Akkaya, Voigt, Shah 1/7 Document 1

Nondestructive measurement of concrete strength gain by an ultrasonic wave reflection method

Y. Akkaya1,2, T. Voigt2, K. V. Subramaniam3 and S. P. Shah2 .

ABSTRACT

A one-sided, nondestructive, ultrasonic technique for monitoring the setting and hardening process of concrete has recently been developed. The technique is based on monitoring the reflection coefficient of ultrasonic transverse waves at the surface of a laboratory scale hardening concrete in steel molds. The technique has been shown to reliably estimate the rate of strength gain of concrete under isothermal and outdoor conditions. Results of an experimental study to investigate the influence of curing temperature and mix design on the rate of strength gain and the ultrasonic transverse wave reflection loss are presented in this paper. Simultaneous measurements of wave reflection loss and compressive strength have been performed on various concrete compositions under different curing conditions. The ultrasonic technique is shown to produce reliable estimates of the rate of strength gain at early ages.

RÉSUMÉ

Une technique de contrôle de la cristallisation du béton a récemment été développée. Cette méthode non destructive et ne requérant qu’une seule surface d’essai est fondée sur l’étude de la diminution de la réflexion des ultrasons sur la surface du béton en cours de cristallisation. L’influence de la température de cristallisation et de la formulation du béton sur la vitesse de durcissement et l’atténuation de la réflexion des ondes ultrasoniques transversales a été mise en évidence par le biais d’une étude expérimentale dont les résultats sont présentés. La méthodologie de cette étude consiste en la mesure simultanée de la réflexion des ultrasons et de la résistance en compression du béton sous différentes conditions de cristallisation. Il a ainsi été démontré que cette technique de contrôle produisait des estimations fiables de la vitesse de durcissement du béton aux jeunes ages, dans un environnement isotherme comme sous des conditions extérieures.

1. INTRODUCTION

The evaluation of mechanical properties of concrete by nondestructive techniques is one of the most challenging tasks in modern civil engineering. Several techniques that meet this demand are currently in use. Some of them are based on propagation of ultrasonic waves. Others are focused on measuring the thermal history or certain mechanical quantities, such as penetration depth or pullout force of concrete. Further techniques deal with microwaves, electrical impedances and acoustic emissions. This paper will concentrate on ultrasonic techniques.

Many ultrasonic methods are based on the through-transmission of stress waves of various frequencies. Boutin and Arnaud [1] generated longitudinal waves (L-waves) of low frequencies using a vibroscope. The time of transition between fluid and solid state of

cellular cement paste was determined by measuring the L-wave velocity. A new device for monitoring the hydration of cement mortar that measures the transit time and the energy of an L-wave pulse propagating through a mortar sample has been introduced by Reinhardt et al. [2]. With this device the setting and hardening process of mortar can be evaluated. Other investigators have applied both, longitudinal and transverse waves (T-waves) to examine the hydration of cementitious materials. Sayers and Grenfell [3] found a linear relationship between the effective bulk and shear moduli determined by pulse velocities. D’Angelo et al. [4] detected a considerably higher sensitivity of T-waves to the hydration process compared to L-waves. Boumiz et al. [5] studied the development of elastic modulus, shear modulus and Poisson’s ratio as functions of time and degree of hydration.

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Other methods are based on the measurement of the reflection of an ultrasonic pulse at an interface between a buffer and a sample material. Papadakis [6] reported one of the first applications of this method in 1968. A sample material was bonded to a solid buffer-rod to measure the ultrasonic attenuation in the sample and the reflection coefficient at the buffer-sample interface.

Based on this method, Stepišnik et al. [7] monitored the reflection of a T-wave pulse at the interface between a quartz bar and cement paste to asses the development of the reflection coefficient and the shear modulus in time. This method has been advanced further by Valic [8]. Öztürk et al. [9] and Rapoport et al. [10] introduced a similar procedure wherein the reflection of T-waves at a steel-concrete interface are monitored and correlated with the progress in hydration. This method has been demonstrated to have a high potential to future field application. Recently, Chotard et al. [11] published data that correlate measurements of the wave reflection technique with observed trends in the hydration process of calcium aluminate cements determined with techniques such as X-ray diffraction, scanning electron microscopy, differential thermal analysis, and thermogravimetry .

