NDT&E International 44 (2011) 728–735

Contents lists available at ScienceDirect

NDT&E International

0963-86

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ndteint

Damage detection in concrete using coda wave interferometry

Dennis P. Schurra, Jin-Yeon Kima, Karim G. Sabrab, Laurence J. Jacobsb,n

a School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USAb Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA

a r t i c l e i n f o

Article history:

Received 29 April 2011

Received in revised form

11 July 2011

Accepted 20 July 2011Available online 2 August 2011

Keywords:

Coda wave interferometry

Diffuse ultrasound

Acoustoelasticity

Concrete

Damage detection

95/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ndteint.2011.07.009

esponding author. Tel.: þ1 404 894 2344; fax

ail address: laurence.jacobs@ce.gatech.edu (L

a b s t r a c t

Coda wave interferometry (CWI) is a nondestructive evaluation technique for monitoring wave velocity

changes in a strongly heterogeneous medium as demonstrated in previous seismic and acoustic

experiments. The multiple-scattering effect in such a medium promotes the rapid formation of a diffuse

field, and waves can travel much longer than the direct path, and thus are more sensitive to small

changes occurring in the medium. This research applies the CWI technique in conjunction with

acoustoelastic measurements to characterize two different types of damage in concrete: damage due to

thermal shock and dynamic cyclic loading. The diffuse ultrasonic signals are taken at different levels of

compressive stress and then relative velocity changes are extracted using the CWI technique. The

relative velocity change (or the material nonlinearity) increases considerably with increasing damage

level in most samples for both types of damage. The feasibility and sensitivity of this CWI-based

technique in characterizing damage in cement-based materials are demonstrated.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

In 2006, concrete and cement-based materials were, byvolume, the largest manufactured in the world [1]. Due to thisprevalence, concrete structures such as buildings, bridges, roads,and parking garages are currently of special focus from a struc-tural health monitoring perspective. Therefore, development ofnondestructive evaluation techniques for cement-based materialsis attracting much attention, especially for a quantitative evalua-tion of small-scale damage in the microstructure. Detection ofdamage at an early stage of degradation may significantly reducemaintenance costs and prevent a catastrophic failure of thesestructures. Cracks at this stage are much smaller than the size ofaggregate, and thus cannot be reliably detected and characterizedwith the conventional techniques based on ultrasonic velocityand/or attenuation measurements. Examples of typical damageinclude thermally induced microcracks and chemo-mechanicaldamage due to the alkali-silica reaction (ASR) (see, for example,Chapter 5 in Ref. [1]). Numerous new nondestructive evaluationtechniques have recently been developed for a quantitativeevaluation of these types of damage [2–4]. Among others, diffuseultrasonic techniques have been successful in detecting damagein a laboratory environment (see, for example, Ref. [4]), showing ahigh potential for in-field measurements of real concretestructures.

ll rights reserved.

: þ1 404 894 0168.

.J. Jacobs).

It has been known that the later arrival signals (the so-calledcoda waves) in a diffuse acoustic/seismic signal carry rich infor-mation about the medium and effort has been made to developtechniques to systematically extract useful information fromdiffuse coda waves for the last several decades [5–7]. Sniederet al. [6] developed a technique called coda wave interferometry

(CWI) to determine changes in the seismic velocity by correlatingtwo nearly identical signals obtained from two closely spacedsensors at different times. Lobkis and Weaver [7] proposed anefficient signal processing technique called the stretch technique

that uses the entire length or a large part of the recordedwaveforms instead of just a small portion. In an ultrasonic CWImeasurement, by launching ultrasonic waves and comparing twocoda waves measured at different conditions (e.g. at differentstress levels) the relative changes in wave velocity can beextracted. The velocity changes may be caused by damage and/or microstructure modifications in the medium at the wavelengthscale. Recently, a few researchers have applied the CWI techniqueto concrete samples. Larose and Hall [8] proposed an ultrasonicCWI experimental method based on the use of the stretchtechnique and demonstrated high accuracy of their experimentalmethod in measuring the stress-dependent velocity changes inconcrete. Payan et al. [9] performed CWI measurements on aconcrete sample using ultrasonic waves polarized in three per-pendicular directions and obtained a complete set of nonlinearelastic parameters. Their interesting results show that even in thismultiple-scattering environment, ultrasonic diffuse waves havethe memory of their initial polarization for a certain period oftime; this fact was exploited to determine the dependence of the

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735 729

velocity changes on the polarization for a given loading direction.More recently, Lillamand et al. [10] conducted experimentssimilar to those of Payan et al. [9] and observed that velocitychanges in concrete are about ten times higher than those inmetals.

