Accelerated Determination of ASR

Susceptibility During Concrete Prism 

Testing Through Nonlinear Impact

Resonance Ultrasonic Spectroscopy

PUBLICATION NO. FHWA-HRT-13-085 OCTOBER 2013

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
 

FOREWORD 

Accurate, reliable, and timely laboratory assessment of concrete mixtures—aggregates combined 

with cementitious materials—is a critical component in ensuring the durability of concrete 

infrastructure from the adverse effects of the alkali-silica reaction (ASR). Currently, the 

“Concrete Prism Test” (American Society of Testing and Materials (ASTM) C1293) is the most 

reliable standard test method for assessing the suitability of materials and materials combinations 

for resistance to damage by ASR. However, the main drawback of this method is the 1- to 2-year 

duration required for the test. This research study evaluates a new nonlinear acoustic technique 

for characterization of ASR damage in standard concrete prism specimens. Nonlinear impact 

resonance acoustic spectroscopy offers fast and reliable measurement of the material 

nonlinearity. Microstructural changes that occur as a result of ASR cause an increase in the 

measured nonlinearity, which can be used as a measure of the amount of ASR-induced damage. 

This study evaluates 10 concrete mix designs with varying ASR reactivity. Both standard 

expansion tests and nonlinearity measurements are performed on the specimens. This report 

presents the results of those tests to illustrate the utility of this new method as a complementary 

technique for damage assessment of laboratory concrete prisms specimens. This report is 

intended for those who assess aggregate reactivity by ASTM C1293 or ASTM C1260. 

 Jorge E. Pagán-Ortiz 

 Director, Office of Infrastructure 

 Research and Development 

Notice 

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for its 

contents or use thereof. This report does not constitute a standard, specification, policy, or 

regulation. 

The U.S. Government does not endorse products or manufacturers. Trade and manufacturers’ 

names appear in this report only because they are considered essential to the object of the 

document. 

Quality Assurance Statement 

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement. 
TECHNICAL REPORT DOCUMENTATION PAGE 

1. Report No. 

FHWA-HRT-13-085 

2. Government Accession No. 3. Recipient’s Catalog No. 

4. Title and Subtitle 

Accelerated Determination of ASR Susceptibility During 

Concrete Prism Testing Through Nonlinear Resonance 

Acoustic Spectroscopy 

5. Report Date 

October 2013 

6. Performing Organization Code: 

7. Author(s) 

Krzysztof J. Lesnicki, Jin-Yeon Kim, Kimberly E. Kurtis, 

and Laurence J. Jacobs 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 

Georgia Institute of Technology 

790 Atlantic Drive 

Atlanta, George 50332-0355 

10. Work Unit No. 

11. Contract or Grant No. 

DTFH61-08-R-00010 

12. Sponsoring Agency Name and Address 

Office of Infrastructure Research & Development 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101-2296 

13. Type of Report and Period Covered 

Interim Report 

July 2009–June 2012 

14. Sponsoring Agency Code 

15. Supplementary Notes 

The Contracting Officer’s Representatives are Y.P. Virmani, HRDI-60, and Fred Faridazar, HRDI-20. We are 

grateful to FHWA’s ASR Technical Working Group for its valuable comments in addition to providing 

suggestions throughout the performance period. 

16. Abstract 

Accurate, reliable, and timely laboratory assessment of concrete mixtures—aggregates combined with 

cementitious materials—is a critical component in ensuring the durability of concrete infrastructure from the 

adverse effects of the alkali-silica reaction (ASR). Currently, the “Concrete Prism Test” (ASTM C1293) is the 

most reliable standard test method for assessing the suitability of materials and materials combinations for 

resistance to damage by ASR. However, the main drawback of this method is the 1- to 2-year duration required 

for the test. This research study evaluates a new nonlinear acoustic technique for characterization of ASR damage 

in standard concrete prism specimens. Nonlinear impact resonance acoustic spectroscopy offers a fast and 

reliable measurement of the material nonlinearity. Microstructural changes that occur as a result of ASR cause an 

increase in the measured nonlinearity, which can be used as a measure of the amount of ASR-induced damage. 

This study evaluates 10 concrete mix designs with varying ASR reactivity. Both standard expansion tests and 

nonlinearity measurements are performed on the specimens. This report presents the results of those tests to 

illustrate the utility of the new method as a complementary technique for damage assessment of laboratory 

concrete prisms specimens. 

17. Key Words 

Nonlinear Acoustics, Vibration, Concrete, Alkali 

Silica Reaction, ASR 

18. Distribution Statement 

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161. 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages 

76 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 
ii 
iii 

TABLE OF CONTENTS 

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

CHAPTER 2. THEORETICAL BACKGROUND FOR NONLINEAR ACOUSTICS ......... 3

CHAPTER 3. SAMPLE PREPARATION ................................................................................. 7

MIX DESIGNS .......................................................................................................................... 7

CONCRETE PRISM SAMPLES .......................................................................................... 11

CHAPTER 4. NONLINEAR MEASUREMENT TECHNIQUES ......................................... 13

NRUS TEST SETUP............................................................................................................... 13

NRUS Results ....................................................................................................................... 16

Limitations of NRUS ............................................................................................................ 19

NIRAS TEST SETUP ............................................................................................................. 20

Preliminary NIRAS Results .................................................................................................. 21

Validation of NIRAS Test Setup .......................................................................................... 26

Attachment Method for Accelerometer ................................................................................ 28

Robustness of NIRAS Test Setup ......................................................................................... 35

Validation of Linear Assumption .......................................................................................... 39

SETUP SUMMARY ................................................................................................................ 40

CHAPTER 5. PETROGRAPHIC METHODS ........................................................................ 41

PETROGRAPHIC SAMPLE PREPARATION .................................................................. 41

INTERPRETATION OF PETROGRAPHIC IMAGES ..................................................... 41

CHAPTER 6. RESULTS ............................................................................................................ 43

EXPANSION RESULTS ........................................................................................................ 43

NIRAS RESULTS ................................................................................................................... 45

CORED SAMPLE RESULTS ................................................................................................ 53

PETROGRAPHY TO COMPLEMENT NIRAS RESULTS .............................................. 54

CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS ........................................... 63

CONCLUSIONS ..................................................................................................................... 63

RECOMMENDATIONS FOR FURTHER RESEARCH ................................................... 64

REFERENCES ............................................................................................................................ 65
iv 

LIST OF TABLES 

Table 1. ASTM C1260 results for the aggregates examined ........................................................ 10

Table 2. Mix design matrix for NIRAS and ASTM C1293 concrete prisms ............................... 10

Table 3. Chemical analysis data for Type I cement ...................................................................... 11

Table 4. Mix designs and expansions for Jobe concrete prism samples used for comparison 

between NRUS and NIRAS .............................................................................................. 13

Table 5. Summary of reactivity classifications based on AMBT, CPT, and NIRAS ................... 48
v 

LIST OF FIGURES 

Figure 1. Equation. Nonlinear stress–strain relationship ................................................................ 3

Figure 2. Equation. Relationship between frequency shift and strain amplitude ........................... 3

Figure 3. Equation. Relationship between the frequency shift, the scaled hysteresis parameter, 

and the signal amplitude ..................................................................................................... 4

Figure 4. Equation. Relationship between change in damping and strain amplitude ..................... 4

Figure 5. Equation. Relationship between the change in damping and the signal amplitude ......... 4

Figure 6. Equation. Integral to calculate “cumulative” nonlinearity .............................................. 5

Figure 7. Equation. Approximation of integral to calculate”cumulative” nonlinearity using a 

Riemann sum ...................................................................................................................... 5

Figure 8. Photo. Las Placitas gravel aggregate as received ............................................................ 8

Figure 9. Photo. Spratt limestone aggregate as received ................................................................ 8

Figure 10. Photo. Adairsville limestone (coarse) aggregate as received ........................................ 8

Figure 11. Photo. Adairsville limestone (fine) aggregate as received ............................................ 9

Figure 12. Photo. Alabama sand aggregate as received .................................................................. 9

Figure 13. Photo. Illinois gravel aggregate as received .................................................................. 9

Figure 14. Graph. ASTM C1293 expansions of concrete prisms used in prior project ................ 13

Figure 15. Illustration. NRUS setup schematic ............................................................................ 14

Figure 16. Photo. NRUS test setup ............................................................................................... 14

Figure 17. Equation. Linear resonance frequency ........................................................................ 15

Figure 18. Equation. First compressional resonance frequency ................................................... 15

Figure 19. Graph. FFT for ASR-01 sample using NRUS ............................................................. 17

Figure 20. Graph. FFT for ASR-02 sample using NRUS ............................................................. 17

Figure 21. Graph. FFT for ASR-06 sample using NRUS ............................................................. 18

Figure 22. Graph. Results of frequency sweep for ASR-01 (NRUS) ........................................... 18

Figure 23. Graph. Results of frequency sweep with increasing voltage (NRUS) for ASR-01, 

ASR-02, and ASR-06........................................................................................................ 19

Figure 24. Graph. Frequency shift variation for ASR-02 sample using NRUS ........................... 20

Figure 25. Photo. NIRAS test setup .............................................................................................. 21

Figure 26. Illustration. NIRAS setup schematic ........................................................................... 21

Figure 27. Graph. Typical NIRAS signal in time and frequency domains ................................... 22

Figure 28. Graph. Frequency spectrum for recorded acceleration signal ..................................... 23

Figure 29. Graph. FFT for ASR-01 sample using NIRAS ........................................................... 23

Figure 30. Graph. Normalized frequency versus amplitude for ASR-01 sample (a linear fit 

to the data produces results in a measured nonlinearity of 3.7831) .................................. 24

Figure 31. Graph. FFT for ASR-02 sample using NIRAS ........................................................... 24

Figure 32. Graph. FFT for ASR-06 sample using NIRAS ........................................................... 25

Figure 33. Graph. Normalized frequency shift versus amplitude for ASR-01, ASR-02, and 

ASR-06 samples using NIRAS ......................................................................................... 25

Figure 34. Graph. FFT for aluminum sample ............................................................................... 26

Figure 35. Graph. Normalized frequency shift versus amplitude for aluminum sample .............. 26

Figure 36. Equation. Modulus of elasticity ................................................................................... 27

Figure 37. Equation. Correction factor for fundamental flexural mode ....................................... 27

Figure 38. Photo. Bracket used for casting accelerometer attachment ......................................... 29

Figure 39. Photo. Cast accelerometer attachment for Sample 1 ................................................... 29

Figure 40. Photo. Cast accelerometer attachment for Sample 2 ................................................... 30
vi 

Figure 41. Photo. Cast accelerometer attachment for Sample 3 ................................................... 30

Figure 42. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 23 days 

of age ................................................................................................................................. 31

Figure 43. Graph. FFT and frequency shift in linear format for Sample 1 at 23 days of age ....... 31

Figure 44. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 30 days 

of age ................................................................................................................................. 32

Figure 45. Graph. FFT and frequency shift in linear format for Sample 1 at 30 days of age ....... 32

Figure 46. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 65 days 

of age ................................................................................................................................. 33

Figure 47. FFT and frequency shift in linear format for Sample 1 at 65 days of age ................... 33

Figure 48. Graph. FFT and frequency shift in the frequency domain for Sample 2 at 65 days 

of age ................................................................................................................................. 34

Figure 49. Graph. FFT and frequency shift in linear format for Sample 2 at 65 days of age ....... 34

Figure 50. Graph. FFT and frequency shift in the frequency domain for Sample 3 at 65 days 

of age ................................................................................................................................. 35

Figure 51: Graph. FFT and frequency shift in linear format for Sample 3 at 65 days of age ....... 35

Figure 52. Graph. Variability of NIRAS measurements ............................................................... 36

Figure 53. Illustration. Schematic showing tested positions ......................................................... 36

Figure 54. Graph. Variability for Position 1 ................................................................................. 37

Figure 55. Graph. Variability for Position 2 ................................................................................. 37