Additional methods are available that are based on the measurement of the fundamental resonant frequencies of concrete specimens. The natural vibrational resonance frequencies are a function of the elastic material constants, mass density, and geometry of the specimen. From the resonant frequencies measured on a specimen vibrating in longitudinal or transverse mode the dynamic Young’s modulus can be calculated. Measuring the fundamental torsional frequency allows the calculation of the dynamic shear modulus. This method, which is described in ASTM C215 [12], requires the estimation of Poisson’s ratio. Leming et al. [13], Mantrala et al. [14], and Nagy [15] applied this test to determine the dynamic Young’s and shear modulus of concrete specimens of various shapes at various ages. Kolluru et al. [16] advanced the methodology by developing an algorithm to calculate the dynamic Young’s modulus and dynamic Poisson’s ratio from the first and second longitudinal resonance frequencies obtained from a single measurement on a concrete standard cylinder. Xianyu [17] et al. used this modified technique to monitor the development of the elastic properties of concrete at early ages. The resonant frequency method has the advantage to evaluate the elastic properties of the entire specimen. Therefore influences of local material inhomogeneities can be minimized. Limitations of the method are its dependency to the specimen geometry and that it is not possible to apply it in-situ on the structure.

2. EVALUATION OF CONCRETE STRENGTH BY NONDESTRUCTIVE METHODS

The most common in-situ method to predict the strength gain of concrete at early ages is the maturity method [18]. In this method, the maturity is calculated from the thermal history of the hardening concrete and related to the compressive strength. Once the maturity-strength relationship for a certain concrete mix is obtained in the laboratory, the method is relatively easy to apply in the field. However, the method underlies certain limitations. Each concrete composition has its own maturity-strength relationship and this relationship has to be determined in the laboratory individually. Additionally, the accuracy of the strength prediction is affected by the temperature and humidity differences between laboratory and site conditions.

Another alternative is to assess the strength of early age concrete with ultrasonic wave propagation techniques. Several methods that relate the ability of cementitious materials to transmit ultrasonic waves and their compressive strength gain can be found in the literature. Keating et al. [19] investigated the relationship between ultrasonic longitudinal pulse velocity and cube strength for cement slurries in the first 24 hours. For concrete cured at room temperature, it was noted that the relative change in the pulse velocity in the first few hours is higher than the observed rate of strength gain. However, a general correlation between these two parameters could be deduced.

Another study about the interdependence between the velocity of L-waves and compressive strength has been presented by Pessiki and Carino [20]. Within the scope of this work concrete mixtures with different water-cement ratios and aggregate contents cured at three different temperatures were examined. The L-wave velocity was determined by using the impact-echo method in a time range of up to 28 days. At early ages the L-wave velocity increases at a faster rate when compared with the compressive strength and at later ages the strength is the faster developing quantity. L-wave velocity is found to be a sensitive indicator of the changes in the compressive strength up to 3 days after mixing.

Popovics et al. [21] determined the velocity of L-waves and surface waves by one-sided measurements. Additionally, L-wave velocity was measured by through-thickness measurements for verification purposes. It was observed that the surface wave velocity is indicative of changes in compressive strength up to 28 days of age. The velocity of L-waves obtained by one-sided measurements was found to be not suitable for following the strength development because of its inherent large scatter when compared with the through-thickness velocity measurements.

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In a recent study conducted by Subramaniam et al. [22] the field applicability of a test technique based on monitoring the reflections of T-waves at a steel-concrete interface in predicting the strength gain in a structure was investigated. The observed trends in the reflection of T-waves at the steel-concrete interface were shown to correlate well with the observed in-situ strength development of concrete. Finally, the percentage change in the WRF reading was shown to be identical to the percentage change in the in-situ strength gain of concrete.