The objective of this research is to develop a robust andreliable CWI-based technique for measuring stress-induced rela-tive velocity changes and to apply the technique to evaluatedifferent types of damage in concrete. The present technique usesa measurement setup and data processing technique similar to [8]and devices developed in our previous work [4]. Damage due tothermal shock and mechanical cyclic loading are considered todemonstrate the applicability and effectiveness of the developedmeasurement procedure.

2. Theoretical background and methodology

2.1. The acoustoelastic effect

The relationship between stress (or strain) and elastic wavevelocity is known as the acoustoelastic effect. Hughes and Kelly[11] derived equations for the speed of elastic waves in a stressedsolid based on the well-known Murnaghan’s theory of finitedeformation [12]. The acoustoelastic effect is treated here as afirst order perturbation, i.e. only small stress increments areconsidered. Furthermore, the strain effects (i.e. change in propa-gation distance) on the propagating elastic waves are smaller byan order of magnitude than the stress effects and thus can beignored [13]. The acoustoelasticity theory can be used to deter-mine the linear change in the propagation velocity of a specificwave mode under a given stress increment Ds (with reference tothe unstressed medium). More generally, the acoustoelastic effectcan be modeled as a simple stretch or compression of the wholemeasured waveform in the time domain [13,14]. Under thisgeneral formalism, the relationship between the waveform hk(t),measured for a small stress increment Ds(k) (indexed by theparameter k) and the reference waveform h0(t), recorded whenthe material is in its reference state (i.e. under no incrementalstress), can be approximated as:

hkðtÞ ¼ h0ðtð1�uðkÞÞÞþnðtÞ, ð1Þ

where n(t) accounts for additional variations, such as electronicnoise and weak decorrelation (or distortion) of the waveform hk(t)– with respect to h0(t) – not accounted for by the stretchparameter u(k)

51. This stretch parameter is assumed to beproportional to the stress increment Ds(k) to the first order:

uðkÞ ¼ ADsðkÞ: ð2Þ

The acoustoelastic constant A between the stretch parameteru(k) and the stress increment Ds(k) will vary depending on thespecific polarization direction and the orientation of the localstress field as well as the second- and third-order elastic con-stants of the material. The stretch parameter u(k) correspondsphysically to the relative velocity change of the propagatingwaves. Note that u(k)o0 (or u(k)40) corresponds to a compressive(or tensile) stress. Eq. (2) provides a simplified first-order modelfor the acoustoelastic effect on the entire recorded time domainwaveform. It should be noted that an analytical derivation of theacoustoelastic constant A in Eq. (2) is possible only for simplewaveforms or experimental geometry [13,14]. For more compli-cated recorded waveforms, such as reverberant or diffuse elasticfields where many modal components exist and interfere, theacoustoelastic constant A needs to be determined experimentallyfirst (e.g. via a calibration procedure), if an absolute value of thestress increment Ds(k) is desired. Otherwise, Eq. (2) only provides

a means for measuring relative stress increment Ds(k) (e.g. withrespect to an unstressed material), which would still be sufficientfor structural monitoring purposes [13].