Figure 56. Graph. Variability for Position 3 ................................................................................. 38

Figure 57. Graph. Variability for Position 4 ................................................................................. 38

Figure 58. Graph. Variability for damaged sample (note difference in y-axis scale) .................. 39

Figure 59. Graph. Results for higher amplitude excitation for ASR-06 ....................................... 40

Figure 60. Graph. Results for higher amplitude excitation for Mix 4 reference stored at 

ambient conditions ............................................................................................................ 40

Figure 61. Photo. Unpolished stained section ............................................................................... 42

Figure 62. Photo. Polished stained section ................................................................................... 42

Figure 63. Graph. ASTM C1293 expansion results up to 400 days ............................................. 44

Figure 64. Graph. ASTM C1293 expansion results up to 100 days ............................................. 44

Figure 65. Graph. ASTM C1293 expansion results up to 750 days for NR, MR, and SCM 

mixes ................................................................................................................................. 45

Figure 66. Graph. Example of extraction of nonlinearity parameter for Mix 3 at 47 days .......... 46

Figure 67. Graph. NIRAS results up to 750 days ......................................................................... 47

Figure 68. Graph. NIRAS results up to 100 days ......................................................................... 47

Figure 69. Graph. NIRAS results for reference mixes.................................................................. 49

Figure 70. Graph. Nonlinearity comparison between reference and tested samples for 

HR Mix 4 at 250 days ....................................................................................................... 49

Figure 71. Graph. Comparison between reference and tested samples for HR Mix 4 at 

250 days in the frequency domain .................................................................................... 50

Figure 72. Graph. Cumulative nonlinearity .................................................................................. 52

Figure 73. Graph. Cumulative nonlinearity for NR and MR mixes ............................................. 52

Figure 74. Graph. Changes in linear resonance frequency ........................................................... 53

Figure 75. Graph. Nonlinear measurement results on I-75 core ................................................... 54

Figure 76. Graph. Nonlinear measurement results on HWY 316 core ......................................... 54

Figure 77. Photo. Petrographic image for Mix 2 at 1 day ............................................................. 55
vii 

Figure 78. Photo. Petrographic image for Mix 2 at 9 days ........................................................... 56

Figure 79. Graph. Comparison of expansion and nonlinearity results for Mix 2 ......................... 56

Figure 80. Graph. Comparison of expansion and nonlinearity results for Mix 4 ......................... 57

Figure 81. Photo. Image 1 of recast Mix 4 at 12 days .................................................................. 58

Figure 82. Photo. Image 2 of recast Mix 4 at 12 days .................................................................. 58

Figure 83. Photo. Image 1 of recast Mix 4 at 26 days .................................................................. 58

Figure 84. Photo. Image 2 of recast Mix 4 at 26 days .................................................................. 59

Figure 85. Photo. Image 1 recast Mix 4 at 40 days ....................................................................... 59

Figure 86. Photo. Image 2 recast Mix 4 at 40 days ....................................................................... 59

Figure 87. Photo. Image 1 of recast Mix 4 at 54 days .................................................................. 60

Figure 88. Photo. Image 2 of recast Mix 4 at 54 days .................................................................. 60

Figure 89. Photo. Image 1 of recast Mix 4 at 62 days .................................................................. 60

Figure 90. Photo. Image 2 of recast Mix 4 at 62 days .................................................................. 61

Figure 91. Photo. Image 1 of recast Mix 7 at 218 days ................................................................ 61

Figure 92. Photo. Image 2 of recast Mix 7 at 218 days ................................................................ 62

Figure 93. Photo. Image 1 for recast reference Mix 7 at 218 days ............................................... 62

Figure 94. Photo. Image 2 for recast reference Mix 7 at 218 days ............................................... 62
viii 

LIST OF ABBREVIATIONS AND SYMBOLS 

Abbreviations 

AMBT Accelerated Mortar Bar Test 

ASR Alkali-Silica Reaction 

ASTM Refers to ASTM International (formerly American Society for Testing and 

Materials) standards 

CPT Concrete Prism Test 

FA Fly Ash 

FFT Fast Fourier Transform 

GDOT Georgia Department of Transportation 

HR Moderately to Highly Reactive aggregates according to their ASR behavior 

HWY Highway 

I-XX I represents interstate, numbers following denote specific interstate 

kSA kiloSamples 

MR Potentially (or May be) Reactive aggregates according to their ASR behavior 

NDE Nondestructive Evaluation 

NDT Nondestructive Testing 

NEWS Nonlinear Elastic Wave Spectroscopy 

NIRAS Nonlinear Impact Resonance Acoustic Spectroscopy 

Nm Nanometer 

NR Non-Reactive aggregates according to their ASR behavior 

NRUS Nonlinear Resonance Ultrasound Spectroscopy 

NWMS Nonlinear Wave Modulation Spectroscopy 

SCM Supplementary Cementing Materials 

SD Standard Deviation 

SNR Signal-to-Noise Ratio 

UV Ultraviolet 

UV-C light Ultraviolet Radiation at 0.00001 inches (254 nanometers) 

Symbols 

 Stress 

E0 Linear Elastic Modulus 

 Coefficient of Quadratic Anharmonicity 

 Coefficient of Cubic Anharmonicity 

 Strain 

 Measure of the Material Hysteresis 

 Strain Amplitude 

 Strain Rate 

0f Linear Resonance Frequency 

f Resonance Frequency at Increased Excitation Amplitude 

C1 Coefficient Proportional to Material Hysteresis 

A Signal Amplitude 
ix 

η Scaled Hysteresis Parameter 

 0 Linear Damping Rate 

 Damping Rate at Increased Excitation Amplitude 

C3 Coefficient Proportional to Material Hysteresis 

Ω Nonlinear Damping Parameter 

C Cumulative Nonlinearity 

t Time, Thickness 

L Specimen Thickness in Direction of Wave Propagation 

v Wave Speed 

0t Time of Arrival at Receiving Transducer 

E Young’s Modulus of Elasticity 

m Mass 

b Width 

L Length 

t Thickness 

f f Fundamental Resonant Frequency of Bar in Flexure

T1 Correction Factor for Fundamental Flexural Mode 

 Poisson’s Ratio 

1 

CHAPTER 1. INTRODUCTION 

Durability is a major concern for infrastructure throughout the United States, as well as the rest 

of the world. One form of deterioration that may affect concrete structures is the alkali-silica 

reaction (ASR). This reaction typically takes a long period of time to cause damage that is 

visually apparent or that affects the serviceability of the structure; however, prevention of the 

reaction is critical to ensuring a long service life. This issue is particularly relevant in regions 

where there is a reliance on marginal aggregate resources, where low-alkali cement and 

appropriate supplementary cementing materials (SCM) are not readily available, and where there 

is significant exposure to external alkali sources, such as deicing salts and chemicals. However, 

interest in prolonging service life, increasing cement alkali contents, increasing cement content 

in concrete (and hence increasing alkali contents in concrete), as well as regional exhaustion of 

nonreactive aggregate sources, have all resulted in an need for more rapid and reliable methods 

for assessment of the resistance of concrete mixtures to alkali-silica reaction. Hence, it is 

becoming increasingly important to be able to assess a specific combination of materials to 

ensure their long-term durability in the field. 

The ASR occurs between reactive siliceous mineral components of some aggregates and the 

alkaline pore solution present in cement-based materials (where the surrounding environment 

may contribute additional alkali ions). The result is a gel that swells in the presence of sufficient 

amounts of moisture, leading to concrete expansion, cracking, increased permeability, and 

decreased mechanical strength and stiffness.(1,2) Concrete, a brittle material, is particularly 

susceptible to cracking as a result of swelling of the gel because of its low tensile strength as well 

as weaker interfacial zones at the cement and aggregate boundary. 

Currently, ASR susceptibility is assessed through length change in the concrete or mortar 

specimens over time while subjected to accelerated conditions. In the United States, the most 

common standard procedures for this type of test are the “Concrete Prism Test” (CPT), described 

in ASTM International (ASTM, formerly American Society of Testing and Materials) C1293, 

and the “Accelerated Mortar Bar Test” (AMBT), described in ASTM C1260.(3,4) The AMBT is a 

considerably quicker test but it has not been proven reliable in all cases. Also, the aggregate must 

be crushed and sieved to a specified gradation for this test; therefore, the results may not reflect 

field performance of the uncrushed aggregate. The most accurate method, with respect to field 

performance, is the CPT.

(5) To evaluate aggregate reactivity, the test duration is 1 year; to 

evaluate mitigation measures, the duration is 2 years. Expansion of concrete prisms stored over 

water at 100 o

F (38 oC) is monitored, with expansion of greater than 0.04 percent by the end of 

the test indicative of alkali reactivity. The prisms should be prepared using cement with total 

equivalent alkali content (Na2Oe) of 0.9±0.1 percent, with additional alkali added to the mix 

water to bring the total equivalent alkali content to 1.25 percent by mass of cementitious 

materials. The additional internal source of alkali and the elevated temperature are intended to 

accelerate the reaction while maintaining good correlation with field performance. 

One issue with the test is the long test duration, which is viewed as a significant drawback.(5)

Another drawback of the test is the use of the final expansion measurement as the sole measure 

of reactivity. For example, it can be difficult to interpret the potential of concrete mixtures for 

reactivity in the field, especially for CPT results close to the expansion limit of 0.04 percent. A 

direct measurement of damage would be an improvement. While there have been attempts to 
2 

relate the degree of reaction to expansion, there remains significant discussion centered on the 

designation of appropriate expansion limits as well as the appropriate duration of laboratory 

testing, particularly for AMBT, to define aggregate reactivity.(6) This further suggests that more 

accuracy in the screening of aggregate for ASR is necessary. 

Flaws in materials, including microcracking and interfacial debonding, increase the material’s 

nonlinearity, which can be detected by nondestructive evaluation (NDE) techniques. In addition, 

the changes in nonlinear elastic properties are generally orders of magnitude greater than the 

changes in linear elastic properties.(7) Because the changes in nonlinear properties are more 

pronounced, there is an opportunity for earlier, as well as more accurate, damage detection using 

NDE techniques. Measurement of the nonlinear behavior can be accomplished using several 

different techniques, such as nonlinear wave modulation spectroscopy (NWMS), second 

harmonic generation, nonlinear resonance ultrasound spectroscopy (NRUS), and the technique 

that has been developed by the present investigators—the nonlinear impact resonance acoustic 

spectroscopy (NIRAS).(8,9) NRUS uses the thickness resonance of a longitudinal ultrasonic wave, 

and its accuracy depends on exciting this single frequency, which is in the ultrasonic range. In 

contrast, NIRAS excites structural resonances and depends on the cross-sectional area, length, 

and boundary conditions. These resonant peaks are relatively easy to excite and can be well 

spaced, depending on specimen geometry. Finally, NWMS uses multiple acoustic inputs to 

create a modulated signal and measures changes in these modulated signals. Of these, 

researchers have already applied NRUS to concrete samples with thermal damage, reinforced 

concrete beams, bone with mechanical damage, and slate with mechanical damage. (See 

References 10–13.) With regard to ASR damage, NWMS techniques have been applied to 

AMBT specimens and have shown potential for earlier detection of damage.(14,15) Originally, the 

group planned to use the NRUS technique, but the results showed inconsistencies for this 

prismatic sample geometry; hence, NIRAS is used for assessment of ASR damage in CPT 

samples because of the simplicity of the setup and the consistency and clarity of the results. 

The NIRAS technique is based on the same basic principles as NRUS. Damaged specimens 

exhibit nonlinear behavior that is reflected in a decrease in resonance frequency with an increase 

in the level of excitation.(9,13) For low levels of strain excitation, researchers have shown that 

there is a linear relationship between the relative frequency shift and the excitation amplitude.(13)

Because hysteresis effects are dominant in microcracked materials, the ratio of the relative 

frequency shift to excitation amplitude can be taken as a parameter proportional to one of the 

nonlinear elastic properties of materials, called the nonlinear hysteresis strength.(13) This 

hysteresis strength increases with accumulated damage and can be used as a quantitative measure 

of ASR damage. 