3. WAVE PROPAGATION THEORY

3.1 Sound waves at boundaries When an ultrasonic wave travelling through a

medium hits an interface, defined as a boundary between two materials with different acoustic properties, it is partially reflected back and partially transmitted into the medium on the other side of the interface. The reflection coefficient r describes the amount of wave energy, which is reflected at that interface. For L- and T-waves r is determined by the acoustic impedances of the materials that form the interface. When a wave is reflected at a boundary between Material 1 and Material 2, r is

1122

1122

i

r

vvvv

AA

rρ+ρρ−ρ

== (1)

where ρ1 and ρ2 are the density of the materials and v1 and v2 are the wave velocity of L- or T-waves respectively. The reflection coefficient can also be determined from the amplitudes of the incident (Ai) and the reflected wave (Ar).

3.2 Derivation of elastic moduli From elasticity and acoustics, two elastic moduli can

directly be derived from density and wave velocity. When the velocity of L- and T-waves in a material are known, the longitudinal and shear modulus can be calculated as follows:

2LvL ⋅ρ= (2) 2TvG ⋅ρ= (3)

Where L is the longitudinal modulus (Young's modulus), G the shear modulus and vL and vT the velocity of L- and T-waves respectively. The moduli L and G are related to the direction of particle motion caused by L- and T-waves. The longitudinal modulus relates strain to longitudinally applied stress. The shear modulus describes the elastic behavior of a material subjected to shear strain.

It follows from Equation 1, 2 and 3 that, dependent on the wave type, the reflection coefficient is governed

by the development of the longitudinal or shear modulus. This proves that r is related to physical properties of the tested material. Consequently, establishing a relationship between r and a certain mechanical parameter of the test material (e.g. concrete) is not empiric but physically founded.

4. EXPERIMENTAL METHOD AND APPARATUS

4.1 Experimental procedure The investigations described in this paper are based

on wave reflection measurements with T-waves. The principle of the applied method is to evaluate reflections of ultrasonic waves at the interface between concrete and a buffer material. A T-wave pulse is transmitted into the buffer material, reflected at the interface between the buffer material and concrete and received at the same side from where it was sent. In all the experiments the bottom plate of a steel mold has been used as the buffer material.

The reflections of the T-wave pulse are acquired in time domain and transformed into the frequency domain by a fast Fourier transform algorithm. Since the amplitude of the incident wave can not be determined reliably, the amplitude ratio of the second to the first reflection is calculated. Basically, this ratio corresponds to the reflection coefficient r (Equation 1). However, the signals contain several influences, e.g. losses due to transducer-steel coupling as well as material and geometric losses in steel. A self-compensating method is used to eliminate those effects. The complete numerical procedure, which was applied in this paper to calculate r is explained by Öztürk et al.9 and Rapoport et al.10.

The wave reflection measurements start immediately after casting. As long as the concrete is in a liquid state, r will be unity, since T-waves can propagate only in solids and the entire wave energy is reflected back from the steel-concrete interface. As the concrete hardens its ability to transmit T-waves increases. Therefore, more and more wave energy is transmitted into the concrete and r decreases.

The reflection coefficient as described above represents a loss in amplitude of the second reflection relative to the first reflection at a given time t. In ultrasonics amplitude ratios are usually measured in decibel. The reflection coefficient r expressed in decibel becomes the reflection loss RL. With Ar1 and Ar2 as the amplitudes of the first and second reflection at time t, the reflection loss RL(t)is calculated as

( )( )tAtA

log20(t) Rr1

r2L ⋅−= (4)

For all further elaborations in this paper, the reflection coefficient is expressed in terms of the reflection loss.

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4.2 Experimental test setup In the test procedure, an ultrasonic T-wave

transducer is attached to a steel plate with a thickness of 1.15 cm. The ultrasonic signal with a center frequency of 2.25 MHz generated by the transducer propagates through the steel plate and is reflected at the steel-concrete interface. The reflected signals are captured by the same transducer. The signals collected by the pulser/receiver are then transferred to a laptop computer, which performs the data evaluation using a data acquisition and analysis program written using LabVIEW™. The equipment allows simultaneous measuring from two channels. Consequently, with the test setup described in this paper it is possible to follow the real-time development of the reflection loss at two different points at the same time. A photograph of the semi-portable test setup for continuous monitoring and automated data acquisition and analysis is shown in Figure 1.