As an illustration of the generality of the above formulation, itcan be noted that Eq. (1) takes a simple form when the recordedwaveform h0(t), between a source-receiver pair, separated by adistance L, contains only a single broadband wave or mode arrival(e.g. longitudinal wave in an isotropic and homogenous elasticsolid). In this case, the reference waveform can be simplymodeled as h0(t)¼d(t�L/V(0)), where d(t) denotes the Dirac deltafunction and V(0) denotes the propagation velocity in the refer-ence stress state of the material. Furthermore, by using thescaling property of the Dirac delta function (stating thatd(at)¼(1/a) � d(t), for an arbitrary scalar parameter a), Eq. (1)reduces to:

hkðtÞ ¼1

ð1�uðkÞÞd t�

L

V ð0Þð1�uðkÞÞ

� �, ð3Þ

which indicates that the modified propagation velocity, V(k)

associated with a given stress increment Ds(k) is V ð0Þð1�uðkÞÞ. Inthis simple case, the stretch parameter u(k) represents the relativevariation of propagation velocity, ðV ð0Þ�V ðkÞÞ=V ð0Þ. Eq. (3) is com-monly used to describe the classical formulation of the acoustoe-lastic effect [13,14]. In practice, Eq. (3) indicates that, to the firstorder, the stress increment Ds(k) can be measured either from thechange in the propagation velocity of a given transient wave ormode component.

When measuring complex recorded waveforms (resultingfrom the mixing of several wave types and polarizations), suchas the ultrasonic diffuse fields measured in this study, the moregeneral model stated in Eq. (1) represents then an extension tothe classical formulation of the acoustoelastic effect [11], as givenby Eq. (3). In this case, it can be shown that the relative wavevelocity change u(k) is directly proportional to the mode-averagednonlinear elastic parameter [11,12]. For example, in the one-dimensional case, the relationship is written as:

uðkÞ ¼V ð0Þ�V ðkÞ

V ð0Þ¼ ADsðkÞ ¼ �b

EDsðkÞ, ð4Þ

where b is the nonlinear elastic parameter, and E is the elasticmodulus. Consequently, in this research, the nonlinearity of theconsidered medium (b) is characterized by measuring the varia-tions of the relative velocity on the applied external stress (A) asshown in Eq. (4).

Physically speaking, changes in material nonlinearity result fromsmall variations in the microstructure of the tested sample. Indeed,various damage phenomena can affect the microstructure of thetested sample (e.g. thermal loading [7]). The previous discussionfocused on variations of the relative velocity due to applied externalstress (see Eq. (2)). But the theoretical model defined by Eq. (1) is notlimited to a specific damage mechanism. Indeed, the stretch para-meter uðkÞ51 can be measured to estimate the level of nonlinearitiesinduced by thermal loading as will be shown in the experimentalsection.

2.2. Implementation of the coda wave interferometry

Following the previous literature, the stretch technique(defined in Eq. (1)) is implemented in practice by stretching (orsqueezing) the waveform hk(t), obtained at a given stress ortemperature increment k to match a reference waveform h0(t).The stretch factor of the time axis is noted by u. The quality of thematch between the stretched and reference waveforms is

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735730

quantified with the following cross-correlation function [7]:

CCkðuÞ ¼

R T0 hk½tð1�uÞ�h0ðtÞdtffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR T

0 h2k ½tð1�uÞ�dt

R T0 h2

0ðtÞdtq

:ð5Þ

The cross-correlation function CCk(u) is computed over aduration T of the measured waveforms hk(t) and h0(t). Early andlate parts might be discarded due to poor signal-to-noise ratio ofthe measurements. The stretch parameter u, which maximizes theCCk(u)-function provides an estimate of the actual relative velocitychange u(k) and is used for further processing

uðkÞ ¼maxuAG

CCkðuÞ, ð6Þ

where G is the domain of u. The stretching technique implies thelinear stretching of the whole waveform hk, which is in accor-dance with the acoustoelastic theory of Section 2.1. The stretchingtechnique has recently been used by Larose and Hall [8] whonoted that this stretching technique can be more precise than thedoublet technique [4] by several orders of magnitude. The currentresearch employs the stretching technique to determine the slopeA of the variations in the measured relative velocity changes u(k)

for different levels of compressive load.

