering Solutions

SCI Structural Condition Index

VBA Visual Basic for Applications

v

TABLE OF CONTENTS

List of Tables………………………………………………………………………….. vii

List of Figures……………………………………………………………………........ xiii

Acknowledgements…………………………………………………………………….. xvi

CHAPTER 1. INTRODUCTION……………………………………………………… 1

1.1. Background…………………………………………………………………. 1

1.2. Objectives………………………………………………………………… 7

1.3. Scope……………………………………………………………………… 8

CHAPTER 2. LITERATURE REVIEW……………………………………………… 10

2.1. Background……………………………………………………………….. 10

2.2. Concrete Properties……………………………………………………….. 10

2.3. Concrete Pavement Fatigue ………………………………………………. 12

2.3.1. Stress Ratio Models……………………………………………….. 12

2.3.2. Slab Fatigue……………………………………………………….. 14

2.3.3. Variable Amplitude Loading……………………………………… 15

2.3.4. Mechanistic Approach……………………………………………. 15

2.3.5. Numerical Approach (Finite-Element Methods)…………………. 16

2.3.6. Fuzzy Logic……………………………………………………….. 16

2.4. Airbus A-380 and Boeing 777……………………………………………. 16

2.5. Current FAA Design Procedure…………………………………………… 18

2.6. Structural Condition Index……………………………………………….. 19

2.7. Strain Gage Characterization…………………………………………….. 19

2.8. Summary of Important Findings from Literature Review………………. 20

CHAPTER 3. FULL-SCALE TESTING OF UNBONDED OVERLAYS ..………….. 22

3.1. NAPTF …………………………………………………………………….. 22

3.2. Pavement Cross-Sections…………………………………………………. 23

3.3. Types of Loading and Aircraft Gears……………………………………. 25

3.4. Instrumentation…………………………………………………………… 29

3.4.1. Strain Gages……………………………………………………….. 29

3.4.2. KM-100B………………………………………………….............. 30

3.5. Performance……………………………………………………………….. 41

CHAPTER 4. METHODOLOGY …………………………………………………... 42

4.1. Overview of Proposed Methodology……………………………………... 42

4.2. Detailed Processing of Data………………………………………………. 43

4.2.1 Data Extraction/Filtering………………………………………….. 44

4.2.2. Responses from Track 0…………………………………………... 44

4.2.3 Matlab Programming……………………………………………… 45

4.2.3.1 Type 1 for North Test Items………………………………. 50

4.2.3.2 Type 2 for North Test Items ………………………………. 53

4.2.3.3 Type 3 for North Test Items ………………………………. 55

4.2.3.4 Type 4 for North Test Items ……………………………… 56

vi

4.2.3.5 Type 1, 2, 3 and 4 for South Test Items…………………… 58

4.2.4 Statistical Analysis…………………………………………………. 60

CHAPTER 5. ANALYSIS …………………………………………………................. 62

5.1. Relationship of Components of Strain Gage Response to Peak Strain….. 62

5.2. Relationships between Peak Strain and other Components of Strain Gage

Response…………………………………………………………………... 72

5.3. Strain Gage Response with Change in Loading and Cross-Sections………. 80

5.4. Performance……………………………………………………………… 86

5.4.1. At the Top of Overlay……………………………………………… 86

5.4.2. At the Bottom of Overlay…………………………………………. 88

5.4.3. At the Top of Underlay……………………………………………. 89

5.4.4. At the Bottom of Underlay……………………………………….. 90

5.5. Summary…………………………………………………………………... 91

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS ……………………. 93

6.1. Findings…………………………………………………………………… 93

6.2. Conclusions………………………………………………………………… 96

6.3. Recommendations…………………………………………………….......... 99

REFERENCES………………………………………………………………………… 101

APPENDIX A. Strain gage coordinates and calibration factor…………………….. 111

APPENDIX B. Matlab Codes ……………………………………………………….. 114

APPENDIX C. Mean and Standard Deviation for Selected Gages …………………. 127

APPENDIX D. Performance Prediction………………………………………………. 174

vii

List of Tables

Table 1. Vehicle Passes Utilized for this Study

Table 2. Summary of Design Test Items for Baseline Experiment

Table 3. Loading Sequences

Table 4. KM-100B Specifications (KM Strain transducers manual, 2010).

Table 5. SCI and Date History with First Crack and SCI=80

Table 6. Linear Relation Chart for Even-numbered Passes with Area as Y and Strain as X

for EG-O-N1-1B

Table 7. Linear Relation Chart for Odd-numbered Passes with Area as Y and Strain as X

for EG-O-N1-1B

Table 8. Average, Median and Standard Deviation of the Peak Strain and Area for Odd-

numbered Passes for EG-O-N1-1B.

Table 9. Average, Median and Standard Deviation of the Peak Strain and Area for Even-

numbered for EG-O-N1-1B

Table 10. Linear Relation Chart for Even-numbered Passes with Area as Y and Strain as

X for EG-O-N1-1T

Table 11. Linear Relation Chart for Odd-numbered Passes with Area as Y and Strain as X

for EG-O-N1-1T


numbered Passes for for EG-O-N1-1T


numbered Passes for EG-O-N1-1T

Table 14. Correlation between Peak Strain and Cumulative Area

Table 15. Correlation between % Recovery and Cumulative Area

Table 16. Correlation between Peak Strain and Cumulative Area by Strain Gage

Locations

viii

Table 17. Correlation between Peak Strain and % Recovery by Strain Gage Locations

Table 18. Correlation between Peak Strain and Duration by Strain Gage Locations

Table 19. Correlation between % Recovery and Area by Strain Gage Locations

Table 20. Correlation between Different Components of Peak Responses

Table 21. Regression Statistics for Analysis of % Recovery, Duration and Number of

Axles as Predictors for Peak Strain(Y)

Table 22. Correlation between Different Components of Strain Gage Responses from Top

of Underlay

Table 23. Regression Statistics for Analysis of % Recovery, Duration and Number of

Axles as Predictors for Peak Strain(Y)

Table 24.Mean and Standard Deviation of Components of Gages’ Response at Top of

Overlay

Table 25. Mean and Standard Deviation of Components of Gage Response at Bottom of

Overlay

Table 26. Mean and Standard Deviation of Components of Gage Response at Top of

Underlay


Underlay

Table 28. Regression Statistics for Analysis of Performance with Peak Strain and %

Recovery and Number of Axles at Top of Overlay

Table 29. Regression Statistics for Analysis of Performance with Pre-Tension area, Post-

Tension Area, Cumulative Compression Area and Number of Axles at Top of

Overlay

Table 30. Regression Statistics for Analysis of Performance with Pre-Compression Area,

Post-Compression Area, Cumulative Tension Area and Number of Axles at

Bottom of Overlay

ix

Table 31. Regression Statistics for Analysis of Performance with Pre-Tension Area, Post-

Tension Area, Cumulative Compression Area and Number of Axles at Top of

Underlay

Table 32. Regression Statistics for Analysis of Performance with Peak Strain and %

Recovery and Number of Axles at Bottom of Underlay.


Post-Compression Area, Cumulative Tension Area and Number of Axles at

Bottom of Underlay

Table 34. Mean and Standard Deviation of Key Components of Strain Gage Responses

Table 35. Coordinates and Calibration Factor for Strain Gages Installed at Test Item N1

Table 36. Coordinates and Calibration Factor for Strain Gages Installed at Test Item S1





Table 41. Average, Median and Standard Deviation of the Peak Strain(microStrain) and

Area for Even-numbered Passes for EG-U-N1-1 B and EG-U-N1-1 T

Table 42. Linear Relation Chart for Even-numbered Passes for EG-U-N1-1 B and EG-U-

N1-1 T with Area as Y and Strain as X


numbered Passes for EG-U-N1-1 B and EG-U-N1-1 T

Table 44. Linear Relation Chart for Odd-numbered Passes for EG-U-N1-1 B and EG-U-



numbered passes for EG-U-N1-3 B and EG-U-N1-3T

Table 46. Linear relation chart for Odd-numbered Passes for EG-U-N1-3 B and EG-U-


x

Table 47. Average, Median and Standard deviation of the Peak Strain and Area for

Even-numbered passes for EG-O-N2-2 B and EG-O-N2-2 T

Table 48: Linear Relation Chart for Even-numbered Passes for EG-O-N2-2 B and EG-O-


Table 49. Average, Median and Standard Deviation of the Peak Strain and Area for

Even-numbered passes for EG-U-S1-2 B and EG-U-S1-2 T

Table 50. Linear relation chart for Even-numbered Passes for EG-U-S1-2 B and EG-U-

S1-2 T with Area as Y and Strain as X


numbered passes for EG-U-S1-2 B and EG-U-S1-2 T

Table 52. Linear relation chart for Odd-numbered Passes for EG-U-S1-2 B and EG-U-











Even-numbered passes for EG-O-S1-2 B and EG-O-S1-2 T

Table 58. Linear relation chart for Even-numbered Passes for EG-O-S1-2 B and EG-O-



numbered passes for EG-O-S1-2 B and EG-O-S1-2 T

Table 60. Linear relation chart for Odd-numbered Passes for EG-O-S1-1 B and EG-O-


xi


Even-numbered passes for EG-O-S1-3 B and EG-O-S1-3 T

Table 62. Linear relation chart for Even-numbered Passes for EG-O-S1-3 B and EG-O-




Table 64. Linear relation chart for Even-numbered Passes for EG-O-N2-2 B and EG-O-



numbered passes for EG-O-N2-2 B and EG-O-N2-2 T

Table 66. Linear relation chart for Odd-numbered Passes for EG-O-N2-1 B and EG-O-













numbered passes for EG-U-N3-1 B and EG-U-N3-1 T

Table 73. Linear relation chart for Odd-numbered Passes for EG-U-N3-1 B and EG-U-



Even-numbered passes for EG-U-N3-2 B and EG-U-N3-2 T

xii

Table 75. Linear relation chart for Even-numbered Passes for EG-U-N3-2 B and EG-U-



numbered passes for EG-O-N3-3 B and EG-O-N3-3 T

Table 77. Linear relation chart for Odd-numbered Passes for EG-O-N3-3 B and EG-O-


















xiii

List of Figures

Figure 1. Test item layout with as-built thicknesses.

Figure 2. Typical strain gage response as shown in FAA TenView.

Figure 3-a. Strain gage response components.

Figure 3-b. Cumulative area of a strain gage response shown as shaded portion of the

curve.

Figure 4. Typical arrangement for twin dual tandem and triple dual tandem aircraft gears.

Figure 5. Experimental design configuration, showing transverse joint spacings (Stoffels

et al., 2008).

Figure 6. End view of longitudinal joint locations for overlay and underlay slabs (Stoffels et

al., 2008).

Figure 7. Loading plan.

Figure 8. Wander pattern and track frequencies (Stoffels et al., 2008).

Figure 9. Schematic diagram of strain gage model KM-100B (KM Strain transducers manual,

2010).

Figure 10-a. Strain gage locations for a test item, longitudinal design view

Figure 10-b. Strain gage locations for a test item, transverse design view.

Figure 11.Expected peak strain condition for a mid-slab edge strain gage during loading.

Figure 12. Nomenclature for strain gage identification.

Figure 13-a. Strain gage instrumentation plan for the underlay of the pavement for test

items N1 and S1 (courtesy, prime contractor QES).

Figure 13-b. Strain gage instrumentation plan at the underlay of the pavement for test


Figure 13-c. Strain gage instrumentation plan at the underlay of the pavement for test


xiv

Figure 14-a. Strain gage instrumentation plan at the overlay of the pavement for test


Figure 14-b. Strain Gage instrumentation plan at the overlay of the pavement for test


Figure 14-c. Strain Gage instrumentation plan at the overlay of the pavement for test

items N3 and S3 (courtesy, prime contractor QES)

Figure 15. Flowchart of proposed methodology.

Figure 16. Flowchart of detailed process.

Figure 17. Strain gage average responses from one wander of ramp-up loading for gages

in test item north 1 with triple dual tandem loading (courtesy, Lin Yeh).

Figure 18. Baseline for a strain gage response.

Figure 19. Peak strains and strain between axles for a strain gage response from triple

dual tandem loading.

Figure 20. Peak strains and strain between axles for a strain gage response from twin dual

tandem loading.

Figure 21. Cumulative area for a strain gage response from triple dual tandem loading.

Figure 22. Pre-stress area for a strain gage response from triple dual tandem loading.

Figure 23. Post-stress area for a strain gage response from triple dual tandem loading.

Figure 24. Duration for a strain gage response from triple dual tandem loading.

Figure 25. Strain gage response from triple dual tandem loading, type 1.




Figure 29. Strain gage response from twin dual tandem loading, type 1 and 2.

Figure 30. Strain gage response from twin dual tandem loading, type 3.

xv

Figure 31. Linear relationship between cumulative area and peak strain for EG-O-N1-1B.

Figure 32. Cumulative area plot for odd-numbered passes(west to east) for EG-O-N1-1B.

Figure 33. Peak strain plot for odd-numbered passes(west to east) for EG-O-N1-1B.

Figure 34. Cumulative area plot for even-numbered passes(east to west) for EG-O-N1-

1B.

Figure 35. Peak strain plot for even-numbered passes(east to west) EG-O-N1-1B.

Figure 36. Linear relationship between cumulative area and peak strain for EG-O-N1-1T.

Figure 37. Cumulative area plot for odd-numbered passes (west to east) for EG-O-N1-1T.

Figure 38. Peak strain plot for odd-numbered passes (west to east) for EG-O-N1-1T.

Figure 39. Cumulative area plot for even-numbered passes (east to west) for EG-O-N1-

1T.

Figure 40. Peak strain plot for even-numbered passes (east to west) for EG-O-N1-1T.

Figure 41. Gage locations used for analysis.

xvi

ACKNOWLEDGMENTS

I wish to thank all those who helped me. Without them, I could not have completed this

project. This thesis utilized data collected during previous research sponsored by the

FAA and the Innovative Pavement Research Foundation (IPRF). I would like to thank my

adviser, Dr Shelley Stoffels. Dr. Stoffels’ motivation and help kept me going through the

project. I would also like to thank Dr. Mansour Solaimanian, Dr Farshad Rajabipour and

Dr. Angelica Palomino for serving as members on my thesis committee and providing

assistance with my thesis. I would also like to acknowledge Lin Yeh, Nima Ostadi,

Dinesh Ayyala and Nitya Ramadoss for their support throughout my graduate career at

the Pennsylvania State University. Finally, I would like to thank the Federal Aviation

Administration (FAA), the Innovative Pavement Research Foundation (IPRF) and the

prime contractor for the full-scale testing project, Quality Engineering Solutions Inc.

(QES), for making this study possible.

1

CHAPTER 1. INTRODUCTION

1.1 Background

Aviation activity in the United States accounts for approximately forty percent of all

commercial aviation and fifty percent of all general aviation activity in the world (FAA,

2008). As a key industry in the United States, air transportation has a significant impact

on the economy. Air transportation faces the high cost of shutdowns due to rehabilitation

of airfield pavements, which also results in unnecessary delays to the traveling public.

Military airfields face similar problems when operational efficiency is affected by poor

pavement condition. Therefore, airfield pavements should be designed for better

performance and constructed with a high degree of quality (Kohn and Tayabji, 2003).

Concrete has been widely used in the construction of airport pavements because of its

durability and capacity to sustain large loads (Portland Cement Association, 2010).

Crack generation and propagation are among the most serious problems in concrete

pavements (Darestani, 2007; Hossain et al., 2003). Therefore, safe operation of aircrafts

requires airfield pavement condition assessment with timely performance of pavement

maintenance and repair (Greene et al., 2004). Pavement distress, structural capacity,

friction, and roughness are important factors for condition assessment (Greene et al.,

2004). Once the pavement condition is properly assessed, appropriate maintenance and

rehabilitation can be programmed and designed.

With the onset of a new generation of aircraft gears, including large multi-axled gears,

such as the triple dual tandem, airport pavement design assumptions need to be re-

2

examined to determine the potential effects of gear spacing and load levels on the

development of stresses and resulting fatigue life of concrete slabs (Roesler, Hiller, and

Littleton, 2004). Extensive research on stress development and fatigue of airport concrete

slabs has been performed, including the work from Westergaard (1926), the Lockbourne

and Sharonville test sections (Parker et al. 1979), the PCA design for airfields (Packard

1973, 1974), and the work by Rollings (1981, 1986, 1990, 1998, 2001) for the U.S. Army

Corps of Engineers (USACOE). Airfield concrete pavement fatigue has been extensively

studied by Smith and Roesler (2003) and Littleton (2003) (Roesler, Hiller, and Littleton,

2004).

Although portland cement concrete pavements have been used for the construction of

airfield pavements for many decades, and typically perform well, eventually all

pavements require rehabilitation or replacement. An unbonded concrete overlay offers an

attractive alternative for its use as an airfield pavement rehabilitation technique for

several reasons. Unbonded concrete refers to concrete pavement constructed over an

existing concrete pavement. The concrete layers are separated by an interlayer, typically

of hot-mix asphalt concrete, which acts as a shear zone, enabling the concrete layers to

move independently of each other. This is why the term unbonded is used (Pavement

Technology Advisory, 2005). One of the reasons unbonded concrete overlays are suitable

for airfield pavements is that, by leaving the existing pavement in place, the in situ

conditions of subgrade and base layers are essentially undisturbed, minimizing any

opportunity for additional consolidation or settlement to take place. Another advantage is

that the existing pavement can be taken into consideration in structural design, typically

resulting in a thinner and less costly required pavement layer (Stoffels et al., 2008),

3

which may be especially important for the heavy loads and thick pavement structures

typically required for airfields.

The Innovative Pavement Research Foundation (IPRF) has an objective of improving the

current understanding of the influence of design parameters on unbonded concrete

overlays of airfield pavements, thus enabling improvement of design methodologies and

consideration of the new aircraft. In 2005, IPRF contracted for a study to prioritize and

conduct the necessary research activities for the design of unbonded concrete overlays for

airfields, including a series of full-scale tests to be built at the Federal Aviation

Administration (FAA) National Airfield Pavement Test Facility (Stoffels et al., 2008).

The construction of the first of the IPRF unbonded overlays took place between

November 2005 and May 2006. Three 6000-ft2 pavement cross-sections, with thicker

overlay on thinner underlay, equal thicknesses of overlay and underlay, and thinner

overlay on thicker underlay, were built, as shown in Figure 1. The full-scale loading was

performed from July 2006 until November 2006 to study the effects of the relative

thickness of the overlay and underlay, the correspondence between predicted and

measured responses, the relative effects of two gear configurations, and the relationship

of the failure mechanisms in the existing pavement and overlay.

4

Figure 1. Test item layout with as-built thicknesses.

Pavement instrumentation has recently become an important tool to monitor in-situ

pavement material performance and quantitatively measure pavement system response to

loading. Sensors, such as strain gages, have become available to monitor the health of the

pavement and its performance (Weinmann et al., 2004). Embedded strain gages have

been used to capture horizontal and vertical deformations of the pavement due to load on

the surface of the pavement. Strain gage response has been used to determine the effect of

static and fatigue cracks on a pavement (Roesler and Barenberg, 1999). The strain

responses can be used to verify the assumptions in mechanistic response models, whether

finite element or closed form solutions, and for development of relationships between

load-induced responses and structural performance.

In the IPRF unbonded overlay studies at the NAPTF, strain gages were installed in an

attempt to capture critical pavement responses under both twin dual tandem and triple

dual tandem gears. Strain responses from the strain gages were recorded. A typical

response from one of the stain gages is shown in Figure 2.

5

Figure 2. Typical strain gage response as shown in FAA TenView.

Most of the previous studies on strain response in concrete pavements have focused on

the peak measured response from the strain gages, as defined in Figure 2. Peak strain

response has been used widely in different models to study the fatigue behavior and life

for the pavement. For this thesis, different components of strain response were analyzed

and compared to peak strain and to observed performance, to determine whether

additional valuable information can be extracted from the strain gage data. For example,

some of the components of strain gage response used are illustrated in Figure 3. Those

components include the peak values of strain for each axle of the gear, the recovery

between axles, the pre-stress and post-stress peaks, duration and the areas of the various

portions of the strain responses. Details of the strain response components are developed

and described in Chapter 4.

6

Figure 3-a. Strain gage response components.

Figure 3-b. Cumulative area of a strain gage response shown as shaded portion of the

curve.

Although the responses from strain gages have been widely used, literature on the

repeatability of these measurements is limited (Gokhale et al., 2009). Factors, such as

inherent construction-related variability in pavement structure and materials, presence or

absence of moisture, layer thicknesses, joint position, slab curling, and gage orientation,

affect the variability of the responses from in-situ instrumentation. Therefore, for this

Pre-stress area Post-stress area

7

study, strain responses are considered on a statistical basis, rather than by detailed

comparison of selected typical responses.

The complete strain response was considered by statistical characterization of the various

peaks and component areas. By considering only the highest peak, other peaks and

recovery areas which may have potential information relative to pavement performance,

are neglected. Thus, different strain gage components, such as strain values for individual

axles, cumulative area, pre-stress area, post-stress area, % recovery and duration, are

characterized and correlated with the peak strain response for the strain gage. A

preliminary analysis of pavement performance was established with various identified

strain gage components.

1.2. Objectives.

The overall objective of this research is to examine and characterize the strain gage

responses from the full-scale testing of unbonded concrete overlays at the FAA NAPTF.

The responses are characterized not just in terms of peak strain, but in terms of multiple

peak values, recovery, and component areas of the responses. No such characterization

for concrete pavements has been found in the literature review. Therefore, the

development of the characterization of stain gage response is the primary objective and

product of this research.

The following questions are addressed using statistical characterization of the interpreted

strain data.

8

• Do the various components of the strain gage response, including peak strain

values for individual axles, cumulative area, pre-stress area, post-stress area,

percent recovery and duration, directly relate to the peak strain?

• How do the components of strain gage response change with different gear

configurations and different pavement cross-sections?

• If not directly related to peak strain, how do the components of the strain gage

response relate to observed performance in terms of cracking or structural

condition?

1.3. Scope

For this thesis, study is limited to analysis of the FAA NAPTF unbonded concrete

overlay strain gage data. Data before the first visually-observed crack was considered, as

these responses are most consistent and relate most directly to those that would be

predicted using a closed-form solution or finite element program for design purposes. For

the original study of the experiment, data was collected in different loading paths

consistent with the wander patterns on an airfield. The total number of loading passes

prior to the first observed crack for each test item is enumerated in Table 1. A test item is

defined as a unique combination of structural cross-section and gear configuration.

