TECHBRIEF Accelerated Determination 

of Asr Susceptibility During 

Concrete Prism Testing 

Through Nonlinear Resonance

Ultrasonic Spectroscopy 

FHWA Publication No.: FHWA-HRT-13-086 

FHWA Contact: Paul Virmani, HRDI-60, (202) 493–3052, 

paul.virmani@dot.gov; Fred Faridazar, HRDI-20, 

(202) 493-3076, fred.faridazar@dot.gov

This document is a technical summary on a Federal 

Highway Administration (FHWA) project that is fully 

documented in a separate report under the same title 

(FHWA-HRT-13-085). 

Introduction

The alkali-silica reaction (ASR) is one form of deterioration that may significantly reduce the service life of 

concrete structures. Currently, ASR susceptibility of 

aggregate sources is most commonly assessed through 

length change in the concrete or mortar specimens 

over time while subjected to standardized acceleratory conditions. The standard concrete prism test (i.e., 

ASTM International (formerly American Society for 

Testing and Materials (ASTM) C1293) is considered the 

most representative of field performance.(1)

However, one significant practical drawback of that 

test is its long duration, which is 1 year to assess 

aggregate reactivity and 2 years to assess mitigation 

measures. The standard accelerated mortar bar 

tests (AMBT) are considerably quicker to perform 

but have not proven reliable in all cases, leading some 

agencies and owners to implement alternate test 

durations and/or expansion limits. 

For both the standard mortar and the concrete tests, 

another issue is the use of a final expansion meaResearch, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.fhwa.dot.gov/research
2

surement as the sole measure of 

aggregate reactivity, leading to difficulties 

in predicting field performance when 

final expansion results are ambiguous 

(e.g., very close to the limits, or on an 

upward trajectory). The objective of this 

research is to develop a reliable measurement technique that can more quickly 

quantify damage associated with ASR in 

concrete specimens while also providing 

an assessment of the accumulated damage. The developed technique, nonlinear 

impact resonance acoustic spectroscopy 

(NIRAS), is based on measurements of the 

nonlinear acoustic or vibration responses 

of concrete specimens.

The research has been coducted on 

laboratory-cast concrete prism specimens 

containing both fine and coarse aggregates obtained from different sources to 

provide a spectrum of reactivity for 

assessment through the developed 

NIRAS technique. The NIRAS measurements were performed while the 

specimens were undergoing the ASTM 

C1293 concrete prism test (CPT), and 

the results from NIRAS measurements 

are compared with those expansion results. 

Approach

Sample Preparation: Mix Design and 

Concrete Prism Specimens

All specimens were cast according to the 

ASTM C1293 standard. The mix design 

matrix, shown in table 1, was developed to 

examine a range of ASR behavior, including 

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 FA

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

(crushed) 25% Class FA

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

NR = nonreactive 

MR = potentially or “may be” reactive 

HR = moderately to highly reactive 

FA = fly ash

Table 1. Mix design matrix for NIRAS and ASTM C1293 concrete prisms
3

the combination of two non-reactive aggregates (Mix 1) and the use of aggregates 

termed “moderately to highly reative” 

(HR) and “potentially (or may be) reactive” 

(MR) aggregates in combination with nonreactive aggregate (NR). Expansion at 

14 days was measured during ASTM C1260 

testing (see table 2).(2) 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. Considering the ASTM C1260 

results, along with historical aggregate 

standard test results and field performance history of these aggregates, 

the aggregates were classified 

preliminarily as NR, MR, or HR. Table 2 

presents these classifications, along 

with other details on the concrete 

prism mixtures, including the sample 

naming scheme. The nonreactive 

aggregate used in all the mix designs is a 

limestone from Adairsville, GA. In 

addition, an ASTM C 150 Type I cement 

with alkali equivalent of 0.88 percent, 

meeting the ASTM C1293 requirements, 

was used in casting CPT samples; the alkali 

content of the concrete was “boosted” 

to 1.25 percent by mass cementitious 

materials, in accordance with the standard.

As specified in ASTM C1293, concrete 

prisms (3 by 3 by 11.25 inches (76 by 76 by 

285 mm)) were cast with a water-to-cement 

ratio of 0.45. The gradation for coarse 

aggregate was as specified in ASTM C1293. 