4.3 Experimental program In order to establish the effects of mix design and

curing temperature of the concrete on the strength gain and change of reflection loss, the experiments have been conducted in two phases. Different curing procedures, mix-designs and materials are used in each phase. In the first phase, the influence of curing temperature on the rate of strength gain predicted by the wave reflection measurements was investigated by using controlled-temperature curing rooms. Three temperatures are used for this purpose: 4oC, 22oC and 30oC. Crushed limestone, with a maximum aggregate size of 24 mm was used as coarse aggregate in this phase.

In Phase II, the influence of varying temperature on the rate of strength gain of concrete and the ultrasonic wave reflection response was studied. In this phase, experiments are carried out under outdoor conditions with concrete specimens being cured in the open. Gravel, with a maximum aggregate size of 16 mm was

used as coarse aggregate in this phase. In both phases, river sand was used as fine aggregate. The cement type used in both phases was Type I. The concrete mix

designs, which were used in Phase I and II are given in Table 1.

The strength development of each concrete mixture composition was determined using standard cylinders (76 mm diameter and 152 mm height). At least 5 specimens are tested at different times during the initial development of the strength (usually between 13-24 hours after casting). The temperature development was also monitored inside the concrete. Thermocouples are placed in the concrete and data are collected in a data-logger.

For all the concrete mixtures tested in this program, the wave reflection measurements were

performed according to the procedure described in the previous section. In Phase I of the experimental work the wave reflections were monitored continuously after casting. In Phase II, the wave reflection was monitored in a discontinuous manner, and the value of RL(t) was recorded at discrete time intervals. Discontinuous sampling of the wave reflection data allows acquiring data from multiple sensors using a single channel data acquisition system. The feasibility of practical implementation of this procedure was explored in Phase II of the experimental work. The discrete reflection loss data collected at distinct times can be interpolated with a mathematical model to obtain a continuous measure for the change of WRF with time.

Table 1 – Mix design and material properties of the concrete specimens used in the experiments

Phase Mix Water/ cement

Water/ (cement +fly ash)

Coarse/ total

aggregate

Total aggregate

volume

Cement/ (cement +fly ash)

1 0.55 0.55 0.63 70 1.00 I

2 0.54 0.40 0.61 68 0.74 1 0.71 0.39 0.40 52 0.55 2 0.46 0.36 0.52 61 0.79 3 0.50 0.31 0.52 61 0.61 4 0.49 0.39 0.52 67 0.80 5 0.54 0.35 0.47 64 0.65

II

6 0.50 0.31 0.52 61 0.61

Fig. 1 - Equipment used in the experiments

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5. EXPERIMENTS UNDER ISOTHERMAL CONDITIONS

5.1 Development of reflection loss Examples of the reflection loss development of the

concrete specimens cured under controlled temperatures are presented in Fig. 2. In Fig. 3 the appropriate temperature development is given. As it can be seen from the figure, the specimens maintained a constant temperature in the curing rooms. The test results reveal that different hydration behaviors caused by different curing temperatures are reflected in the reflection loss graphs.

Fig. 2 – Reflection loss development of concrete I-2 under controlled conditions

Fig. 3 – Concrete temperature for controlled conditions

5.2 Correlation of reflection loss and strength

In this section, the relation between measured reflection loss and the compressive strength development of the concrete is presented. In Fig. 4 the early age compressive strength development of the I-2 concrete cured at three different temperatures is plotted. The corresponding reflection loss measurements for the same concrete compositions are shown in Fig. 5. It can be seen that the rate of strength

development is affected by the curing temperature. Concrete cured at the highest ambient temperature starts developing strength first and has the highest rate of change. The concrete cured at the lowest temperature starts last with the lowest growth rate. The reflection loss follows exactly the same trend.