3. Experiment

3.1. Samples and ultrasonic measurement

Concrete samples are cast to perform ultrasonic measure-ments for different damage types that can cause velocity changes.The mix design follows the American Standard for Testing and

Material standard, ASTM C1293 [15] and the mixing procedure The

American Concrete Institute (ACI) standard. The water to cementratio is 1 by volume. The cement used is the Type I Portlandcement. Mix design of the samples is shown in Table 1. Thedimensions of all samples are 30.5 cm�7.6 cm�7.6 cm(12�3�3 inches). The largest dimension of aggregate is about4 cm. Samples T1, T2, and T3 are used for the thermal damagemeasurements, while C1 and C2 are used for the mechanicaldamage measurements. The bottom and top surfaces of thesamples are polished to avoid an imperfect contact with loadingplates when the samples are compressed, as well as to achievetwo parallel faces (Fig. 1). It should be mentioned that thedimension in the sample cross section is less than two timeslarger than the largest dimension of aggregate. The size of thesamples is not big enough to be considered statistically homo-geneous in their microstructure and thus no single sample canrepresent not only the microstructure, but also the mechanicaland ultrasonic properties of the entire batch of samples. This factinevitably can cause a large sample-to-sample variation in theresults obtained.

A small specially designed aluminum cone is attached to thereceiver surface using superglue to achieve a point-like detectionand thus to avoid the phase cancellation of the received diffusewaves [4]. The radius of the circular contact area is about 1 mm.The receiver transducer with the attached cone is held by a fixture

Table 1Mix design of concrete samples.

Component Value

Cement (kg) 0.84119

Water (kg) 0.3789

Coarse aggregate (kg) 2.2133

Fine aggregate (Adairsville) (kg) 1.3216

Water–cement ratio by volume 1.0002

and clamped on the concrete sample, for the receiver to beperfectly perpendicular to the sample surface at all times duringthe experiment. Another fixture with a retainer spring that isdesigned to apply a constant force onto the transmitting trans-ducer is also used. Use of these fixtures guarantees a consistentcontact and repeatable ultrasonic measurement. Both transducersare placed in the center of two neighboring faces of the sample toensure that the ultrasonic transducers are sufficiently far awayfrom the sample ends where the compression force is applied andthus local damage may develop, and also to minimize capturingthe ballistic waves. The local damage, or any change at the sampleends will not affect the diffuse field due to the high attenuation inthe frequency range used in the experiment (200–800 kHz) (or ashort transport mean free path). Therefore, the diffuse waves willprobe only the volume near the transducers and will not besensitive to the remote damage. The requirement for separationdistance between the two transducers will be discussed further inthe next section.

A schematic of the acoustoelastic measurement setup is shownin Fig. 1. An arbitrary function generator, Agilent 33250A, pro-vides the input signal, a linear frequency modulated up-chirpsignal with a peak-to-peak amplitude of 10 Vpp beginning at200 kHz and ending at 800 kHz. Both the transmitter and receiverare Panametrics V103 broadband transducers with a centerfrequency 1 MHz. The received signal is amplified with a pre-amplifier (the receiver part of Panametrics 5058PR) in order toimprove signal-to-noise ratio. The input (s(t)) and output(received and then amplified) signal (r(t)) are digitized by aTektronix TDS5043B digital oscilloscope and saved for furtherdata processing.

3.2. Procedure to impart damage and mechanical loading for

acoustoelasticity measurements

Two different types of damage in concrete (or changes in themicrostructure) are examined: thermal shock damage anddamage due to dynamic mechanical loading. Each experimentincludes one common step: the compressive loading on thesample to make the acoustoelasticity measurements as shownin Fig. 2(a). The concrete samples are compressed with steps of100 kPa each, and a total of 11 steps on a load frame (SATEC 22EMF). The maximum load capacity of this machine is 97.8 kN(22 lbf) and thus about 23.5% of the maximum capacity of theloading machine is activated. At each load step level, k, theultrasonic signals rk and sk are acquired and saved. The appliedstress where the ultrasonic measurements are made is in the3–4 MPa range for both the thermal and mechanical damagedsamples. The ultrasonic results at stress levels below 3 MPa arenot consistent enough, possibly due to some initial settling in ofthe inherently more resilient components of the concrete, such asthe loose interfaces between the cement matrix and aggregate (whichare aligned perpendicular to the loading direction) that can be closedat a relatively low compressive load. This effect is seen also inFig. 4 and 7 of Shokouhi et al. [16]; the slope at lower loads isdifferent from that at higher loads. One additional point is that weobserved that our loading machine is not in its best condition, and itshowed some inconsistency at the beginning of the loading.