9

Table 1. Vehicle Passes Utilized for this Study

Test Item Cross Section Loading

Condition

Total Passes

before First

Observed

Crack

Passes Directly

over Strain

Gage

North 1 (N1) Thick overlay over

thin underlay

Triple dual

tandem 2046 281

South 1 (S1) Thick overlay over

thin underlay

Twin dual

tandem 2456 211

North 2 (N2)

Equal thicknesses

of overlay and

underlay

Triple dual

tandem 2046 211

South 2 (S2)

Equal thicknesses

of overlay and

underlay

Twin dual

tandem 4356 550

North3 (N3) Thin overlay over

thick underlay

Triple dual

tandem 2456 211

South 3 (S3) Thin overlay over

thick underlay

Twin dual

tandem 2456 340

Peak strain responses from all tracks for all gages were analyzed for initial loading,

which was performed with wheel loads of less than 40,000 pounds, as compared to the

extended fatigue loading at 50,000-pound wheel loads. Code in Excel’s Visual Basic for

Applications was developed to verify which strain gage responses were of the greatest

magnitude. The model was developed with the help of Pennsylvania State University’s

doctoral candidate Lin Yeh. It was found that the greatest responses occurred when the

outside wheel track was directly over the strain gages. Detailed characterization of the

strain responses was limited to those passes, as indicated in the final column of Table 1.

10

CHAPTER 2. LITERATURE REVIEW

2.1. Background.

Between 1927 and 1928, the first concrete airfield pavement was constructed at the Ford

Terminal, Dearborn, Michigan. Since then concrete pavements have been widely used at

both civilian and military airfields in the United States. The use of concrete for the

construction of runways, taxiways, and apron areas at airports has been popularized.

Naturally, there has been a great deal of evolution in the design and construction methods

applied to airport pavements. This evolution has been fueled by experience, field trials,

practice, and application of theoretical predictions (Kohn and Tayabji, 2003).

Furthermore, for many airfield applications, portland cement concrete is the preferred

material due to its much greater resistance to heat and fuel, in comparison to asphalt

concrete.

2.2 Concrete Properties.

Concrete properties such as concrete strength, modulus of elasticity, coefficient of

thermal expansion, shrinkage and concrete fatigue life play important roles to study the

possible fatigue failure mode of concrete pavements (Darestani, 2007). Tensile stresses at

the bottom of the concrete slab are generated by bending from the applied load on the

pavement. The load is transferred to sublayers by the bending action. In addition,

downward bending at slab corners or counter-flexure beyond the loaded area may induce

surface tensile stresses. Cracks on the top or bottom of the concrete surface are generated

when the flexural strength is exceeded by the stress induced by the applied load, or more

11

commonly from fatigue under repeated loading. Cracks propagate into the depth of the

concrete slab from the surface of the pavement, or vice versa. This is one of the main

reasons behind concrete deterioration, and thus flexural strength or modulus of rupture is

considered a major concrete property. Flexural Strength plays an important role in

concrete pavement design guides (Darestani, 2007), and in construction material

specifications for airfields.

Modulus of elasticity is a property of the concrete which reflects the stiffness of concrete

under static load. For a concrete of a given strength, Neville (1996) pointed that a higher

aggregate content results in higher modulus of elasticity of the concrete because normal

weight aggregate had a higher elastic modulus than hydrated cement paste (Tia et al.,

2005). Modulus of elasticity is dependent on the concrete materials and mix proportions

(ACI, 1992; Darestani, 2007). Thermal coefficient of the concrete depends on the

concrete constituents and moisture contents (Neville, 1983). Concrete’s coefficient of

thermal expansion is dependent on the coefficient of thermal expansion of cement paste

and aggregates. Cement paste has a coefficient of thermal expansion between 11×10-6

and 20×10-6

mm/mm/°C which is greater than aggregate thermal expansion coefficient

(Meyers, 1951). The type and percentage of aggregates in a concrete mix, associated with

curing method, can affect the magnitude of coefficient of thermal expansion in concrete

as thermal movement of the cement paste is restrained by aggregates (Darestani, 2007).

Three types of concrete shrinkage have been identified, namely, plastic shrinkage, drying

shrinkage, and carbonation shrinkage (Nawy, 2001). Plastic shrinkage happens during the

first hours after placing fresh concrete in the forms. It is affected by the ratio of the

12

surface area to the thickness of the concrete elements. Drying shrinkage, on the other

hand, occurs during the final setting of concrete when the cement hydration process is

nearing its completion. It is a decrease in the volume of the concrete element due to the

evaporation of moisture. Reaction between carbon dioxide (CO2) in the atmosphere and

calcium hydroxide in the cement paste causes carbonation shrinkage (Nawy, 2001;

Darestani, 2007). Shrinkage cracking may play a role in the initiation of subsequent load-

related cracking.

2.3. Concrete Pavement Fatigue.

Fatigue is failure of structural elements due to repeated loads, when the magnitude of

applied load is not large enough to cause immediate failure in the elements. Repeated

loads such as cyclic loads result in fatigue failure of the concrete under a load less than its

flexural strength (Karimov, 2004; Darestani, 2007). The maximum stress experienced by

the concrete during loading has been widely studied to define fatigue. A number of such

models for concrete fatigue have been developed.

2.3.1. Stress Ratio Models. Stress ratio (SR) has been defined as the ratio of the

maximum tensile bending stress experienced by the concrete slab to the concrete modulus

of rupture. Rao (2004) also described several fatigue curves for concrete pavement,

which have been developed using field and laboratory data that relate the stress ratio to

the number of loads until failure. These include the following (Rao et al., 2004).

1) Zero-Maintenance Design Beam Fatigue Model (Darter et al., 1976, 1977) ―

Concrete beams were used to develop this model. Complete beam fracture was taken as

13

the failure criterion. Bending beam equations were used to calculate the load stresses at

the bottom of the beam.

log Nf = 17.61 – 17.61 SR (1)

Where, Nf = Number of stress applications to failure for the given stress ratio SR.

2) Calibrated Mechanistic Design Field Fatigue Model (Salsilli et al., 1993). This

was developed using Corp of Engineers (COE) field aircraft data and American

Association of State Highway Officials (AASHO) Road Test data. Fifty percent slab

cracking was taken as the failure criteria in this method. The finite element program,

“ILLI-SLAB” was used to calculate load and temperature curling stresses at the edge.

log � = ��. �� (��)�.��

�.�� (2)

Where, P = Cracking probability.

3) ERES/COE Field Fatigue Model (Darter, 1988). This model was also developed

using Corp of Engineers (COE) field aircraft data. Similar to the Calibrated Mechanistic

Design Field Fatigue Model, the failure criterion was defined as fifty percent slab

cracking. Instead of ILLI SLAB as used in Calibrated Mechanistic Design Field Fatigue

Model, influence chart software, known as H-51 (Rao et al., 2004), was used to find

stress at the slab edge. In order to account for load transfer and support conditions, stress

was reduced by a factor of 0.75.

log N = 2.13 SR-1.2

(3)

14

4) Foxworthy Field Fatigue Model (Foxworthy 1985). This model is similar to

Calibrated Mechanistic Design Field Fatigue Model. It was developed using Corp of

Engineers (COE) field aircraft data. Similar to the Calibrated Mechanistic Design Field

Fatigue Model, the failure criterion was defined as fifty percent slab cracking. ILLI

SLAB was used to find load stress at the slab edge.

log � = 1.323 ! ��" + 0.588 (4)

5) PCA Beam Fatigue Model (Packard et al., 1983) ― This model is similar to the

Zero-Maintenance Design Beam Fatigue Model. Concrete beams were used to develop

this model. Complete beam fracture was taken as the failure criterion. Bending beam

equations were used to calculate the load stresses at the bottom of the beam.

log N = 11.737 - 12.077 SR for SR ≥0.55 (5)

N= � '.�(��)*��.'��(�

�.��+for 0.45 < SR < 0.55 (6)

N = unlimited for SR ≤0.45.

2.3.2. Slab Fatigue. Fatigue curves for beams always show lesser resistance to the

cracking as compared to fatigue curves as predicted for slabs (Roesler, 2006). Therefore,

fatigue curves for slabs cannot be predicted from beam fatigue curves, and this has been

confirmed by full scale testing on concrete slabs (Roesler et al., 1998, 2004, 2005).

Gaedicke (2009) studied a fracture-based method to predict the fatigue crack growth of

small-scale specimens which is extended to predict the crack growth in concrete slabs

supported by a soil foundation. Gaedicke (2009) developed fatigue model in which

concrete slabs were tested in the cyclic loading at the same level. This methodology

15

allows for the future prediction of the remaining fatigue life of new and partially-cracked

concrete slabs for a variety of pavement applications (Gaedicke et al., 2009).

2.3.3 Variable Amplitude Loading. Highways and airport pavements are subjected to

millions of cycles of repeated axle loads. Repetitive loading tends to deteriorate both

stiffness and the strength of the concrete as a result of accumulated damage (Yun et al.,

2005). Since most of the studies are based on constant amplitude loading instead of

variable amplitude loading, Yun (2005) studied accumulated damage and methods of

concrete testing under variable loading. Yun (2005) adopted the linear damage theory by

Miner, 1945 (Yun et al., 2005), nonlinear theory proposed by Oh, 1991 (Yun et al., 2005)

and the equivalent damage theory proposed by Marin (Yun et al., 2005). Yun (2005)

found that split tensile test results were equivalent to or better than the flexural tensile test

results for application to the equivalent damage theory. Thus, remaining life of concrete

under fatigue damage could be predicted by splitting tensile test (Yun et al., 2005).

2.3.4 Mechanistic Approach. Hiller and Roesler (2005) developed a mechanistic

approach in conjunction with Miner’s Hypothesis to calculate fatigue damage for

California rigid pavements. Hiller and Roesler (2005) predicted the location and

magnitude of concrete damage by using concrete fatigue transfer functions accounting for

stress range or maximum stress. It was observed that factors such as effective built-in

temperature difference, steer-drive axle spacing, load transfer level, lateral wheel wander

distribution, and climatic region controlled critical damage location and magnitude. Top-

down and bottom-up transverse, longitudinal, and corner cracking occurred in the slabs

with curling (Hiller and Roesler, 2005).

16

2.3.5 Numerical Approach (Finite-Element Methods). Kuo et al. (2004) investigated

the effects of impact load by landing of heavy aircrafts in which “the angle of landing by

a single-wheel impact load is greater than the static load for the same aircraft, with

inclusion of the effects of the shock-absorption system” on the runways. From the

numerical model calculated by Kuo et al. (2004), theoretical stresses and strains that were

computed by existing elastic-layer and finite-element computer programs indicated that

tensile strength is ten times more than that of static loading for the base of asphalt layer

and compression strains at the top of the subgrade (Kuo et al., 2004).

2.3.6 Fuzzy Logic. Tigdemir (2002) used fuzzy logic for estimating fatigue life from

deformation measurement by employing theory of fuzzy sets and by representing fatigue

life and deformation relations as a set of fuzzy rules. Fatigue life and deformation are

intimately related phenomena and a model involving a relationship between them can

best be derived by methods that explicitly take vagueness into account (Tigdemir et al.,

2002).

2.4. Airbus A-380 and Boeing 777

With local and regional aviation going through rapid changes, airline companies are

trying to improve their efficiency in order to remain profitable. Therefore, introduction of

supersized aircrafts like the new Airbus aircraft has been welcomed by many in the

aviation industry. But the introduction of new super-sized aircrafts has been challenging

to the civil engineering profession. Different landing gear configurations, in different

aircraft such as the Boeing 777 and the Airbus A-380, also affect the assumptions by

which engineers design the airport pavements (Khoon and Meng, 2005). Thus, loading

17

type and repetition have been important to a civil engineer in the fatigue study of airfield

pavements. Loading due to operation of a particular aircraft is dependent on the number

of the aircraft passes, the number and the spacing of the wheels on the aircraft main

landing gear, the width of tire-contact area, and the lateral distribution of the aircraft

wheel-paths relative to pavement centerline or guideline marks (HoSang, 1975).

Design and evaluation of an aircraft pavement has been based on the theoretical analysis

of the structural thickness coupled with full-scale tests on in-service pavements. The most

important considerations in the design methods are the gear and wheel arrangements

(Khoon and Meng, 2005). Previous design guides given by FAA made assumptions with

respects to wheel and gear configurations such as single wheel gear, dual wheel gear,

dual tandem gear and also specific charts for wide body aircrafts with double dual tandem

gears such as A-300 and B747. However, gear and wheel arrangement of Airbus A-380

and Boeing 777 with its triple dual tandem main gear are different when compared to

existing super-sized aircraft with twin dual tandem main gears. Triple dual tandem is

unique, with six wheels in the aircraft arranged as three pairs of wheels in a row. Figure 4

shows the arrangement for twin dual gear and triple dual gear for an aircraft. The

spacings vary between aircraft, and these spacings are not exactly representative of any

specific aircraft. They are, however, the exact gear configurations used during the full-

scale testing of unbonded overlays at the NAPTF.

18

Figure 4. Typical arrangement for twin dual tandem and triple dual tandem aircraft gears.

2.5. Current FAA Design Procedure

FAARFIELD (FAA Rigid and Flexible Iterative Elastic Layered Design) is an FAA

thickness design program that incorporates 3D finite element structural response

computations for rigid pavements and rigid overlays, and layered elastic analysis for

flexible pavements and overlays. FAARFIELD accompanies the FAA design procedure

AC 150/5320-6E. In FAARFIELD, thickness of the different layers can be input with

their modulus properties. It also requires the input of aircraft gears with wheel load

configurations and loads. After entering all the data and executing the program,

FAARFIELD gives the estimated life of the pavement. In order to do so, FAARFIELD

makes use of the 3D finite element programs (NIKE3D and INGRID) originally

developed by the U.S. Dept. of Energy Lawrence Livermore National Laboratory

(LLNL). These programs have been modified by the FAA for pavement analysis (FAA

2010). The 3D finite element program is used to compute the stresses in the rigid

Tire Contact Area: 214.6 in2

19

pavements and rigid overlays. During execution, FAARFIELD fetches the peak strain in

order to calculate the estimated life of the pavement.

2.6 Structural Condition Index

Rollings (1988) developed the Structural Condition Index (SCI) based on visual surveys

of the pavement condition. SCI is defined as a function of the number, width and type of

structural distresses in a pavement. SCI is derived from the distress definitions and deduct

values as determined by ASTM D 5340 Airport Pavement Condition Index Surveys

(Rollings, 1988). The Pavement Condition Index (PCI) is a numerical indicator that rates

the surface condition of the pavement. An objective and rational basis for determining

priorities and maintenance and repair needs is provided by the PCI (Standard Test

Method for Airport Pavement Condition Index Surveys, 2004). SCI is the component of

the PCI which addresses structural damage.

2.7. Strain Gage Characterization

There have been very few attempts to characterize strain gage response components such

as cumulative area, pre-stress area, post-stress area, % recovery and duration. Chou and

Wang (2005) analyzed data recorded by H-bar strain gauges, which were installed at

various depths of concrete pavement, generated by the taxing aircraft, including the

variation of strain induced by aircraft of different gear configurations. They concluded

that by looking at strain gage response, the main gear configuration of an aircraft can be

identified with a number of peaks. They also added that the time point when the peak

strain happened could be used to figure out the location of the loading.

20

Guo et al. (2002) studied the strain gage responses from three types of portland cement

concrete pavements, built at the Federal Aviation Administration’s (FAA) National

Airport Pavement Test Facility (NAPTF) in 2000, with traffic loads consisting of four-

and six-wheel carriages at 45,000 lbs. Though the data from 462 strain gages was

recorded during testing, Guo et al. (2002) could only study a small portion of the data.

Peak strain responses from all the axles in a gear configuration were studied to analyze

the corner crack in the pavement. They concluded that the measured strain gage

responses contain significant information which can help understand slab behavior under

simulated aircraft traffic loading.

It is evident that in these prior studies, peak strain has been widely investigated regarding

its effect on pavement structural responses and fatigue performance. Peak strain is

typically used because it defines the maximum stress developed during the course of

loading, which is considered as a critical component affecting the pavement life. . In

addition, with the assumptions needed for traditional closed-form solutions for concrete

slab analysis, results were often inherently limited to maximum values (Westergaard,

1948; Ioannides, 1985).

2.8. Summary of Important Findings from Literature Review

It can be summarized from the above literature that current procedures to develop

different fatigue models principally utilize the maximum peak strain response from

application of a gear load. There has been no or minimal attempt to consider the

accumulated peak responses from different gear configurations, the recovery between

axles, or the total strain amplitudes. Different types of models have been developed

21

including mechanistic approaches and different numerical approaches such as fuzzy logic

and finite element methods. All the models found during this literature review use peak

strain response, irrespective of the different gear configuration or different pavement

cross section. The FAA has upgraded FAARFIELD extensively to match the new gear

configuration and its impact on the calculation on the life of the pavement, and has made

the computer program part of the design procedure, as opposed to reliance on design

charts. FAARFIELD also relies on the peak strain response as the important factor in the

calculation of pavement estimated life, which may or may not be appropriate for all gear

configurations. FAARFIELD, however, is calibrated by the results of past field and

accelerated tests and performance observations.

22

CHAPTER 3. FULL-SCALE TESTING OF UNBONDED OVERLAYS

The Innovative Pavement Research Foundation (IPRF), in cooperation with the FAA,

with an objective of improving the current design methodology and understanding of the

influence of design parameters for airfield unbonded concrete overlays, initiated full-

scale testing at the NAPTF. Three different thickness concrete airport pavement sections

were constructed over the same subgrade with medium support. The sensor installation

included strain gages, linear position transducers and pressure cells to capture critical

pavement responses under twin dual tandem and triple dual tandem gears. The prime

contractor was Quality Engineering Solutions Inc. (QES). The Baseline Experiment was

initiated in September 2005 and the SCI Validation Study began in 2007. These results

serve to help in the future validation/calibration of concrete pavement structural response

models, and, hence, aid in the development of better tools for the design/evaluation of

airport pavement systems.

3.1. NAPTF

The FAA operates a state-of-the-art, full-scale pavement test facility dedicated solely to

airport pavement research which was constructed in April 1999. The National Airport

Pavement Test Facility (NAPTF) is located at the William J. Hughes Technical Center

near Atlantic City, New Jersey. High quality, accelerated test data from rigid and flexible

pavements are acquired at the facility by simulating aircraft traffic. NAPTF has a fully

enclosed instrumented test track, computerized data acquisition system, controlled

aircraft wander simulation, a test vehicle capable of simulating aircraft weighing up to

1.3 million pounds, wheel loads independently adjustable up to 75,000 pounds per wheel

23

and up to 20 test wheels capable of being configured to represent two complete landing

gears (FAA 2010).

3.2. Pavement Cross-Sections

An approximately 300-foot test pavement was constructed as a baseline experiment at

FAA’s testing facility. It was constructed on the medium subgrade, and had three

structural cross-sections as shown in Figures 5 and 6 (Stoffels et al., 2008). The

underlying slabs were not designed to be distressed (no shattered or cracked slabs), but to

have different joint matching conditions to determine how underlying discontinuities

(including cracks) affect the overlay’s performance. Having an intact underlay also

allows investigation of deterioration of the underlying pavement due to overlay loading

(Stoffels et al., 2008).

Thus, the final design for the Baseline Experiment consisted of six test items of 12 slabs

each. The test items were separated by transition slabs in both the longitudinal and

transverse directions. By providing two test items in each structural section, different

loading configurations could be applied. Figure 5 shows the three structural cross-

sections, numbered 1, 2 and 3 from west to east. Numbers in Figure 5 and Figure 6

indicate the width of the slabs in feet. Joint patterns were established to create matched

and mismatched joints in the underlying slab and the concrete overlay as shown in

Figures 5 and 6. All longitudinal joints are mismatched or offset as shown in Figure 6.

The transverse joints have some matched and some offset as shown in Figure 5. The

underlay joints were sawcut and not doweled. All overlay joints, both transverse and

longitudinal, were doweled and sawcut. The structural cross-section was loaded from

24

west to east and east to west. This may affect the strain gage response. For example, the

strain gage installed to the left of any joint in either overlay or underlay will be loaded

first before any of the axles reach the joint, while the same strain gage, when the test

vehicle is traveling in the reverse direction, will record the strain after the axles of vehicle

pass the matched or mismatched joint.

Figure 5 shows the transverse cross-section, indicating that each test item has two 12.5-ft

wide lanes, with a 10-ft transition slab between the test items. The test items are also

summarized in Table 2.

Figure 5. Experimental design configuration, showing transverse joint spacings. (Stoffels

et al., 2008).

Figure 6. End view of longitudinal joint locations for overlay and underlay slabs. (Stoffels et al.,

2008).

25

Table 2. Summary of Design Test Items for Baseline Experiment

Test Item

Designation

As-Built

Overlay

Thickness

(in)

As-Built

Underlay

Thickness

(in)

Nominal

Interlayer

Thickness

(in)

Planned Gear

Loading

North 1 (N1) 8.65 6.30 1.00 Triple Dual Tandem

South 1 (S1) 8.65 6.30 1.00 Twin Dual Tandem





3.3. Types of Loading and Aircraft Gears.

The NAPTF test vehicle has two carriages, which can be used for loading simultaneously

or independently. Each carriage also has flexibility in the choice of gear configuration,

the selection of wheel load level, and in carriage position. During loading, the FAA

personnel at the NAPTF monitored the control of the wheel load level and carriage

position. The wheel load levels were within control throughout the experiment, and thus

only the target wheel loads are reported here. Tire pressures were also monitored, with an

unloaded inflation pressure of 233 psi. The use of a constant inflation pressure means that

contact areas vary with load level. The test speed was three miles per hour. The gear

configurations used at the NAPTF during this experiment are illustrated in Figure 4 and

Figure 7.

26

Figure 7. Loading plan.

For failure loading, the triple dual tandem gear was used on the north test items, and the

twin dual tandem gear was used on the south test items. The remaining gears were used

only for preloading and static testing. The twin dual tandem and triple dual tandem gears,

while representative of true aircraft, do not have the exact dimensions of in-service

aircraft. The gear positions have been established such that the wheel and axle spacings

27

are the same for all configurations. The dual wheels are spaced at 54 inches center-to-

center. The spacing between axles is 57 inches, as illustrated in Figure 4.

The transverse position of the carriages was shifted between passes to simulate vehicle

wander. A wander pattern consisted of 66 passes, with each passage of the test vehicle to

the east being counted as a pass, and the return to the west counting as a second pass. The

carriage completed the two-pass down and back cycle before being shifted. A wander

pattern consisting of nine carriage (gear) positions, each shifted by 10.25 inches, was

used for all dynamic loading with the test vehicle. This wander pattern was previously

used by the FAA at the NAPTF, and was determined to be a reasonable estimation of real

airfield wander patterns. By using the same pattern, the ability to compare failure data

across construction and testing cycles at the NAPTF is also improved. The standard

wander pattern and track frequencies are shown in Figure 8.

Test vehicle loading of the test items occurred in a number of stages. The dates and wheel

loads for each stage of loading are summarized in Table 3. The number of wanders and

dates for the failure loading varied by test item. During the loading, when the direction

was from west to east, the data was recorded as odd-numbered passes. Then the load was

returned from east to west and recorded as even-numbered passes.

28

Figure 8. Wander pattern and track frequencies. (Stoffels et al., 2008).