For as-received fine aggregates and 

crushed coarse aggregates used as fines, 

the gradation is adjusted to obtain a fineness modulus of 2.71 for consistency 

among the concretes. The samples were 

initially cured for 24 hours in a moist 

environment and subsequently stored 

over water in a sealed container, at 100.4° F 

(38° C), to accelerate ASR. 

NIRAS Measurement: Theoretical 

Background and Damage Parameter

Microcracks distributed in concrete can be 

envisioned as forming a network of soft 

bonding elements that are the source of 

the strong nonlinear acoustic behavior 

of concrete. Using the phenomenological 

Aggregate Source 14-day AMBT Expansion (%) 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. ASTM C1260 results for the aggregates examined
4

model for hysteresis and classical 

nonlinear constitutive relations, the 

general nonlinear stress–strain relationship 

can be shown as the equation in figure 1:(3,4)

where s is stress,  is strain; E0 is the linear 

elastic modulus; b and d are the coefficients 

of quadratic and cubic nonlinearity; a is the 

measure of the material hysteresis; D is 

the strain amplitude (during a dynamic 

excursion);  is the strain rate; and 

sgn () = 1 if  > 0, –1 if  < 0, and 0 if 

 = 0. One of the consequences of this 

nonlinear stress–strain relationship is 

the excitation amplitude dependent resonance frequency of a concrete specimen. 

Figure 2 shows resonance spectra obtained 

for different levels of excitation of a CPT 

specimen. The resonance frequency of the 

specimen (represented as a peak in each 

spectrum) shows a downward shift with 

the increase of impact strengths. It has 

been shown that the amount of the downward shift is proportional to the amount of 

damage occurring in the specimen in terms 

of the density of microcracks. 

Therefore, a nonlinearity parameter that 

characterizes the amount of damage at 

a certain instant is defined as shown in 

equation in figure 3:(4)

where ƒ0 is the linear resonance frequency, ƒ

is the resonance frequency at an increased 

excitation amplitude, and A is the amplitude 

Figure 2. Graph. Shift of resonance frequency for increasing excitation strength (measurements performed on a typical 

CPT specimen).

?

?

? ? ?

s 5  ? E0 [1 1 b 1 d2 1 a(D 1  ? sgn ()) ] ?

Figure 1. Equation. Nonlinear stress–strain relationship

5( ƒ0 ƒ )A

Figure 3. Equation. Nonlinearity parameter characterizing 

amount of damage

ƒ0
5

of excitation. Note that  is the negative of 

the slope of (ƒ0 – ƒ) versus the amplitude (the 

y-axis) in figure 2.

Because the nonlinearity is attributed to 

nonlinear interactions (clapping and 

Hertzian contact) of crack surfaces, relatively large and open cracks will not 

contribute to nonlinearity. Under this 

assumption, the above nonlinearity 

parameter can be thought of as an 

“instantaneous” measure of nonlinearity. A 

“cumulative” nonlinearity (c) or damage 

parameter can then be measured by integration, using the equation shown in figure 4.

These two parameters are used in this 

research as indicators of the amount of damage due to ASR that has accumulated in the 

specimens.

NIRAS Measurement: Experimental 

Method and Procedure

The experimental setup is similar to the 

ASTM C215 procedure for the measurement of the transverse resonance 

frequency.(5) The specimen is placed on a 

1.5-inch (38 mm) thick support mat to 

allow the specimen’s free vibrations. A 

5-oz. (140-g) hammer is used to strike the 

sample in its center, as shown in figure 

5. A miniature accelerometer (PCB 353B13) 

is attached using super glue to one end 

of the specimen, at the midline, where 

the response is at a maximum for the 

transverse mode. The NIRAS measurements 

begin 1 minute after the attachment of 

Figure 5. Photo. NIRAS test setup

c5t∫

0

()d

Figure 4. Equation. Integral to calculate “cumulative” 