The aim of the current research is to develop NIRAS as a reliable, nonlinear ultrasonic 

measurement technique that can more quickly quantify damage associated with ASR in concrete 

specimens. The results of these measurements of nonlinearity in concrete prisms undergoing 

ASR are compared with expansion. In addition, the research focuses on developing an 

understanding of the sensitivity of the technique as well as the reaction through petrographic 

analysis. This report describes the NIRAS technique that has been developed for quantifying 

ASR damage in concrete prisms subjected to standard accelerated laboratory test conditions. 
3 

CHAPTER 2. THEORETICAL BACKGROUND FOR NONLINEAR ACOUSTICS 

It is well known that cracks within a material decrease its resonance frequency by decreasing the 

overall stiffness of the structure. In addition to this linear change in frequency, researchers have 

demonstrated that cracks are also responsible for nonlinear effects, including the strain amplitude 

dependent resonance frequency shift.(16,17) Microcracks inside a material form a network that acts 

as a nonlinear bond system. The nonlinear behavior of this bond system can be attributed to 

Hertzian contact of crack faces and/or opening and closing of cracks in response to wave motion. 

Using the phenomenological model for hysteresis and classical nonlinear constitutive 

relationships, researchers have shown that the nonlinear stress–strain relationship can be shown 

as the equation in figure 1.(9,13). 

   1      sgn  2

0   E      

Figure 1. Equation. Nonlinear stress–strain relationship 

where 

 = stress, 2

m

N 

E0 

= linear elastic modulus, 2

m

N

 = coefficient of quadratic anharmonicity 

 = coefficient of cubic anharmonicity 

 = strain

L

L

, where L is length

 = measure of the material hysteresis 

 = strain amplitude 

 = strain rate, 

second



sgn()  1 if   0 , -1 if   0, and 0 if   0

Assuming that effects of hysteresis are dominant in microcracked materials, the relationship 

between frequency shift and strain amplitude shown in figure 2 is valid for low levels of strain 

excitation.(13) 

   1

0

0 C

f

f f

Figure 2. Equation. Relationship between frequency shift and strain amplitude 

where 

0f 

= linear resonance frequency, Hz 

f = resonance frequency at increased excitation amplitude, Hz 
4 

C1 = coefficient proportional to material hysteresis 

At higher amplitudes, there will also be an additional quadratic term for the strain amplitude

2

1 D  ; however, because the experiments are performed at low levels of strain excitation, this 

higher-order term can be ignored. In these experiments, the amplitude of the signal, A , which is 

proportional to the strain amplitude,  , is measured instead of the strain amplitude. As a result, 

the absolute hysteresis parameter, , is not measured. Instead, a scaled hysteresis parameter

proportional to  is used as a measure of the material’s nonlinearity. The relationship used in 

this investigation is given by the equation shown in figure 3. 

A

f

f f   

0

0

Figure 3. Equation. Relationship between the frequency shift, the scaled hysteresis 

parameter, and the signal amplitude 

Chapter 4 explains in detail the extraction of the parameter  from recorded data. An additional 

effect observed for hysteretic materials is the increase in damping for the sample. The equation 

in figure 4 shows that a linear relationship exists between the change in damping and the strain 

amplitude.(13) 





     3

0

0 C

Figure 4. Equation. Relationship between change in damping and strain amplitude 

where 

 0 = linear damping rate 

 = damping rate at increased excitation amplitude 

C3 = coefficient proportional to material hysteresis 

Because the signal amplitude is proportional to strain amplitude, the relationship between the 

change in damping and the signal amplitude is the equation shown in figure 5: 

 A 

0

0



 

Figure 5. Equation. Relationship between the change in damping and the signal amplitude 

where  is termed the nonlinear damping parameter. 

Because the nonlinearity is attributed to nonlinear interaction of cracks, relatively large and open 

cracks will not contribute to nonlinearity. Under this assumption, the nonlinearity parameter can 

be thought of as an “instantaneous” measure of nonlinearity. Because the measurements for 
5 

tracking nonlinearity in CPT samples are taken at rather long intervals of time, the “cumulative” 

nonlinearity  C can be measured by integration, as shown in the equation in figure 6. 

 

t

C d

0

 ( ) 

Figure 6. Equation. Integral to calculate “cumulative” nonlinearity 

With experimental data, a Riemann sum can be used to approximate this integral (see figure 7). 



    

N

i

C i i i i t t t t

2

1 1 ( )( ( ) ( )) 2

1

  

Figure 7. Equation. Approximation of integral to calculate”cumulative” nonlinearity using 

a Riemann sum 

7 

CHAPTER 3. SAMPLE PREPARATION 

MIX DESIGNS 

For this study, the researchers chose aggregate sources that would provide a range of alkali 

reactivity for assessment using the NIRAS technique. The aggregate sources were selected after 

discussion with the teams at Clemson University and University of Texas at Austin, as well as 

with input from members of Federal Highway Administration’s Technical Working Group on 

ASR. Some of the same aggregate sources were examined by while maintaining a range of alkali 

reactivity. 

The reactivity of the aggregates, shown in their “as received” condition in figure 8, figure 9, 

figure 10 through figure 13, was initially assessed by AMBT. Each of the aggregates was 

crushed, when necessary, to fit the grading requirements prescribed in ASTM C1260. The 

dimensions of mortar bars created were 1 by 1 by 11.25 inch(es) (25 by 25 by 285 mm). For each 

mix design, three samples were created. The samples were cured at about 100-percent relative 

humidity and 73.4 °F (23 °C) for 24 hours. After demolding, the samples were cured for an 

additional 24 hours while immersed in tap water at 176 °F (80 °C). The initial length 

measurements were performed after this curing period. ASR was then induced in the mortar bars 

by immersing them in a 1N sodium hydroxide (NaOH) solution at 176 °F (80 °C). The samples 

were removed from the NaOH solution at regular intervals for expansion measurements as 

prescribed by ASTM C1260. 

Table 1 presents the average expansion of the three samples at 14 days. Again, these results were 

used as an initial means for assessing the reactivity of the individual aggregates used in the 

concrete prisms. According to ASTM C1260, expansion at the end of the test that is less than 

0.10 percent indicates innocuous behavior, expansion greater than 0.20 percent indicates 

potentially deleterious expansion, and expansion between 0.10 and 0.20 percent may be 

innocuous or deleterious in field behavior. 

In this research, all specimens for evaluation by NIRAS and CPT were cast according to the 

ASTM C1293 standard. The mix design matrix, described in table 2, was developed to examine a 

range of ASR behavior, including the combination of two non-reactive aggregates (Mix 1), and 

the use of aggregates termed here as “moderately to highly reactive” (HR) and “potentially (or 

may be) reactive” (MR) aggregates, each in combination with the same non-reactive aggregate 

(NR). (The nonreactive aggregate used in all the mix designs is a limestone from Adairsville, 

GA.) Considering the ASTM C1260 results, along with historical aggregate standard test results 

and field performance history of these aggregates, each of the aggregates was preliminarily 

classified as NR, MR, or HR. Table 2 gives these classifications, along with other details about 

the concrete prism mixtures, including the sample naming scheme. 

In addition, an ASTM C150 Type I cement with alkali equivalent of 0.88 percent, meeting the 

ASTM C1293 requirements, was used in the casting of CPT samples; the alkali content of the 

concrete was “boosted” to 1.25 percent by mass cementitious materials, in accordance with the 

standard. 
8 

Table 3 summarizes the physical and chemical properties of this cement. 

Figure 8. Photo. Las Placitas gravel aggregate as received 

Figure 9. Photo. Spratt limestone aggregate as received 

Figure 10. Photo. Adairsville limestone (coarse) aggregate as received 
9 

Figure 11. Photo. Adairsville limestone (fine) aggregate as received 

Figure 12. Photo. Alabama sand aggregate as received 

Figure 13. Photo. Illinois gravel aggregate as received 
10 

Table 1. ASTM C1260 results for the aggregates examined 

Aggregate Source

14-day AMBT 

Expansion (percent) AMBT Classification 

Limestone, GA 0.0787 Innocuous 

Las Placitas, NM gravel 0.8533 Potentially deleterious 

Spratt limestone, Canada 

(crushed) 0.2661 Potentially deleterious 

Alabama sand, AL 0.1555 Innocuous or potentially deleterious 

Central Illinois sand, IL 0.2088 Potentially deleterious 

Table 2. Mix design matrix for NIRAS and ASTM C1293 concrete prisms 

Mix ID Coarse Aggregate Fine Aggregate 

Supplementary 

Cementing 

Materials

Mix 1 NR/NR Limestone, GA Limestone, GA — 

Mix 2 HR/NR Las Placitas, NM gravel Limestone, GA — 

Mix 3 NR/HR Limestone, GA Las Placitas, NM gravel 

(crushed) — 

Mix 4 HR/NR Spratt limestone, 

Canada Limestone, GA — 

Mix 5 NR/HR Limestone, GA Spratt limestone, Canada 

(crushed) — 

Mix 6 NR/MR Limestone, GA Alabama sand, AL — 

Mix 7 NR/MR Limestone, GA Central Illinois Sand, IL — 

Mix 8 HR/NR—25% FA Spratt limestone, 

Canada Limestone, GA 25% Class F FA 

Mix 9 NR/HR—25% FA Limestone, GA Spratt limestone, 

Canada(crushed) 25% Class F FA 

Mix 10 NR/HR—25% FA Las Placitas, NM gravel Limestone, GA 25% Class F FA 

NR = nonreactive 

MR = potentially or “may be” reactive 

HR = moderately to highly reactive 

FA = fly ash 

— = no supplementary cementing materials 
11 

Table 3. Chemical analysis data for Type I cement 

Chemical Requirements 

ASTM C114 

Test Result, 

(percent by mass) 

Specification Limits 

Type 1 

ASTM C150 

(percentage by mass)

Silicon Dioxide (SiO2) 19.11 — 

Aluminum Oxide (Al2O3) 4.99 — 

Ferric Oxide (Fe2O3) 3.55 — 

Calcium Oxide (CaO) 60.66 — 

Magnesium Oxide (MgO) 3.24 — 

Sulfur Trioxide (SO3) 3.96 3.0 maximum 

Ignition Loss 2.71 3.0 maximum 

Insoluble Residue 0.24 0.75 maximum 

Carbon Dioxide—CO2 Percentage 1.71 — 

Limestone Percentage 4.1 5 maximum 

CaCO3 Percentage in Limestone 94.5 70 minimum 

Tricalcium Silicate (C3S) 42.9 — 

Tricalcium Aluminate (C3A) 7.0 < 8 

C3S + 4.75C3A 76 100 maximum 

Equivalent Alkalis (Na2O+.658K2O) 0.88 — 

Chloride (Cl) 0.01 — 

— No specification 

CONCRETE PRISM SAMPLES 

All CPT samples were prepared using the ASTM C1293 testing procedure. Each sample, with a 

water-to-cement ratio of 0.45, is 3 inches long with a 3-inch square cross section (76 by 76 by 

285 mm). The gradation for coarse aggregate was as specified in ASTM C1293. For fine 

aggregates, the gradation was adjusted through sieving or crushing to achieve a fineness modulus 

of 2.71. This was done to minimize any variability in NIRAS and expansion measurements that 

may have arisen owing to differences in fine aggregate gradation. For each mix design, eight 

specimens were cast, six with studs for expansion measurements and two without studs for 

petrographic examination. The samples were initially cured for 24 hours in a moist environment 

for 23.5  0.5 hours. After demolding, the initial lengths of three samples were recorded. 