Fig. 4 – Strength development for high strength concrete in the first three days

Fig. 5 – Reflection loss development of concrete I-2 under controlled conditions

In order to predict the strength development with the reflection loss measurements a correlation between these two quantities needs to be established. The relationship between strength and reflection loss for a sample experiment is given in Fig. 6. Strength and reflection loss show a linear relationship. By means of the plotted trend line the reflection loss value for the time ts when the strength starts to develop can be found (Fig. 6). Using this value the gain in reflection loss relative to the time ts when strength starts increasing can be calculated. The relationship between strength and the reflection loss gain is linear and passes from the origin (Fig. 6). The gain of reflection loss is calculated with the following equation:

∆RL(t) = RL(t) – RL(ts) (5)

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where ∆RL(t) is the total gain of reflection loss at time t with respect to the value at time ts, RL(t) and RL(ts) the reflection loss at time t and ts respectively.

Fig. 6 – Relationship between strength and reflection loss

Time ts can be assumed to depend on the curing conditions and mix compositions of the concrete and consequently has to be determined for each experiment individually. In Fig. 6 it is shown how time ts can be determined based on the entire development of strength and reflection loss. However, for possible field applications it is necessary to define ts only using the reflection loss measurements. Therefore, the next step in the procedure consists of determining this theoretical value of ts from the observed trends of the reflection loss.

Fig. 7 – Example of numerical determination of time ts from measured reflection loss data

The reflection loss development of one of the experiments is shown in Figure 7(a). It can be observed that the reflection loss response exhibits an inflection point in the early ages. The inflection point corresponds to a maximum in the numerical derivative

of the reflection loss data. This maximum in the derivative is labeled point I in the graph and the time corresponding to the inflection point in the reflection loss is denoted as tI. At point I the reflection loss has its highest rate of change.

The development of the very early age compressive strength of the same concrete is plotted in Figure 7(c) for comparison. The observed trend in the compressive strength gain can be extrapolated to obtain the time ts when concrete theoretically begins gaining strength (as shown in the Figure). Data analysis of all the tested concrete mixtures in this program revealed that ts is consistently a fixed multiple of tI obtained from reflection loss measurements. It was established that time tI multiplied by 1.15 corresponds to the time ts, the time when strength starts increasing.

After determining time ts the gain of reflection loss can be calculated and the ∆reflection loss-strength (∆RL−S) relationship for each conducted experiment can be plotted (Fig. 8). It is obvious that there is a unique relationship between the reflection loss gain and compressive strength for each conducted experiment. A linear function that passes from the point of origin can be fitted to each single data set. The function of the ∆RL−S relationship has the following equation:

Scalc(t) = m · [RL(t) – RL(ts)] (6)

where, Scalc(t) is the calculated strength, RL(t) and RL(ts) the measured reflection loss at time t and ts respectively, and m is the factor of proportionality, i.e., the slope of the function.

Fig. 8 – ∆RL-S relationships for mixes cured at constant temperatures conditions

5.3 Prediction of compressive strength

The ∆RL −S relationship (Equation 6) established in the previous section can now be used to predict the compressive strength development. Time ts and subsequently RL(ts) can readily be extracted from the reflection loss measurements as shown. For any time t (where t>ts) the strength can be calculated using the measured reflection loss value at that time. The

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calculation is exemplary shown in Table 2, where Scalc(t) and Smeas(t) are the calculated and measured strength values respectively.

Table 2 – Exemplary calculation of strength prediction

t (hours)

RL(t) (dB) ?RL(t)

(dB) Scalc(t) (MPa) Smeas(t)

(MPa) 16 1.59 0.74 10.48 10.90 18 1.73 0.87 12.37 13.36 20 1.84 0.99 13.98 14.53 36 2.38 1.53 21.57 20.94 48 2.58 1.73 24.40 23.42 72 2.80

–RL(ts)=

1.95

×m=

27.50

≅

28.04 RL(ts) = 0.85 db m = 14.14

The procedure for determining the strength at any given time hence requires an estimate of the coefficient m. If the strength of concrete is determined at any time t (where t>ts) through a direct measurement, the value of m can be calculated. Since this value of m is shown to be invariant with time, it can be used for predicting the further strength gain in concrete. Consequently the prediction procedure presented in this paper requires at least one reliable compressive strength value. This value can be considered as a calibration value, which includes the specific properties of the tested concrete composition.

The predicted strength values shown in this section are calculated based on the ∆RL−S relationship evaluated from the entire reflection loss and strength developments. The measured and predicted strength of the concretes cured under the temperatures 22ºC and 30ºC are shown in Fig. 9.