Table 3. Loading Sequences (Stoffels et al., 2008)

Dates Wanders Wheel Loads

(lbs) Purpose

3/14/2006 44 passes 10000 Seating Load on Underlay

3/14/2006 to 3/15/2006 4 15000 Gear Response Loading on

Underlay

3/15/2006 NA 10000 Static Loading on Underlay

5/22/2006 to 5/23/2006 88 passes 10000 Seating Load on Overlay

5/23/2006 NA 15000 Static Loading on Overlay

5/23/2006 to5/24/2006 4 20000 Gear Response Loading on

Overlay

7/6/2006 NA 20000 Interaction Loading

7/6/2006 to7/12/2006

1

2

3

20000

30000

40000

Ramp-Up Loading

7/25/2006 to10/31/2006 Varied 50000 Failure Loading

29

3.4. Instrumentation.

3.4.1. Strain Gages. Although other instrumentation was utilized for the full-scale

testing, this thesis study focused exclusively on the strain gage responses. Strain gages

were used to measure the strain near the top and bottom of the slab. The frequency at

which the strain gage response was captured was 20 Hz. The number of data samples for

a stain gage ranged between 700 to 1000 for one pass of loading, thus data captured for a

strain gage response has a total duration of 35 seconds to 50 seconds. For this study,

strain gage model KM-100B by manufacturer Tokyo Sokki Kenkyujo was used.

A pair of embedded strain gages was installed at each location to measure strain near the

top and bottom of the slab in the longitudinal direction of the pavement. These gages

were usually located at the mid slab (transverse center of the slab) of the loaded joint.

Embedded strain gages were installed during the paving operation. During the slab

construction, the cans were used to install the strain gages in the pavement. These

instrumentation cans were carefully hand filled with concrete completely encasing the

strain gages. Next, concrete was piled around the cans to hold them in place. In order to

keep the instrumentation wiring out of the underlying slabs, trenches were dug in the base

course and wires placed within them. Prior to placement of the underlying slab, these

trenches were backfilled with concrete sand and compacted using hand tampers. Rebar

chairs were used to make certain the top gages were set at the proper height, one inch

below the top surface of the pavement layer. A spacer was used to make sure that the

bottom gage was completely covered by concrete and any part of the gage could not rub

against the surface of the substrate layer when the slab moves (Stoffels et al., 2008).

30

3.4.2. KM-100B. The KM-100B strain gage is designed to measure strain in materials

like concrete which undergo a transition from a complaint state to a hardened state. They

are impervious to moisture absorption and are stable for long-term strain measurement.

Figure 9 provides the schematic diagram of model KM-100B. The weight of the strain

gage is 75g. Table 4 gives the specification for the gage (KM Strain transducers manual,

2010). The wires for the full-bridge gages were run through channels in the asphalt

concrete interlayer to the sides of the pavement sections. The connections were

completed and the data acquired through the in-place system and computers at the

NAPTF.

Figure 9. Schematic diagram of strain gage model KM-100B (KM Strain transducers

manual, 2010).

Table 4. KM-100B Specifications (KM Strain transducers manual, 2010).

Capacity -5000X10-6

to +5000X10-6

Gauge length 100mm

Rated output(approximately) 2.5mV/V (+5000X10-6

)

Apparent elastic modulus 40N/mm2

Temperature range -20oC to 80

oC

Input/Output 350 ohm Full bridge

31

Strain generated in the specimen is transmitted to the gage (foil or wire resistor) when

expansion or contraction occurs. As a result, the resistor experiences a change in

resistance. This change is proportional to the strain as indicated in the following equation

Strain= Calibration Factor ∗ 2 ∗ ∆eE (7)

Where, ∆e:Voltage output; E:Exciting voltage(input voltage=5V),

Calibration factors for all strain gages are included in Appendix A.

For the baseline unbonded concrete overlay experiment, strain gages were installed in the

longitudinal direction of the pavement, placed in-situ near the top of the unbonded

overlay, the bottom of the overlay, the top of the underlay and the bottom of the underlay.

There were two additional strain gages installed at the top and bottom of underlay for test

item 2, as shown in Figure 10. Figure 10 shows the instrument locations relative to the

transverse and longitudinal end views of the pavement sections.

Figure 10-a. Strain gage locations for a test item, longitudinal design view.

asphalt

32

Figure 10-b. Strain gage locations for a test item, transverse design view.

Figure 11 shows a schematic diagram of the concrete slab of unbonded overlay over

underlay. When the surface of the overlay is loaded, the top of the overlay and the top of

the underlay go into compression, and the bottom of the overlay and the bottom of the

underlay go into tension. Due to the compression and tension, resistance of a strain gage

installed at top and bottom of overlay and underlay, shown in Figure 11, changed and

output voltage was recorded for the change in resistance. The output voltage was later

converted to engineering units by using equation 7. Appendix A gives the coordinates for

each strain gage.

Asphalt

concrete

33

Figure 11.Expected peak strain condition for a mid-slab edge strain gage during loading.

Individual strain gages were identified using the nomenclature shown in Figure 12.

Figure 13 shows the top-view instrumentation plan view of strain gage locations installed

in the underlying pavement, while Figure 14 provides the instrumentation locations for

the overlay. Figures 13 and 14 also show the locations for the linear position transducers

(LPT) installed in the experiment. The LPTs were also named in the same format as

strain gage, as shown in Figure 12, by replacing “EG” with “LPT.” However, the LPTs

have not been used for any study in the experiment.

34

Figure 12. Nomenclature for strain gage identification.

EG-O-N1-1B

Overlay as O

and Underlay

as U Bottom as B and Top as T

Test Item where strain

gage is installed Embedded

strain gage

35

Figure 13-a. Strain gage instrumentation plan for the underlay of the pavement for test items N1 and S1

(courtesy, prime contractor QES).

indicates strain gage location

36

Figure 13-b. Strain gage instrumentation plan at the underlay of the pavement for test items N2 and S2



37

Figure 13-c. Strain gage instrumentation plan at the underlay of the pavement for test items N3 and S3



38

Figure 14-a. Strain gage instrumentation plan at the overlay of the pavement for test items N1 and S1



39

Figure 14-b. Strain Gage instrumentation plan at the overlay of the pavement for test items N2 and S2



40

Figure 14-c. Strain Gage instrumentation plan at the overlay of the pavement for test items N3 and S3



41

3.5. Performance

Performance of the pavement was considered with number of passes to the first crack, and to

the point when SCI (Structural Condition Index) was equal to 80. At an SCI value of 80, the

pavement has started to crack and has one or two corner breaks or small cracks. Table 5

shows the SCI history for the test items with the interpolated number of passes required to

reach the SCI of 80 (Stoffels, 2008).

Table 5. SCI and Date History with First Crack and SCI=80

First Crack SCI=80

Test Item Passes Date Passes Date

North 1 2046 8/1/2006 2456 8/3/2006

South 1 2456 8/3/2006 3762 8/9/2006

North 2 2046 8/1/2006 2456 8/3/2006

South 2 4356 8/10/2006 5524 9/14/2006

North 3 2456 8/3/2006 2574 8/8/2006

South 3 2456 8/3/2006 3432 8/8/2006

42

CHAPTER 4. METHODOLOGY

4.1. Overview of Proposed Methodology

In order to achieve the objectives of this research, the methodology was developed as shown

in the following flowchart, Figure 15.

Figure 15. Flowchart of proposed methodology.

Characterize the Responses in Pavement from Embedded

Concrete Strain Gages

• Visual examination is performed for strain gage responses

from different locations.

• Ramp-up data was analyzed to check if response from

vehicle passes directly over the strain gages is highest as

compared to response from other vehicle wander patter

• Key response components are identified. For example.

• Peaks of pre-compression

• Peaks of tensile responses for each axle

• Recovery between axles

• Area of strain time response components

Examine Relationships between the Components of Responses

Relationships of the characterized strain response components are

examined statistically. For example:

• Peak strain vs. strain area

• Peak strain vs. percent recovery

• Component areas vs. percent recovery

Consider the Impacts of Gear and

Structural Cross-Section on the

Relationships between the Components

of Responses

Relationship to the Observed

Performance

Preliminary analysis of strain gage

response components is related to

observed performance of the structures.

43

4.2. Detailed Processing of Data

Strain responses from gages were collected in binary format for each pass. Each generated

pass has six files; each file containing specific sets of gages. In order to extract, analyze and

interpret the strain data, methods were followed as shown in the following flowchart, Figure

16.

Figure 16. Flowchart of detailed process.

Statistical analysis is done

to find relationship between

peak strain, % recovery and

other components of

responses. Relationship to

performance is also found. Functional

strain gage

response is

taken as input

Peak strain and

components of the

responses are found

Matlab is used to

process the file

Output is found

and analyzed

Stop

The components of

strain gage responses

are taken as input

Start

Binary data from

Strain gages is taken

as input

Engineering data is

obtained as excel

files

Data is fed in

TenView

Does pass

represent the

pass above the

strain gage?

Matlab is used to

process the input data The Excel file is

taken as input

Does strain

gage have

response?

Excel sheet is

taken as input

Skip this file and

Check another file

NO

YES

Skip this gage and

Check another

NO

YES

44

4.2.1. Data Extraction/Filtering. Extracting strain gage data from binary files is the first

step. Before the first crack, there were a total of 4356 vehicle passes. Each pass has 6 files

containing gage responses from different locations. FAA Tenview takes nearly 7 min to

extract one binary file to an Excel spreadsheet. In order to extract the entire datasets, it would

have taken over 508 hours of continuous extraction. Since FAA Tenview was not designed to

extract more than one file at time (the code was principally written for visually monitoring

data near the time of collection), it was necessary to modify and automate Tenview to increase

the speed and to extract all the possible passes. After Tenview was modified, responses were

removed from the gages other than strain gages, and stored for later analysis efforts. Then data

from vehicle passes directly above the strain gages were selected as input for the subsequent

steps.

4.2.2. Responses from Track 0. Since, track 0 (track number for the wander position when

the outside wheel track of the gear passes directly over the strain gages) responses were used

to process and analyze datasets, it was verified that the responses from track 0 yielded higher

response values as compared to responses from other datasets.

Before the full-scale baseline experiment started on 25th

July, 2006, the cross-sections were

preloaded with triple dual tandem and twin dual tandem gears at wheel loads in incremental

increases as listed in Table 3. The responses captured by the gages were used to check if the

track, when vehicle passes directly over the strain, gives higher and better peak strain

response. Peak strain response from all the gages was calculated for all passes. Then average

was taken for one full wander which contains a total of 66 passes for each gage and every

track. Figure 17, as prepared by doctoral candidate Lin Yeh, shows the response for test item

45

1 from triple dual tandem loading. Similar plots were prepared for all test items to verify that

responses were consistently higher at track 0 for all wheel loads, cross-sections and gage

positions

Figure 17. Strain gage average responses from one wander of ramp-up loading for gages in

test item north 1 with triple dual tandem loading (courtesy, Lin Yeh).

4.2.3. Matlab Programming. Development and programming of this methodology was a

primary part of the thesis work. In addition, potential descriptive components of the total

strain gage responses were developed, including peak values, recovery between axles, and

area components of the strain response. Initially, Visual Basic was used to further analyze the

data and find peak responses. Because of its capability as engineering software, Matlab was

chosen to do all the subsequent analysis including the computation of peak responses and the

-150

-100

-50

0

50

100

150

-4 -3 -2 -1 0 1 2 3 4

Str

ain

Gage

Aver

age

Res

pon

se o

f on

e w

an

der

of

40k

(mic

roS

train

)

Track Number

EG-U-N1-1 B EG-U-N1-1 T EG-U-N1-2 B EG-U-N1-2 TEG-U-N1-3 B EG-U-N1-3 T EG-O-N1-1 B EG-O-N1-1 TEG-O-N1-2 B EG-O-N1-2 T EG-O-N1-3 B EG-O-N1-3 T

46

component areas under the strain responses. Matlab programming helped to remove the strain

gage responses which were either bad or had no data. Also, it helped to automate the data as

two responses from strain gages at two different locations were not the same in pattern.

Initially, portions of the strain response graphs were defined. The definitions used are as

follows:

Baseline: As shown in Figure 18, baseline of a strain gage response is the value shown by an

unloaded strain gage. The baseline is used as a relative x-axis to calculate peak strain and

other components of the strain gage response.

Figure 18. Baseline for a strain gage response.

Percent recovery: Figure 19 shows a typical strain gage response when it was loaded with

triple dual tandem gear. As a result of loading by three axles, three strain peaks were

generated, shown in Figure 19 as “peak 1”, “peak 2” and “peak 3”. When the loading shifted

from one of three axles to the second axle, the pavement recovered with strain gage for that

time period. The recovery was recorded by the strain gage and is shown in Figure 19 as

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800 900

mic

roS

train

Number of Cycles

Baseline

47

“Remaining strain 1” and “Remaining strain 2”. In case of loading by twin dual tandem as

shown in Figure 20, two peak strain and one strain between axles were recorded. Average of

“Peak 1”, “Peak 2” and “Peak 3” was taken with the average of “Remaining strain 1” and

“Remaining strain 2” to define percent recovery in equation 1.

Figure 19. Peak strains and strain between axles for a strain gage response from triple dual

tandem loading.

Figure 20. Peak strains and strain between axles for a strain gage response from twin dual

tandem loading.

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800 900

mic

roS

train

Number of Cycles

Remaining Strain 1

Remaining Strain 2

Peak1Peak 2 Peak 3

-356

-354

-352

-350

-348

-346

-344

-342

-340

-338

0 100 200 300 400 500 600 700 800 900

mic

roS

train

Number of Cycles

Peak1 Peak2

Remaining Strain 1

48

% Recovery = 100 ∗ 9:;<=�; >;=?�9:;<=�; *;@=ABAB� )C<=AB9:;<=�; >;=? (8)

Cumulative strain area: Cumulative area of a strain gage response is the area between

baseline and the curve, shown as the shaded portion of a strain gage response in Figure 21.

Cumulative area, as a whole, represents time of loading, the strain response due to loading,

and recovery between axles.

Figure 21. Cumulative area for a strain gage response from triple dual tandem loading.

Pre-stress area: Pre-stress area of a strain gage response is the shaded portion of a strain gage

response as shown in Figure 22. The pres-stress component of curve is obtained due to the

flexural property of the concrete. When the load was just outside of the strain gage area, it

produced counter-flexure/reverse bending, causing strain gage to record pre-stress as

compression when concrete was going to be loaded in tension as shown in Figure 22.

49

Figure 22. Pre-stress area for a strain gage response from triple dual tandem loading.

Post-stress area: Post-stress area of a strain gage response is the shaded portion of a strain

gage response as shown in Figure 23. The post-stress component of the curve is obtained due

to the flexural property of the concrete. After the load was removed from the strain gage,

concrete, being a stiff material, jumped to recover its initial position. Due to this phenomenon,

post-stress was recorded by the strain gage.

Figure 23. Post-stress area for a strain gage response from triple dual tandem loading.

Duration: Duration is defined as the time period of loading on the strain gages by the triple

dual tandem or twin dual tandem gear as shown in Figure

Figure 24. Duration for a strain gage response from triple dual tandem loading.

In order to complete the Matlab programming

strain responses, it was necessary to recognize all types of patterns of observed responses

from the strain gages. Fortunately, it was possible to categorize the strain responses into a

reasonable number of response patterns. The discussion of typical procedures to obtain the

needed response components for the various patterns is provided in the following sections.

Code to find peaks and areas can be found in Appendix

4.2.3.1 Type 1 for North Test Item

A typical type 1 curve for triple dual tandem loading is shown in Figure 2

responses for which “peak 1”, “peak 2” and “peak 3”, shown in Figure 2

discerned. The recovery between axles

responses that are principally tensile or compressive strain.

0

5

10

15

20

25

30

35

40

0 100

mic

roS

train

50

Duration is defined as the time period of loading on the strain gages by the triple

dual tandem or twin dual tandem gear as shown in Figure 24.

. Duration for a strain gage response from triple dual tandem loading.

he Matlab programming to extract all the desired components from the

, it was necessary to recognize all types of patterns of observed responses


easonable number of response patterns. The discussion of typical procedures to obtain the


Code to find peaks and areas can be found in Appendix B.

North Test Items.

A typical type 1 curve for triple dual tandem loading is shown in Figure 25.

“peak 1”, “peak 2” and “peak 3”, shown in Figure 2

The recovery between axles, shown in Figure 25, is partial. Type 1 includes both

responses that are principally tensile or compressive strain.

200 300 400 500 600 700

Number of Cycles

Duration is defined as the time period of loading on the strain gages by the triple

. Duration for a strain gage response from triple dual tandem loading.

to extract all the desired components from the

, it was necessary to recognize all types of patterns of observed responses


easonable number of response patterns. The discussion of typical procedures to obtain the


. Type 1 includes

“peak 1”, “peak 2” and “peak 3”, shown in Figure 25, can be clearly

Type 1 includes both

700 800 900

51


The peak of the curve in Figure 25 is found by the following method.

1. Graph is normalized to remove noise from the curve.

2. Normalization is done by taking average of any continuous 12 points on the curve and

replacing it with first of the 12 points. Any point “i” on the curve is replaced by the

average of point “i” and 11 points following the point “i”.

3. First differentiation of the normalized curve is done.

4. After first differentiation, zero is found on the curve and second differentiation of the

curve is second for the points where first differentiation of the curve is equal to zero.

5. If second differential is less than zero then the point is top peak and if the second

differential is greater than zero then the point is bottom peak.

52

Area under the curve for strain responses of the type shown in Figure 25 is calculated by the

following methods.

1. First “base-line” for the curve is chosen by taking the average of first 100 value or last

100 values (average for last 100 values were taken in this case to find baseline). Red

horizontal line in Figure 25 resembles the baseline for the curve.

2. Graph was normalized using Matlab to remove noise.

3. In order to find the area of the curve, “base – line” for a graph is shifted to 0.

4. The graph is then divided in two graphs, one above base line and other below base

line.

5. The graph above base-line is named as Graph A and the graph below baseline as

Graph B.

6. Peak Values for Graph B (graph below “base-line”) are found.

7. Then area under the curve B was found using peak value. The Area is divided into

three areas, Area 1 (area between baseline and curve from point B1 to B2), Area2

(area between baseline and curve from point B2 to B3) and Area3 (area between

baseline and curve from point B3 to B4).

a) Type 1 has three top peak and four bottom peaks for the curve B.

b) In order to find the area1, area2 and area3, it is important to know the B1, B2, B3

and B4.

8. Same steps are followed for Graph A, i.e., peak values were found and the area under

the curve, i.e., pre-stress area and post-stress area, show in Figure 25, was found using

the peak value.

53

a) For pre-stress and post-stress, Graph A for every type has same combination of

two top peaks, shown as A1 and A2 in Figure 25, and four bottom peaks, when

strain is equal to baseline. So, there was no change in argument for this for any

types of the curve.

To find area values B1, B2, B3 and B4 are calculated. These values are used to calculate

recovery between axles.

4.2.3.2 Type 2 for North Test Items.

Type 2 curves are similar to type 1, except that full recovery of tensile or compressive strains

may occur between some axles, shown in Figure 26 as remaining strains touching the

baseline.


Area under the above curve for this type is calculated by following methods.

54


100 values (average for last 100 values were taken in this case to find baseline).




line.


Graph B.






a) Type 2 has three top peak and four bottom peaks for the curve B similar to TYPE1.

b) In order to find the area1, area2 and area3, it is important to know the B1, B2, B3

and B4.


the curve, i.e., pre-stress area and post-stress area, as shown in Figure 26, were found

using the peak value.

a) For pre-load and post-load, Graph A for every type has same combination of two top

peaks, A1 and A2 in Figure 26, and four bottom peaks, when strain is equal to

baseline. So, there was no change in argument for this for any types of the curve.

55

4.2.3.3 Type 3 for North Test Items

Responses were characterized as type 3 if a strain reversal (from either tension to compression

or from compression to tension) occurred between axles, shown by remaining strain 1 and

remaining strain 2 in Figure 27.








line.

56


Graph B.






a) Type 3 has three top peak and six bottom peaks for the curve B

b) In order to find the area1, area2 and area3, it is important to know the B1, B2, B3,

B4, B5 and B6.




b) For pre-stress and post-stress, Graph A for every type has same combination of two

top peaks, A1 and A2 in Figure 27, and four bottom peaks, when strain is equal to


4.2.3.4 Type 4 for North Test Items.

Responses were characterized as type 4 if a strain reversal (from either tension to

compression, or from compression to tension), shown by remaining strain2 in Figure 28,

occurred between only a single set of axles.

57








line.


Graph B.


58





a) Type 4 has three top peak and five bottom peaks for the curve B

b) In order to find the area1, area2 and area3, it is important to know the B1, B2, B3,

B4, B5 and B6.




c) For pre-stress and post-stress, Graph A for every type has same combination of two

top peaks, A1 and A2 in Figure 28, and four bottom peaks, when strain is equal to


4.2.3.5 Types 1, 2 and 3 for South Test Items.

Loading on the south test items was conducted with a twin dual tandem gear with two axles.

As a result, responses captured by the strain gages have 5 peaks which are categorized in

following types from 1 to 4. Finding areas for these types is similar to finding areas for the

response patterns observed in the north test items.

The following types of strain response patterns can be related to the typical response pattern

types for the north test items.

59

Figure 29. Strain gage response from twin dual tandem loading, type 1 and 2.

Figure 30. Strain gage response from twin dual tandem loading, type 3.

60

4.2.4. Statistical Analysis

After extracting and filtering data, statistical analysis on the data was done to extract

information from the data sets. There were a total of 64 strain gages installed for the Baseline

Experiment. It was important to analyze and characterize all the strain gages and to check the

behavior of the peak values, recovery between axles, and area components of the strain

response for each of the strain gages. Statistical analysis was done in Excel with the help of

Excel’s Visual Basic for Applications (VBA).

After characterizing the components of strain gage responses in terms of both mean and

standard deviation, each of the components was correlated to check its dependency on other

components. Then regression analysis was done on key components which are independent to

each other. To do the correlation and regression analysis, the whole dataset was divided by

pavement cross-section and loading configuration.

Strain gage response components were analyzed with number of passes to reach an SCI value

of 80 for the preliminary examination of the performance of the pavement at different cross-

sections with the two loading conditions. The numbers of passes to an SCI value of 80 were

chosen above number of passes to first crack because the first crack was not always seen

immediately during the course of loading on the test items. Practically, it was therefore not

possible to obtain the exact number of passes to the first crack. However, the number of

passes to “SCI=80” could be interpolated from SCI values at the end of loading for each day.

The effect of number of axles was included in all attempts to develop regression models for

the test items. This was necessary for a number of reasons, including that the total applied

61

gear load was directly proportional to the number of axles. For all regression models and

correlations, Excel 2007 was used with Visual Basic for Applications (VBA).

62

CHAPTER 5. ANALYSIS

The methodology provided in Chapter 4 was utilized to process all the strain gage responses,

and to extract the descriptive statistics for individual gages and for subsets of gages by

position and test item. The subsequent statistical correlations and analyses of those strain

components are discussed in the following sections.

5.1. Relationship of Components of Strain Gage Response to Peak Strain

Figure 31 shows the linear relationship between linear relationship between peak strain

response and cumulative area. From Figure 31, it can be observed that there is fairly constant

relationship between cumulative area and the peak response.