Subsequently, those samples, along with one sample for petrography, were transferred to a 

container that is kept at 100.4 °F (38 °C) in an environmental chamber. The container also allows 

the elevation of the specimens above water, providing high relative humidity, which is necessary 

for inducing ASR. The remaining specimens were kept for reference at room temperature; when 

examined, these samples of the same composition as mixes 1 through 10 (table 2) but stored at 

ambient conditions are hereafter referred to as “reference” samples. 

13 

CHAPTER 4. NONLINEAR MEASUREMENT TECHNIQUES 

Two nonlinear acoustic test setups—NRUS and NIRAS—were developed and compared with 

one another, using an existing set of concrete prism samples (ASR-01, ASR-02, and ASR-03) 

that had experienced varying amounts of expansion (see figure 14). The following sections 

describe the setups for NRUS and NIRAS. The three existing concrete prism samples examined 

using these methods had been subjected to 2 years of ASTM C1293 testing and subsequently 

stored for approximately 1 year at ambient conditions. All of these concrete samples contained a 

reactive sand from El Paso, TX (Jobe) but with different binder compositions. Figure 14, the 

expansion plot, shows expansions at the end of the 2-year test, but prior to storage in the 

laboratory. Table 4 shows the binder compositions for these three mixtures, along with the 

expansion measured after 2 years of testing. 

Figure 14. Graph. ASTM C1293 expansions of concrete prisms used in prior project 

Table 4. Mix designs and expansions for Jobe concrete prism samples used for comparison 

between NRUS and NIRAS 

Sample Mix Design

ASTM C1293

2-Year Expansion (percent)

ASR-01 No SCMs 0.543

ASR-02 8% metakaolin 0.048

ASR-03 25% Class C FA 0.347

NRUS TEST SETUP 

The original proposal considered using the NRUS method, and the initial set of measurements 

used the NRUS method for nonlinear parameter measurements. Figure 15 shows a representative 

schematic of the NRUS test setup, and figure 16 shows the physical test setup. 
14 

Figure 15. Illustration. NRUS setup schematic 

Concrete

sample

Function generator

Oscilloscope

Transducers

Figure 16. Photo. NRUS test setup 

A function generator is used to create a sinusoidal input signal with 10-second duration. The 

sinusoidal signal is swept in frequency in a user-specified range around an expected resonance 

frequency of the sample. The input signal is fed through an amplifier and then transmitted 

through an ultrasonic longitudinal transducer (Ultran® GRD100-D50) to the concrete sample. 

The transmitted signal is then received by an identical ultrasonic transducer connected to an 

oscilloscope (Tektronix® TDS 5034B) and sampled at a rate of 125 kiloSamples/second (kSa/s). 

In addition, vacuum grease is used on the surfaces of both transducers to improve the 

transmission and reception of the signal. To ensure the same contact force during the 

measurement each time, the transducers are clamped to the sample. Data recorded using the 
15 

oscilloscope is then analyzed using a developed analysis code, based on the software package 

Matlab®, on a computer. 

With this setup, the first compressional wave resonance mode is excited, which can be calculated 

using the measured compressional wave speed (or the time of flight). The time of flight can be 

measured using a single transducer that sends a compressional wave through the thickness of the 

specimen. The time it takes for the signal to travel to the specimen boundary and reflect back to 

the source is the time of flight, t . Assuming a free surface boundary, the equation in figure 17 

gives the linear resonance frequency. 

L t

v f 21

2 0  

Figure 17. Equation. Linear resonance frequency 

where 

L = specimen thickness in direction of wave propagation, meters 

v = wave speed, 

s

m

t = time of flight, seconds 

However, because of the attenuation in the relatively large CPT specimens, there is no clear 

reflection of the source wave. Alternatively, two transducers are employed, and the time of 

arrival of the signal at the receiving transmitter is used to measure the first compressional 

resonance frequency, as shown in the equation in figure 18. 

0

0

1

L t

v f  

Figure 18. Equation. First compressional resonance frequency 

where 0t = time of arrival at receiving transducer, seconds 

Using the time of arrival, the resonance frequency was determined to be about 23 to 

25 kilocycles per second (23 to 35 kHz), but when the frequency sweep was performed in this 

range, there was no clear peak in signal amplitude as expected for resonance. Therefore, the 

frequency was progressively increased until a significant increase in signal amplitude was 

detected. In other words, a sinusoid at a constant amplitude (voltage) and frequency was used as 

an input, and the amplitude of the transmitted signal was monitored as the input frequency was 

increased. The frequency at the observed amplitude increase was assumed to correspond to the 

first compressional resonance mode. The frequency sweep was then set to the range around this 

frequency, and the input voltage was progressively increased from about 10 to 190 volts. (All the 

measured data fall in this range but the same voltages are not used for different specimens.) The 

signal in the time domain was then analyzed with a fast Fourier transform (FFT) to obtain the 

frequency spectrum. 
16 

NRUS Results 

The results of the FFT analysis for ASR-01, ASR-02, and ASR-06 are shown in figure 19, figure 

20, and figure 21, respectively. The amplitude in the frequency domain is representative of the 

input signal amplitude, in volts, at a given frequency. The frequency at which the largest 

amplitude magnitude is measured (“output”), when applying a voltage varying from 10 to 

190 volts, is then assumed to be the resonance frequency. The resonance frequency at the lowest 

excitation is assumed to be the linear resonance frequency, 0f . The left side of the equation 

shown in figure 3 is then calculated by taking the difference between the linear resonance 

frequency and the frequency at the current excitation level, f  f 0 , as shown in figure 19. 

Further details can be found in Reference 10. 

The calculated difference, f  f 0 , is then normalized by the linear resonance frequency and 

plotted against amplitude, as shown in figure 22. The nonlinear parameter, , is then the slope of 

the data as dictated by the equation in figure 3 and illustrated in figure 22. 

Figure 23 presents the results for the three specimens tested together, along with the expansion 

recorded at 720 days and measured nonlinearity. Using the nonlinear parameter, each sample is 

clearly differentiated, showing distinguishable nonlinearity levels. Surprisingly, comparing 

NRUS results with the expansion values last recorded at 720 days, there is a discrepancy. The 

ASR-01 sample had more expansion at 720 days compared with ASR-06 but the measured 

ASR-06 nonlinearity is higher. 

However, it is important to consider that the expansion results were not obtained at the same 

time as the nonlinearity measurements. Even though both ASR-01 and ASR-06 were well 

beyond the 0.04-percent expansion limit at 2 years of CPT, it is not clear how any further 

development of damage has progressed in the samples over this last year of ambient storage. 

Therefore, a comparison of expansion values from the end of the CPT test with nonlinearity 

measured by NRUS may not be valid. 
17 

Figure 19. Graph. FFT for ASR-01 sample using NRUS 

Figure 20. Graph. FFT for ASR-02 sample using NRUS 
18 

Figure 21. Graph. FFT for ASR-06 sample using NRUS 

Figure 22. Graph. Results of frequency sweep for ASR-01 (NRUS) 
19 

Figure 23. Graph. Results of frequency sweep with increasing voltage (NRUS) for ASR-01, 

ASR-02, and ASR-06 

Limitations of NRUS 

While the NRUS method distinguished between the different concrete mixtures, the peak 

assumed to be a resonance mode had a higher frequency than expected based on time of flight 

measurements. This local peak could not be confirmed to correspond to resonance frequencies or 

their harmonics. Because it is unclear where this local peak in the frequency domain originated, 

there is a question of robustness and reliability of the technique. In addition, there were 

difficulties with consistency in the measurements, as illustrated in figure 24. Measurements for 

the ASR-02 sample were repeated by reassembling the setup between measurements. Between 

each measurement trial, the transducers were removed from the specimen, the specimen and 

transducers were cleaned, and the specimen was again coupled to the transducers using vacuum 

grease. It was found that the results were not consistent when the setup was reassembled, 

producing considerable scatter. It is speculated that this could result from changes in the 

boundary (transducer to sample coupling) conditions caused by reassembling the test setup. 
20 

Figure 24. Graph. Frequency shift variation for ASR-02 sample using NRUS 

NIRAS TEST SETUP 

Because of inconsistent results obtained with the NRUS technique, an alternate method of 

excitation was attempted. The new technique uses the natural vibration of the specimen as the 

probing signal and is termed NIRAS, first introduced for assessment of alkali reactivity of 

aggregates by Chen et al.(9) Instead of using a frequency sweep employing transducers in 

ultrasonic frequency range, the sample is excited with a low amplitude impact. The setup is 

similar to the ASTM C215 procedure for the measurement of the transverse resonance 

frequency.(18) The specimen is placed on a 1.5-inch (38 mm) thick support mat to allow free 

vibration. A 5-oz. (140-g) hammer is used to strike the sample in the center of the specimen, as 

shown in figure 25. An accelerometer (PCB 353B13) is attached using super glue to one end of 

the specimen, at the center, where the response is at a maximum for the transverse mode. The 

sample is tested 1 minute after the attachment of the accelerometer, and the signal is then 

captured using a TektronixTM TDS5034B oscilloscope and analyzed using Matlab®. The 

schematic for this setup is shown in figure 26. The signal duration captured by the oscilloscope is 

0.4 seconds, which allows a complete decay of the response signal, with a sampling rate of 

500 kSa/s. The signal is then “zero-padded” and analyzed in Matlab® using the FFT. The “zeropadding” increases the signal duration by appending trailing zeros at the end of the signal. This 

increases the apparent resolution in the frequency domain, allowing more accurate identification 

of the resonance peak frequency. The signal processing for both the NRUS and NIRAS 

techniques is essentially the same, and both rely on the same nonlinear resonance theory. 

However, as is demonstrated throughout this chapter, the NIRAS technique proves to be much 

more repeatable and robust. 
21 

Figure 25. Photo. NIRAS test setup 

Figure 26. Illustration. NIRAS setup schematic 

Preliminary NIRAS Results 

The NIRAS technique was also initially applied to the Jobe aggregate concrete prism samples 

(see table 4) to assess the performance of the technique. The impact excites the specimen’s 
22 

natural vibration. Figure 27 shows the typical signal captured by the accelerometer in both the 

time and frequency domains (for ASR-01 in this case). Notice that the signal is a simple 

decaying oscillation. Figure 27 also shows that the captured signal has a high signal-to-noise 

ratio (SNR) and that the frequency spectrum has a clearly defined resonance peak. The high SNR 

can be seen in the time domain signal, which has significantly higher amplitude than the noise 

before the impact (i.e., before 0.04 seconds). 

Figure 27. Graph. Typical NIRAS signal in time and frequency domains 

Figure 28 shows a larger portion of the spectrum, demonstrating that the fundamental resonance 

mode is the only mode excited with this technique. The spectrum is shown up to 10 kHz because 

this is the maximum frequency that can be excited with the impact hammer. There is some lowfrequency content at the beginning of the signal, which can be induced by the vibration of the 

support or equipment near the testing area. However, these low frequencies will not affect the 

results because the resonance occurs at considerably higher frequencies. For testing of 

nonlinearity, the procedure is repeated 10 times, with progressive increases in the strength of the 

impact. Figure 29 shows the result for the concrete prism ASR 1. Just as in the NRUS 

measurements, the lowest amplitude resonance frequency is assumed to be the linear resonance 

frequency, 0f . The difference between this linear resonance frequency and the frequency at a 

higher amplitude impact, f  f 0 , is normalized by the linear frequency and plotted against the 

recorded signal amplitude in figure 30. A linear fit is used for the data in this plot to find the 

nonlinearity parameter, which is simply the slope. The results, in the frequency domain, of 

applying the technique to the ASR-02 and ASR-06 samples are also shown in figure 31 and, 

figure 32, respectively. 