nonlinearity
6

the accelerometer, and the signals are 

then captured using an oscilloscope 

(Tektronix TDS5034B) and analyzed 

using Matlab®. The signal duration captured by the oscilloscope is 0.4 s, which 

allows a complete decay of the response 

signal (see the signal shown on the 

oscilloscope screen in figure 5), with 

a sampling rate of 500 kilo Samples/

second (kSa/s). The signal is then 

“zero-padded” and analyzed using 

the fast Fourier transform. Figure 2 

shows a set of typical resonance spectra 

measured from a CPT specimen. The 

downward shift of resonance frequency 

is obvious in the figure. The quantities 

ƒ0 and (ƒ0 – ƒ) can be easily extracted 

from this figure, and then the nonlinearity parameter  can be calculated using 

the equation in figure 3. The repeatability 

and robustness of the NIRAS measurement setup were validated using an aluminum specimen with similar dimensions. 

Results

Expansion Results

This section briefly presents the expansion 

measurement results for the concrete 

mixtures described in table 2. Results 

of all the expansion measurements 

are shown in figure 6, with figure 7 

showing more detail for the lowerexpanding mixes. (Note that the legend 

for the two figures is the same. 

Also, the difference in y-axis scaling 

between the two figures should be noted.) 

When expansion during CPT exceeds 

0.04 percent by 1 year, aggregates are 

classified as reactive. For assessments 

of mitigation measures, such as the 

use of fly ash (FA), the limit is 0.04 percent 

at 2 years.

The preliminary AMBT results and the CPT 

results for the HR mixtures, as well as the 

NR Mix 1, generally show good agreement. 

That is, the aggregates identified as 

Figure 6. Graph. All ASTM C1293 expansion results
7

“potentially deleterious” in AMBT—

those used in mixes 2, 3, 4, and 

5—are identified through CPT as 

“reactive.” Through comparison, Mix 7 

was also identified as “reactive” by CPT. 

The expansion in Mix 7 exceeded the CPT 

limit at about 150 days, but its potential for 

reaction is less clear in the ABMT, with a 

14-day expansion at just about 0.2 percent, 

putting it in the “innocuous to or potentially 

deleterious” category. This discrepancy 

demonstrates some of the challenges associated with characterizing aggregates from 

their expansion.

 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. 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, 

again perhaps demonstrating some of the 

challenges associated with determining 

reactivity through expansion measurements alone. 

The 25-percent replacement of cement with 

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. In comparison, mixes 4 

and 5, which use the same aggregate, 

crossed the limit before 100 days. 

NIRAS Results

Figure 8 presents the NIRAS results. The 

measured nonlinearity parameter, for 

the same three specimens as were used 

for the CPT expansion measurements, is 

Figure 7. Graph. Greater detail in ASTM C1293 expansion results for the less expansive mixes 
8

averaged and plotted at each test date. 

For this representation, the nonlinearity 

parameter is shown as a function of the time 

that samples were exposed to ASTM C1293 

testing conditions. 

Based on these results, derived from 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. 

However, significant further investigation—including ruggedness testing, roundrobin 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 considered 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 nonreactive and reactive mixtures. 

For aggregates initially classified as HR, 

once again measures of expansion and 

nonlinearity are in agreement. 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, 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 non-linearity 

of both Mix 1 and Mix 6 specimens has 

remained very close to zero throughout 

Figure 8. Graph. NIRAS results for all mixtures
9

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 

Deleterious Nonreactive Nonreactive

Mix 7 Potentially Deleterious Reactive Nonreactive

Table 3. Summary of reactivity classifications based on AMBT, CPT, and NIRAS

the year of testing, indicating these are 

nonreactive aggregates. Although 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. 

In some cases, there is an indication of earlier detection of reactivity using nonlinearity 

measured through NIRAS. Comparing data 

for Mix 2 in figure 6 and figure 8, 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. Mix 7 

is the only mix for which the nonlinearity 

measurements contradict expansion 

measurements. The expansion limit has 

been crossed for that mix but nonlinearity remains negligible throughout the 

1-year test. Independent petrographic 

study on this mix validates the nonlinear 

measurements (see full report for details). 

Table 3 summarizes the AMBT, CPT, and 

NIRAS results for the aggregates examined. 