Table 6 includes the slope, intercept and R2 between cumulative area (Y) and peak strain (X)

for even-numbered passes for every loading date before first crack was developed. From the

table, it can be observed that cumulative area and the peak strain hold a fairly linear

relationship. Table 7 shows a similar relationship for odd-numbered passes.

63

Figure 31. Linear relationship between cumulative area and peak strain for EG-O-N1-1B.

Table 6. Linear Relation Chart for Even-numbered Passes with Area as Y and Strain as X for

EG-O-N1-1B

Date Slope Intercept R-Sq

25-Jul-06 37.91315 546.4988 0.735922

26-Jul-06 -4.86397 -969.346 0.084751

27-Jul-06 18.23942 -161.754 0.751819

28-Jul-06 23.68282 8.328725 0.679803

31-Jul-06 19.47439 -135.745 0.968097

1-Aug-06 31.90612 229.7597 0.836906

Table 7. Linear Relation Chart for Odd-numbered Passes with Area as Y and Strain as X for

EG-O-N1-1B


25-Jul-06 31.11671 353.3732 0.912336

26-Jul-06 36.2161 485.089 0.96907

27-Jul-06 30.31745 149.5481 0.411033

28-Jul-06 16.45665 -403.791 0.417443

31-Jul-06 22.24185 -349.741 0.738427

1-Aug-06 45.76946 758.1759 0.757807

y = 16.609x - 221

R² = 0.7302

y = 14.066x - 491.51

R² = 0.5175

-1400

-1200

-1000

-800

-600

-400

-200

0

-60 -50 -40 -30 -20 -10 0C

um

ula

tiv

e A

rea

(m

icro

Str

ain

-sec

-Hz)

Peak Strain (microStrain)

EG-O-N1-1 B

Even Numbered Passes(East to West)

Odd Numbered Passes(West to East)

64

Figures 32 and 33 show the change in the cumulative area and change in peak strain,

respectively, with accumulation of loading passes. In both plots, zero is plotted when there is

a bad response, and thus the peak reponse or the cumulative area of the chart can the found. It

can be easily concluded from the figures that both charts have similar patterns.

Figure 32. Cumulative area plot for odd-numbered passes(west to east) for EG-O-N1-1B.

Figure 33. Peak strain plot for odd-numbered passes(west to east) for EG-O-N1-1B.

-1400

-1200

-1000

-800

-600

-400

-200

0

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Cu

mu

lati

ve

Are

a(m

icro

Str

ain

-sec

-Hz)

Cumulative Passes

EG-O-N1-1 B

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

-60

-50

-40

-30

-20

-10

0

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Pe

ak

Str

ain

(m

icro

Str

ain

)

Cumulative Passes

EG-O-N1-1 B

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

65

Figure 32 and Figure 33 are summarized in Table 8. In Table 8, average, median and standard

deviation for the peak strain and cumulative area can be found. The ratio of the average,

median and standard deviation of the peak strain and the area is taken to observe if the

relationship is constant in both datasets. It can be observed that the ratio, which ranges

between 0.02 to 0.04, is found to be fairly constant for all the dates.


numbered Passes for EG-O-N1-1B.

Date

Peak Strain

(microStrain

)

Cumulative Area

(microStrain-sec-

Hz)

(Peak Strain)/

(Cumulative

Area)

25-Jul-06

Average -47.81 -1134.17 0.04

Median -48.15 -1147.69 0.04

Standard Deviation 2.49 81.28 0.03

26-Jul-06

Average -42.03 -1039.63 0.04

Median -44.29 -1130.16 0.04


27-Jul-06

Average -41.47 -1107.71 0.04

Median -41.44 -1120.80 0.04


28-Jul-06

Average -39.31 -1050.73 0.04

Median -39.53 -1047.51 0.04


31-Jul-06

Average -28.24 -977.91 0.03

Median -30.22 -1034.92 0.03


1-Aug-06

Average -36.35 -905.38 0.04

Median -36.34 -895.35 0.04


Figure 34 and Figure 35 show the change in the cumulative area and change in peak strain,

respectively, with advancement in loading for the loading passes which are east to west. In

both plots, zero is plotted when there is a bad response, and thus the peak reponse or the

66

cumulative area of the chart can the found. It can be easily concluded from these figures that

that both charts display a similar pattern. It can also be validated by the fact that area and peak

strain have a fairly linear relationship between them.

Figure 34. Cumulative area plot for even-numbered passes(east to west) for EG-O-N1-1B.

Figure 35. Peak strain plot for even-numbered passes(east to west) EG-O-N1-1B.

-1400

-1200

-1000

-800

-600

-400

-200

0

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Cu

mu

lati

ve

Are

a(m

icro

Str

ain

-se

c-H

z)

Cumulative Passes

EG-O-N1-1 B

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

-40

-35

-30

-25

-20

-15

-10

-5

0

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Pe

ak

Str

ain

(m

icro

stra

in)

Cumulative Passes

EG-O-N1-1 B

26

th J

uly

27

th J

uly

1st

Au

g

25

th J

uly

28

th J

uly

31

th J

uly

67

Figure 34 and Figure 35 can be summarized, as in Table 9. In Table 9, average, median and

standard deviation for the peak strain and cumulative area can be found. The ratio of the

average, median and standard deviation of the peak strain and the area is taken to observe if

the relationship is constant in both datasets. It can be observed that the ratio, which ranges

between 0.03 to 0.05, is found to be fairly constant for all the dates.


numbered for EG-O-N1-1B

Date

Peak Strain

(microStrain

)

Cumulative Area

(microStrain-sec-

Hz)

(Peak Strain)/

(Cumulative

Area)

25-Jul-06

Average -35.23 -789.09 0.04

Median -35.22 -793.53 0.04


26-Jul-06

Average -32.82 -809.73 0.04

Median -35.09 -785.00 0.04


27-Jul-06

Average -34.33 -787.92 0.04

Median -34.29 -780.51 0.04


28-Jul-06

Average -32.28 -756.20 0.04

Median -32.28 -753.09 0.04


31-Jul-06

Average -21.92 -562.60 0.04

Median -24.93 -623.98 0.04


1-Aug-06

Average -28.54 -680.68 0.04

Median -28.54 -682.28 0.04


The same steps are followed for the gage EG-O-N1-1 T, which is at the top of the overlay in

test item N1 for the first gage location. Similar results were obtained, noting that both the

cumulative area and peak strain represent compression.

68

Figure 36. Linear relationship between cumulative area and peak strain for EG-O-N1-1T.

Table 10. Linear Relation Chart for Even-numbered Passes with Area as Y and Strain as X for

EG-O-N1-1T


25-Jul-06 15.02375 966.1083 0.126205

26-Jul-06 18.94456 745.1289 0.95373

27-Jul-06 41.05093 -572.955 0.988942

28-Jul-06 35.74301 -537.484 0.02068

31-Jul-06 34.69165 31.29665 0.868023

1-Aug-06 23.56772 424.009 0.60587

y = 23.504x + 461.87

R² = 0.779

y = 28.713x + 187.6

R² = 0.8526

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60 70 80 90

Cu

mu

lati

ve

Are

a (

mic

roS

tra

in-s

ec-

Hz)

Peak Strain(microStrain)

Even Numbered Passes(East to West)

Odd Numbered Passes(West to East)

EG-O-N1-1 T

69

Table 11. Linear Relation Chart for Odd-numbered Passes with Area as Y and Strain as X for

EG-O-N1-1T


25-Jul-06 15.59121 836.0566 0.721136

26-Jul-06 49.95582 -1003.17 0.950624

27-Jul-06 44.60814 -726.611 0.95393

28-Jul-06 -3.36224 2146.333 0.023538

31-Jul-06 39.09608 -124.715 0.94174

1-Aug-06 46.99594 -1050.08 0.811839

Figure 37. Cumulative area plot for odd-numbered passes (west to east) for EG-O-N1-1T.

0

500

1000

1500

2000

2500

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Cu

mu

lati

ve

Are

a (

mic

roS

tra

in-s

ec-

Hz)

Cumulative Passes

EG-O-N1-1 T

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

70

Figure 38. Peak strain plot for odd-numbered passes (west to east) for EG-O-N1-1T.


numbered Passes for for EG-O-N1-1T

Date

Peak Strain

(microStrain

)

Cumulative Area

(microStrain-sec-

Hz)

(Peak Strain)/

(Cumulative

Area)

25-Jul-06

Average 53.24 1666.09 0.03

Median 53.45 1667.00 0.03


26-Jul-06

Average 54.43 1717.34 0.03

Median 53.94 1710.37 0.03


27-Jul-06

Average 56.30 1784.84 0.03

Median 56.18 1775.49 0.03


28-Jul-06

Average 60.69 1942.29 0.03

Median 60.14 1939.42 0.03


31-Jul-06

Average 41.33 1491.14 0.03

Median 40.76 1281.70 0.03


1-Aug-06

Average 63.73 1945.05 0.03

Median 63.71 1949.80 0.03


0

10

20

30

40

50

60

70

80

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Pe

ak

Str

ain

(mic

roS

tra

in)

Cumulative Passes

EG-O-N1-1 T

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

71

Figure 39. Cumulative area plot for even-numbered passes (east to west) for EG-O-N1-1T.

Figure 40. Peak strain plot for even-numbered passes (east to west) for EG-O-N1-1T.

0

500

1000

1500

2000

2500

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Cu

mu

lati

ve

Are

a(m

icro

Str

ain

-sec

-Hz)

Cumulative Passes

EG-O-N1-1 T

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

0

10

20

30

40

50

60

70

80

90

0 132 264 396 528 660 792 924 1056 1188 1320 1452 1584 1716 1848 1980 2112 2244

Pe

ak

Str

ain

(mic

roS

tra

in)

Cumulative Passes

EG-O-N1-1 T

25

th J

uly

26

th J

uly

27

th J

uly

28

th J

uly

31

th J

uly

1st

Au

g

72


numbered Passes for EG-O-N1-1T

Date

Peak Strain

(microStrain)

Cumulative Area

(microStrain-sec-

Hz)

(Peak Strain)/

(Cumulative

Area)

25-Jul-06

Average 55.96 1806.83 0.03

Median 56.15 1801.46 0.03


26-Jul-06

Average 50.98 1710.90 0.03

Median 57.35 1844.29 0.03


27-Jul-06

Average 62.02 1973.12 0.03

Median 62.48 1976.71 0.03


28-Jul-06

Average 69.18 1935.29 0.04

Median 69.48 2159.26 0.03


31-Jul-06

Average 39.70 1408.43 0.03

Median 41.50 1275.18 0.03


1-Aug-06

Average 76.12 2217.95 0.03

Median 76.05 2212.81 0.03


The same type of analysis was performed for all the gages at different locations for different

cross-section with different loading conditions. It was found that peak strain holds a strong

relationship with cumulative area. The results from the individual gage analyses are included

in Appendix C.

5.2. Relationships between Peak Strain and other Components of Strain Gage Response

In order to show correlation between peak strain and other components of the peak responses,

the following data groups were prepared:

• Gages on top of overlay in test items 1 (thick overlay over thin underlay)

73

• Gages on top of overlay in test items 2 (equal thickness overlay and underlay)

• Gages on top of overlay in test items 3 (thin overlay over thick underlay)

• Gages on top of overlay in north test items (triple dual tandem)

• Gages on top of overlay in south test items (twin dual tandem)

• Gages on bottom of overlay in test items 1 (thick overlay over thin underlay)

• Gages on bottom of overlay in test items 2 (equal thickness overlay and underlay)

• Gages on bottom of overlay in test items 3 (thin overlay over thick underlay)

• Gages on bottom of overlay in north test items (triple dual tandem)

• Gages on bottom of overlay in south test items (twin dual tandem)

• Gages on top of underlay in test items 1 (thick overlay over thin underlay)

• Gages on top of underlay in test items 2 (equal thickness overlay and underlay)

• Gages on top of underlay in test items 3 (thin overlay over thick underlay)

• Gages on top of underlay in north test items (triple dual tandem)

• Gages on top of underlay in south test items (twin dual tandem)

• Gages on bottom of underlay in test items 1 (thin overlay over thin underlay)

• Gages on bottom of underlay in test items 2 (equal thickness overlay and underlay)

• Gages on bottom of underlay in test items 3 (thin overlay over thick underlay)

• Gages on bottom of underlay in north test items (triple dual tandem)

• Gages on bottom of underlay in south test items (twin dual tandem)

• Gages by their particular location, as shown in Figure 41 by pavement cross-section

• Gages by their particular location, as shown in Figure 41 by loading condition

74

Figure 41. Gage locations used for analysis.

Correlation charts between peak strain and cumulative area, peak strain and % recovery, peak

strain and duration and % recovery and area was tabulated for different test items and

different loading conditions for top of overlay, top of underlay, bottom of overlay, and bottom

of underlay. There was no correlation found between peak strain and duration, and a very

weak correlation was found between peak strain and % recovery. Also, a strong correlation

was obtained between peak strain and cumulative area as shown in Table 14. In Table 14, data

grouped by test items contain the particular test item with both north and south loading

conditions, while data grouped by loading condition include all test items (the three structural

cross-sections) subjected to the particular loading.

75

Table 14. Correlation between Peak Strain and Cumulative Area

Correlation

Coefficient

Groups

Test Item 1 Test Item 2 Test Item 3 North Loading South Loading

>=0.95 Bottom of Overlay Bottom of

Underlay Bottom of

Overlay

>=0.90

and <0.95

Top of Overlay,

Top of Underlay,

Bottom of Underlay

Bottom of

Overlay

Top of

Overlay,

Bottom of

Underlay

Bottom of

Overlay, Bottom

of Underlay

>=0.85

and <0.90

Top of Overlay,

Top of Underlay Bottom of

Underlay

Bottom of

Overlay, Top

of Underlay

Top of Overlay,

Top of Underlay

>=0.80

and <0.85 Top of Overlay

>=0.75

and <0.80

Top of

Underlay

Correlation coefficient between % recovery and cumulative area was found to be varied. It

ranges from 0.85 to as low as 0.05. This relationship is summarized in Table 15.

Table 15. Correlation between % Recovery and Cumulative Area

Correlation

Coefficient Groups

Test Item 1 Test Item 2 Test Item 3 North South

>=0.80 and

<0.85 Top of Underlay

>=0.70 and


>=0.65 and


>=0.55 and

<0.60

Bottom of

Underlay

>=0.50 and

<0.55

Bottom of

Overlay, Bottom

of Underlay

Bottom of

Underlay Bottom of

Overlay Top of Overlay

>=0.45 and

<0.50

Bottom of

Underlay Bottom of Overlay

>=0.40 and

<0.45 Top of Overlay

<0.35 Top of Overlay,

Bottom of

Overlay

Top of Overlay,

Top of Underlay Bottom of

Overlay

Top of Overlay,

Top of Underlay,

Bottom of Underlay

76

Correlation for each gage located at a particular relative location, as shown in Figure 41, is

also completed. The correlation tables for those components can be found in tables 16 through

19.

Table 16. Correlation between Peak Strain and Cumulative Area by Strain Gage Locations

Correlation

Coefficient

Groups


=1 6 12 2, 5, 6, 7, 13 5 12

>=0.95 1, 10, 11, 13 3, 11 3, 8, 11 7

>=0.90 and <0.95 4, 11 4, 6, 7 4 2 1, 4, 5, 13

>=0.85 and <0.90 1, 5, 8, 12 3, 5, 8, 14 1 6, 13, 14

>=0.80 and <0.85 13 2 12 3

>=0.75 and <0.80 7 8 6, 8, 10

>=0.70 and <0.75 1, 10 2, 9, 11

>=0.65 and <0.70 2,3, 9

>=0.60 and <0.65 12 4

>=0.35 and <0.40

>=0.05 and <0.35 9 7, 9

<0.05 9

Table 17. Correlation between Peak Strain and % Recovery by Strain Gage Locations

Range of

Correlation

Coefficient

Groups


1

>=0.95 2, 7, 11

>=0.90 and <0.95 11

>=0.85 and <0.90 10, 13, 3, 5

>=0.80 and <0.85 8, 12, 13 8

>=0.75 and <0.80 7 6 5

>=0.70 and <0.75 5 4, 12

>=0.65 and <0.70 6 4 3, 12

>=0.60 and <0.65 13 11

>=0.55 and <0.60 9 10 14

>=0.50 and <0.55 4, 7 4, 6

>=0.45 and <0.50 1

>=0.40 and <0.45 7 8, 12

>=0.35 and <0.40 6 11

<0.35 1, 2, 3, 8,

12

1, 2, 3, 5, 8, 9, 11 1, 9, 14 2, 4, 5, 6, 9,

13

1, 2, 3, 7, 9, 10,

13

77

Table 18. Correlation between Peak Strain and Duration by Strain Gage Locations

Correlation

Coefficient

Groups


=1 7

>=0.95 11

>=0.90 and <0.95 13 8, 10

>=0.85 and <0.90 13 5

>=0.80 and <0.85 7 2

>=0.75 and <0.80 1 8, 12 5 5

>=0.70 and <0.75 13 10

>=0.65 and <0.70 2, 3 3 11 8

>=0.60 and <0.65 7, 9 4

>=0.55 and <0.60 8 3 14

>=0.50 and <0.55 4

>=0.45 and <0.50 4 9 12

>=0.40 and <0.45 1 3 8, 11

>=0.35 and <0.40 6, 7, 9

<0.35 5,6, 11, 12 2, 5, 9, 11,

12, 14 1, 2, 6

1, 4, 6, 7, 9,

13

1, 2, 3, 4, 6,

10, 12, 13

Table 19. Correlation between % Recovery and Area by Strain Gage Locations

Correlation

Coefficient

Groups


=1

>=0.95 7, 11

>=0.90 and <0.95 11 10 12 8, 10

>=0.85 and <0.90 13 3, 5 7

>=0.80 and <0.85 7 2, 8 5

>=0.75 and <0.80 6, 13

>=0.70 and <0.75 5, 7 12 9, 9, 12

>=0.65 and <0.70 6, 9 4 3, 11

>=0.60 and <0.65 4

>=0.55 and <0.60 2, 3

>=0.50 and <0.55 4 13

>=0.45 and <0.50 4, 8 2, 3

>=0.40 and <0.45 4

>=0.35 and <0.40 1, 13 1, 5, 8, 14 6, 7, 12

<0.35 12 2, 3, 6, 9, 11 1 1, 2, 5, 6, 13 1, 8, 9, 10, 11, 14

78

Multiple regression analysis of peak strain response was done by taking the strain gage

components as predictors. Since it was found that peak strain is strongly correlated to

cumulative area, also shown by individual gages, as described in section 5.1., cumulative area

was not taken as one of the predictors for the multiple regression analysis, as it would neglect

other factors used in the analysis. Therefore, the regression analysis of peak strain(Y) was

done with % recovery, duration and number of axles.

It was found that the R2

value for multiple regression analysis depended on the correlation of

variables used in regression analysis. For example, Table 20 shows the correlation between

different variables, and regression analysis for the components of gage response from the top

of the overlay in test items 3. As included in the table, correlation between peak strain and %

recovery, and for duration and number of axles is poor. The R2

for regression analysis of %

recovery, duration and number of axles as predictors for peak strain(Y) is 0.09, as shown in

Table 21, thus showing no relation by mimicking the correlation found independently.

Table 20. Correlation between Different Components of Peak Responses

Passes

to First

Crack

Passes to

SCI=80 Peak Strain

(microStrain) %

Recovery

Duration

(sec)

Cumulative

Area

(microStrain-

sec-Hz)

Number

of Axles

Passes to First Crack 1

Passes to SCI=80 1 Peak Strain

(microStrain) -0.22 1

% Recovery 0.39 -0.09 1

Duration(sec) -0.08 0.22 -0.03 1 Cumulative Area

(microStrain-sec-Hz) -0.6 0.82 -0.36 0.18 1

Number of Axles -1 0.22 -0.39 0.08 0.6 1

79

Table 21. Regression Statistics for Analysis of % Recovery, Duration and Number of Axles as

Predictors for Peak Strain(Y)

Regression Statistics

Multiple R 0.3

R Square 0.09

Adjusted R Square 0.09

Standard Error 19.76

Observations 1095

But, on other hand, for cases in which any of the variables, % recovery, duration and number

of axles, are strongly related to peak strain as in Table 22, then R2

for multiple regression

analysis is found to be high. For example, Table 23 shows the correlation and regression

statistics between the components of the strain gages from the top of the underlay in test items

2. Peak strain is fairly well correlated to % recovery, duration and number of axles, and thus

impact of the correlation can be seen in the R2.

Table 22. Correlation between Different Components of Strain Gage Responses from Top of

Underlay Passes

to First

Crack

Passes

to

SCI=80


Cumulative

Area (microStrain-

sec-Hz)

%

Recovery

Duration (sec)

Number

of

Axles

Passes to First

Crack 1.00

Passes to SCI=80 1.00 1.00 Peak Strain

(microStrain) 0.75 0.75 1.00

Cumulative Area

(microStrain-sec-

Hz)

0.47 0.47 0.86 1.00

% Recovery -0.58 -0.58 -0.69 -0.74 1.00 Duration (sec) -0.92 -0.92 -0.56 -0.25 0.39 1.00 Number of Axles -1.00 -1.00 -0.75 -0.47 0.58 0.92 1.00

80

Table 23. Regression Statistics for Analysis of % Recovery, Duration and Number of Axles as

Predictors for Peak Strain(Y)


Multiple R 0.84

R Square 0.71

Adjusted R

Square 0.71

Standard Error 5.64

Observations 2874

Also, multiple regression analysis was done for % recovery (Y) with the predictors as area

components. There was no relationship found for that analysis.

5.3. Strain Gage Response with Change in Loading and Cross-Sections.

To show how the components of strain gage responses changes with different gear

configuration with different pavement cross-section, mean and standard deviation of

components of gage response at top of overlay, top of underlay, bottom of overlay, and

bottom of underlay are tabulated in Tables 24 through 27. Mean and standard deviation of

gage response components for every individual gage were also calculated.