 FFT
23 

Figure 28. Graph. Frequency spectrum for recorded acceleration signal 

Figure 29. Graph. FFT for ASR-01 sample using NIRAS 
24 

Figure 30. Graph. Normalized frequency versus amplitude for ASR-01 sample (a linear fit 

to the data produces results in a measured nonlinearity of 3.7831) 

Figure 31. Graph. FFT for ASR-02 sample using NIRAS 
25 

Figure 32. Graph. FFT for ASR-06 sample using NIRAS 

Figure 33 plots the normalized frequency against amplitude for all three samples. These results 

show that the sample with the least expansion, ASR-02, is well-differentiated from the more 

expansive mixes, ASR-01 and ASR-06. However, contrary to expansion results, the results from 

both the NRUS and NIRAS techniques suggest that the ASR-06 sample is more damaged than 

ASR-01 because the nonlinearity of ASR-06 is greater. However, as previously mentioned, the 

comparison may not be valid because the samples may have experienced further damage during 

1 year of ambient storage after conclusion of the ASTM C1293 exposure and testing. 

Figure 33. Graph. Normalized frequency shift versus amplitude for ASR-01, ASR-02, and 

ASR-06 samples using NIRAS 
26 

Validation of NIRAS Test Setup 

To ensure that the measured nonlinearity is solely due to the material behavior, the linearity of 

the entire experimental measurement setup, which includes a few electronic devices, was 

confirmed using a linear elastic material. By convention, the test set up was validated through 

measurements of a linear elastic aluminum (6061) prism. This prism is of similar dimensions,

3 by 3 by 12 inches (76.3 by 76.3 by 304 mm) to the concrete samples. The results in figure 34 

and figure 35 illustrate that for an undamaged and isotropic sample, there is no detectable change 

in the resonance frequency. 

Figure 34. Graph. FFT for aluminum sample 

Figure 35. Graph. Normalized frequency shift versus amplitude for aluminum sample 

This also shows that there are no spurious nonlinear effects from the instrumentation. Also, note 

that the resonance peak for aluminum is significantly sharper than broad peaks recorded for 

concrete caused by lower attenuation. In addition, because of the lower attenuation, the natural 
27 

vibration takes longer to decay, so the window was extended to 2 seconds with a 250 kSa/s 

sampling rate. 

To confirm the resonance peak measurements taken using the impact testing method, the 

equation (see figure 36) provided in ASTM E1876 was used to calculate the modulus of 

elasticity with the measured resonance frequency.(19) 

1

2 3

0.9465 T

t

L

b

mf E f





 



















 

Figure 36. Equation. Modulus of elasticity

where 

E = Young’s modulus of elasticity, Pa 

m = mass of the bar, g 

b = width of bar, mm 

L = length of bar, mm 

t = thickness of bar, mm 

f f = fundamental resonant frequency of bar in flexure, Hz 

T1 = correction factor for fundamental flexural mode given by the equation in figure 37

 

 

  



























 



   





 



  







 



   

 



    

2

2

4

2

2 4

2

1

1 6.338 1 0.1408 1.536

8.340 1 0.2023 2.173

1 6.585 1 0.0752 0.8109 0.868

L

t

L

t

L

t

L

t T

 

 

 

Figure 37. Equation. Correction factor for fundamental flexural mode

where  is Poisson’s ratio. 

These calculations were performed for aluminum, whose modulus of elasticity is well known to 

be close to 10152.64 ksi (70 GPa). The calculation with the measured weight and resonance 

frequency yielded a modulus of elasticity of 10075.77 ksi (69.47 GPa). This result shows the 

accuracy of determining the resonance frequency of a material with the impact method. Taking 

10152.64 ksi (70 GPa) as an accepted value yields less than 1-percent error using the impact 

testing method. If these calculations are applied to CPT samples, making reasonable assumptions 

about the Poisson’s ratio and dynamic modulus, the calculated resonance frequencies are in the 

same range as the measured ones. Note that the standard ASTM C215 has similar equations for 

calculating the dynamic modulus of elasticity using resonance frequency. The difference 

between ASTM C215 and ASTM E1876 is in the calculation of a correction factor. The 

correction factor in ASTM C215 is specific to concrete while the correction factor in 
28 

ASTM E1876 is more general and can be used with higher values of Poisson’s ratio. In fact, 

using the properties of the concrete prism and the correction factor from ASTM E1876 yields a 

similar result to following the procedure described in ASTM C215. 

Attachment Method for Accelerometer 

Alternative attachment techniques have been explored in an effort to improve robustness of the 

NIRAS technique. Casting a screw attachment into the sample was investigated to test whether 

improvements in consistency could be achieved. The very reactive Las Placitas aggregate was 

used in this assessment. The casting of the screw attachment was achieved using a bracket, 

which held the attachment during the casting, as shown in figure 38. Inconsistencies were noted 

in the embedment depth and bonding of the cast screw attachment to the concrete for the three 

samples, as shown in figure 39, figure 40, and figure 41. Consequently, the results were also 

varied. Figure 42 and figure 43 show the FFT and frequency shift for sample 1 at an early age, 

where the standard deviation (SD) is about 29 percent from the mean, but for a later age, shown 

in figure 44 and figure 45, the SD from the mean is only about 2 percent. Also, note that the 

accelerometer could not be attached using an adhesive in the same spot as the cast attachment, 

and this can also be a source of variability between the attachment methods. 

Because the screw attachment was steel and could also be used as an attachment for a magnet, 

this coupling technique was also investigated. Figure 46 through figure 51 show the results at 

65 days for all three samples with all three coupling techniques. The SD is 26.51 percent for 

figure 46 and figure 47, 19.92 percent for figure 48 and Figure 49, and 20.03 percent for figure 

50 and figure 51. 

Based on the current results, there does not seem to be an apparent advantage to casting a 

screw/magnet attachment into the specimens. In fact, looking at figure 50 and figure 51, some 

irregularities in the FFT signal are noticeable for the screw attachment that are not seen for the 

magnet or adhesive attachment. Consequently, for the remainder of the project, the focus will to 

increase the robustness of using an adhesive attachment; the adhesive attachment also has the 

advantage of being semi-permanent and can be readily applied to concrete cores. 
29 

Figure 38. Photo. Bracket used for casting accelerometer attachment 

Figure 39. Photo. Cast accelerometer attachment for Sample 1 

CPT Mold

Bracket

Accelerometer 

Attachment 
30 

Figure 40. Photo. Cast accelerometer attachment for Sample 2 

Figure 41. Photo. Cast accelerometer attachment for Sample 3 
31 

Key — = Screw Linear Ft where η = 2.65 

--- = Adhesive Linear Fit where η = 1.75 

Figure 42. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 

23 days of age 

Figure 43. Graph. FFT and frequency shift in linear format for Sample 1 at 23 days of age 
32 

Key — = Screw Linear Ft where η = 4.271 

 --- = Adhesive Linear Fit where η = 4.1487 

Figure 44. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 

30 days of age 

Figure 45. Graph. FFT and frequency shift in linear format for Sample 1 at 30 days of age 
33 

Key — = Screw Linear Ft where η - 6.4684 

--- = Adhesive Linear Fit where η = 4.5441 

Figure 46. Graph. FFT and frequency shift in the frequency domain for Sample 1 at 

65 days of age 

Figure 47. FFT and frequency shift in linear format for Sample 1 at 65 days of age 
34 

Key — = Screw Linear Ft where η - 2.6125 

--- = Adhesive Linear Fit where η = 1.8657 

Figure 48. Graph. FFT and frequency shift in the frequency domain for Sample 2 at 

65 days of age 

Figure 49. Graph. FFT and frequency shift in linear format for Sample 2 at 65 days of age 
35 

Key — = Screw Linear Ft where η = 2.9783 

--- = Adhesive Linear Fit where η = 2.1516 

Figure 50. Graph. FFT and frequency shift in the frequency domain for Sample 3 at 

65 days of age 

Figure 51: Graph. FFT and frequency shift in linear format for Sample 3 at 65 days of age 

Robustness of NIRAS Test Setup 

The consistency of the NIRAS setup was also tested by repeating measurements on the same 

sample 10 times on mature specimens in a brief time span, removing the accelerometer and regluing it each time the slope, which represents nonlinearity, was recorded. The sample tested was 

one of the Mix 1 reference samples (see table 2). The result is shown in figure 52, which 

demonstrates about 10-percent SD from the mean nonlinearity (AVG). 
36 

 

Figure 52. Graph. Variability of NIRAS measurements 

This procedure was repeated on a second sample from the Mix 1 reference batch at four 

positions; a schematic is shown in figure 53. Figure 54 and figure 55 show the results for 

Positions 1 and 2, respectively, and the results for Positions 3 and 4 are shown in figure 56 and 

figure 57, respectively. 

Figure 53. Illustration. Schematic showing tested positions 

AVG
37 

Figure 54. Graph. Variability for Position 1 

Figure 55. Graph. Variability for Position 2 

AVG

AVG
38 

Figure 56. Graph. Variability for Position 3 

Figure 57. Graph. Variability for Position 4 

Note that the mean values for Positions 1 and 2 are very close together. This makes sense 

because these positions are on the same prism surface but at opposite ends, so the same vibration 

mode is being measured. The SD for these positions is also practically the same. However, this 

SD is higher than the previously reported 10 percent shown in figure 52. This may be because 

these positions had been previously tested very frequently and a debonder (e.g., acetone) was not 

always used to remove the old adhesive. This resulted in a deteriorated surface at those positions, 

which may explain the higher SD. Positions 3 and 4 were tested for the first time, so the surface 

condition was relatively smooth, and the results show a markedly improved SD. Also, as before, 

the mean value is very close for the two positions because they are on the same surface of the 

prism. The average nonlinearity for the 10 data sets for Positions 3 and 4 is higher than the 

nonlinearity for Positions 1 and 2. This result is expected because both the material itself and the 

AVG

AVG
39 

damage are not perfectly isotropic so these modes will not be purely symmetric. As a result, the 

excitation of a different surface can result in the vibration of a different cross-section property, 

which can cause measurement variability. 

The samples used for these measurement variability experiments were undamaged samples with 

relatively low nonlinearity; therefore, a set of measurements was also made on a damaged 

sample with relatively high nonlinearity. The result, shown in figure 58, gives a linear 

relationship and an SD in measurements that are comparable to results for the sample with low 

nonlinearity. (Note that the y-axis scale for figure 58 is different than for figure 54 through figure 

57.) 

Figure 58. Graph. Variability for damaged sample 

(note difference in y-axis scale) 

Validation of Linear Assumption 

As noted in the theoretical background section of this report, the nonlinear parameter used in this 

study is extracted by assuming a linear relationship between frequency shift and strain amplitude. 

This is thought to hold true for low levels of strain amplitude. A question that arises from that 

assumption concerns the limit to which that statement holds true. This limit was tested on 

samples with relatively high (ASR-06) and low nonlinearity (Mix 4 reference, stored at ambient 

conditions). The results demonstrate that the limit is not the same for both samples. The highly 

nonlinear sample shown in figure 59 deviates from the linear relationship at a relatively low 

amplitude but there is no deviation for the sample with low nonlinearity, shown in figure 60. 

Note that both samples were excited to the same level of impact excitation but the response of a 

highly nonlinear specimen has lower amplitude than that of one with low nonlinearity owing to 

peak broadening (greater damping). These results demonstrate that for a highly nonlinear sample, 

the relationship between frequency shift and amplitude is linear for amplitudes lower than 

5 x 10-3 volts The relationship remained linear for all levels of excitation for the sample with low 

nonlinearity. In all other measurements in this project, the impact excitation was kept low 

enough to avoid a nonlinear relationship between frequency shift and amplitude. 

AVG
40 

Figure 59. Graph. Results for higher amplitude excitation for ASR-06 

Figure 60. Graph. Results for higher amplitude excitation for Mix 4 reference stored at 

ambient conditions 

SETUP SUMMARY 

These results show the ability of the nonlinear resonance techniques to distinguish the less 

damaged (i.e., lower slope) samples from the highly damaged (i.e., higher slope) samples and 

suggest the potential of this approach for damage assessment in concrete. Because the results of 

NIRAS are clear and consistent, the NIRAS technique has been applied to all the mixtures listed 

in table 3.
41 

CHAPTER 5. PETROGRAPHIC METHODS 

In addition to expansion measurements, a limited petrographic analysis is performed on 

companion CPT samples as a complementary assessment of the progression of damage. 