Fig. 9 – Prediction of compressive strength for concrete I-1 under controlled conditions

6. EXPERIMENTS UNDER VARIABLE CURING CONDITIONS

To verify and validate the results presented above, experiments have been conducted under outdoor

conditions. Examples of the temperature developments of the specimens cured under outdoor conditions are given in Fig. 10. They show significant changes and are dominated by the day/night cycle. The maximum temperature difference is about 17 ºC. The reflection loss development of three concrete mixes subjected to outside conditions can be found in Fig. 11.

Fig. 10 – Concrete temperature for uncontrolled conditions

Fig. 11 – Reflection loss development of concrete under uncontrolled conditions

Fig. 12 – ∆RL−S relationships for concrete cured under outdoor conditions

The ∆RL−S relationships for all performed outdoor experiments are shown in Fig. 12. As it can be seen, the

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changing temperatures did not influence the linear relation between strength and reflection loss. The prediction of compressive strength is analogous to the procedure described above. Three examples of the strength prediction are given in Fig. 13.

Fig. 13 – Prediction of compressive strength for concrete under uncontrolled conditions

7. ACCURACY OF STRENGTH PREDICTIONS

To evaluate the proposed strength prediction and allow a comparison with other predictive methods the accuracy of the prediction shall be quantified and discussed in this section. The calculated versus measured strength values for all twelve conducted experiments are plotted in Fig. 14. It can be seen that the trend line of the data points (dashed) is very close to the line of equality (solid). For quantification of the prediction the Relative Standard Error of Estimate (RSEE) will be observed. The RSEE is calculated with the following equation:

n

%100S

SS

RSEE

n

1i

2

meas,i

calc,imeas,i∑=

⋅

−

= (7)

where Si,meas and Si,calc are the measured and calculated strength values at a certain time and n is the number of considered data sets. The RSEE values for each conducted experiment as well as for the entirety of the experiments are given in Table 3.

In a recently published review article, Popovics [23] discusses the accuracy of strength predictions made by ultrasonic pulse velocity methods. He concludes that predictions based on through transmission experiments can currently achieve an accuracy of ±20 percent under laboratory conditions. The results presented within this paper show that the described method could considerably improve the estimation error.

Table 3. Relative Standard Error of Estimate for the tested

concrete mixes

Phase Mix RSEE (%)

1 @ 4ºC 9.14 1 @ 22ºC 13.17 1 @ 30ºC 4.32 2 @ 4ºC 29.71 2 @ 22ºC 8.64

I

2 @ 30ºC 6.22 1 2.20 2 3.84 3 3.20 4 8.90 5 21.40

II

6 11.75

Phase I + II 13.70

Fig. 14 – Calculated versus measured strength values for all experiments

8. CONCLUSIONS

1. The reflection loss of T-wave reflections at a steel concrete interface is sensitive to the hydration of concrete. The compressive strength development and the reflection loss gain measured at the surface of the concrete specimen are linearly related at early ages. Changing curing temperatures and different concrete mix designs and materials do not affect the linearity of the correlation in this time range.

2. Once the reflection loss change of the concrete is calibrated to the strength gain of the concrete, it can be used to predict the concrete strength at early ages.

3. The described method of ultrasonic reflection loss measurement can be used to predict the time of initiation of the concrete strength gain (time ts) nondestructively. Further research is needed to

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understand the microstructural changes of the concrete at this time.

4. Discontinuous reflection loss measurements can be performed and a mathematical model can be applied to predict the complete behavior of the reflection loss change in time.

5. Further studies are needed to improve the technique. The effect of the microstructural properties of the interface between concrete and steel plate can be investigated by using multiple probes. Investigations are necessary to establish the thickness of the concrete surface layer that affects the reflection factor. Additionally the correlation between the measured surface layer properties and the bulk properties of the tested concrete has to be examined.

6. The paper presents results of laboratory-scale experiments performed on steel molds under controlled and uncontrolled conditions. By using a simple steel plate, which is attached to the surface of any concrete structure, the technique could be transformed into a field applicable method. However, prior field application, further research concerning the issues mentioned in the previous paragraph has to be done.