81

Table 24.Mean and Standard Deviation of Components of Gages’ Response at Top of Overlay

Structural Cross-section 1 Structural Cross-section 2 Structural Cross-section 3

North

Loading(N1)

South

Loading (S1)

North

Loading (N2)

South

Loading (S2)

North

Loading (N3)

South

Loading (S3)

Mean StDev Mean StDev Mean StDev Mean StDev Mean StDev Mean StDev

Pre-stress Peak

(microStrain) -22 10 -15 1 -11 3 -9 2 -11 3 -11 6

Peak 1

(microStrain) 62 17 44 7 45 4 34 4 57 10 45 16

Remaining peak 1

(microStrain) 22 20 16 4 12 7 8 7 11 9 -1 11

Peak 2

(microStrain) 56 17 44 8 40 4 31 4 52 10 36 14

Remaining peak 2

(microStrain) 17 18 N/A N/A 10 7 N/A N/A 8 8 N/A N/A

Peak 3


Post-stress Peak

(microStrain) -18 9 -14 1 -8 2 -5 4 -7 2 -7 5

Pre-Tension Area

(microStrain-sec-

Hz)

-524 265 -442 38 -185 51 -163 69 -72 35 -169 197

Post-Tension Area

(microStrain-sec-

Hz)

-708 341 -484 45 -416 115 -297 117 -453 125 -314 178

Average Peak

(microStrain) 58 16 44 8 41 4 33 4 52 10 40 14

Average

"Recovery "

Strain

(microStrain)

19 19 16 4 11 7 8 7 10 8 -1 11

Peak Strain

(microStrain) 62 16 45 8 45 4 34 4 57 10 45 16

% Recovery 70% 24% 65% 6% 74% 17% 75% 20% 83% 13% 99% 19%

Table 24 includes the mean and standard deviation of various components of strain gage

response at the top of the overlay slab. The average and standard deviation of the response

components for loading by the triple dual tandem gear (N1) were higher than for the loading

by the twin dual tandem gear (S1) for structural cross-section 1, that is thicker overlay over

thinner underlay. For structural section 2, i.e., equal thickness of overlay and underlay, the

average of the strain gage response components was higher for the north test item (N2), i.e.,

loading with the triple dual tandem, as compared to loading by the twin dual tandem gear

82

(S2). But the standard deviation of the components was found to be almost the same for both

loading conditions. For structural cross-section 3, i.e., thinner overlay over thicker underlay,

the average of the components, except pre-tension area and % recovery, was higher for the

north test item (N3), i.e., loading with the triple dual tandem, as compared to loading by the

twin dual tandem gear (S3). However, the standard deviation of the components was higher

for loading by the twin dual tandem gear (S3) than for loading by the triple dual tandem gear

(N3).


Overlay


North

Loading(N1)

South

Loading (S1)

North

Loading (N2)

North

Loading(N1)

South

Loading (S1)

North

Loading (N2)


Pre-stress Peak

(microStrain) 29 5 25 4 18 5 17 4 19 5 37 9

Peak 1

(microStrain) -35 45 -25 11 -18 5 -22 9 -43 27 -19 10

Remaining peak 1

(microStrain) 5 22 0 Mean -2 3 5 8 10 6 32 8

Peak 2

(microStrain) -34 47 -32 14 -18 5 -25 11 -45 26 -27 9

Remaining peak 2

(microStrain) 1 24 N/A N/A -5 4 N/A N/A 7 5 N/A N/A

Peak 3

(microStrain) -45 51 N/A N/A -21 6 N/A N/A -54 29 N/A N/A

Post-stress Peak

(microStrain) 15 3 16 4 9 3 10 6 13 3 29 9

Pre-compression Area

(microStrain-sec-Hz) 1116 683 876 174 633 252 602 185 724 146 666 361

Post-compression Area


Average Peak

(microStrain) -38 47 -28 12 -19 5 -23 10 -47 27 -23 5

Average "Recovery "

Strain

(microStrain)

3 23 0 4 -3 3 5 8 8 6 32 8

Peak Strain

(microStrain) -33 45 -25 11 -18 5 -21 10 -43 27 -15 6

% Recovery 128% 25% 101% 22% 85% 17% 137% 56% 126% 18% 250% 59%

Table 25 provides the mean and standard deviation of components of strain gage response at

the bottom of the overlay. The average and standard deviation of the response components for

83

loading with the triple dual tandem gear (N1) were higher than for the loading with the twin

dual tandem (S1) for structural cross-section 1, i.e., thicker overlay over thinner underlay

except for the post-compression area which had lower average and standard deviation for

loading by triple dual tandem. For structural cross-section 2, i.e., equal thickness of overlay

and underlay, the average of the strain gage response components was lower for north test

item (N2) , i.e., loading with triple dual tandem, as compared to loading by twin dual tandem

(S2) gear except for the pre-compression area which had higher average and standard

deviation for loading by triple dual tandem (N2). For structural cross-section 3, i.e., thinner

overlay over thicker underlay, pre-compression area showed higher mean and lower standard

deviation for north test item (N3). Post-compression area, % recovery and average peak

average “remaining” strain showed lower mean and standard deviation for north test item

(N3) than south test item (S3). Peak strain for north test item (N3) showed higher mean and

standard deviation than strain for south test item (S3).

84

Table 26. Mean and Standard Deviation of Components of Gage Response at Top of Underlay


North

Loading(N1)

South

Loading (S1)

North

Loading (N2)

North

Loading(N1)

South

Loading (S1)

North

Loading (N2)


Pre-stress Peak

(microStrain) -22 8 -20 3 -23 7 -18 4 -24 6 -19 3

Peak 1

(microStrain) 17 8 33 8 23 10 41 6 31 10 44 10

Remaining peak 1

(microStrain) 0 6 18 3 1 8 18 10 18 8 34 5

Peak 2

(microStrain) 19 8 48 10 24 10 52 6 39 12 54 11

Remaining peak 2


Peak 3


Post-stress Peak

(microStrain) -14 6 -12 4 -13 5 -9 6 -14 3 -13 3

Pre-tension Area

(microStrain-sec-Hz) -676 265 -569 117 -610 192 -509 136 -801 236 -615 146

Post-tension Area


Average Peak

(microStrain) 23 8 40 9 27 9 47 6 38 11 49 10

Average "Recovery "

Strain

(microStrain)

2 5 18 3 3 7 18 10 21 9 34 5

Peak Strain

(microStrain) 33 10 48 10 35 9 52 6 44 13 54 10

% Recovery 95% 18% 54% 10% 97% 31% 62% 18% 46% 8% 30% 6%

Table 26 includes the mean and standard deviation of components of gage response at top of

underlay. The average and standard deviation of pre-tension area, post-tension and %

recovery for loading by triple dual tandem gear (N1) were higher than the loading by twin

dual tandem (S1) for structural cross-section 1, i.e., thicker overlay over thinner underlay

except. The average peak had lower mean and standard deviation for north test item (N1).

Peak Strain had lower peak and same standard deviation for south test item (S1) and north test

item (N1). For structural cross-section 2, i.e., equal thickness of overlay and underlay, and

structural cross-section 3, i.e., thinner overlay over thicker underlay, the same relationships

were observed as in the case of structural cross-section 1.

85


Underlay


North

Loading(N1)

South

Loading (S1)

North

Loading (N2)

North

Loading(N1)

South

Loading (S1)

North

Loading (N2)


Pre-stress Peak

(microStrain) 17 5 16 4 23 4 17 2 13 4 16 3

Peak 1

(microStrain) -16 8 -29 13 -17 5 -28 9 -14 7 -25 3

Remaining peak 1

(microStrain) -1 6 -16 7 8 4 -8 10 -6 5 -18 1

Peak 2

(microStrain) -14 8 -32 15 -13 4 -31 11 -15 7 -28 3

Remaining peak 2

(microStrain) 0 8 N/A N/A 9 5 N/A N/A -7 5 N/A N/A

Peak 3

(microStrain) -19 10 N/A N/A -17 5 N/A N/A -16 7 N/A N/A

Post-stress Peak

(microStrain) 9 3 10 4 16 3 12 7 8 2 10 2



Post-compression Area


Average Peak

(microStrain) -16 8 -31 14 -16 4 -30 10 -15 7 -26 2

Average "Recovery "

Strain

(microStrain)

0 7 -16 7 9 4 -8 10 -7 4 -18 1

Peak Strain

(microStrain) -12 7 -29 14 -13 4 -28 9 -13 6 -25 2

% Recovery 124% 64% 48% 6% 162% 36% 78% 27% 59% 12% 30% 5%

In Table 27, for gages at bottom of underlay the average and standard deviation of post-

compression area and % recovery for loading by triple dual tandem gear (N1) were higher

than the loading by twin dual tandem (S1) for structural cross-section 1, i.e., thicker overlay

over thinner underlay. The average and standard deviation of average peak, average

“remaining” strain and peak strain for loading by triple dual tandem gear (N1) were lower

than the loading by twin dual tandem (S1) for a structural cross-section 1. For structural cross-

section 1, a lower average and higher standard deviation for pre-compression area were

86

observed for loading by triple dual tandem gear (N1). For structural cross-section 2, i.e., equal

thickness of overlay and underlay, the same relationship was observed as was seen with test

item 1, except for pre-compression area, which has the same average and higher standard

deviation for loading by triple dual tandem (N2), as compared to loading by twin dual tandem

(S2). For structural cross-section 3, i.e., thinner overlay over thicker underlay, the mean of all

the components except % recovery was lower for loading by triple dual tandem (N3). In

addition, the standard deviation of all the components except post-compression area was

higher for loading by triple dual tandem (N3).

5.4. Performance Relationships

After finding that peak strain response is not directly related to other components of strain

gages except cumulative area, relationship of performance (defined as number of passes when

SCI=80) is done with components of strain gage response. For this analysis, all possible

permutations of predictors are taken with number of axles as one of the fixed predictors.

Although number of axles showed strong correlation with the performance for all the gages, it

also defines loading type and total gear load. All resulting potential performance equations

can be found in Appendix D.

5.4.1. At the Top of Overlay: Equation 9 shows the relationship with peak strain and %

recovery and number of axles. Regression statistics for this relationship are given in Table 28.

Its R2 is 0.72 with standard error =689.68. This equation indicates reduced performance with

increased compressive peak strain (microStrain), increased recovery between axles, and

increased number of axles. This is in agreement with a rational understanding of the

87

performance characteristics, as higher compressive strain at the top of the overlay typically

correlates directly with higher tensile strain below.

Performance= -18.0696 (Peak Strain) – 5.52 (% Recovery) - 1893.5 (Number of Axles) +

9587.60 (9)

Table 28. Regression Statistics for Analysis of Performance with Peak Strain and % Recovery

and Number of Axles at Top of Overlay


Multiple R 0.85

R Square 0.72

Adjusted R

Square 0.72


Observations 4674

Another relationship, which was found to give a better R2, is for prediction of performance by

using area components, i.e., pre-tension area (microStrain-sec-Hz), post-tension area

(microStrain-sec-Hz) and cumulative compression area (microStrain-sec-Hz), with number of

axles as predictors in the model. Equation 10 shows the relationship of the performance with

area components. Table 29 shows the regression statistics for the analysis with R2= 0.70 and

standard error= 711.34. This equation is also consistent with engineering expectations with

regard to cumulative area and number of axles. However, the improved performance with

increased pre-stress and post-stress areas is not expected.

Performance= 0.58 (Pre-Tension Area) + 0.42 (Post-Tension Area) - 0.22 (Cumulative

Compression Area) -1782.75(Number of Axles) + 8692.87 (10)

88

Table 29. Regression Statistics for Analysis of Performance with Pre-Tension area, Post-

Tension Area, Cumulative Compression Area and Number of Axles at Top of Overlay


Multiple R 0.84

R Square 0.70

Adjusted R

Square 0.70


Observations 4674

5.4.2. At the Bottom of Overlay: No rational regression relationship could be obtained for

performance by the predictors - peak strain (microStrain), % recovery and number of axles.

This is unexpected, as peak tensile strain at the bottom of the overlay would be expected by

mechanics to have the strongest negative influence on performance. However, the regression

equations developed showed improved performance with increased peak tensile strain. A

reasonable R2 is found for prediction of performance by using area components, i.e., pre-

compression area (microStrain-sec-Hz), post-compression area (microStrain-sec-Hz) and

cumulative tension area (microStrain-sec-Hz), with number of axles as predictors in the

model. Equation 11 shows the relationship of the performance with area components. Table

30 shows the regression statistics for the analysis with R2= 0.68 and standard error= 717.60.

However, this relationship also shows improved performance with increased cumulative

tensile strain area, although this is more than offset by the decreased performance with the

compression areas.

Performance= -0.05 (Pre-Compression Area) -0.41(Post-Compression Area) + 0.005

(Cumulative Tension Area) -2193.49(Number of Axles) + 9240.2 (11)

89


Post-Compression Area, Cumulative Tension Area and Number of Axles at Bottom of

Overlay


Multiple R 0.82

R Square 0.68

Adjusted R

Square

0.68


Observations 4580

5.4.3. At the Top of Underlay: No rational regression relationship could be obtained for

performance by the predictors - peak strain (microStrain), % recovery and number of axles for

top of underlay.

A good R2 is found for prediction of performance by using area components, i.e., pre-tension

area (microStrain-sec-Hz), post-tension area (microStrain-sec-Hz) and cumulative

compression area (microStrain-sec-Hz), with number of axles as predictors in the model.

Equation 12 shows the relationship of the performance with area components. Table 31 shows

the regression statistics for the analysis with R2= 0.69 and standard error= 724.47.

Performance= 0.55(Pre-Tension Area) + 0.82(Post-Tension Area) +0.065 (Cumulative

Compression Area) -1982.06(Number of Axles) + 9111.31 (12)

Table 31. Regression Statistics for Analysis of Performance with Pre-Tension Area, Post-

Tension Area, Cumulative Compression Area and Number of Axles at Top of Underlay


Multiple R 0.83

R Square 0.69

Adjusted R Square 0.69


Observations 6198

90

5.4.4. At the Bottom of Underlay: No clearly rational relationship could be obtained for

performance by the predictors of peak strain (microStrain), % recovery and number of axles.

However, the developed equation is shown as equation 13. Regression statistics for this

relationship are given in Table 32. Its R-sq is 0.69 with standard error =706.53. This

relationship indicates decreased performance with higher peak strain and great number of

axles, as anticipated. However, the relationship also shows improved performance with

increased percent recovery. While not anticipated, the higher percent recovery may be

correlated with other parameters, such as structural cross-section, Further investigation is

warranted.

Performance= -23.5 1(Peak Strain) + 7.63 (% Recovery) - 2059.42(Number of Axles) +

7664.72 (13)

Table 32. Regression Statistics for Analysis of Performance with Peak Strain and % Recovery

and Number of Axles at Bottom of Underlay


Multiple R 0.83

R Square 0.69

Adjusted R

Square 0.69


Observations 6013.00

A reasonable R2 is found for prediction of performance by using area components, i.e., pre-

compression area (microStrain-sec-Hz), post-compression area (microStrain-sec-Hz) and

cumulative tension area (microStrain-sec-Hz), with number of axles as predictors in the

model. Equation 14 shows the relationship of the performance with area components. Table

32 shows the regression statistics for the analysis with R2= 0.62 and standard error= 779.28.

However, this relationship again shows improved performance with increased cumulative

91

tensile strain area, although this is more than offset by the decreased performance with the

compression areas.

Performance= -0.08(Pre-Compression) -0.05(Post-Compression) + 0.11(Cumulative Tension

Area) -2169.31(Number of Axles) + 9120.64 (14)


Post-Compression Area, Cumulative Tension Area and Number of Axles at Bottom of

Underlay


Multiple R 0.79

R Square 0.62

Adjusted R

Square 0.62


Observations 6013

5.5. Summary

From the above analysis, it can be summarized that peak strain from a gage’s response has a

strong correlation with cumulative area. It does not hold a strong relationship with other

components of a strain gage response, as found by multiple regression analysis of peak strain

with different components of strain gage response.

Also, no relationship was found between % recovery and other different components of the

gages responses. Mean and standard deviation of various components of strain gage response

were calculated and tabulated to show the variation of the components with different cross-

sections under different loading conditions. Those summary statistics are provided in tables 24

through 27.

92

Performance relationships were established, with different components of the strain gage

response and number of axles as one of the fixed predictors in the relationship. It was found

that performance has the strongest relationship with the predictors of peak strain, % recovery

and number of axles. Performance also showed relationships with different area components,

such as cumulative area, pre-strain and post-strain area, and number of axles. However, the

relationships, especially with peak tensile strain, did not always follow the rational pattern

anticipated by mechanics.

93

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS

6.1. Findings

This study focuses on the characterization of the strain gage response. It also addresses the

relationships of peak strain response with different components of strain gage response.

Preliminary analysis of unbonded concrete overlay performance is also attempted using the

components of strain gage response.

In chapter 5, different components of the strain gage responses were compared and analyzed

for the three unbonded concrete overlay structural cross-sections and two loading conditions,

triple dual tandem and twin dual tandem. The following are the findings of that analysis:

• For each and every gage, peak strain and cumulative area show a similar trend with

change in number of passes, for constant speed of loading.

• Peak strain and cumulative area show strong correlation for all test items and south

loading conditions for gages at top of overlay, bottom of overlay, top of underlay and

bottom of underlay. Correlation coefficients range between 0.95 and 0.85 for all

loading conditions and test items analyzed here, except for gages at the top of overlay

and underlay for test item 3 as shown in Table 14.

• Since the loading speed was constant, there was no correlation found between peak

strain and duration. Hence under constant speed conditions, duration did not provide

any further information beyond what could be found from the peak strain.

94

• Correlation between % recovery and cumulative area was found to vary within a wide

range, from as low as 0.05 to as high as 0.85. Groups by loading condition show low

correlation as compared to groups characterized by cross-sections.

• Means and standard deviations for key components of stain gage response are shown

in Table 34.

95

Table 34. Mean and Standard Deviation of Key Components of Strain Gage Responses

Location Strain Gage' Components


North Loading

(N1)

South Loading

(S1)

North Loading

(N2)

North Loading

(N1)

South Loading

(S1)

North Loading

(N2)


Top of

Overlay



Post- compression Area


Peak Strain (microStrain) 62 16 45 8 45 4 34 4 57 10 45 16

% Recovery 70% 24% 65% 6% 74% 17% 75% 20% 83% 13% 99% 19%

Bottom of

Overlay





Peak Strain (microStrain) -33 45 -25 11 -18 5 -21 10 -43 27 -15 6

% Recovery 128% 25% 101% 22% 85% 17% 137% 56% 126% 18% 250% 59%

Top of

Underlay





Peak Strain (microStrain) 33 10 48 10 35 9 52 6 44 13 54 10

% Recovery 95% 18% 54% 10% 97% 31% 62% 18% 46% 8% 30% 6%

Bottom of

Underlay





Peak Strain (microStrain) -12 7 -29 14 -13 4 -28 9 -13 6 -25 2

% Recovery 124% 64% 48% 6% 162% 36% 78% 27% 59% 12% 30% 5%

96

• Performance defined as number of passes when SCI=80 is analyzed by relating it

with components of strain gage response. Performance has the strong relationship

with the predictors as peak strain and % recovery and number of axles only for

gages at the top of overlay, and the other sets of predictors as the area components

and the number of axles. R2 values for analysis done for the gages at the top of

overlay, bottom of overlay, top of underlay and bottom of underlay range between

0.62 and 0.72, with the adjusted R2 ranging from 0.62 to 0.72

6.2. Conclusions

Three questions were formulated to convey the objectives of the research. These

questions are answered as follows:

Do the various components of the strain gage response such as peaks, recovery, duration

and area directly relate to the peak strain?

From the analysis and the findings, it can be concluded that peak strain holds a strong

relationship with cumulative area. Doing analysis for each and every gage, it was found

that peak strain and cumulative area show the same trend with change in passes, with the

mean, median and standard deviation ratio of the peak strain and cumulative area to be

same. This type was expected for the loading direction as speed of a vehicle was

constant. Therefore it can be concluded, since the speed and loading of the vehicles was

constant for a particular gage, that cumulative area is a representative of a peak strain for

this particular experiment.

97

But peak strain did not show the same strong relationship with other components of the

gage responses. This implies that if other components of response may have a strong

influence on the fatigue or cracking behavior of the concrete pavement, then they must be

considered independently under this type of loading. The peak strain would not then

serve as an adequate proxy even with calibration.

As expected, the cumulative area did not show good correlation with strain gage response

components except to the peak strain. In general, cumulative area showed the same

behavior as the peak strain. Though the cumulative area represented duration of loading,

recovery between axles and strain responses due to axle loadings, it did not share any

strong relation with the components individually. This was expected because of the high

influence of peak strain on the cumulative area. Since duration depended on the speed of

loading, it was expected and observed that the duration did not show any relation with

peak strain.

How do the components of strain gage response change with different gear

configurations and different pavement cross-sections?

Mean and standard deviation for different components were obtained for each structural

cross-section (the numbered test items) at both loading conditions. It was observed that

peak strain, % recovery, average peak and pre-stress area and post-stress area show

changes as observed in Table 33 with change in the cross-section and loading conditions.

98

Though the loading by an axle is the same for different gear configurations, average peak

and recovery for a test item showed different average and standard deviation for loading

by the triple dual tandem gear and the twin dual tandem gear.

If not directly related to peak strain, how do the components of the strain gage response

relate to number of passes before cracking?

As anticipated for the small number of test items, only a preliminary answer to this

question could be obtained. Conducting multiple regression analysis, relation of the

observed performance, defined as passes to SCI=80, with the area components and the

number of axles was predicted. Performance could be predicted using peak strain and

percent recovery and number of axles for top of the overlay only. From this, it can be

concluded that performance of the pavement is dependent on area components and the

peak components.

The strain gages were installed at what were anticipated by accepted models to be the

critical locations for tensile strains that would result in transverse bottom-up cracking.

However, observed cracking patterns on the pavement were predominantly longitudinal,

and a mix of top-down and bottom-up cracking. Therefore, the strain gages were not

found to be installed at the what would have been the critical locations for the particular

experiment. This may partially explain some of the unexpected regression relationships.

It also illustrates one of the key problems with instrumented pavement designs for which

the behavior is not fully understood. Of course, those are the pavement sections from

which the most knowledge may be gained by utilizing instrumentation.

99

6.3. Recommendations

For this research, baseline experiment data from the unbonded concrete overlay

experiment at the NAPTF was used and strain responses were characterized for three

different unbonded concrete overlay cross-sections and for two different loading

conditions. Results were limited to those particular sets of data, and to the particular

locations of these strain gages, which may not have been at the most critical locations or

orientations. However, this research builds a foundation for the future work and

recommendations.

Data used in this work was simulated using two gear configurations on three structural

cross-sections. The gear configurations did not exactly reflect real aircraft, and were

limited to only twin dual tandem and triple dual tandem with each wheel load being

50,000 lbs. In order to show more varied relations, responses from real in-service aircraft

gears with varied loading conditions could be used to capture responses on other concrete

pavement structures. The FAA has instrumented concrete pavements; data from the

Denver International Airport is available.

Also, responses used in the datasets were limited to those before the first crack was

developed. Responses with the change in SCI value could also be analyzed to study

changes in response components with crack generation. After the Baseline Experiment

was over, the overlay was removed leaving the deteriorated underlay in place. A new

concrete overlay was placed over the undisturbed underlay. This study could also be

extended to the weakened support conditions in that study.

100

Perhaps the most significant conclusion of this research is that peak strain did not serve

as a full representation of strain gage response for these complex loading and structural

conditions. In addition, the preliminary statistical relationships with performance

indicated that other variables, such as % recovery between axles, may be important. This

study limited scope to the statistical characterization of the strain responses. Other

analytical approaches such as Finite Element Method and Artificial Intelligence should

be undertaken to analyze the effects of the responses. Those approaches may help to

develop future design procedures that include additional important components of

response to complex loads, instead of limiting use to only peak strain behavior.

101

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111

APPENDIX A: Strain gage coordinates and calibration factor

Structural Cross-section 1

Table 35. Coordinates and Calibration Factor for Strain Gages Installed at Test Item N1.