Companion samples for petrography were cast from each of the mixes tested by NIRAS and 

CPT. The petrographic examination relies on the use of a fluorescent stain that can be used to 

quickly identify the presence of ASR gel. The uranyl acetate staining technique was introduced 

by Natesaiyer and Hover, and it has also been appended to ASTM C856 Standard Practice for 

the Petrographic Examination of Hardened Concrete.(20,21) From previous studies, it has been 

determined that silica gel possesses the capability of adsorption of ions as well as ion exchange. 

When the ASR gel is formed in concrete, the cations present may include calcium, sodium, and 

potassium. Through ion exchange, the uranyl ion, in uranyl acetate stain solution, can replace the 

cations present in the gel. Because the uranyl ion fluoresces green when excited by ultraviolet 

radiation at 0.00001 inches (254 nm) (UV-C light), the silica gel in concrete can be easily 

identified with a UV-C light source after staining. However, it has been found that siliceous, not 

necessarily reactive, aggregates also fluoresce because the silica surface always contains free 

OH- groups with adsorbed cations, which can be replaced by the uranyl ion.(21) This can cause 

complications with the analysis of the images because the fluorescence of the aggregate can 

make it difficult to distinguish between the aggregate and reaction rims. Despite this limitation, 

the technique is still useful for tagging possibly relevant features in the microstructure, which 

simplifies the petrography. 

PETROGRAPHIC SAMPLE PREPARATION 

Whenever petrography is performed, a 0.5-inch-thick rectangular sample is cut, using a table 

saw, from the concrete prism. The sample is rinsed briefly with de-ionized water and placed in a 

fume hood, as a safety precaution to prevent inhalation. The 0.11 N uranyl acetate solution is 

applied to the freshly cut surface using a pipette and allowed to rest for 1 minute. Next, the 

surface is thoroughly rinsed with de-ionized water, and the sample is placed under a microscope. 

A heavy tarp is placed over the microscope instead of using a dark room. A UV lamp is used to 

illuminate the surface of the sample and a built-in camera (SPOTTM Insight color camera) is used 

to capture the image from the microscope (Leica® MZ6 stereomicroscope). The initial 

petrography was conducted using a handheld UV lamp (UVP Model UVSL-14P) and, in an 

effort to improve image quality, a higher-intensity pen-ray lamp (UVP Model 11SC-1), with 

short wavelength filter, has been used in the later stages of petrographic examination. 

INTERPRETATION OF PETROGRAPHIC IMAGES 

Note that the results presented in this report were obtained on unpolished sections. The loss of 

the gel was a concern at the start of the petrographic examination, and it was decided to forego 

polishing to limit this loss. However, in an effort to improve image quality, polishing was tried 

on an ASR damaged Las Placitas sample. Observation of fluorescing ASR gel suggests that the 

sample preparation methods used are appropriate for these types of samples. Figure 61 shows a 

representative unpolished stained section for a concrete prism with a reactive aggregate, and 

figure 62 shows a polished section for the same concrete prism (different section). The concrete 

prism is a recast version of Mix 2. Additional specimens for Mix 2 were cast to allow imaging 

during the initial stages of the reaction. When comparing the images in figure 61 and figure 62, 
42 

there does not appear to be any evidence of loss of ASR gel. In fact, figure 62 shows a relatively 

large crack that is still stained after polishing. When comparing the quality of the images, the 

unpolished section does not appear as clear as the polished section. For the unpolished section, it 

is difficult to achieve good focus, especially at higher magnifications, resulting in diminished 

image quality. For the polished section, the image is not only in focus but the stained features are 

more distinct. In the polished section, it is possible to see microcracks at the edge of the 

macrocrack. Based on these results, for future petrographic examination, the samples will be 

polished before staining. 

 

500 microns = 0.19685 inches

Figure 61. Photo. Unpolished stained section

 

500 microns = 0.19685 inches

Figure 62. Photo. Polished stained section 
43 

CHAPTER 6. RESULTS 

EXPANSION RESULTS 

This section presents the expansion measurement results for the concrete mixtures described in 

table 2. Note that in this study, the expansion measurements are taken more frequently than 

required in the ASTM C1293 standard. Figure 63 shows the results of the expansion 

measurements for the HR mixtures. Comparing the results from ASTM C1260 (table 2) and the 

measured expansions in figure 63, it is evident that there is good agreement for the classification 

of the HR mixtures (i.e., mixes 2 through 5). Figure 64 shows results up to 100 days to facilitate 

identification of the specimen age at which the 0.04-percent expansion limit, indicating 

aggregate reactivity, is crossed. Mixes 2 through 5 have expansions that cross this limit during 

the test period. Also, the relatively rapid expansion rate for these mixes further suggests the 

relatively high reactivity of these aggregates. There also appears to be some observation of more 

rapid and, in one case, larger expansion when the reactive aggregate is crushed and used as the 

fine in the mixture. This is demonstrated when comparing mixes 2 and 3 as well as mixes 4 

and 5. However, an exception to this observation is the behavior for Mix 4 when recast, to better 

evaluate the early (<100 days of age) expansion behavior; that sample set has an 

uncharacteristically high rate of expansion compared with previous results for Mix 4. The 

underlying cause for this difference in behavior between the two sample sets is not clear; it may 

simply be related to the variability inherent in concrete and in reactive aggregates in particular. 

Results for the NR Mix 1, the MR mixes 6 and 7, and SCM-containing mixes 8 and 9 are 

presented in figure 65. The average expansion of mixes 1 and 6 has not crossed the expansion 

limit at 1 year; therefore, these are classified as nonreactive by the CPT standard. Mix 6 was 

expected to experience more expansion than Mix 1 because, according to ASTM C1260, the 

aggregate in Mix 6 was classified as innocuous or potentially deleterious. According to these 

concrete prism results, the aggregate is nonreactive but it does come very close to the expansion 

limit, demonstrating perhaps some of the challenges associated with determining reactivity 

through expansion measurements alone. The 25-percent replacement of cement with fly ash (FA) 

in mixes 8 and 9 appears to be effective in mitigating expansion with the Spratt aggregate 

because the expansion limit has not been crossed. For comparison, mixes 4 and 5, using the same 

aggregate, crossed the limit before 100 days. Mix 7 crossed the limit at about 150 days and can 

be classified as reactive using the CPT standard. 
44 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 50 100 150 200 250 300 350 400

Expansion (%)

Specimen Age (days)

Mix 2 HR (Las Placitas)/NR Mix 3 NR/ HR (Las Placitas)

Mix 4 HR (Spratt)/NR Mix 4 (recast)

Mix 5 NR/ HR (Spratt) ReactiveAgg Expansion Limit

Figure 63. Graph. ASTM C1293 expansion results up to 400 days 

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100

Expansion [%]

Specimen Age [days]

Mix 2 HR (Las

Placitas)/NR

Mix 3 NR/ HR

(Las Placitas)

Mix 4 HR

(Spratt)/ NR

Mix 4 (recast)

Mix 5 NR/ HR

(Spratt)

ReactiveAgg

Expansion Limit

Figure 64. Graph. ASTM C1293 expansion results up to 100 days 
45 

Figure 65. Graph. ASTM C1293 expansion results up to 750 days for NR, MR, and SCM 

mixes 

NIRAS RESULTS 

NIRAS results are presented in a similar manner as the expansion measurements, that is the 

average measured nonlinearity, performed on the same three samples as CPT expansion, is 

plotted versus age at each test date. With this representation, the nonlinearity parameter is shown 

as a function of time that samples were exposed to ASTM C1293 testing conditions. For Mix 4, 

note that because the NIRAS measurements did not start on Mix 4 until after the expansion was 

greater than 0.04 percent, that mix was recast to gather early age data for that mix. 

As an example of how the nonlinearity of a given sample at a given age is determined, consider 

Mix 3 at 47 days. The data analysis process for one of the Mix 3 prisms is shown in figure 66. 

The impact response for 10 separate hits is recorded and converted to the frequency domain, as 

described previously. The frequency shift is then normalized and plotted against the excitation, 

as shown in figure 66. The nonlinearity parameter () is the slope of the data on this plot; in this 

case,  is found to be 5.6082. For the other samples, the nonlinearity parameters were measured 

to be 7.2799 and 5.6941. The average of these nonlinearity parameters is 6.19. 
46 

Figure 66. Graph. Example of extraction of nonlinearity parameter for Mix 3 at 47 days 

This average nonlinear parameter, along with SD at each measurement age, is then plotted versus 

age, as in figure 67. The average nonlinearity parameter of 6.19 at 47 days can be seen in figure 

67 and corresponds to the maximum nonlinearity measured for Mix 3. Figure 67 shows the 

results up to 750 days while figure 68 shows a more detailed view, only up to 100 days, to better 

show early age behavior. 

From these results, performed on a limited range of aggregates and with a limited range of binder 

compositions, a preliminary limit of 0.2 during the standard test duration has been proposed to 

distinguish between alkali reactive and non-reactive aggregates, cast, and tested according to 

ASTM C1293. Figure 67 shows this limit. However, significant further investigation—including 

ruggedness testing, round-robin testing of precision and bias, and a comprehensive assessment of 

more aggregate types—is clearly needed to determine the microstructural changes that contribute 

nonlinearity, as well as to better assess what level of nonlinearity can be used to distinguish 

between innocuous aggregates and those detrimental to long-term performance. 

The results show that the NIRAS technique confirms the ASTM C1293 reactivity classification 

based on expansion results for the HR mixtures. For aggregates initially classified as HR, as with 

AMBT, measures of CPT expansion and nonlinearity are in agreement, as summarized in table 5. 

However, in some cases, there is an indication of earlier detection of reactivity using NIRAS. 

Comparing Mix 2 in figure 64 and figure 68, it can be seen that the NIRAS technique is capable 

of identifying ASR sooner than the expansion measurements; nonlinearity is detected at 8 days 

while the expansion limit is crossed at about 25 days. However, further investigations are clearly 

needed in this area to determine what kind of microstructural changes cause nonlinearity as well 

as what level of nonlinearity can be considered detrimental. These investigations will enable us 

to describe the damage in concrete in a more quantitative manner and to give a definitive 

criterion for reactivity of an aggregate, considering its microstructure and chemical properties. 
47 

Figure 67. Graph. NIRAS results up to 750 days 

Figure 68. Graph. NIRAS results up to 100 days 
48 

Table 5. Summary of reactivity classifications based on AMBT, CPT, and NIRAS 

Sample 

Aggregate 

reactivity 

based on 

ASTM C1260 

Aggregate 

reactivity 

based on 

ASTM C1293 

Aggregate 

reactivity 

based on 

NIRAS 

Mix 1 Innocuous Nonreactive Nonreactive 

Mix 2 Potentially 

Deleterious Reactive Reactive 

Mix 3 Potentially 

Deleterious Reactive Reactive 

Mix 4 Potentially 

Deleterious Reactive Reactive 

Mix 5 Potentially 

Deleterious Reactive Reactive 

Mix 6 

Innocuous or 

Potentially 

Reactive 

Nonreactive Nonreactive 

Mix 7 Potentially 

Deleterious Reactive Nonreactive 

Table 5 also summarizes results for the NR Mix 1 and the MR Mix 6. For both Mix 1 and Mix 6, 

the average expansion of the specimens at 1 year is very close to the 0.04-percent expansion 

limit in ASTM C1293 but does not exceed that limit, indicating a nonreactive aggregate by that 

measure. The classification of aggregate in Mix 6 is more ambiguous because it exceeded the 

lower 0.1-percent expansion limit in AMBT. NIRAS shows the nonlinearity of both Mix 1 and 

Mix 6 specimens has remained very close to zero throughout the year of testing, indicating these 

are nonreactive aggregate. While the expansion for any concrete sample, including the 

nonreactive mixes, increases as the duration of the test increases, the nonlinearity does not 

change for a nonreactive aggregate, providing a more definitive and accurate result. 