ACKNOWLEDGEMENTS

This research was supported by the Center for Advanced Cement-Based Materials and the Infrastructure Technology Institute of Northwestern University. Special appreciation should be given to Dr. John S. Popovics for his valuable comments.

REFERENCES

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[4] D’Angelo, R., Plona, T.J., Schwartz, L.M., Coveney, P., ‘Ultrasonic measurements on hydrating cement slurries’, Advanced Cement Based Materials 2 (1) (1995) 8-14.

[5] Boumiz, A., Vernet, C., Tenoudji, F.C., ‘Mechanical properties of cement pastes and mortars at early ages, evolution with time and degree of hydration’, Advanced Cement Based Materials 3 (3/4) (1996) 94-106.

[6] Papadakis, E.P., ‘Buffer-rod system for ultrasonic attenuation measurements’, Journal of Acoustical Society of America 44 (5) (1968) 1437-1441.

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[9] Öztürk, T., Rapoport, J., Popovics, J.S., Shah, S.P., ‘Monitoring the setting and hardening of cement-based materials with ultrasound’, Concrete Science and Engineering 1 (2) (1999) 83-91.

[10] Rapoport, J., Popovics, J.S., Subramaniam, K.V., Shah, S.P., ‘The use of ultrasound to monitor the stiffening process of portland cement concrete with admixtures’, ACI Materials Journal 97 (6) (2000) 675-683.

[11] Chotard, T., Gimet-Breart, N., Smith, A., Fargeot, D., Bonnet, J.P., Gault, C., ‘Application of ultrasonic testing to describe the hydration of calcium aluminate cement at the early age’, Cement and Concrete Research 30 (3) (2001) 405-412.

[12] ASTM C 215, 1998, ‘Test method for fundamental transverse, longitudinal, and torsional frequencies of concrete specimens’ Annual Book of Standards, Volume 04.02, Concrete and Aggregates, ASTM, Philadelphia, PA.

[13] Leming, M.L., Nau, J.M., Fukuda, J., ‘Nondestructive determination of the dynamic modulus of concrete disks’ ACI Materials Journal 95 (1) (1998) 50-57.

[14] Mantrala, S.K., Vipulanandan C., ‘Nondestructive evaluation of polyester polymer concrete’ ACI Materials Journal 92 (6) (1995) 660-668.

[15] Nagy, A., ‘Determination of E-modulus of young concrete with nondestructive method’ ASCE Journal of Materials in Civil Engineering 9 (1) (1997) 15-20.

[16] Kolluru, S.V., Popovics, J.S, Shah, S.P., ‘Determining elastic properties of concrete using vibrational resonance frequencies of standard test cylinders’ Cement, Concrete, and Aggregates, 22 (2) (2000) 81-89.

[17] Xianyu, J., Li, Z., ‘Dynamic property determination for early-age concrete’ ACI Materials Journal 98 (5) (2001) 365-370.

[18] Carino, N.J., ’The maturity method: theory and application’, Cement, Concrete, and Aggregates 6 (2) (1984) 61-73.

[19] Keating, J., Hannant, D.J., Hibbert, A.P., ‘Correlation between cube strength, ultrasonic pulse velocity and volume change for oil well cement slurries’, Cement and Concrete Research 19 (5) (1989) 715-726.

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[20] Pessiki, S.P., Carino, N.J., ’Setting time and strength of concrete using the impact-echo method’, ACI Materials Journal 85 (5) (1988) 389-399.

[21] Popovics, J.S., Song, W., Achenbach, J.D., Lee, J.H., Andre, R.F., ‘One–sided wave velocity measurement in concrete’, Journal of Engineering Mechanics 124 (12) (1998) 1346-1353.

[22] Subramaniam, K.V., Mohsen, J.P., Shaw, C.K., Shah, S.P., ‘An ultrasonic technique for monitoring concrete strength gain at early age’, ACI Materials Journal (2002), in press.

[23] Popovics, S., ‘Analysis of the concrete strength versus ultrasonic pulse velocity relationship’, Materials Evaluation 59 (2) (2001) 123-129.