Applicability of Coda Wave Interferometry Technique for Measurement of Acoustoelastic Effect of Concrete
Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 428-434, 2014
Applicability of Coda Wave Interferometry Technique for Measurement of Acoustoelastic Effect of Concrete
Sung Woo Shin
Abstract In this study, we examined the applicability of coda wave interferometry (CWI) technique, which was developed to characterize seismic waves, to detect and evaluate change in the velocity of ultrasonic waves in concrete due to acoustoelastic effect. Ultrasonic wave measurements and compressive loading tests were conducted on a concrete specimen. The measured wave signals were processed with CWI to detect and evaluate the relative velocity change with respect to the stress state of the specimen. A phase change due to the acoustoelastic effect of concrete was clearly detected in the late-arriving coda wave. This shows that the relative velocity change of ultrasonic waves in concrete due to the acoustoelastic effect can be evaluated successfully and precisely using CWI.
Keywords: Concrete NDE, Coda Wave, Coda Wave Interferometry, Acoustoelastic Effect, Ultrasonic Velocity
1. Introduction effect of concrete is lower than 0.01%/MPa [5]. On the other hand, nevertheless of constant Stress states in concrete structures can be stress state, an usual velocity measurement error changed due to cracking, overloading, support of a conventional time-of-flight (TOF) method, settlements, corrosion of reinforcements, to name which is commonly used for wave velocity a few. The change of the stress state may measurement of concrete, is often higher than reduce the load carrying capacity of the structure 1% [6]. Obviously it is inacceptable to monitor and can lead to structural failure. Therefore, the change of stress state in concrete using TOF monitoring the changes of the stress state in a based ultrasonic wave velocity measurement. certain critical member of a structure is important Coda wave interferometry (CWI) is a prom- task to assess the safety of the structure. ising technique to monitor small wave velocity It is well known that the ultrasonic wave change in complex medium such as soil and velocity of a solid medium changes with the concrete. CWI technique was originally developed stress state of the medium [1]. This stress for detection and quantification of small temporal dependence of the wave velocity is so called as change between two seismic waves originating the acoustoelastic effect [2]. Many research have from the same source [7]. As originated from been devoted to develop the acoustoelastic based seismology, coda wave means a tail of seismo- stress monitoring techniques for steel structural gram after an earthquake. When seismic (or members [3]. However, those for concrete struc- ultrasonic) wave propagates through a complex tural members have not been much interested in heterogeneous medium, multiple scattering occurs research community as the relative velocity due to heterogeneities of the medium. These change with respect to the stress change in a multiply scattered wave components (i.e. coda concrete medium is very small [4]. For example, wave) travelled longer distance than the directly the relative velocity change due to acoustoelastic propagated wave components (i.e. ballistic wave).
[Received: November 7, 2014, Revised: December 15, 2014, Accepted: December 16, 2014] Department of Safety Engineering, Pukyong National University, 45 Yongso-ro, Busan 608-737, Korea (E-mail: [email protected]) ⓒ 2014, Korean Society for Nondestructive Testing Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 428-434 2014 429
Therefore, coda wave forms later part of where subscripts and denote wave polariza- measured wave signal while ballistic wave forms tion and propagation directions, respectively. early part. Coda wave has more information on is normal stress in direction 1. and are the medium than ballistic wave as it travelled the stressed and the stress-free (or initial) wave longer distance and interacted more with the velocities of a medium, respectively. is the medium. Therefore, a small change in the acoustoelastic coefficient which depends on the medium, that is hardly detected in ballistic Lame's second order and the Murnaghan's third wave, becomes detectable in coda wave [7]. order elastic constants [11]. As seen in Eq. (1), CWI technique utilizes a complex medium (e.g. it is obvious that the wave velocity is depending concrete) as an interferometer of coda wave in on the stress state (i.e. ) in the medium. Eq. order to detect and quantify small temporal (1) can be re-written as change of a complex medium [8]. The CWI technique has recently been applied (2) for various problems in damage detection of concrete [9]. In this study, the applicability of the CWI technique to detect ultrasonic wave Therefore, if the acoustoelastic coefficient of a velocity change due to the stress state change of medium is known, the current stress state () of concrete is investigated. the medium can be estimated by measuring the current and the initial wave velocities of the 2. Theoretical Basis medium. This is the basic idea of the acousto- elastic based stress monitoring technique. As shown in equation (2), the acoustoelastic 2.1 Acoustoelastic Based Stress Monitoring coefficient of an interesting medium must be known in advance to monitor the stress state of The classical theory of ultrasonic wave the medium based on wave velocity measure- propagation assumes a linear elastic behavior of ments. Since the acoustoelastic coefficient of a