The only mix for which the nonlinearity measurements are contrary to expansion results is 

Mix 7, as shown in table 5. The expansion limit has been crossed for that mix but nonlinearity 

remains negligible throughout the test period. Petrography has been performed on this mix in an 

attempt to assess the validity of the various results for this aggregate. Those results are presented 

in the “Petrography Results” section of this chapter. 

Nonlinearity was also measured on reference samples held at ambient laboratory conditions (i.e., 

not exposed to ASTM C1293 accelerated environmental conditions). Figure 69 shows those 

results. All the values of nonlinearity for reference mixtures are considerably lower than what 

measurements for reactive mixtures that have undergone CPT. For example, the results for 

Mix 4, for both CPT and reference samples, are shown in figure 70 and figure 71. Notice that in 

addition to a negligible frequency shift, the reference sample has a sharper resonance at a higher 

frequency due to lower attenuation. 
49 

Figure 69. Graph. NIRAS results for reference mixes 

Figure 70. Graph. Nonlinearity comparison between reference and tested samples for HR 

Mix 4 at 250 days 
50 

Figure 71. Graph. Comparison between reference and tested samples for HR Mix 4 at 

250 days in the frequency domain 

It is interesting to note that in figure 68 and figure 69, mixtures tested at the first day show some 

nonlinearity that then decreases down to zero through subsequent testing. This can be caused by 

the continued hydration of the cement after demolding, which decreases the inherent material 

nonlinearity by eliminating defects present initially (i.e., before the material nonlinearity due to 

ASR becomes dominant). The results for the reference mixes are surprising for the NR mixture, 

because slightly lower nonlinearity is detected for the specimens subjected to CPT. (However, it 

should be noted that in both environments, the nonlinearity for the NR mix is very low.) The 

difference in the measurements could be related to variations in inherent defects between the two 

sample groups or, perhaps more likely, by more limited cement hydration during storage at drier 

ambient conditions, compared with the moist conditions during CPT. Because the CPT sample 

group has abundant moisture available to promote cement hydration (which could fill early age 

cracking and porosity), NR concrete can achieve more complete hydration and hence lower 

nonlinearity than the reference sample group, for which the drier conditions would limit 

hydration. Because the reference samples undergo only 1 day of moist curing, it is possible that 

the inadequate hydration can be the cause of the slight nonlinearity in the nonreactive reference 

mixtures. Overall, however, the results indicate that it may be possible to extend the use of this 

technique to investigations of the cement hydration process, as well as self-healing in 

cementitious systems. 

In addition, the observed decrease in the nonlinearity parameter for reactive mixes at later ages 

should be considered. This underlying cause for the decrease at later ages is not yet fully 

understood, but it is postulated this may be related to cracks growing to larger sizes (i.e., wider 

cracks). The measured nonlinearity comes from the nonlinear behavior of cracks, through the 

interaction of crack surfaces. When a crack becomes too large, the crack faces may no longer 

interact and, as a result, no longer contribute to nonlinearity. It is important to notice that this 

decrease in nonlinearity appears to occur at about the same time the expansion rate starts to 

decrease and level off. Perhaps the same phenomenon is responsible for the eventual decrease in 

expansion rate and decrease in nonlinearity observed in the results. 
51 

Another way to represent the nonlinearity data—and one that shows even greater distinction 

between the reactive and nonreactive aggregates—is through a measure of accumulated damage, 

c. This approach is described in chapter 2. Figure 72 shows accumulated damage for all 

samples, while figure 73 shows a detailed view of the results for the NR and MR mixtures. Using 

the accumulated damage for these NR and MR mixtures, some distinction can be made between 

the mixtures that was not clear from the instantaneous nonlinearity in figure 67 and figure 68. 

One observation from comparing these results is that nearly the same levels of accumulated 

damage and instantaneous nonlinearity have developed in HR Mix 4 (initial and recast samples). 

This result can be seen in figure 67, figure 68, and figure 72. The expansion measurements, 

figure 63 and figure 64, show more variable results when comparing the recast Mix 4 with the 

initially cast batch. However, with both methods of assessment, the aggregate is clearly reactive. 

As noted earlier, the expansion measurements seem to indicate a faster rate of reaction when the 

reactive aggregate is used as a fine aggregate as compared with its use as a coarse aggregate; an 

exception is the case of the recast Mix 4. With the NIRAS measurements, particularly in the 

assessment of accumulated damage, there is no observable trend with the size of the reactive 

aggregate. This can be beneficial in laboratory testing because there is no effect of gradation on 

the results of reactivity classifications, offering benefits for the assessment of job mixtures and 

potentially eliminating the needed for crushing and/or grading prior to assessment. 

The SD, represented by error bars in figure 67 and figure 68, shows the variability among the 

measurements made on three samples for each mix at each age. Both the expansion 

measurements and measurements of c have a general trend of increasing SD with increasing 

expansion or nonlinearity. Because of inherent heterogeneities, the cast prisms are not identical 

to each other, even within the same mix. As a result, each sample represents a different material 

system that can accumulate damage in different ways. Because of the high sensitivity of NIRAS, 

the SD is larger for reactive mixes. 

Because the lowest amplitude impact is assumed to be the approximate linear resonance 

frequency, this measure can also be used to track changes to the specimens. In general, these 

data, shown in figure 74, complement the nonlinearity measurements. Examining data for 

mixes 5, 8, and 9 from figure 67, figure 68, and figure 74, it is observed that these mixes start 

with a low linear resonance frequency and relatively high nonlinearity after demolding. 

Subsequently, the linear resonance frequency increases (presumably because of an increase in 

elastic modulus due to hydration) and nonlinearity decreases. This data supports the postulated 

explanation for relatively high initial nonlinearity and slightly higher nonlinearity for nonreactive 

reference mixes. Overall, an observed decrease in linear resonance frequency also relates to an 

increase in nonlinearity, demonstrating an inverse relationship between changes in linear 

resonance frequency and nonlinearity parameter. It is important to observe that the changes in 

nonlinearity are significantly larger than the changes in the linear resonance frequency. This 

comparison, demonstrates that nonlinearity can be used to more accurately assess changes in the 

specimens than changes in linear resonance frequency. 
52 

Figure 72. Graph. Cumulative nonlinearity 

Figure 73. Graph. Cumulative nonlinearity for NR and MR mixes 
53 

Figure 74. Graph. Changes in linear resonance frequency 

CORED SAMPLE RESULTS 

To assess whether the NIRAS technique might be used to examine ASR damage in the field or 

on samples obtained from in-service structures, cored samples obtained from two different 

pavements were also tested. The cores were supplied by the Georgia Department of 

transportation (GDOT). One core was taken from I-75 and another was taken from Highway 

(HWY) 316. The concrete from HWY 316 is suspected to have ASR damage, while that from 

I-75 was not expected to have ASR, based on external petrographic analysis. The cores were 

tested in the same manner and with the same setup as described in Chapter 4. The nonlinearity 

results for I-75 and HWY 316 are shown in figure 75 and figure 76, respectively. 

These results clearly show that HWY 316 has a significantly higher nonlinear parameter, 

indicating that it has experienced damage. While the cause of damage is unclear, the 

measurements suggest that the result is an extensively microcracked road. This technique offers 

an extremely rapid and non-subjective evaluation of cores that can be used to evaluate field 

concrete. 
54 

Figure 75. Graph. Nonlinear measurement results on I-75 core 

Figure 76. Graph. Nonlinear measurement results on HWY 316 core 

PETROGRAPHY TO COMPLEMENT NIRAS RESULTS 

As described in chapter 5 of this report, complementary assessment of the progression of damage 

in the concretes was performed through petrographic assessment of concrete prisms from various 
55 

mixes and after various CPT durations. These results can be used to better understand the data 

obtained through CPT and NIRAS evaluation. 

For HR Mix 2, the results of the preliminary petrographic examination, using the uranyl acetate 

stain on a prism, are shown in figure 77 and figure 78. For this mix, a set of five prisms was 

recast—with three used for expansion and two for petrography—to obtain early age images. 

Comparing figure 77 and figure 78 shows a clear difference in the petrographic features at 

different specimen ages. At 1 day, the representative cross-section in figure 77 shows only a light 

staining of the paste but no signs of ASR gel. At 9 days, as shown in figure 78, there is clear 

evidence of reaction rims forming around some aggregates, indicating ASR activity. These 

results are consistent with the nonlinearity results for Mix 2, for which the measurements show a 

detectable nonlinearity at the first measurement at 8 days. Figure 79 shows the expansion 

measurements for the originally cast Mix 2 samples and for the recast Mix 2 set. In addition, the 

nonlinearity of the original Mix 2 samples is plotted on the secondary axis. These results show 

that nonlinearity measurements appear to indicate reactivity at earlier ages than the expansion 

results; that is, the expansion limit is not crossed until about 13 days and 20 days for the recast 

and original Mix 2 samples, respectively, while the proposed nonlinearity limit or 0.2 was 

already exceeded by the time of the first NIRAS measurement, at 8 days. 

At later ages, petrographic examination shows substantial staining throughout the concrete 

matrix, making it difficult to determine which microstructural changes are most influencing the 

nonlinearity measurements. As mentioned earlier, Mix 4 had been recast to gather nonlinearity 

data for the early ages because this mixture had been originally cast before the development of a 

nonlinear measurement setup. In addition to gathering nonlinear data, expansion measurements 

were also collected for these recast samples, and petrography was performed regularly. The 

expansion and nonlinearity results are shown together in figure 80. 

 

1 mm = 0.03937 inches

Figure 77. Photo. Petrographic image for Mix 2 at 1 day 
56 

1 mm = 0.03937 inches

Figure 78. Photo. Petrographic image for Mix 2 at 9 days 

Figure 79. Graph. Comparison of expansion and nonlinearity results for Mix 2 
57 

Figure 80. Graph. Comparison of expansion and nonlinearity results for Mix 4 

The results show that the recast Mix 4 prisms had a considerably higher expansion rate, crossing 

the limit at only 20 days while the originally cast mixture crossed at about 95 days. For the 

NIRAS measurements, the nonlinearity starts to develop at about 50 days. At 12 days, although 

there is a small amount of staining of the paste, there is no fluorescence, as shown in figure 81 

and figure 82. At 26 days, overall, there is little fluorescence, with only a few instances of 

fluorescence shown in figure 83 and figure 84. At 40 days, there is still little fluorescence in the 

sample; only a few instances are found, shown in figure 85 and figure 86. These results are not 

consistent with expansion results because much more fluorescence is expected once the 

expansion limit is crossed. Note the nonlinearity remains low for these ages. At 54 days, there is 

significantly more fluorescence but it appears inside the aggregates, which was not observed in 

other aggregate sources examined (see figure 87 and figure 88). At about this time, nonlinearity 

starts to increase. At 62 days, the fluorescence is even more common and consistent with the 

increase in nonlinearity (see figure 89 and figure 90). 
58 

1 mm = 0.03937 inches

Figure 81. Photo. Image 1 of recast Mix 4 at 12 days 

1 mm = 0.03937 inches

Figure 82. Photo. Image 2 of recast Mix 4 at 12 days 

1 mm = 0.03937 inches 

Figure 83. Photo. Image 1 of recast Mix 4 at 26 days 
59 

1 mm = 0.03937 inches 

Figure 84. Photo. Image 2 of recast Mix 4 at 26 days 

1 mm = 0.03937 inches 

Figure 85. Photo. Image 1 recast Mix 4 at 40 days 

1 mm = 0.03937 inches 

Figure 86. Photo. Image 2 recast Mix 4 at 40 days 
60 

1 mm = 0.03937 inches 

Figure 87. Photo. Image 1 of recast Mix 4 at 54 days 

1 mm = 0.03937 inches 

Figure 88. Photo. Image 2 of recast Mix 4 at 54 days 

1 mm = 0.03937 inches 

Figure 89. Photo. Image 1 of recast Mix 4 at 62 days 
61 

1 mm = 0.03937 inches 

Figure 90. Photo. Image 2 of recast Mix 4 at 62 days 

Petrography was also performed on Mix 7. Again, all samples were recast. At 218 days, after the 

expansion limit had been crossed, as shown in figure 91 and figure 92, some staining of certain 

aggregates is apparent but there is no evidence of reaction rims or cracks. This technique was 

also applied to the reference Mix 7 for comparison, as shown in figure 93 and figure 94. When 

compared, the photos of Mix 7 and those of reference Mix 7 show little difference between the 

features of the concrete exposed to accelerated conditions and that stored at ambient conditions. 