For reactive mixes, in addition to the early 

increase in nonlinearity, a decrease in the 

nonlinearity parameter has been observed 

at later ages. This decrease is not yet fully 

understood, but it is postulated that a 

decrease in nonlinearity could be accompanied by increasing size (e.g., width) 

of cracks. The measured nonlinearity 

comes from the nonlinear behavior of 

cracks through the interaction of crack surfaces. As a result, when a crack widens, the 

crack faces may no longer interact and will 

contribute less to measured nonlinearity. 
10

It is also noteworthy 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. 

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. Taking the 

measured nonlinearity as an instantaneous 

measure, the data are integrated, as 

described above, to find the accumulated 

damage, as shown in figure 9. Using the 

accumulated damage for these mixtures, 

some distinctions can be seen between the 

mixtures that could not be seen from the 

instantaneous nonlinearity in figure 8. The 

expansion measurements, figure 6, show 

measurement variations for the recast 

Mix 4 and the original Mix 4. Although the 

cause of this discrepancy is unknown, it 

is evident that nonlinearity measurements remain relatively unaffected and may 

be more robust.

The expansion measurements seem to 

indicate a faster rate of reaction when the 

reactive aggregate is used as a fine aggregate compared with when used as received 

(a coarse aggregate). An exception is the 

recast Mix 4, which shows no observable 

effect of the size of the reactive aggregate 

on the NIRAS measurements. This can be 

beneficial in laboratory testing because 

these results suggest that there is no effect 

of aggregate size on the results of reactivity 

classifications. Further testing is needed to 

validate these observations, however.

Figure 9. Graph. Cumulative nonlinearity for all mixes
11

The standard deviation, represented by 

error bars, shows the variability in the three 

samples tested for each mix. Both the 

expansion measurements and measurements of  show a general trend of 

increasing standard deviation with increased 

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 higher sensitivity of NIRAS, the standard 

deviation is larger for reactive mixes. 

Conclusions

• NIRAS measurements have shown a clear 

distinction between reactive and nonreactive aggregates and concrete 

mixtures. For more reactive cases, there 

is evidence of earlier detection of 

ASR-related damage with the NIRAS 

testing technique than with concrete 

prism expansion. 

• NIRAS has also been proven to be a 

powerful non-destructive testing 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.

• With some aggregate types, a higher rate 

of expansion is measured with aggregate 

that has been crushed than in the asreceived 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 timeconsuming crushing and grading processes.

• Two nonlinearity parameters are defined: 

one () that characterizes the rate of 

damage development at a certain instant 

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 alkalireactive 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. 
12

OCTOBER 2013 FHWA-HRT-13-086

HRDI-60/10-13(600)E

Researcher—This study is being performed by School of Civil and Environmental Engineering, 

Georgia Institute of Technology, 790 Atlantic Dr., Atlanta, Georgia 30022-0355, Phone (404) 385-0825. 

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distribution is being made to the Divisions and Resource Center.

Availability—This TechBrief may be obtained from the FHWA Product Distribution Center by email 

to report.center@dot.gov, fax to (814) 239-2156, phone to (814) 239-1160, or online at http://www.fhwa.

dot.gov/research. 

Key Words—alkali-aggregate reaction, AAR, alkali-silica reaction, ASR, concrete, durability, fly ash, 

non-destructive testing

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References

1. ASTM C1293, “Standard Test Method 

for Determination of Length Change of 

Concrete Due to Alkali-Silica Reaction,” 

ed. West Conshohocken, PA: ASTM 

International. 2008.

2. ASTM C1260, “Standard Test Method for 

Potential Alkali Reactivity of Aggregates 

(Mortar-Bar Method),” ed. West 

Conshohocken, PA: ASTM International. 

2007.

3. 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.

4. 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 Nonlinear 

Resonance Acoustic Spectroscopy,” 

Research in Nondestructive Evaluation,

Vol. 12, pp. 31–42. 2000.

5. ASTM C215, “Standard Test Method for 

Fundamental Transverse, Longitudinal, 

and Torsional Resonant Frequencies 

of Concrete Specimens,” ed. West 

Conshohocken, PA: ASTM International. 

2008.