solids. Under this assumption, the wave velocity material cannot be determined analytically, an of a solid medium is independent of the stress experiment to establish the velocity-stress relation state of the medium. However, when a solid should be performed. For this purpose, an index material exhibits nonlinear elastic behavior, for relative velocity change ( ) is introduced higher-order terms to describe nonlinear behavior as should be included in the stress-strain relation and in this case the wave velocity becomes stress dependent [1]. Hughes and Kelly derived (3) the stress-velocity relationship of uni-axially loaded isotropic medium based on Murnaghan's This suggests that the acoustoelastic coefficient theory of nonlinear elasticity [10]. Recently, () can be determined by estimating the slope Hughes and Kelly's stress-velocity model has of relation [11]. been further generalized using the first order In this study, the applicability of CWI linearization as technique for an accurate measurement of in concrete is investigated since the conventional (1) TOF method is inacceptable to use for the accurate measurement of in concrete. 430 Sung Woo Shin
2.2 Coda Wave Interferometry Technique Since , finally we obtain
The theory of CWI technique is briefly (9) introduced here. For more details about the Eq. (9) suggests that can be estimated by technique, see the state-of-the-art paper by stretching (or compressing) the unperturbed wave Snieder [8]. signal to match a perturbed wave signal [8]. The Suppose that in a medium the wave velocity quality of the match between the stretched is perturbed with the perturbation , and the unperturbed wave signal and the perturbed wave relative velocity change is the same at every signal within time-window , in which location in the medium. The unperturbed travel time of the wave is given by possesses coda wave, can be quantified with the following cross-correlation function as (4) where is wave path. The perturbed travel (10) time to the first order in the velocity perturbation is given by where is a stretching parameter [8]. Finally, (5) can be found among all values of that maximize the correlation coefficient as [8] Since is assumed to be constant, Eq. (5) can be re-arranged using Eq. (4) as max (11) (6) Eqs. (10) and (11) are two keys of CWI technique to detect and quantify small temporal This indicates that the travel time perturbation change of ultrasonic waves propagated through a increases linearly with the arrival time. complex medium. In this study, Eqs. (10) and Therefore, the travel time perturbation such as (11) are applied to detect and quantify the due to the acoustoelastic effect is more clearly relative velocity change of ultrasonic wave identified in the coda wave than the ballistic propagated through concrete. wave as the coda wave arrives later than the ballistic wave [8]. 3. Experimental Program Due to the acoustoelastic effect of a medium, the travel time of ultrasonic wave 3.1 Experimental Setup propagated through the medium is perturbed with from the unperturbed wave. Thus, the A test concrete specimen was prepared. relationship between the unperturbed and the Type I Portland cement, fine sand, and crushed perturbed signals can be written as gravel with nominal maximum size of 20 mm
(7) were used to make a concrete specimen. The length of the specimen is 300 mm and the Eq. (7) can be re-written using Eq. (6) as square sectional area is 150 mm by 150 mm.
Water/cement ratio of the specimen is 0.4 by (8) weight. The specimen was casted and cured in a Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 428-434 2014 431
3.2 Test Procedures
In order to obtain the relative velocity change () with respect to the stress state of a concrete specimen, ultrasonic wave measure- ments are executed during the uni-axial com- pression tests on the specimen. Load-controlled compression test was performed on the test specimen. Step loading with 0.1 MPa increment ranging from 5 to 6 MPa was applied. Since formation of crack can affect wave behaviors in concrete, stress ranges from 5 to 6 MPa, which is well below the matrix cracking strength (about 14 to 18 MPa) of the test specimen, was chosen in order to ensure elastic behavior of the
Fig. 1 Test specimen with ultrasonic transducers concrete specimen. Ultrasonic tests were performed at each loading step. The applied controlled curing room for 28 days before load is maintained constant during the ultrasonic testing. A companion cylinder specimen was measurement. After the ultrasonic test, the also produced for the compressive strength test. compressive load is slowly increased to the next Measured compressive strength of companion step load and then the ultrasonic measurement is cylinder specimen is 29.2 MPa. repeated. A pair of ultrasonic transducers with a central frequency 100 kHz (Model : Olympus 4. Results and Discussions V1011) was used for transmitting and receiving of ultrasonic waves. Both transducers were 4.1 Detection of Small Temporal Change of attached on the middle of two opposite sides of Ultrasonic Wave in Concrete the specimen (see Fig. 1). Therefore, the direc- tion of wave propagation (2 direction) is set to Typical ultrasonic signals measured at be perpendicular to the direction of loading different stress states (5.0 MPa, 5.5 MPa and (1 direction). Note that since the transducer used 6.0 MPa) are shown in Figs. 2-4. As seen in in this study generates compressional ultrasonic Fig. 2, those three signals seem to be very wave, the mode of the wave velocity becomes similar over the entire duration of the signals.