For the thermal shock damage samples, ultrasonic measurementsare performed 4 times during the entire thermal exposure period. Thesamples are kept in a thermal chamber at 120 1C for 3 h to induce freewater evaporation, for a total of 9 h in the chamber as shown inFig. 2(b). After the period in the thermal chamber, the samples arestored at room temperature for 24 h in order for the sample to fullycool down before the ultrasonic measurements. The water evapora-tion during the thermal shock cycles is known to produce micro-cracks and pores in the concrete microstructure [9].

Fig. 1. Experimental setup for the CWI-based acoustoelasticity measurement.

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735 731

For the mechanical damage samples, 12 consecutive compres-sion cycles are performed to introduce any change in the micro-structure as shown in Fig. 2(c). The range and pattern of the unitcyclic load are the same as in the acoustoelastic measurement(Fig. 2(a)) and the ultrasonic measurements are taken at everycycle. The maximum load is about 10% of the yield strength of theconcrete sample and is apparently too low to produce anysubstantial progressive damage. Nonetheless, as concrete isloaded numerous times in a row, there can be some small changesin its properties, for example in the Young’s modulus [1]. Themain objective of the cyclic loading experiment is to see if theproposed ultrasonic technique is sensitive enough to detect suchsmall changes in the microstructure.

3.3. Data pre-processing

In many ultrasonic measurements, a short pulse signal is usedas the excitation signal and then a frequency domain deconvolu-tion technique is applied to obtain the impulse response function.Another method is the so-called pulse compression technique inwhich the input is a long chirp signal in an arbitrary shape andduration. To achieve the impulse response function, hk(t), theoutput signal rk (t) is cross-correlated with the input signal sk (t):

hkðtÞ ¼ rkðtÞnskðtÞ, ð7Þ

where n is the cross-correlation operator. This operation is alsoknown as matched filtering. Due to the longer signal length and the

Fig. 2. Profiles for thermal and mechanical loading: (a) load profile for acoustoelastic measurements (single compression cycle); (b) temperature profile for the thermal

shock damage; and (c) profile for the cyclic compressive loading.

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735732

higher energy input at each frequency component as compared to theshort pulse signal, the method of matched filtering provides a highersignal to noise ratio. The impulse response function calculated fromthe measured diffuse field signal, obtained at 3 MPa, is taken as thereference h0. Fig. 3 shows a typical impulse response functionobtained using matched filtering.

After matched-filtering, the obtained impulse responses (hk(t) andh0(t)) are cross-correlated according to Eq. (5) in the time range up to0.6 ms. The relative velocity changes uðkÞ are plotted against theapplied stress (Ds(k)) to determine the slope A from a linear curvefitting. Each set of data during the compressive loading provides oneslope, for one damage state. Finally, all the slopes are plotted againstthe exposure time in the thermal chamber or the number ofcompressive cycles.

4. Results

4.1. Measurement repeatability

Eqs. (1) and (2) show that the higher the compressive stress is,the faster the waves travel through the concrete. Therefore, one

can expect a negative relative velocity change as the compressivestress increases (A in Eq. (4) is thus positive). The range ofresulting slopes (the acoustoelasticity constant) measured forthe undamaged concrete samples is 0.6–1.2�10�6 and this isclose to the published value 1.0�10�6 for a concrete sample withsimilar material contents [8]. Using the nominal value of theYoung’s modulus, 36 GPa of the concrete samples used in thisresearch, and following the procedure to calculate the nonlinear-ity parameter [8], the average nonlinearity parameter obtained is�36 which is fairly close to that in [8] (�40), but lower than thatof Shokouhi et al. [16] (�75), and much lower than that of Payanet al. [9] (�157). These inconsistencies need to be investigated,especially if there is any dependence on the measurementtechnique used. One has to consider the effect of temperatureon the relative velocity changes, since it has been shown thatdiffuse waves are also sensitive to the ambient temperaturevariation [17]. Since one compression loading takes less than12 min, the thermal diffusion from the air into the concretesample will be slow and can be neglected. Also, the roomtemperature is measured in every ultrasonic measurement. Theaverage fluctuation of the room temperature is quite small, in the