Sensor Test Item Overlay/Underlay Xloc ft Yloc ft Zloc in Calibration

Factor

EG-O-N1-1 B N1 Overlay 338.75 -17.25

0.818

EG-O-N1-1 T N1 Overlay 338.75 -17.25

0.812

EG-O-N1-2 B N1 Overlay 363.75 -17.25

0.806

EG-O-N1-2 T N1 Overlay 363.75 -17.25

0.808

EG-O-N1-3 B N1 Overlay 376.25 -17.25

0.817

EG-O-N1-3 T N1 Overlay 376.25 -17.25

0.81

EG-U-N1-1 B N1 Underlay 338.75 -17.5 -5.5 0.787

EG-U-N1-1 T N1 Underlay 338.75 -17.5 -1.17 0.79

EG-U-N1-2 B N1 Underlay 366 -17.5 -5.5 0.804

EG-U-N1-2 T N1 Underlay 363.75 -17.5 -1.17 0.786

EG-U-N1-3 B N1 Underlay 370 -17.5 -5.5 0.782

EG-U-N1-3 T N1 Underlay 370 -17.5 -1.17 0.808

Table 36. Coordinates and Calibration Factor for Strain Gages Installed at Test Item S1.

Sensor Test

Item Overlay/Underlay Xloc ft Yloc ft

Zloc

in

Calibration

Factor

EG-O-S1-1 B S1 Overlay 338.75 17.25

0.814

EG-O-S1-1 T S1 Overlay 338.75 17.25

0.817

EG-O-S1-2 B S1 Overlay 363.75 17.25

0.813

EG-O-S1-2 T S1 Overlay 363.75 17.25

0.818

EG-O-S1-3 B S1 Overlay 376.25 17.25

0.808

EG-O-S1-3 T S1 Overlay 376.25 17.25

0.817

EG-U-S1-1 B S1 Underlay 338.75 17.5 -5.5 0.79

EG-U-S1-1 T S1 Underlay 338.75 17.5 -1.17 0.785

EG-U-S1-2 B S1 Underlay 366 17.5 -5.5 0.786

EG-U-S1-2 T S1 Underlay 363.75 17.5 -1.17 0.782

EG-U-S1-3 B S1 Underlay 370 17.5 -5.5 0.786

EG-U-S1-3 T S1 Underlay 370 17.5 -1.17 0.801

112



Sensor Test

Item Overlay/Underlay Xloc ft Yloc ft Zloc in

Calibration

Factor

EG-O-N2-1 B N2 Overlay 428.75 -17.25

0.817

EG-O-N2-1 T N2 Overlay 428.75 -17.25

0.825

EG-O-N2-2 B N2 Overlay 441.25 -17.25

0.809

EG-O-N2-2 T N2 Overlay 441.25 -17.25

0.809

EG-O-N2-3 B N2 Overlay 466.25 -17.25

0.817

EG-O-N2-3T N2 Overlay 466.25 -17.25

0.808

EG-U-N2-1 B N2 Underlay 428.75 -17.5 -7 0.787

EG-U-N2-1 T N2 Underlay 428.75 -17.5 -1.17 0.797

EG-U-N2-2 B N2 Underlay 441.25 -17.5 -7 0.796

EG-U-N2-2 T N2 Underlay 441.25 -17.5 -1.17 0.79

EG-U-N2-3 B N2 Underlay 466.25 -17.5 -7 0.801

EG-U-N2-3 T N2 Underlay 466.25 -17.5 -1.17 0.795

EG-U-N2-4 B N2 Underlay 472.5 -17.5 -7 0.8

EG-U-N2-4 T N2 Underlay 472.5 -17.5 -1.17 0.792


Sensor Test


Calibration

Factor

EG-O-S2-1 B S2 Overlay 428.75 17.25

0.808

EG-O-S2-1 T S2 Overlay 428.75 17.25

0.81

EG-O-S2-2 B S2 Overlay 441.25 17.25

0.806

EG-O-S2-3 B S2 Overlay 466.25 17.25

0.814

EG-O-S2-3 T S2 Overlay 466.25 17.25

0.82

EG-U-S2-1 B S2 Underlay 428.75 17.5 -7 0.79

EG-U-S2-1 T S2 Underlay 428.75 17.5 -1.17 0.794

EG-U-S2-2 B S2 Underlay 441.25 17.5 -7 0.792

EG-U-S2-2 T S2 Underlay 441.25 17.5 -1.17 0.794

EG-U-S2-3 B S2 Underlay 466.25 17.5 -7 0.801

EG-U-S2-3 T S2 Underlay 466.25 17.5 -1.17 0.797

EG-U-S2-4 B S2 Underlay 472.5 17.5 -7 0.801

EG-U-S2-4 T S2 Underlay 472.5 17.5 -1.17 0.795

113



Sensor Test


Calibration

Factor

EG-O-N3-1 B N3 Overlay 518.75 -17.25

0.813

EG-O-N3-1 T N3 Overlay 518.75 -17.25

0.812

EG-O-N3-2 B N3 Overlay 543.75 -17.25

0.817

EG-O-N3-2 T N3 Overlay 543.75 -17.25

0.814

EG-O-N3-3 B N3 Overlay 556.25 -17.25

0.814

EG-O-N3-3 T N3 Overlay 556.25 -17.25

0.809

EG-U-N3-1 B N3 Underlay 518.75 -17.5 -9.5 0.787

EG-U-N3-1 T N3 Underlay 518.75 -17.5 -1.17 0.795

EG-U-N3-2 B N3 Underlay 546 -17.5 -9.5 0.803

EG-U-N3-2 T N3 Underlay 543.75 -17.5 -1.17 0.786

EG-U-N3-3 B N3 Underlay 550 -17.5 -9.5 0.796

EG-U-N3-3 T N3 Underlay 550 -17.5 -1.17 0.781


Sensor Test


Calibration

Factor

EG-O-S3-1 B S3 Overlay 518.75 17.25

0.813

EG-O-S3-1 T S3 Overlay 518.75 17.25

0.81

EG-O-S3-2 B S3 Overlay 543.75 17.25

0.812

EG-O-S3-2 T S3 Overlay 543.75 17.25

0.795

EG-O-S3-3 B S3 Overlay 556.25 17.25

0.804

EG-O-S3-3 T S3 Overlay 556.25 17.25

0.817

EG-U-S3-1 B S3 Underlay 518.75 17.5 -9.5 0.789

EG-U-S3-1 T S3 Underlay 518.75 17.5 -1.17 0.794

EG-U-S3-2 B S3 Underlay 546 17.5 -9.5 0.797

EG-U-S3-2 T S3 Underlay 543.75 17.5 -1.17 0.79

EG-U-S3-3 B S3 Underlay 550 17.5 -9.5 0.796

EG-U-S3-3 T S3 Underlay 550 17.5 -1.17 0.792

114

APPENDIX B. Matlab Codes

Matlab Code to find peaks.

1. function [p,t]=findpeaks(s)

2. warning off

3. ds=diff(s);

4. ds=[ds(1);ds];%pad diff

5. filter=find(ds(2.end)==0)+1;%%find zeros

6. ds(filter)=ds(filter-1);%%replace zeros

7. ds=sign(ds);

8. ds=diff(ds);

9. t=find(ds>0);

10. p=find(ds<0);

Matlab code to find area.

1. function [Area peak]=getArea(mat,name)

2.

3. H = fspecial('average',12);

4. filteredData=imfilter(mat,H,'replicate');

5. %m1=mean(filteredData(1.100));

6. % if(m1>0 || m2>0)

7. % m=min(m1,m2);

8. % else

9. % m=max(m1,m2);

10. % end

11. %m=m1;

12. m=getBaseline(mat);

13. filteredData=filteredData-m;

14. topFData=filteredData;

15. bottomFData=filteredData;

16. topFData(topFData<0)=0;

17. bottomFData(bottomFData>0)=0;

18. topFData(abs(topFData/max(abs(topFData)))<.15)=0;

19. bottomFData(abs(bottomFData/max(abs(bottomFData)))<.15)=0;

20.

21. Area=zeros(6,1);

22. peak=zeros(7,1);

23.

24. if isempty(regexp(name,'EG[a-zA-Z0-9\- ]+B','once'))

25. [p k]=findpeaks(topFData);

115

26. maxt=zeros(2,1);

27. bottomFData=abs(bottomFData);

28. [p1 k1]=findpeaks(bottomFData);

29. if isempty(regexp(name,'EG-[UOuo2]-S[a-zA-Z0-9\- ]','once'))

30. if( length(p)>2)

31. if(length(k)==6)

32. Area(1)=trapz(topFData(k(1).k(2)));



35.

36. peak(2)=filteredData(p(1));

37. peak(3)=filteredData(round(0.5*(k(2)+k(3))));




41. end





46.






52. end





57.






63. end

64. end

65. else

66. if( length(p)>1)




70. Area(3)=0;

71.

116




75. end




79. Area(3)=0;

80.




84. end



87. Area(2)=0;

88. Area(3)=0;

89.


91. peak(3)=0;

92. peak(4)=0;

93. end

94. end

95. end

96.

97. if(length(p1)>1)

98.

99. maxt(1)=p1(1);

100. for maxt_check=1.length(p1)

101. if bottomFData(maxt(1))<bottomFData(p1(maxt_check))

102. maxt(1)=(p1(maxt_check));

103. end

104. end

105.

106. if maxt(1)==p1(length(p1))

107. maxt(2)=p1(1);

108. else

109. maxt(2)=p1(length(p1));

110. end


112. if bottomFData(maxt(2))<bottomFData(p1(maxt_check)) &&

(p1(maxt_check))~=(maxt(1)) && abs((p1(maxt_check))-(maxt(1)))>10


114. end

115. end

116. if(abs(maxt(1)-maxt(2))>10)

117

117. % area6 is time

118. Area(6)= abs(maxt(1)-maxt(2));

119. peak(1)=filteredData(maxt(1));



122. else


124. end

125.

126. if maxt(1)>maxt(2)

127. kt=maxt(2);

128. maxt(2)=maxt(1);

129. maxt(1)=kt;

130. end

131.

132. new_k1=k1(bottomFData(k1)==0);

133. % new_k1.array=[];

134. % cou=1;

135. % for c=1.length(k1)

136. % if(bottomFData(k1(c))==0)

137. % new_k1(cou)=k1(c);

138. % cou=cou+1;

139. % end

140. % end

141. if(length(new_k1)>1)

142. mp1=abs(new_k1(1)-maxt(1));

143. mp1_k1=new_k1(1);

144. for maxt_check=1.length(new_k1)

145. if mp1 > abs(new_k1(maxt_check)-maxt(1))

146. mp1_k1=new_k1(maxt_check);

147. end

148. end

149.

150. if mp1_k1==new_k1(1)


152. mp1_k2=new_k1(2);

153. else


155. mp1_k2=new_k1(1);

156. end


158. if mp1 > abs(new_k1(maxt_check)-maxt(1)) &&

mp1_k1~=new_k1(maxt_check)


160. end

161. end

118

162.

163. if(mp1_k1>mp1_k2)

164. kp=mp1_k1;

165. mp1_k1=mp1_k2;

166. mp1_k2=kp;

167. end

168. Area(4)=trapz(topFData(mp1_k1.mp1_k2));

169.


171. mp1_k1=new_k1(1);




175. end

176. end

177. if mp1_k1==new_k1(1)


179. mp1_k2=new_k1(2);

180. else


182. mp1_k2=new_k1(1);

183. end





187. end

188. end

189.

190. if(mp1_k1>mp1_k2)

191. kp=mp1_k1;

192. mp1_k1=mp1_k2;

193. mp1_k2=kp;

194. end


196. end

197. end

198. end

199.

200. end

201.

202.

203. if isempty(regexp(name,'EG[a-zA-Z0-9\- ]+T','once'))

204.

205. [p k]=findpeaks(bottomFData);

206. [p1 k1]=findpeaks(topFData);

119

207.


209. if( length(k)>2)

210. if(length(p)==6)

211. Area(1)=trapz(bottomFData(p(1).p(2)));



214.

215. peak(2)=filteredData(k(1));

216. peak(3)=filteredData(round(0.5*(p(2)+p(3))));




220. end





225.






231. end





236.






242. end

243. end

244. else

245. if(length(k)>1)




249. Area(3)=0;

250.



120


254. end



257. Area(2)=0;

258. Area(3)=0;

259.


261. peak(3)=0;

262. peak(4)=0;

263. end




267. Area(3)=0;

268.




272. end

273. end

274. end

275. if(length(p1)>1)

276. maxt(1)=p1(1);


278. if topFData(maxt(1))<topFData(p1(maxt_check))


280. end

281. end

282.

283. if maxt(1)==p1(length(p1))

284. maxt(2)=p1(1);

285. else

286. maxt(2)=p1(length(p1));

287. end


289. if topFData(maxt(2))<topFData(p1(maxt_check)) &&

(p1(maxt_check))~=(maxt(1)) && abs((p1(maxt_check))-(maxt(1)))>10


291. end

292. end

293.

294. if(abs(maxt(1)-maxt(2))>10)

295. % area6 is time

296. Area(6)= abs(maxt(1)-maxt(2));


121



300. else


302. end

303.

304. if maxt(1)>maxt(2)

305. kt=maxt(2);

306. maxt(2)=maxt(1);

307. maxt(1)=kt;

308. end

309. new_k1=k1(topFData(k1)==0);

310. % cou=1;

311. % for c=1.length(k1)

312. % if(topFData(k1(c))==0)

313. % new_k1(cou)=k1(c);

314. % cou=cou+1;

315. % end

316. % end

317. %

318. if(length(new_k1)>1)


320. mp1_k1=new_k1(1);




324. end

325. end

326.

327. if mp1_k1==new_k1(1)


329. mp1_k2=new_k1(2);

330. else


332. mp1_k2=new_k1(1);

333. end





337. end

338. end

339.

340. if(mp1_k1>mp1_k2)

341. kp=mp1_k1;

342. mp1_k1=mp1_k2;

122

343. mp1_k2=kp;

344. end


346.


348. mp1_k1=new_k1(1);




352. end

353. end

354. if mp1_k1==new_k1(1)


356. mp1_k2=new_k1(2);

357. else


359. mp1_k2=new_k1(1);

360. end





364. end

365. end

366.

367. if(mp1_k1>mp1_k2)

368. kp=mp1_k1;

369. mp1_k1=mp1_k2;

370. mp1_k2=kp;

371. end


373. end

374. end

375. end

376. end

377.

378. end

379.

Matlab code to print Area on Excel.

1. clc;

2. clear all;

123

3. foldername='F.\Baseline Extracted Data\vishal';

4. datsName=getUnique(strcat(foldername,'\*.xls'));

5.

6. for cnt=1.size(datsName,1)

7. % FOr each date

8. listf=subdir(strcat(foldername,'\*',datsName(cnt,.),'*.xls'));

9. foldernum=regexp(listf(1).name,'[a-zA-Z0-9,\-]+.xls');

10. datefolder=listf(1).name(1.foldernum-2);

11. Passnum=unique(getPassNum(strcat(datefolder,'\*.xls')));

12. cntp_count=0;

13. for cntp=1.numel(Passnum)

14. % for each pass

15. if getTrackPass(cntp)==1

16. listp=(subdir(strcat(datefolder,'\*p',num2str(Passnum(cntp)),'.xls')));

17. mat.array=[];

18. mat.arrayName=[];

19. for cntps=1.numel(listp)

20. % for each file of pass

21. disp(strcat('Reading file . ',num2str(cntps),32,' for Pass.

',num2str(Passnum(cntp)),32,' on Date . ',datsName(cnt,.)));

22. [num,txt] = xlsread(listp(cntps).name);

23. % tmp=repmat(Passnum(cntp),size(num,1),1);

24. % num=[tmp num];

25. txt=char(txt(1,2.end-1));

26. try

27. mat.array=[mat.array num];

28. catch

29. [r1 c1]=size(num);

30. [r2 c2]=size(mat.array);

31. if r1<r2

32. mat.array=[mat.array(1.r1,.) num];

33. else

34. mat.array=[mat.array num(1.r2,.)];

35. end

36. end

37. txt1=[];

38. for cntt=1.size(txt,1)

39. txt1(cntt,.)= makeuniformName(txt(cntt,.));

40. end

41. mat.arrayName=[mat.arrayName;txt1];

42. end

43. Headerstr=makeuniformName('Pass Number');

44.

45. k=1;

46. cntp_count=cntp_count+1;

47. for cntRes=1.size(mat.arrayName,1)

124

48. if isempty(regexp(char(mat.arrayName(cntRes,.)),'EG[a-zA-Z0-9\- ]',

'once'))

49. else

50. [Area

peak]=getArea(mat.array(.,cntRes),char(mat.arrayName(cntRes,.)));

51. Area1(cntp_count,1)=Passnum(cntp);

52. Area1(cntp_count,k+1)=Area(1);





57. Sum123(cntp_count,1)=Passnum(cntp);

58. Sum123(cntp_count,k+1)=Area(1)+Area(2)+Area(3);





63. time(cntp_count,1)=Passnum(cntp);

64. time(cntp_count,k+1)=Area(6);

65.

66. peak1(cntp_count,1)=Passnum(cntp);

67. peak1(cntp_count,k+1)=peak(1);













80.

81. Headerstr=[Headerstr;char(mat.arrayName(cntRes,.))];

82. k=k+1;

83. end

84. end

85. end

86. end

87. %writing area data

88. xlswrite(strcat('Results\Area-',datsName(cnt,.),'-file.xls'),

cellstr(Headerstr(1.min(size(Headerstr,1),256),.))','Sheet1','A1');

89. %write the data directly underneath the column headers

125


num2cell(Area1(.,1.min(size(Headerstr,1),256))),'Sheet1','A2');

91.






95.






99.






103.






107.


cellstr(Headerstr(1.min(size(Headerstr,1),256),.))','SUM123','A1');



num2cell(Sum123(.,1.min(size(Headerstr,1),256))),'SUM123','A2');

111.


cellstr(Headerstr(1.min(size(Headerstr,1),256),.))','time','A1');



num2cell(time(.,1.min(size(Headerstr,1),256))),'time','A2');

115.

116. %writing peaks data.

117. xlswrite(strcat('Results\peaks-',datsName(cnt,.),'-file.xls'),




num2cell(peak1(.,1.min(size(Headerstr,1),256))),'Sheet1','A2');

120.

126






124.






128.






132.






136.






140.






144. end

145.

127

APPENDIX C: Means and Standard Deviations for Selected Gages

Table 41. Average, Median and Standard Deviation of the Peak Strain(microStrain) and

Area for Even-numbered Passes for EG-U-N1-1 B and EG-U-N1-1 T

EG-U-N1-1 B

EG-U-N1-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

Peak Strain Cumulative

Area

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -23.44 -479.65 0.05 31.97 799.07 0.04

Median -23.49 -479.11 0.05 32.02 800.31 0.04

Standard

Deviation 1.20 29.83 0.04 1.03 75.79 0.01

7/26/2006

Average -16.22 -348.76 0.05 26.71 613.90 0.04

Median -14.55 -370.79 0.04 29.21 603.90 0.05

Standard

Deviation 3.67 113.55 0.03 6.54 86.55 0.08

7/27/2006

Average -11.97 -155.06 0.08 34.89 797.76 0.04

Median -11.93 -151.22 0.08 34.84 800.04 0.04

Standard

Deviation 0.61 25.53 0.02 1.27 23.84 0.05

7/28/2006

Average -11.48 -129.19 0.09 35.57 798.38 0.04

Median -11.48 -128.59 0.09 35.57 791.47 0.04

Standard

Deviation 0.16 5.42 0.03 0.88 33.47 0.03

7/31/2006

Average -15.32 -383.76 0.04 31.88 837.96 0.04

Median -16.30 -374.26 0.04 31.38 799.55 0.04

Standard

Deviation 1.41 57.17 0.02 1.78 84.55 0.02

8/1/2006

Average -13.39 -194.28 0.07 36.23 815.75 0.04

Median -13.36 -194.80 0.07 36.27 812.38 0.04

Standard

Deviation 0.29 7.55 0.04 0.60 15.61 0.04

128

Table 42. Linear Relation Chart for Even-numbered Passes for EG-U-N1-1 B and

EG-U-N1-1 T with Area as Y and Strain as X

Date EG-U-N1-1 B EG-U-N1-1 T

7/25/2006

slope 24.48 53.81

intercept 94.28 -920.98

R-sq 0.97 0.53

7/26/2006

slope 20.26 5.24

intercept -20.20 474.02

R-sq 0.43 0.16

7/27/2006

slope 40.72 15.35

intercept 332.35 262.36

R-sq 0.95 0.66

7/28/2006

slope 14.69 31.77

intercept 39.39 -331.86

R-sq 0.18 0.70

7/31/2006

slope -5.58 14.46

intercept -469.27 377.05

R-sq 0.02 0.09

8/1/2006

slope 23.12 11.50

intercept 115.37 399.05

R-sq 0.81 0.19

129



EG-U-N1-1 B

EG-U-N1-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -22.33 -613.49 0.04 29.92 839.69 0.04

Median -22.57 -615.79 0.04 29.40 840.52 0.03

Standard

Deviation 1.90 93.46 0.02 1.59 53.64 0.03

7/26/2006

Average -14.08 -304.99 0.05 28.59 694.24 0.04

Median -12.24 -205.29 0.06 27.38 693.55 0.04

Standard

Deviation 3.86 177.32 0.02 2.98 44.73 0.07

7/27/2006

Average -10.07 -131.74 0.08 30.18 825.99 0.04

Median -10.33 -134.36 0.08 30.20 846.16 0.04

Standard

Deviation 0.96 25.43 0.04 0.60 91.98 0.01

7/28/2006

Average -9.41 -110.18 0.09 30.37 808.87 0.04

Median -9.70 -113.64 0.09 30.38 841.72 0.04

Standard

Deviation 0.92 11.30 0.08 0.92 106.44 0.01

7/31/2006

Average -15.75 -376.99 0.04 28.02 853.43 0.03

Median -16.19 -372.40 0.04 27.88 847.49 0.03

Standard

Deviation 1.41 85.63 0.02 1.09 51.88 0.02

8/1/2006

Average -12.67 -165.48 0.08 33.80 865.87 0.04

Median -12.62 -163.28 0.08 33.58 838.22 0.04

Standard

Deviation 0.32 7.97 0.04 1.00 65.25 0.02

130

Table 44. Linear Relation Chart for Odd-numbered Passes for EG-U-N1-1 B and



7/25/2006

slope 47.36 26.71

intercept 444.01 40.56

R-sq 0.93 0.63

7/26/2006

slope 45.08 9.13

intercept 329.59 433.17

R-sq 0.96 0.37

7/27/2006

slope 25.63 61.82

intercept 126.30 -1039.86

R-sq 0.93 0.16

7/28/2006

slope -3.34 35.06

intercept -141.64 -255.98

R-sq 0.07 0.09

7/31/2006

slope 38.98 -17.69

intercept 236.93 1349.09

R-sq 0.41 0.14

8/1/2006

slope 21.69 54.73

intercept 109.42 -983.93

R-sq 0.78 0.70

131



EG-U-N1-3 B EG-U-N1-3 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -30.47 -1127.65 0.03 35.02 826.09 0.04