. Especially in the early part (ballistic wave part) 8 cycles of Hanning-windowed sine function of measured signals as shown in Fig. 3, it is with an oscillation frequency of 100 kHz was observed that the arrival of ultrasonic wave used as an input wave signal. A waveform is not visibly discernible (almost identical) generator and a power amplifier are used to nevertheless of the different stress states. generate the input. The received wave signal is However, as shown in Fig. 4, notable phase amplified with a preamplifier and digitized with changes of ultrasonic waves with respect to a sampling rate of 1 and a duration of 2 . stress state are clearly seen in the later part The digitized signals are saved in a personal (coda wave part) of the measured wave signals. computer for further signal processing. The results suggest that the conventional TOF 432 Sung Woo Shin
5 1.5 5.0 MPa 5.0 MPa 5.5 MPa 5.5 MPa 4 6.0 MPa 6.0 MPa
1 3
2 0.5
1
0 0 Amplitude (V) Amplitude Amplitude (V) Amplitude -1
-0.5 -2
-3 -1
-4
-1.5 -5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 6.5 7 7.5 8 -4 Lapse Time (sec) -3 Lapse Time (sec) x 10 x 10
Fig. 2 Measured full ultrasonic wave signals for Fig. 4 Later part (from 650 to 800 ) of full three different stress states wave signals presented in Fig 2.
study, the same wave mode () and loading 5 5.0 MPa 5.5 MPa 4 6.0 MPa condition were used. Therefore, it may be
3 concluded that the phase change of coda wave 2 in this study is resulting from the acoustoelastic 1 effect of concrete. 0 Amplitude (V) Amplitude -1
-2 4.2 Evaluation of Acoustoelastic Velocity -3 Change in Concrete
-4
-5 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Lapse Time (sec) -4 x 10 In order to evaluate the acoustoelastic velocity change in concrete, values for Fig. 3 Early part (from 40 to 190 ) of full wave various stress states were estimated. A stretching signals presented in Fig 2 CWI technique, represented in Eqs.(10) and method, which estimates the time of arrival of (11), was applied for this purpose. It is worth the fastest wave (i.e. ballistic wave) from which noting that the ultrasonic signal measured at the the wave velocity is calculated, may not be stress level of 5 MPa was selected as the effective to detect small velocity change in reference signal, , in CWI processing. In concrete. On the contrary, a small temporal order to include coda wave part (see Fig. 4) in change of ultrasonic wave is clearly identify in processing of Eq. (10), the time range ( ) in coda wave part. This result verifies the Eq. (10) was set as . Using Eq. effectiveness of utilizing coda wave to detect a (10), were searched for all ranging small velocity change of ultrasonic wave in from 0 to 0.05 with increment of . Then, concrete. Finally, as seen in Fig. 4, the lapse as shown in Fig. 5, value for a certain stress time of coda wave decreases as compressive level was determined using Eq.(11). stress in concrete increases. It was reported that Fig. 6 shows the estimated values for the wave velocity of mode in concrete various levels of compressive stress in the test increases as compressive stress (perpendicular to concrete specimen. It is clearly seen that the the direction of mode) increases due to value increases as compressive stress increases. acoustoelatic effect of concrete [12]. In this This result suggests that CWI technique can Journal of the Korean Society for Nondestructive Testing, Vol. 34, No. 6: 428-434 2014 433
5. Conclusion
Maximum CC Value at Alpha=0.0003 0.92 In this study, the applicability of CWI 0.91
0.9 technique for measurements of ultrasonic wave 0.89 velocity change due to the acoustoelastic effect 0.88 of concrete was investigated. On the basis of CC Value 0.87
0.86 the results, following conclusions could be 0.85 drawn. 0.84
0.83
0.82 0 1 2 3 4 5 6 (1) Nevertheless of change in stress state in Alpha -4 x 10 concrete, the frist-arrival ballistic wave part
Fig. 5 Example of value determination (for a of measured ultrasonic signals does not case with the stress level of 5.1 MPa) change much (visibly indiscernible) with the stress state of concrete. (2) Significant (visible) phase change with -3 x 10 3.5 Measured Linear Regression respect to the stress state of concrete is 3 occurred in the late-arriving coda wave part
2.5 of measured ultrasonic signals.
2 (3) The relative velocity change due to the acoustoelastic effect of concrete can be Alpha (dV/V) Alpha 1.5 evaluated precisely using CWI technique 1 with a resolution of 0.1 MPa. 0.5 (4) The CWI technique can be used to establish
0 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 relation of concrete and to monitor Stress (MPa) stress change of concrete. Fig. 6 Estimated relative velocity change () with respect to the level of compressive stress Acknowledgment in the test specimen
This work was supported by a Research quantify the relative velocity change of concrete Grant of Pukyong National University (2014 due to the acoustoelastic effect of concrete year). precisely (with resolution of 0.1 MPa). Using linear regression analysis, the acoustoelastic References coefficient ( in Eq. 3), which is represented as a slope in Fig. 6, was estimated. The estimated [1] J. L. Rose, Ultrasonic waves in solid acoustoelastic coefficient is 0.002936 MPa-1 media, pp. 300-307, Cambridge University with high value of correlation coefficient Press, Cambridge, UK (1999) (0.9895). This result indicates that the [2] R. A. Toupin and B. Bernstein, "Sound relation of concrete is linear and also suggests waves in deformed perfectly elastic that CWI technique can effectively be used both materials Acoustoelastic effect," Journal of to establish relation of various types of Acoustical Society of America, Vol. 33, concrete and to monitor stress change of pp. 216-225 (1961) concrete structural members. [3] D. E. Bray and R. K. Stanley, Nonde- 434 Sung Woo Shin
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