Fig. 3. Typical impulse response obtained from matched filtering in Eq. (5). The diffuse envelope for frequency 525 kHz is shown together.

Fig. 4. Repeatability plot showing the maximum variation of the measured relative velocity changes uk.

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735 733

0.2–0.6 1C range depending on time. Another effect is the relativevelocity change through strain. The strain induced relative velo-city change is about 16 times smaller than the stress inducedrelative velocity change, and thus it can be neglected as is5�10�5, which corresponds to an absolute velocity change of0.24 m/s. This is the level of sensitivity of a single measurement.

In the thermal damage experiments, the transducers areremoved from the samples while the samples are in the thermalchamber to avoid damaging the transducers and the transducersare reattached for the next ultrasonic experiment. Due to thisremoval and reattachment of the transducers, errors in therelative velocity change can occur. In a preliminary experiment,the possible errors in the slope are determined. A concrete sampleis compressed and released five times with an interval betweenthe loading/unloading of at least five hours for a full recoveryfrom any slow dynamics effects [18]. The five linear fits from thefive ultrasonic measurements (Fig. 4) have a maximum variationof the relative velocity changes of 8�10�5, which represents themaximum experimental error or the sensitivity of the thermaldamage experiments. As expected, this variation is higher than

the maximum variation for a single loading cycle and is the resultof slight variation of transducer positions as well as the couplingcondition. Nonetheless, the absolute level of experimental errorsis relatively small and acceptable.

One has also to ensure that the diffuse field is fully developedat the receiver. The diffuse behavior of the multiply scatteredultrasonic waves can be described by the diffuse field solution fora three dimensional space given by:

E¼P0

4Dpte�r2=4Dte�at , ð8Þ

where E is the average energy, P0 the released source amplitude, D

the diffusivity, a the dissipation rate, t the time, and r the sourceto receiver distance. Best fit parameters obtained by fitting Eq. (8)to the impulse response function shown in Fig. 3 are:D¼15.15 m2/s and a¼10 s�1 at 530 kHz. The values for D and a

agree well with those in [4]. In Fig. 3, the diffuse envelope isshown together with the recovered impulse response function.Note that while the impulse response function contains frequencycomponents in the 200–800 kHz range, the diffuse envelope is

Fig. 5. Results of the thermal damage experiment. The increase in the acoustoelasticity constant (A) is shown for 3 different specimens. Note that the elastic nonlinearity

parameter (b) is proportional to the measured acoustoelasticity constant (A).

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735734

only for 530 kHz (which is around the center frequency) and isshown as a representative in this frequency range. From thisdiffusivity, the transport mean free path le can be calculatedwhich is the mean distance where the direction of propagation ofthe energy is fully randomized [19]; after this distance, the diffusefield is assumed to begin. To ensure that waves are diffuse beforereaching the receiver, the distance le must be smaller than thesource to receiver distance, which is L¼5.4 cm. The approximateformula for the transport mean free path is given by [19]

le ¼3D

ue, ð9Þ

where ve is the average velocity at which energy is transported.Page et al. [20] experimentally showed that the energy velocity inan ultrasonic diffuse field is very close to the group velocity. FromFig. 3, the group velocity is estimated to be ve¼4752 m/s, whichgives the transport mean free path le on the order of 1 cm. With lebeing smaller than L, the diffuse field is fully developed beforearriving at the receiver. In addition, the distance from thetransmitting transducer to the sample end is about 15 cm; thisdistance is far enough (about 15 times the mean free path) for theexcited ultrasonic diffuse waves to become sufficiently attenu-ated at the sample end.