This petrographic examination does not provide evidence of ASR and, as a result, confirms the 

nonlinearity results but contradicts expansion results. 

1 mm = 0.03937 inches 

Figure 91. Photo. Image 1 of recast Mix 7 at 218 days 
62 

1 mm = 0.03937 inches 

Figure 92. Photo. Image 2 of recast Mix 7 at 218 days 

1 mm = 0.03937 inches 

Figure 93. Photo. Image 1 for recast reference Mix 7 at 218 days

1 mm = 0.03937 inches 

Figure 94. Photo. Image 2 for recast reference Mix 7 at 218 days 
63 

CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS 

CONCLUSIONS 

1. NIRAS measurements have shown a clear distinction between reactive and nonreactive 

aggregates and among concrete mixtures containing reactive aggregate with and without 

mitigation for ASR. For HR cases, there is evidence of earlier detection of ASR-related 

damage with the NIRAS testing technique than with concrete prism expansion. 

2. The NIRAS measurement setup has proven to be a robust and accurate measurement 

technique. The variability between successive measurements has been shown to be less than 

20 percent overall and less than 10 percent with a prepared adhesion surface. 

3. NIRAS has also been proven to be a powerful nondestructive testing (NDT) tool to rapidly 

detect microcrack-type damage (regardless of the cause) in concrete in an early stage of the 

material degradation. Based on the current body of research, this test should be used as a 

supplement to other standard testing. Additional research and testing can be used to assess 

whether NIRAS can be used as an alternative test. 

4. With some aggregate types, a higher rate of expansion is measured with aggregate that has 

been crushed than in the as-received condition, showing a potential effect of aggregate size. 

The NIRAS measurements, however, do not appear to be affected by the reactive aggregate 

size and show the potential to be used to evaluate job-specific aggregates, while also 

eliminating the need for the time-consuming crushing and grading processes. 

5. Complementary petrography, performed by staining the concrete samples with uranyl 

acetate, was used to confirm the presence of ASR gel and cracking within the samples. Based 

on this lack of fluorescence, gel, and cracking, one aggregate identified as non-reactive 

through NIRAS was confirmed to be non-reactive, despite having been identified as 

potentially deleterious and reactive through expansion testing. Further petrographic analysis 

to complement expansion and NIRAS testing will contribute to improving the understanding 

of ASR as well as to improving the understanding of the correlation between the results of 

NIRAS and expansion testing. 

6. Two nonlinearity parameters are defined: one () that characterizes the rate of damage 

development at a certain age and another (c) that characterizes the amount of damage 

accumulated up until that time. Based on the experimental results for a limited number of 

aggregates—albeit with various levels of reactivity—it is proposed that the aggregate under 

assessment can be considered alkali reactive if the nonlinearity parameter of its concrete 

prism specimen measures 0.2 or more at any time during the 12-month test period. 

Nonlinearity parameters between 0.05 and 0.2 may suggest some potential for ASR, and the 

aggregate should be further evaluated. These proposed limits, however, must be verified 

through a more comprehensive evaluation of a broader range of aggregates and also through 

round-robin testing. 
64 

RECOMMENDATIONS FOR FURTHER RESEARCH 

This research has shown that the NIRAS technique has potential as a powerful method for nondestructive evaluation of concrete in the laboratory, in cored samples, and potentially in the field. 

Although applications for detection of ASR-induced damage are the focus of this research, 

results here suggest the technique could be further developed for detection and quantification of 

cumulative damage due to various causes (e.g., fatigue, freeze/thaw, sulfate attack, reinforcement 

corrosion) and also for examination of hydration and self-healing in concrete. 

With regard to ASR, further efforts are needed in several areas. First, additional research is 

needed for continued development and validation of the NIRAS technique with a broader range 

of aggregate mineralogies and reactivities, including assessment of more aggregates when 

assessment by AMBT and CPT is ambiguous. In this research, the nonlinearity measurements for 

an aggregate that was near the expansion limit and was determined to be potentially deleterious 

and reactive by AMBT and CPT, respectively, showed negligible nonlinearity. The lack of ASR 

damage was confirmed through petrographic assessment. Assessment of more aggregates that are 

known to be challenging to classify is warranted, in particular. 

In addition, with further NIRAS assessment it is also important to continue to assess the 

relationship between microstructural changes and changes in nonlinearity, as well as to compare 

results with standard expansion tests and field performance. This correlation among the various 

measures aids not only in the classification of the aggregates, but also in the continued 

assessment of the proposed limit on nonlinearity. In addition, a limit on cumulative nonlinearity 

might also result from further research and development efforts. In particular, the age at which 

aggregate reactivity is identified by NIRAS and expansion testing should be compared over a 

broader range of aggregates to provide additional understanding of the potential benefits of 

NIRAS for early and reliable detection of reactive aggregates. 

Based on those results, a critical next step would be to build a predictive model that captures the 

physics of the damage evolution of ASR. This physics- and chemistry-based material model 

could be used to interpret these experimental results and thus predict the resonance response of 

an ASR-damaged specimen or concrete. This work would result in refinements in the accuracy 

of the identification of reactive aggregate and form the foundation for a device for detection of 

ASR in the field. 

A round-robin test series should also be initiated for concrete prism samples. Such a series would 

involve several laboratories using the NIRAS technique to measure nonlinearity and CPT 

expansion in a pre-determined set of aggregates; these might include some of those identified 

through continued research on aggregates whose reactivity is “ambiguous.” Results could be 

used to establish precision and bias for the test and to refine a standard test procedure. 

Because the NIRAS method appears to be insensitive to reactive aggregate size and because the 

technique was successfully applied to both ordinary concrete and concrete with SCMs, the 

method appears to have potential as a technique for screening job mixes. A research program 

should be established to measure change in nonlinearity over a broad range of concrete, varying 

the aggregate reactivity and gradation, water-to-cement ratio, and binder composition. Exposure 

could be done using CPT or other accelerated testing appropriate for concrete. 
65 

REFERENCES 

1. Farny, J.A. and Kosmatka, S.H., “Diagnosis and Control of Alkali-Aggregate Reactions in 

Concrete,” Portland Cement Association IS413, 1997. 

2. Mehta, P.K. and Montiero, P.J.M., Concrete: Microstructure, Properties, and Materials, 3rd 

ed. New York: McGraw-Hill. 2006. 

3. ASTM C1293, “Standard Test Method for Determination of Length Change of Concrete Due 

to Alkali-Silica Reaction,” ed. West Conshohocken, PA: ASTM International. 2008. 

4. ASTM C1260, “Standard Test Method for Potential Alkali Reactivity of Aggregates (MortarBar Method),” ed. West Conshohocken, PA: ASTM International. 2007. 

5. Folliard, K., Thomas, M.D.A., and Kurtis, K.E., “Guidelines for the Use of Lithium to 

Mitigate or Prevent ASR in Concrete,” Publication No. FHWA-RD-03-047, Federal 

Highway Administration. 2003. 

6. Haha, M. B., Gallucci, E., Guidoum, A., and Scrivener, K.L., “Relation of Expansion Due to 

Alkali Silica Reaction to the Degree of Reaction Measured by SEM Image Analysis,” 

Cement and Concrete Research, Vol. 37, pp. 1,206–1,214. 2007. 

7. Nagy, P.B., “Fatigue Damage Assessment by Nonlinear Ultrasonic Materials 

Characterization,” Ultrasonics, Vol. 36, pp. 375–381. 1998. 

8. Van Den Abeele, K.E.A., Johnson, P.A., and Sutin, A., “Nonlinear Elastic Wave 

Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave 

Modulation Spectroscopy (NWMS),” Research in Nondestructive Evaluation, Vol. 12, 

pp. 17–30. 2000. 

9. Chen, J., Jayapalan, A.R., Kim,J.-Y., Kurtis, K.E., and Jacobs, L.J., “Rapid Evaluation of 

Alkali-Silica Reactivity of Aggregates Using a Nonlinear Resonance Spectroscopy 

Technique,” Cement and Concrete Research, Vol. 40, pp. 914–923. 2010. 

10. Payan, C., Garnier,V., Moysan, J., and Johnson, P.A., “Applying Nonlinear Resonant 

Ultrasound Spectroscopy to Improving Thermal Damage Assessment in Concrete,” Journal 

of the Acoustical Society of America, Vol. 121, pp. EL125–EL130. 2007. 

11. Van Den Abeele, K. and De Visscher, J., “Damage Assessment in Reinforced Concrete 

Using Spectral and Temporal Nonlinear Vibration Techniques,” Cement and Concrete 

Research, Vol. 30, pp. 1,453–1,464. 2000. 

12. Muller, M. Sutin, A., Guyer, R., Talmant, M., Laugier, P., and Johnson, P.A., “Nonlinear 

Resonant Ultrasound Spectroscopy (NRUS) Applied to Damage Assessment in Bone,” 

Journal of the Acoustical Society of America, Vol. 118, pp. 3,946–3,952. 2005. 

13. Van Den Abeele, K.E.A., Carmeliet, J., Ten Cate, J.A., and Johnson, P.A., “Nonlinear Elastic 

Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part II: Single-Mode 
66 

Nonlinear Resonance Acoustic Spectroscopy,” Research in Nondestructive Evaluation, 

Vol. 12, pp. 31–42. 2000. 

14. Chen, J., Jayapalan, A.R., Kim, J.-Y., Kurtis, K. E., and Jacobs, L.J., “Nonlinear Wave 

Modulation Spectroscopy Method for Ultra-Accelerated Alkali-Silica Reaction Assessment,” 

ACI Materials Journal, Vol. 106, pp. 340–348. 2009. 

15. Chen, X.J., Kim, J.-Y., Kurtis, K.E., Qu, J., Shen, C.W., and Jacobs, L.J., “Characterization 

of Progressive Microcracking in Portland Cement Mortar Using Nonlinear Ultrasonics,” 

NDT and E International, Vol. 41, pp. 112–118. 2008. 

16. Morris, W.L., Buck, O., and Inman, R.V., “Acoustic Harmonic Generation Due to Fatigue 

Damage in High-Strength Aluminum,” Journal of Applied Physics, Vol. 50, pp. 6,737–6,741. 

1979. 

17. Solodov, I.Y. and Korshak, B.A., “Instability, Chaos, and “Memory” in Acoustic-WaveCrack Interaction,” Physical Review Letters, Vol. 88, pp. 143,031–143,033. 2002. 

18. ASTM C215, “Standard Test Method for Fundamental Transverse, Longitudinal, and 

Torsional Resonant Frequencies of Concrete Specimens,” ed. West Conshohocken, PA: 

ASTM International. 2008. 

19. ASTM E1876, “Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and 

Poisson’s Ratio by Impulse Excitation of Vibration,” ed. West Conshohocken, PA: ASTM 

International. 2009. 

20. ASTM C856, “Standard Practice for Petrographic Examination of Hardened Concrete,” ed. 

West Conshohocken, PA: ASTM International. 2004. 

21. Natesaiyer, K. and Hover K.C., “Insitu Identification of ASR Products in Concrete,” Cement 

and Concrete Research, Vol. 18, pp. 455–463. 1988. 

HRDI-60/10-13(600)E Recycled

Recyclable