Median -30.46 -1119.58 0.03 34.91 797.32 0.04

Standard

Deviation 0.74 33.00 0.02 0.40 71.66 0.01

7/26/2006

Average -29.61 -1143.04 0.03 32.31 709.88 0.05

Median -32.47 -1247.68 0.03 37.29 765.35 0.05

Standard

Deviation 7.61 367.00 0.02 11.60 219.84 0.05

7/27/2006

Average -29.38 -760.99 0.04 43.48 933.54 0.05

Median -29.57 -676.08 0.04 43.03 939.02 0.05

Standard

Deviation 0.72 151.45 0.00 2.03 74.78 0.03

7/28/2006

Average -29.24 -617.42 0.05 45.58 1025.39 0.04

Median -28.76 -603.66 0.05 45.26 983.70 0.05

Standard

Deviation 0.99 29.31 0.03 1.80 88.98 0.02

7/31/2006

Average -27.46 -684.09 0.04 53.35 1307.33 0.04

Median -24.53 -501.66 0.05 52.69 1287.11 0.04

Standard

Deviation 7.69 267.10 0.03 6.12 203.82 0.03

8/1/2006

Average -37.39 -778.64 0.05 52.37 1429.71 0.04

Median -37.37 -782.93 0.05 52.43 1430.56 0.04

Standard

Deviation 1.99 50.95 0.04 0.68 20.55 0.03

132



EG-U-N1-3 B EG-U-N1-3 T

7/25/2006

slope 35.83 -58.92

intercept -35.96 2889.61

R-sq 0.65 0.11

7/26/2006

slope 47.92 17.16

intercept 276.04 155.59

R-sq 0.99 0.82

7/27/2006

slope -70.47 36.05

intercept -2833.88 -633.28

R-sq 0.11 0.93

7/28/2006

slope 28.36 45.97

intercept 211.71 -1069.86

R-sq 0.92 0.87

7/31/2006

slope 25.07 33.27

intercept 4.28 -467.49

R-sq 0.52 1.00

8/1/2006

slope 25.48 21.78

intercept 174.08 288.88

R-sq 0.99 0.52

133


numbered Passes for EG-U-N1-3 B and EG-U-N1-3T

EG-U-N1-3 B

EG-U-N1-3 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -32.13 -1168.73 0.03 37.62 1140.50 0.03

Median -31.79 -1171.43 0.03 37.88 1129.74 0.03

Standard

Deviation 1.31 31.40 0.04 0.84 55.74 0.02

7/26/2006

Average -35.51 -1303.49 0.03 38.30 1047.16 0.04

Median -35.58 -1271.45 0.03 37.39 1081.34 0.03

Standard

Deviation 3.38 152.47 0.02 2.67 104.30 0.03

7/27/2006

Average -31.09 -934.26 0.03 39.11 1257.91 0.03

Median -31.18 -934.46 0.03 39.26 1258.34 0.03

Standard

Deviation 0.53 31.09 0.02 1.41 83.46 0.02

7/28/2006

Average -30.14 -819.95 0.04 39.74 1346.05 0.03

Median -29.81 -801.33 0.04 38.75 1306.70 0.03

Standard

Deviation 0.93 34.25 0.03 2.07 104.34 0.02

7/31/2006

Average -29.48 -793.22 0.04 32.70 997.05 0.03

Median -29.69 -867.29 0.03 18.97 670.41 0.03

Standard

Deviation 6.49 222.39 0.03 16.04 608.13 0.03

8/1/2006

Average -37.93 -896.71 0.04 46.89 1614.72 0.03

Median -38.20 -898.40 0.04 47.08 1629.98 0.03

Standard

Deviation 1.93 52.30 0.04 1.27 46.56 0.03

134




7/25/2006

slope 15.31 54.82

intercept -676.93 -922.06

R-sq 0.41 0.68

7/26/2006

slope 44.26 -23.70

intercept 268.45 1954.95

R-sq 0.96 0.37

7/27/2006

slope 26.39 57.12

intercept -113.84 -976.02

R-sq 0.21 0.93

7/28/2006

slope 31.16 49.71

intercept 119.11 -629.21

R-sq 0.71 0.97

7/31/2006

slope 33.15 37.76

intercept 184.00 -237.85

R-sq 0.93 0.99

8/1/2006

slope 25.22 34.31


R-sq 0.87 0.87

135


numbered Passes for EG-U-S1-2 B and EG-U-S1-2 T

EG-U-S1-2 B

EG-U-S1-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -16.39 -528.56 0.03 No Response No Response No Response

Median -16.11 -522.42 0.03 No Response No Response No Response

Standard

Deviation 0.78 30.06 0.03 No Response No Response No Response

7/26/2006



Standard


7/27/2006



Standard


7/28/2006



Standard


7/31/2006



Standard


8/1/2006



Standard


8/2/2006



Standard


136

Table 50. Linear Relation Chart for Even-numbered Passes for EG-U-S1-2 B and

EG-U-S1-2 T with Area as Y and Strain as X

Date EG-U-S1-2 B EG-U-S1-2 T

7/25/2006

slope 37.94 No Response

intercept 93.45 No Response

R-sq 0.96 No Response

7/26/2006




7/27/2006




7/28/2006




7/31/2006




8/1/2006




8/2/2006


intercept -261.54 No Response


137



EG-U-S1-2 B

EG-U-S1-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006



Standard


7/26/2006



Standard


7/27/2006



Standard


7/28/2006



Standard


7/31/2006



Standard


8/1/2006



Standard


8/2/2006



Standard


138

Table 52. Linear Relation Chart for Odd-numbered Passes for EG-U-S1-2 B and



7/25/2006




7/26/2006




7/27/2006




7/28/2006




7/31/2006




8/1/2006




8/2/2006




139



EG-U-S1-3 B

EG-U-S1-3 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -55.86 -1652.33 0.03 54.24 1374.42 0.04

Median -56.11 -1653.57 0.03 54.39 1384.89 0.04

Standard

Deviation 0.93 25.85 0.04 1.09 36.30 0.03

7/26/2006

Average -49.37 -1456.62 0.03 53.27 1346.00 0.04

Median -51.54 -1507.85 0.03 54.41 1348.94 0.04

Standard

Deviation 6.68 187.99 0.04 8.13 182.77 0.04

7/27/2006

Average -44.06 -1270.63 0.03 52.06 1260.38 0.04

Median -43.91 -1272.54 0.03 51.53 1240.17 0.04

Standard

Deviation 0.54 18.27 0.03 1.57 52.10 0.03

7/28/2006

Average -42.33 -1211.08 0.03 51.36 1213.33 0.04

Median -41.65 -1191.19 0.03 50.52 1181.37 0.04

Standard

Deviation 1.37 39.19 0.03 2.08 68.03 0.03

7/31/2006

Average -38.23 -1165.72 0.03 49.41 1264.38 0.04

Median -40.21 -1229.12 0.03 50.65 1339.39 0.04

Standard

Deviation 6.10 162.16 0.04 11.44 302.63 0.04

8/1/2006

Average -39.29 -1166.31 0.03 44.45 1217.00 0.04

Median -39.25 -1165.51 0.03 44.49 1215.46 0.04

Standard

Deviation 0.28 9.85 0.03 0.49 16.52 0.03

8/2/2006

Average -43.56 -1251.35 0.03 56.27 1356.64 0.04

Median -43.62 -1252.14 0.03 56.50 1364.13 0.04

Standard

Deviation 0.84 12.68 0.07 1.21 27.92 0.04

140




7/25/2006

slope 26.48 32.36

intercept -173.24 -380.70

R-sq 0.90 0.94

7/26/2006

slope 27.91 21.78

intercept -78.75 185.95

R-sq 0.98 0.94

7/27/2006

slope 30.47 31.95

intercept 72.28 -402.97

R-sq 0.80 0.93

7/28/2006

slope 27.63 31.18

intercept -41.72 -388.09

R-sq 0.93 0.91

7/31/2006

slope 26.34 26.31

intercept -158.57 -35.54

R-sq 0.98 0.99

8/1/2006

slope 24.79 27.96

intercept -192.22 -25.70

R-sq 0.50 0.70

8/2/2006

slope 11.47 21.51

intercept -751.55 146.29

R-sq 0.58 0.87

141



EG-U-S1-3 B

EG-U-S1-3 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -57.47 -1613.33 0.04 59.43 1482.15 0.04

Median -57.79 -1610.63 0.04 59.89 1489.96 0.04

Standard

Deviation 1.21 29.31 0.04 2.00 45.10 0.04

7/26/2006

Average -51.84 -1446.65 0.04 59.52 1459.17 0.04

Median -52.79 -1443.03 0.04 60.90 1490.91 0.04

Standard

Deviation 3.01 65.96 0.05 3.00 63.75 0.05

7/27/2006

Average -44.25 -1210.89 0.04 60.51 1440.43 0.04

Median -44.03 -1207.69 0.04 60.31 1437.33 0.04

Standard

Deviation 0.57 15.32 0.04 1.33 41.34 0.03

7/28/2006

Average -41.98 -1154.50 0.04 58.82 1388.11 0.04

Median -41.65 -1140.87 0.04 58.56 1371.02 0.04

Standard

Deviation 0.95 27.80 0.03 1.14 51.91 0.02

7/31/2006

Average -38.46 -1139.35 0.03 52.60 1350.81 0.04

Median -39.91 -1209.23 0.03 54.36 1420.47 0.04

Standard

Deviation 4.64 150.76 0.03 14.42 328.00 0.04

8/1/2006

Average -40.49 -1118.56 0.04 58.45 1357.05 0.04

Median -40.40 -1116.53 0.04 58.56 1361.25 0.04

Standard

Deviation 0.35 10.63 0.03 0.56 12.80 0.04

8/2/2006

Average -41.70 -1185.14 0.04 59.95 1474.93 0.04

Median -41.72 -1187.33 0.04 60.27 1486.60 0.04

Standard

Deviation 0.53 11.03 0.05 1.10 30.72 0.04

142




7/25/2006

slope 21.42 22.19

intercept -382.22 163.53

R-sq 0.79 0.97

7/26/2006

slope 20.42 20.89

intercept -388.06 215.89

R-sq 0.87 0.96

7/27/2006

slope 21.01 27.80

intercept -281.17 -241.55

R-sq 0.61 0.80

7/28/2006

slope 26.48 41.25

intercept -42.73 -1038.58

R-sq 0.81 0.82

7/31/2006

slope 32.03 22.56


R-sq 0.97 0.98

8/1/2006

slope 21.37 5.62

intercept -253.07 1028.81

R-sq 0.51 0.06

8/2/2006

slope 15.59 26.50

intercept -535.04 -113.54

R-sq 0.57 0.90

143


numbered Passes for EG-O-S1-2 B and EG-O-S1-2 T

EG-O-S1-2 B EG-O-S1-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -56.64 -1157.86 0.05 37.09 971.81 0.04

Median -57.10 -1174.86 0.05 37.03 970.57 0.04

Standard

Deviation 2.41 54.54 0.04 0.39 10.31 0.04

7/26/2006

Average -56.88 -1170.50 0.05 34.87 926.35 0.04

Median -61.82 -1221.98 0.05 36.29 940.13 0.04

Standard

Deviation 10.13 129.61 0.08 3.20 36.65 0.09

7/27/2006

Average -55.85 -1086.33 0.05 35.80 919.75 0.04

Median -56.35 -1106.18 0.05 35.72 921.96 0.04

Standard

Deviation 2.52 64.48 0.04 0.34 9.25 0.04

7/28/2006

Average -51.21 -980.26 0.05 36.17 916.74 0.04

Median -51.53 -989.76 0.05 36.18 919.71 0.04

Standard

Deviation 1.53 42.31 0.04 0.63 19.29 0.03

7/31/2006

Average -36.94 -798.49 0.05 29.74 809.83 0.04

Median -34.31 -829.59 0.04 28.16 795.10 0.04

Standard

Deviation 9.38 111.54 0.08 5.64 107.62 0.05

8/1/2006

Average -42.61 -942.86 0.05 36.21 906.95 0.04

Median -42.55 -940.16 0.05 36.18 906.55 0.04

Standard

Deviation 0.60 21.59 0.03 0.24 8.94 0.03

8/2/2006

Average -52.05 -982.99 0.05 35.20 873.09 0.04

Median -52.56 -988.77 0.05 35.04 872.95 0.04

Standard

Deviation 1.24 23.45 0.05 0.41 11.78 0.03

144

Table 58. Linear Relation Chart for Even-numbered Passes for EG-O-S1-2 B and

EG-O-S1-2 T with Area as Y and Strain as X

Date EG-O-S1-2 B EG-O-S1-2 T

7/25/2006

slope 21.01 21.55


R-sq 0.86 0.68

7/26/2006

slope 12.64 11.08

intercept -451.31 540.01

R-sq 0.98 0.94

7/27/2006

slope 25.50 20.64

intercept 338.32 181.20

R-sq 0.98 0.61

7/28/2006

slope 26.30 26.24

intercept 366.27 -32.50

R-sq 0.90 0.73

7/31/2006

slope 11.04 18.74

intercept -390.70 252.56

R-sq 0.86 0.96

8/1/2006

slope 33.56 30.53

intercept 487.14 -198.48

R-sq 0.87 0.66

8/2/2006

slope 17.46 19.60

intercept -73.97 182.94

R-sq 0.86 0.46

145




Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -57.19 -1169.53 0.05 39.66 1026.44 0.04

Median -57.78 -1179.49 0.05 39.75 1028.20 0.04

Standard

Deviation 2.12 39.70 0.05 0.23 5.85 0.04

7/26/2006

Average -61.65 -1216.09 0.05 38.01 985.67 0.04

Median -62.09 -1222.13 0.05 38.56 1000.11 0.04

Standard

Deviation 1.24 31.22 0.04 1.05 30.07 0.03

7/27/2006

Average -51.07 -1006.49 0.05 37.64 972.33 0.04

Median -51.65 -1030.00 0.05 37.70 973.75 0.04

Standard

Deviation 3.65 78.01 0.05 0.36 9.66 0.04

7/28/2006

Average -44.12 -874.97 0.05 37.88 972.21 0.04

Median -44.60 -862.50 0.05 38.01 972.57 0.04

Standard

Deviation 1.93 49.44 0.04 0.56 14.12 0.04

7/31/2006

Average -29.79 -681.95 0.04 29.22 794.67 0.04

Median -30.72 -676.13 0.05 27.27 799.84 0.03

Standard

Deviation 3.18 93.74 0.03 6.04 145.57 0.04

8/1/2006

Average -41.04 -791.79 0.05 38.60 967.89 0.04

Median -40.91 -785.39 0.05 38.62 971.14 0.04

Standard

Deviation 0.89 26.25 0.03 0.46 10.31 0.04

8/2/2006

Average -42.39 -876.18 0.05 37.27 925.01 0.04

Median -42.70 -887.57 0.05 37.22 924.11 0.04

Standard

Deviation 0.73 25.33 0.03 0.28 8.14 0.03

146

Table 60. Linear Relation Chart for Odd-numbered Passes for EG-O-S1-1 B and



7/25/2006

slope 18.06 11.11

intercept -136.51 585.77

R-sq 0.93 0.19

7/26/2006

slope 21.93 28.02

intercept 136.06 -79.13

R-sq 0.76 0.95

7/27/2006

slope 21.19 21.08


R-sq 0.99 0.62

7/28/2006

slope 21.57 23.71


R-sq 0.71 0.90

7/31/2006

slope 8.90 23.57

intercept -416.82 106.11

R-sq 0.09 0.96

8/1/2006

slope 27.81 16.58

intercept 349.71 327.81

R-sq 0.90 0.54

8/2/2006

slope 33.52 20.82

intercept 544.45 148.89

R-sq 0.92 0.50

147




Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -29.82 -705.68 0.04 50.26 1409.76 0.04

Median -29.52 -693.82 0.04 50.23 1413.76 0.04

Standard

Deviation 2.57 73.29 0.04 0.59 27.66 0.02

7/26/2006

Average -22.74 -514.65 0.04 44.56 1235.83 0.04

Median -23.48 -481.48 0.05 47.71 1305.29 0.04

Standard

Deviation 5.12 101.04 0.05 6.33 137.23 0.05

7/27/2006

Average -21.92 -404.37 0.05 47.90 1267.96 0.04

Median -22.37 -411.55 0.05 47.91 1267.64 0.04

Standard

Deviation 1.93 56.05 0.03 0.74 16.56 0.04

7/28/2006

Average -21.21 -364.74 0.06 50.54 1340.17 0.04

Median -21.67 -376.99 0.06 50.47 1334.70 0.04

Standard

Deviation 1.39 33.66 0.04 0.97 29.18 0.03

7/31/2006

Average -13.81 -309.95 0.04 34.28 925.22 0.04

Median -13.47 -320.74 0.04 34.66 887.91 0.04

Standard

Deviation 4.62 87.25 0.05 5.22 112.69 0.05

8/1/2006

Average -17.22 -314.94 0.05 53.19 1417.38 0.04

Median -17.18 -314.10 0.05 53.21 1418.53 0.04

Standard

Deviation 0.21 7.78 0.03 0.53 13.10 0.04

8/2/2006

Average -19.23 -294.18 0.07 50.08 1334.50 0.04

Median -19.13 -293.01 0.07 50.02 1334.82 0.04

Standard

Deviation 0.39 7.09 0.05 0.68 13.81 0.05

148

Table 62. Linear Relation Chart for Even-numbered Passes for EG-O-S1-3 B and


Date EG-O-S1-3 B EG-O-S1-3 T

7/25/2006

slope 28.39 43.99

intercept 140.86 -800.96

R-sq 0.99 0.89

7/26/2006

slope 17.39 21.65

intercept -119.25 270.97

R-sq 0.78 1.00

7/27/2006

slope 28.63 20.26

intercept 223.02 297.86

R-sq 0.99 0.80

7/28/2006

slope 24.00 28.58

intercept 144.27 -104.41

R-sq 0.98 0.91

7/31/2006

slope 16.57 20.59

intercept -81.22 219.35

R-sq 0.77 0.91

8/1/2006

slope 35.23 23.58

intercept 291.56 163.51

R-sq 0.92 0.91

8/2/2006

slope 15.55 19.05


R-sq 0.72 0.89

149


numbered Passes for EG-O-N2-2 B and EG-O-N2-2 T

EG-O-N2-2 B EG-O-N2-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006



Standard

Deviation 0.37 19.28 0.02

No Response No Response No Response

7/26/2006



Standard

Deviation 2.70 100.32 0.03


7/27/2006



Standard

Deviation 0.76 42.44 0.02


7/28/2006



Standard

Deviation 0.43 16.66 0.03


7/31/2006



Standard

Deviation 3.01 33.30 0.09


8/1/2006



Standard

Deviation 0.54 14.17 0.04


150

Table 64. Linear Relation Chart for Even-numbered Passes for EG-O-N2-2 B and

EG-O-N2-2 T with Area as Y and Strain as X

Date EG-O-N2-2 B EG-O-N2-2 T

7/25/2006




7/26/2006




7/27/2006




7/28/2006




7/31/2006




8/1/2006




151




Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006



Standard

Deviation 0.31 7.50 0.04


7/26/2006



Standard

Deviation 2.44 33.86 0.07


7/27/2006



Standard

Deviation 1.25 28.65 0.04


7/28/2006



Standard

Deviation 0.46 13.65 0.03


7/31/2006



Standard

Deviation 5.09 128.10 0.04


8/1/2006



Standard

Deviation 0.40 14.59 0.03


152

Table 66. Linear Relation Chart for Odd-numbered Passes for EG-O-N2-1 B and



7/25/2006 slope 21.22 No Response



7/26/2006 slope -0.83 No Response


















153




Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average No Response No Response No Response 44.14 1023.52 0.04

Median No Response No Response No Response 44.80 1034.89 0.04

Standard

Deviation No Response No Response No Response

1.57 35.15 0.04

7/26/2006



Standard


2.22 155.64 0.01

7/27/2006



Standard


1.61 166.39 0.01

7/28/2006



Standard


1.14 38.80 0.03

7/31/2006



Standard


11.46 420.38 0.03

8/1/2006



Standard


0.79 257.64 0.00

154



EG-U-S2-1 B

EG-U-S2-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -33.28 -769.38 0.04 51.11 1225.10 0.04

Median -33.35 -775.59 0.04 51.17 1221.81 0.04

Standard

Deviation 1.04 20.52 0.05 0.92 19.18 0.05

7/26/2006

Average -34.58 -787.75 0.04 52.78 1273.68 0.04

Median -34.54 -788.72 0.04 52.97 1276.46 0.04

Standard

Deviation 0.54 16.40 0.03 0.75 25.92 0.03

7/27/2006

Average -35.04 -796.20 0.04 53.52 1300.09 0.04

Median -35.24 -801.38 0.04 53.65 1306.53 0.04

Standard

Deviation 0.55 18.91 0.03 0.74 25.62 0.03

7/28/2006

Average -34.85 -791.76 0.04 53.78 1316.84 0.04

Median -34.95 -792.36 0.04 53.83 1316.02 0.04

Standard

Deviation 0.61 17.62 0.03 0.70 20.68 0.03

7/31/2006

Average -31.11 -775.28 0.04 47.13 1226.77 0.04

Median -32.60 -828.28 0.04 49.09 1344.35 0.04

Standard

Deviation 5.09 99.62 0.05 8.09 188.37 0.04

8/1/2006

Average -32.15 -861.64 0.04 51.35 1443.30 0.04

Median -32.18 -866.03 0.04 51.33 1447.64 0.04

Standard

Deviation 0.46 17.04 0.03 0.40 13.57 0.03

8/2/2006

Average -33.89 -856.83 0.04 51.86 1414.28 0.04

Median -33.94 -865.82 0.04 51.77 1410.37 0.04

Standard

Deviation 0.53 18.28 0.03 0.78 15.95 0.05

8/3/2006

Average -33.82 -779.38 0.04 50.43 1230.38 0.04

Median -33.76 -780.20 0.04 50.46 1229.34 0.04

Standard

Deviation 0.47 13.97 0.03 0.67 25.99 0.03

8/4/2006 Average -34.31 -777.19 0.04 51.58 1248.51 0.04

155

Median -34.34 -775.69 0.04 51.60 1250.87 0.04

Standard

Deviation 0.40 14.57 0.03 0.49 14.77 0.03

8/9/2006

Average -34.13 -769.99 0.04 53.05 1275.46 0.04

Median -34.09 -769.32 0.04 53.04 1279.09 0.04

Standard

Deviation 0.54 15.67 0.03 0.72 28.12 0.03

156




7/25/2006

slope 18.99 19.91

intercept -137.48 207.60

R-sq 0.93 0.90

7/26/2006

slope 28.15 32.90

intercept 185.68 -462.81

R-sq 0.87 0.91

7/27/2006

slope 31.12 32.27

intercept 294.07 -426.94

R-sq 0.83 0.88

7/28/2006

slope 26.40 27.57

intercept 128.10 -165.78

R-sq 0.84 0.86

7/31/2006

slope 18.52 22.65

intercept -199.17 159.39

R-sq 0.90 0.95

8/1/2006

slope 35.95 29.26

intercept 294.01 -59.38

R-sq 0.93 0.74

8/2/2006

slope -5.89 9.29

intercept -1056.39 932.56

R-sq 0.03 0.21

8/3/2006

slope -5.89 9.29

intercept -1056.39 932.56

R-sq 0.03 0.21

8/4/2006

slope 28.99 21.05

intercept 217.57 162.77

R-sq 0.64 0.48

8/9/2006

slope 25.68 36.67

intercept 106.33 -669.57

R-sq 0.79 0.87

157



EG-U-S2-2 B

EG-U-S2-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -47.52 -1317.36 0.04 53.37 1429.15 0.04