4.2. Thermal damage

The ultrasonic results for the thermal damage samples areshown in Fig. 5, which consists of 4 slopes versus the exposuretime for the 3 different samples. The slopes for all three samplesshow a clearly increasing trend. This trend demonstrates that themore thermal damage that is introduced into the concrete, thegreater the measured slope (or the nonlinearity) of the concrete.Fig. 5 also shows the increase of the slopes tends to slow downwith time; this is consistent with the well-known fact that theevaporation of free water occurs in the first a few hours (but withan exact length depending on temperature) and so does thedamage (porosity and microcracks). A complete set of data pointsand curves can be found in Ref. [21].

4.3. Cyclic loading

Fig. 6 shows the ultrasonic results from the cyclic loadingexperiment. These curves also show an increasing trend at thebeginning, and then tend to level off as the number of cyclesincreases, which may be interpreted that the changes in mechan-ical state due to the cyclic loading get saturated. This saturationmay have occurred since the level of the applied cyclic loading isfar below the stress level that can lead to a continuous accumula-tion of damage. Therefore, the concrete samples may have under-gone slight changes in their microstructure only in the first fewcycles. This is, in fact, an unproven conjecture but practicallythere is no other way to characterize these small changes and toprove or disprove the conjecture. Note also that the changes inslope are much smaller than those in the thermal damage case. Acomplete set of data points and fit curves can also be found in Ref.[21].

It is observed that the variations in the results for the twocyclic loading samples are larger than those for the three thermalshock samples. The present cyclic load testing is in fact a high-cycle fatigue test and the poor repeatability of fatigue test results(even for small metallic fatigue samples) is well known. It ispartially due to the different loading conditions that the machineproduces at each different test, as well as the sample-to-samplevariation in material properties. On the contrary, the thermalloading (temperature changes up to 120 1C) are easier to repeatusing a thermal chamber unit with an automatic temperaturecontrol capability. Therefore, the variation in the two differentdamage tests appears to be more due to differences in the testingprocedures, than a physical cause.

5. Conclusion

This research presents initial results to demonstrate thefeasibility of detecting small scale damage in concrete samplesusing the diffuse ultrasound and the coda wave interferometrydata processing technique. The measurement procedure devel-oped in this research is shown to be repeatable and highlysensitive to damage in concrete and thus can be useful forrepetitive measurements during degradation. The slopes (the

Fig. 6. Results of the cyclic loading experiment for two different specimens. The changes in the acoustoelasticity constant (A) are shown for increasing number of cycles.

Note that the elastic nonlinearity parameter (b) is proportional to the measured acoustoelasticity constant (A).

D.P. Schurr et al. / NDT&E International 44 (2011) 728–735 735

acousoelasticity constant A or the nonlinear elastic parameter b)for damaged samples are typically multiple times higher thanthat for the undamaged samples. The results of the thermaldamage experiments show a clear increasing trend, and theincrease is higher than that for the cyclic loading experiment.The slopes of the cyclic loading experiment start to saturate as thenumber of cycle increases

The major advantages of the present experimental techniqueare the relatively simple measurement setup and the sophisti-cated data analysis methods that are based on the well-developedtheoretical foundations (the CWI and the cross-correlation tech-nique to extract the Green’s function from diffuse waves). TheCWI is applied to the signals from the acoustoelastic measure-ments in this research, which makes the technique somewhatimpractical for a large structure. However, in principle, applyingload on the object is not a requirement and the CWI can beapplied to signals due to changes in the medium by any cause(temperature change, elastic modulus change, damage, etc.).Future work includes developing an experimental technique thatimplements the CWI without relying on the acoustoelasticmeasurement.

Acknowledgments

The Deutscher Akademischer Austauschdienst provided partialsupport to DPS. The authors wish to thank Jun Chen and RobertMoser for help with sample preparation and mechanical testing.The authors also would like to thanks Dr. R. Weaver for hisstimulating suggestions during the planning of this study.

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