Median -47.74 -1329.66 0.04 53.90 1449.74 0.04

Standard

Deviation 0.94 36.96 0.03 1.82 48.69 0.04

7/26/2006

Average -46.88 -1310.85 0.04 55.94 1505.48 0.04

Median -46.96 -1317.39 0.04 55.99 1510.89 0.04

Standard

Deviation 0.60 25.77 0.02 0.68 31.05 0.02

7/27/2006

Average -45.98 -1287.37 0.04 56.34 1524.14 0.04

Median -46.06 -1292.19 0.04 56.53 1535.07 0.04

Standard

Deviation 0.51 21.69 0.02 0.77 32.16 0.02

7/28/2006

Average -45.91 -1281.82 0.04 56.07 1521.08 0.04

Median -45.97 -1287.08 0.04 56.36 1530.66 0.04

Standard

Deviation 0.65 25.83 0.03 0.82 31.06 0.03

7/31/2006

Average -42.26 -1266.70 0.03 47.29 1373.96 0.03

Median -45.21 -1337.62 0.03 46.27 1446.26 0.03

Standard

Deviation 5.32 151.65 0.04 7.54 248.27 0.03

8/1/2006

Average -45.84 -1274.29 0.04 54.98 1493.91 0.04

Median -45.99 -1279.21 0.04 55.10 1498.49 0.04

Standard

Deviation 0.45 18.27 0.02 0.67 19.91 0.03

8/2/2006

Average -45.51 -1263.36 0.04 54.76 1499.10 0.04

Median -45.41 -1268.44 0.04 54.82 1493.74 0.04

Standard

Deviation 0.56 24.41 0.02 0.71 29.75 0.02

8/3/2006

Average -45.57 -1271.01 0.04 54.33 1478.47 0.04

Median -45.42 -1264.05 0.04 54.33 1485.12 0.04

Standard

Deviation 0.69 22.55 0.03 0.61 32.65 0.02

8/4/2006 Average -45.46 -1257.58 0.04 55.03 1503.16 0.04

158

Median -45.57 -1258.76 0.04 55.09 1501.68 0.04

Standard

Deviation 0.45 13.02 0.03 0.64 16.40 0.04

8/9/2006

Average -43.38 -1193.35 0.04 56.21 1556.73 0.04

Median -43.66 -1206.01 0.04 56.52 1567.60 0.04

Standard

Deviation 1.40 54.78 0.03 1.40 58.02 0.02

159




7/25/2006

slope 36.51 26.44


R-sq 0.87 0.97

7/26/2006

slope 37.80 42.51

intercept 461.48 -872.70

R-sq 0.77 0.88

7/27/2006

slope 40.24 39.05

intercept 563.06 -675.89

R-sq 0.90 0.88

7/28/2006

slope 38.90 35.56

intercept 504.11 -472.82

R-sq 0.95 0.87

7/31/2006

slope 27.97 32.11

intercept -84.58 -144.58

R-sq 0.96 0.95

8/1/2006

slope 38.07 27.29


R-sq 0.88 0.83

8/2/2006

slope 41.81 39.42

intercept 639.05 -659.44

R-sq 0.91 0.88

8/3/2006

slope 30.56 49.40

intercept 121.81 -1205.84

R-sq 0.86 0.84

8/4/2006

slope 24.03 19.86

intercept -165.15 410.29

R-sq 0.68 0.61

8/9/2006

slope 38.45 40.77

intercept 474.84 -734.80

R-sq 0.97 0.96

160



EG-U-N3-1 B

EG-U-N3-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -15.90 -657.04 0.02 30.35 1141.07 0.03

Median -15.76 -651.72 0.02 30.48 1146.96 0.03

Standard

Deviation 0.57 19.53 0.03 0.34 19.95 0.02

7/26/2006

Average -14.55 -606.74 0.02 31.08 1179.65 0.03

Median -14.58 -612.40 0.02 31.07 1178.76 0.03

Standard

Deviation 0.73 32.44 0.02 0.27 11.44 0.02

7/27/2006

Average -13.31 -543.09 0.02 31.15 1199.07 0.03

Median -13.31 -545.55 0.02 31.08 1196.05 0.03

Standard

Deviation 0.26 20.17 0.01 0.37 15.23 0.02

7/28/2006

Average -12.59 -497.47 0.03 31.38 1218.86 0.03

Median -12.59 -500.74 0.03 31.32 1218.53 0.03

Standard

Deviation 0.37 16.25 0.02 0.30 12.05 0.02

7/31/2006

Average -9.70 -404.67 0.02 22.67 929.34 0.02

Median -11.33 -476.75 0.02 26.76 1087.10 0.02

Standard

Deviation 4.38 185.13 0.02 11.39 470.16 0.02

8/1/2006

Average -12.15 -460.68 0.03 31.70 1167.33 0.03

Median -12.16 -461.65 0.03 31.70 1168.88 0.03

Standard

Deviation 0.19 6.40 0.03 0.30 9.39 0.03

161




7/25/2006

slope 34.03 43.04

intercept -116.10 -165.09

R-sq 0.98 0.54

7/26/2006

slope 43.90 22.26


R-sq 0.98 0.28

7/27/2006

slope 66.06 36.48


R-sq 0.73 0.80

7/28/2006

slope 40.03 21.67


R-sq 0.83 0.29

7/31/2006

slope 41.61 41.07

intercept -1.02 -1.63

R-sq 0.97 0.99

8/1/2006

slope 27.81 8.87

intercept -122.90 886.14

R-sq 0.69 0.08

162



EG-U-N3-2 B

EG-U-N3-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -24.67 -1082.34 0.02 44.74 2190.27 0.02

Median -24.52 -1074.06 0.02 44.91 2197.32 0.02

Standard

Deviation 0.59 23.88 0.02 0.85 41.32 0.02

7/26/2006

Average -23.30 -1031.01 0.02 47.77 2371.51 0.02

Median -23.06 -1024.36 0.02 47.90 2365.05 0.02

Standard

Deviation 0.67 38.09 0.02 0.50 30.49 0.02

7/27/2006

Average -24.35 -1092.11 0.02 52.46 2627.69 0.02

Median -24.35 -1093.87 0.02 52.02 2599.74 0.02

Standard

Deviation 0.28 16.89 0.02 1.56 94.99 0.02

7/28/2006

Average -26.24 -1101.99 0.02 73.27 2833.57 0.03

Median -26.27 -1108.29 0.02 73.84 2882.51 0.03

Standard

Deviation 0.45 19.26 0.02 1.65 109.66 0.02

7/31/2006

Average -21.65 -1000.95 0.02 44.11 2196.31 0.02

Median -22.22 -990.91 0.02 49.94 2467.10 0.02

Standard

Deviation 1.27 84.45 0.02 12.98 707.94 0.02

8/1/2006

Average -25.51 -1162.32 0.02 57.58 2828.78 0.02

Median -25.49 -1160.81 0.02 57.63 2828.59 0.02

Standard

Deviation 0.23 7.58 0.03 0.38 12.14 0.03

163




7/25/2006

slope 39.56 46.53

intercept -106.38 108.80

R-sq 0.94 0.92

7/26/2006

slope 55.20 56.08

intercept 255.37 -307.13

R-sq 0.96 0.85

7/27/2006

slope 52.12 60.10

intercept 177.28 -525.46

R-sq 0.77 0.98

7/28/2006

slope 23.91 57.56

intercept -474.48 -1383.62

R-sq 0.31 0.75

7/31/2006

slope 7.51 54.04

intercept -838.34 -187.27

R-sq 0.01 0.98

8/1/2006

slope 23.32 20.67

intercept -567.59 1638.42

R-sq 0.49 0.41

164




Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006



Standard

Deviation 6.14 215.79 0.03


7/26/2006



Standard

Deviation 4.36 143.85 0.03


7/27/2006



Standard

Deviation 4.15 158.84 0.03


7/28/2006



Standard

Deviation 3.10 109.66 0.03


7/31/2006



Standard

Deviation 27.71 651.91 0.04


8/1/2006



Standard

Deviation 4.96 173.14 0.03


165

Table 77. Linear Relation Chart for Odd-numbered Passes for EG-O-N3-3 B and



7/25/2006




7/26/2006




7/27/2006




7/28/2006




7/31/2006




8/1/2006




166



EG-U-S3-1 B

EG-U-S3-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -36.90 -988.81 0.04 61.20 1794.76 0.03

Median -36.95 -989.24 0.04 61.26 1809.08 0.03

Standard

Deviation 0.24 9.07 0.03 0.94 48.14 0.02

7/26/2006

Average -34.57 -934.61 0.04 63.28 1866.09 0.03

Median -34.50 -932.48 0.04 63.71 1869.31 0.03

Standard

Deviation 1.29 32.08 0.04 1.52 56.30 0.03

7/27/2006

Average -31.87 -885.01 0.04 64.68 1939.10 0.03

Median -31.96 -887.93 0.04 64.47 1915.75 0.03

Standard

Deviation 0.61 14.96 0.04 1.16 52.05 0.02

7/28/2006

Average -31.48 -883.61 0.04 65.53 1976.77 0.03

Median -31.53 -886.32 0.04 65.25 1965.86 0.03

Standard

Deviation 0.28 9.58 0.03 1.36 59.55 0.02

7/31/2006

Average -29.16 -871.67 0.03 59.79 1880.56 0.03

Median -29.43 -861.74 0.03 67.20 2075.70 0.03

Standard

Deviation 1.17 41.50 0.03 10.85 307.73 0.04

8/1/2006

Average -31.87 -916.42 0.03 67.49 2109.05 0.03

Median -31.88 -917.44 0.03 67.55 2104.13 0.03

Standard

Deviation 0.17 7.01 0.02 0.40 15.26 0.03

8/2/2006

Average -30.68 -880.82 0.03 69.39 2145.01 0.03

Median -30.66 -878.09 0.03 69.48 2147.35 0.03

Standard

Deviation 0.18 7.33 0.02 0.61 31.32 0.02

167




7/25/2006

slope 32.67 48.42

intercept 216.42 -1168.80

R-sq 0.72 0.89

7/26/2006

slope 24.63 35.11

intercept -83.34 -355.58

R-sq 0.98 0.90

7/27/2006

slope 23.92 42.89

intercept -122.61 -834.77

R-sq 0.95 0.91

7/28/2006

slope 30.34 42.47

intercept 71.60 -806.61

R-sq 0.81 0.94

7/31/2006

slope 5.20 28.19

intercept -720.11 195.36

R-sq 0.02 0.99

8/1/2006

slope 36.97 29.63

intercept 261.72 109.70

R-sq 0.80 0.59

8/2/2006

slope 28.92 44.15


R-sq 0.48 0.74

168



EG-U-S3-1 B

EG-U-S3-1 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -34.46 -987.09 0.03 65.13 1802.73 0.04

Median -34.62 -990.10 0.03 65.23 1812.38 0.04

Standard

Deviation 0.68 18.49 0.04 0.98 55.57 0.02

7/26/2006

Average -32.82 -942.89 0.03 67.01 1879.16 0.04

Median -32.93 -943.21 0.03 67.14 1878.25 0.04

Standard

Deviation 1.08 26.08 0.04 1.31 51.57 0.03

7/27/2006

Average -30.52 -896.59 0.03 68.40 1938.82 0.04

Median -30.60 -897.76 0.03 68.26 1923.17 0.04

Standard

Deviation 0.56 13.22 0.04 0.99 35.19 0.03

7/28/2006

Average -29.95 -887.54 0.03 68.71 1962.70 0.04

Median -30.01 -889.01 0.03 68.71 1947.81 0.04

Standard

Deviation 0.30 8.72 0.03 1.33 51.38 0.03

7/31/2006

Average -27.98 -888.42 0.03 63.78 1964.67 0.03

Median -28.47 -892.22 0.03 63.87 2157.90 0.03

Standard

Deviation 1.52 55.32 0.03 11.60 330.20 0.04

8/1/2006

Average -30.31 -916.32 0.03 71.03 2088.61 0.03

Median -30.36 -914.40 0.03 71.11 2088.57 0.03

Standard

Deviation 0.17 8.05 0.02 0.36 13.50 0.03

8/2/2006

Average -29.44 -890.32 0.03 72.12 2097.18 0.03

Median -29.42 -891.16 0.03 72.14 2106.48 0.03

Standard

Deviation 0.18 5.29 0.03 0.41 32.40 0.01

169




7/25/2006

slope 26.61 53.79

intercept -70.07 -1700.69

R-sq 0.95 0.90

7/26/2006

slope 23.89 37.94

intercept -158.78 -662.92

R-sq 0.97 0.93

7/27/2006

slope 22.29 32.16

intercept -216.12 -260.69

R-sq 0.88 0.82

7/28/2006

slope 26.68 36.12

intercept -88.54 -518.86

R-sq 0.86 0.88

7/31/2006

slope 29.12 26.75

intercept -73.83 258.63

R-sq 0.64 0.88

8/1/2006

slope 40.63 22.36

intercept 315.04 500.22

R-sq 0.71 0.35

8/2/2006

slope 25.49 60.58

intercept -139.90 -2271.49

R-sq 0.78 0.58

170



EG-U-S3-2 B

EG-U-S3-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -25.28 -792.66 0.03 52.51 1563.64 0.03

Median -25.09 -786.09 0.03 52.29 1558.22 0.03

Standard

Deviation 0.84 27.61 0.03 0.90 35.80 0.03

7/26/2006

Average -24.89 -783.29 0.03 52.52 1566.62 0.03

Median -24.91 -782.14 0.03 52.59 1573.95 0.03

Standard

Deviation 0.30 6.79 0.04 0.51 21.37 0.02

7/27/2006

Average -25.14 -797.92 0.03 52.28 1565.28 0.03

Median -25.16 -797.42 0.03 52.34 1562.59 0.03

Standard

Deviation 0.23 6.82 0.03 0.33 15.04 0.02

7/28/2006

Average -25.27 -800.20 0.03 51.61 1535.27 0.03

Median -25.22 -798.07 0.03 51.39 1530.34 0.03

Standard

Deviation 0.36 13.82 0.03 0.84 31.37 0.03

7/31/2006

Average -25.39 -848.47 0.03 50.82 1615.51 0.03

Median -27.28 -889.57 0.03 53.70 1659.03 0.03

Standard

Deviation 3.35 100.25 0.03 5.73 222.40 0.03

8/1/2006

Average -26.43 -832.75 0.03 50.81 1494.91 0.03

Median -26.41 -833.28 0.03 50.79 1494.88 0.03

Standard

Deviation 0.19 6.96 0.03 0.19 9.46 0.02

8/2/2006

Average -26.38 -825.45 0.03 50.10 1457.13 0.03

Median -26.40 -823.11 0.03 49.89 1454.05 0.03

Standard

Deviation 0.19 8.85 0.02 0.50 24.57 0.02

171




7/25/2006

slope 32.43 39.09

intercept 27.10 -489.25

R-sq 0.97 0.97

7/26/2006

slope 18.76 39.65

intercept -316.34 -515.98

R-sq 0.71 0.90

7/27/2006

slope 26.51 41.39

intercept -131.33 -598.88

R-sq 0.77 0.82

7/28/2006

slope 37.40 36.06

intercept 144.86 -325.86

R-sq 0.93 0.94

7/31/2006

slope 28.88 35.01

intercept -115.14 -163.61

R-sq 0.93 0.81

8/1/2006

slope 25.51 31.55

intercept -158.45 -107.87

R-sq 0.50 0.41

8/2/2006

slope 45.25 45.84

intercept 368.50 -839.58

R-sq 0.90 0.86

172



EG-U-S3-2 B

EG-U-S3-2 T

Date


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)


Cumulative

Area (microStrain-

sec-Hz)

(Peak

Strain)/

(Cumulative

Area)

7/25/2006

Average -26.69 -792.45 0.03 48.24 1609.31 0.03

Median -26.60 -789.05 0.03 48.29 1620.46 0.03

Standard

Deviation 0.52 15.65 0.03 0.54 29.07 0.02

7/26/2006

Average -25.87 -779.62 0.03 48.42 1612.25 0.03

Median -25.87 -776.93 0.03 48.30 1602.37 0.03

Standard

Deviation 0.41 12.45 0.03 0.61 27.50 0.02

7/27/2006

Average -26.06 -792.12 0.03 47.77 1591.65 0.03

Median -26.06 -793.27 0.03 47.68 1584.74 0.03

Standard

Deviation 0.16 7.72 0.02 0.63 28.78 0.02

7/28/2006

Average -25.87 -785.39 0.03 46.73 1560.76 0.03

Median -25.86 -785.90 0.03 46.75 1557.72 0.03

Standard

Deviation 0.20 8.02 0.02 0.69 28.81 0.02

7/31/2006

Average -25.67 -829.50 0.03 44.18 1533.56 0.03

Median -27.59 -878.65 0.03 48.17 1652.75 0.03

Standard

Deviation 3.61 104.37 0.03 8.79 275.29 0.03

8/1/2006

Average -27.04 -813.66 0.03 47.02 1553.02 0.03

Median -27.03 -813.57 0.03 47.07 1542.64 0.03

Standard

Deviation 0.24 8.98 0.03 0.67 28.41 0.02

8/2/2006

Average -26.85 -809.93 0.03 46.19 1539.48 0.03

Median -26.79 -809.32 0.03 46.45 1550.57 0.03

Standard

Deviation 0.21 8.45 0.03 0.71 32.29 0.02

173




7/25/2006

slope 29.04 48.00

intercept -17.21 -705.82

R-sq 0.94 0.79

7/26/2006

slope 28.03 41.79

intercept -54.68 -411.10

R-sq 0.86 0.87

7/27/2006

slope 39.49 43.75

intercept 236.79 -498.19

R-sq 0.70 0.93

7/28/2006

slope 33.53 37.59

intercept 82.13 -195.69

R-sq 0.70 0.81

7/31/2006

slope 27.44 31.28

intercept -125.14 151.35

R-sq 0.90 1.00

8/1/2006

slope 32.63 36.57

intercept 68.78 -166.79

R-sq 0.79 0.75

8/2/2006

slope 30.45 41.61


R-sq 0.58 0.85

174

APPENDIX D: Performance Prediction

Top of Overlay

Performance= -18.0696 (Peak Strain) -551.554 (% Recovery) -1893.5(Number of Axles) +

9587.60


Multiple R 0.85

R Square 0.72

Adjusted R

Square 0.72



Performance= -2157.45 (Number of Axles) + 8956.88


Multiple R 0.82

R Square 0.67

Adjusted R

Square 0.67



Performance= -44.92(Peak Strain) - 180.55 (% Recovery) + 6009.89


Multiple R 0.57

R Square 0.33

Adjusted R

Square 0.33



175

Performance= -17.84 (Peak Strain) -1866.26 (Number of Axles) + 9093.07


Multiple R 0.84

R Square 0.71

Adjusted R

Square 0.71



Performance= -516.87(% Recovery) -2186.54 (Number of Axles) + 9418.64


Multiple R 0.82

R Square 0.68

Adjusted R

Square 0.68



Performance= 0.58 (Area4) + 0.42(Area5) -0.22 (Cumulative Area) -1782.75(Number of

Axles) + 8692.87


Multiple R 0.84

R Square 0.70

Adjusted R

Square 0.70



176

Bottom of Overlay

Performance= 0.50(Peak Strain -125.42 (% Recovery) -2152.56 (Number of Axles) +

9103.88


Multiple R 0.82

R Square 0.66

Adjusted R

Square 0.66



Performance= - -2121.21 (Number of Axles) + 8851.14


Multiple R 0.81

R Square 0.66

Adjusted R

Square 0.66



Performance= 5.70 (Peak Strain) +101.16 (% Recovery) + 3834.78


Multiple R 0.18

R Square 0.03

Adjusted R

Square 0.03





Multiple R 0.81

R Square 0.66

Adjusted R

Square 0.66



177

Performance= -121.24 (% Recovery) -2158.53 (Number of Axles) + 9099.05


Multiple R 0.82

R Square 0.66

Adjusted R

Square 0.66



Performance= -0.05 (Area4) -0.41(Area5) + 0.005 (Cumulative Area) -2193.49(Number

of Axles) + 9240.2


Multiple R 0.82

R Square 0.68

Adjusted R

Square 0.68



178

Top of Underlay

Performance= 12.25(Peak Strain) + 1149.41 (% Recovery) -2152.56 (Number of Axles) +

8066.44


Multiple R 0.85

R Square 0.72

Adjusted R

Square 0.72



Performance= -2177.29 (Number of Axles) + 9025.90


Multiple R 0.82

R Square 0.67

Adjusted R

Square 0.67



Performance= 54.92 (Peak Strain) + 271.06(% Recovery) + 1081.70


Multiple R 0.49

R Square 0.24

Adjusted R

Square 0.24



Performance= 1.16 (Peak Strain) -2160.17 (Number of Axles) + 8931.36


Multiple R 0.82

R Square 0.67

Adjusted R

Square 0.67



179

Performance= 961.06 (% Recovery) -2442.92(Number of Axles) + 9054.82


Multiple R 0.84

R Square 0.71

Adjusted R

Square 0.71



Performance= 0.55(Area4) + 0.82(Area5) +0.065 (Cumulative Area) -1982.06(Number of

Axles) + 9111.31


Multiple R 0.83

R Square 0.69

Adjusted R

Square 0.69



180

Bottom of Underlay

Performance= -23.5 1(Peak Strain) + 763.68(% Recovery) - 2059.42(Number of Axles) +

7664.72


Multiple R 0.83

R Square 0.69

Adjusted R

Square 0.69



Performance= -2107.9 2(Number of Axles) + 8823.16


Multiple R 0.79

R Square 0.62

Adjusted R

Square 0.62



Performance= -76.70(Peak Strain) + 362.44 (% Recovery) + 1989.46


Multiple R 0.61

R Square 0.37

Adjusted R

Square 0.37





Multiple R 0.79

R Square 0.63

Adjusted R

Square 0.63



181

Performance= 688.61 (% Recovery) -2373.32 (Number of Axles) + 8956.13


Multiple R 0.82

R Square 0.67

Adjusted R

Square 0.67



Performance= -0.08(Area4) -0.05(Area5) + 0.11(Cumulative Area) -2169.31(Number of

Axles) + 9120.64


Multiple R 0.79

R Square 0.62

Adjusted R

Square 0.62



Documents

STRAIN-RESPONSE CHARACTERIZATION FOR UNBONDED CONCRETE