Lateral wave
Blackwell echo Specimen
Receiver
Transmitter Wedge
Diffracted waves Transducer
beam profile
H
t0
L
0 D t
tBW
t1
t2
tL
t0
Time Mode converted
Non-destructive testing of cover concrete using spectral analysis of ultrasonic surface waves
Morad GRIMES University of Jijel, Electronic
Department, Algeria grimes_morad@yahoo.fr
Zoubir-Mehdi SBARTAΪ I2M Laboratory, Dept GCE, University of Bordeaux, France
Nabil YACEF University of Jijel, NDT LAB,
Algria
Abstract— Concrete cover evaluation with NDT technique is a critical issue in the diagnosis of structures service life.
Ultrasonic NDT technique is one of the most efficient techniques for concrete strength evaluation. This paper presents the use of spectral analysis of ultrasonic surface waves for the non- destructive evaluation of concrete cover in laboratory. The procedure consists in generation and reception of surface waves using the time of flight diffraction method. After extraction of the lateral wave in the received signal using the matching pursuit method, the phase velocity dispersion characteristic is determined, and concrete cover is characterized.
Keywords—time of flight diffraction; matching pursuit;
concrete cover
I. INTRODUCTION
Non-Destructive Evaluation (NDE) of concrete cover is critical for monitor the integrity and predicts the durability, the corrosion of the concrete structures subject to poor environment. Among the main NDE techniques, the most used are based on ultrasound [1], which apply surface waves, that propagate from the surface of examined material and penetrate the material within the depth close to the wavelength.
In this study, the Spectral Analysis of Surface Save (SASW) method is used. It consists of generation, measurement, and processing of dispersive surface waves.
These waves are generated using the Time of Flight Diffraction method (TOFD). Hence, the received signal is composed of diffraction signals from cracks, refraction signals from subsurface, mode converted signals and lateral signal (surface signal). The later is extracted using the matching pursuit algorithm (MP).
II. THEORITICALBACKGROUND A. Time of Fligth Diffraction
The TOFD technique is based on measurements of the travel time of the echoes diffracted by the defect or by the subsurface. When a wide ultrasonic wave encounters defects, such as cracks or subsurface, the defect/subsurface will oscillate and the wave will be reflected, transmitted and also diffracted at the edges. The diffracted component can therefore be received by suitably positioned ultrasonic transducers. Figure 1 below shows a typical phenomena arising for such an arrangement over a planar specimen containing an embedded crack-like flaw. Where the diffraction
echoes are scattered by the edges of the flaw with 180° phase shift, and caught by the receiver, the lateral wave is
transmitted, which follows the specimen profile and the backwall echo is observed, which corresponds to the specular reflection of the beam over the outer wall of the component.
Figure 1 : Basic principle of the TOFD method
In fig.1,H denotes the thickness of the specimen, 2S the distance between the beam index positions of the two transducers,Dthe depth of the crack from the top surface of the specimen,Lthe length of the crack,t0the travel time of the ultrasound in a wedge,tLthe first arrival time from the lateral
wave signal to the receiver,t1 is the second arrival time from the top-tip diffracted signal to receive,t2the third arrival time from the bottom-tip diffracted signal to receiver andtBWis the fourth arrival time from the back wall echo to receiver.
B. Matchnig pursuit algorithm
Matching pursuit decomposition is an iterative algorithm, introduced by Mallat and Zhang [2], which can decompose any given signal into a set of waves taken from a dictionary.
The MP algorithm decomposes a given signal Sig using a
dictionary Dic belonging to the Hilbert space Hil. The MP offers an approximation of the signalSigas a linear expansion in terms of functions gi called atoms chosen from a complete dictionary. We define the complete dictionary as a family Dic ={gi; i = 0, 1,…, Le} of vectors inHil, such as||gi||=1.
The first step of the MP, the atomg0 which best matches the signal Sig is chosen from dictionary Dic. In each of the consecutive steps, the atomgmis matched to the signalRmSig, which is the residual left after subtracting results of previous iterations:
0
, 1
arg max i D ,
m m m
m m
m
m g i
R Sig Sig
R Sig R Sig g g R Sig
g R Sig g
(1)
After M iterations, the Matching Pursuit decomposes the signalSiginto its elementary components:
1 1
0
,
M m m
m m m
Sig
R Sig g g R Sig
(2)C. Spectral analysis of surface wave
Spectral analysis of surface waves is widely used in Geotechnical and Civil Engineering applications for estimating material properties in layered structures based on the dispersion characteristics of Rayleigh waves [3]. For a given position of the transmitter, two signalsx1(t) and x2(t) are recorded for two different positions of the receiver as shown in Fig.2. These temporal signals are transformed to X1(t) and X2(t) in the frequency domain through the Fast Fourier Transform. The cross power spectrum GX1X2 is defined as X1(f)*. X2(f), where X1(f)* denotes the complex conjugate of X1(f). The phase shift, X1X2, which represents physically the number of cycles frequency between the two receiver locations. The travel timet(f) from receiver 1 to receiver 2 can be computed by:
t(f)=X1X2(f)/(360°f) (3) The surface wave velocity, VR(f ), and the wavelength,(f), can then be determined by :
VR(f) =Dis/t(f) (4)
(f) =VR(f) /f (5)
whereDisis the distance between the two receivers. The plot of surface wave velocityVR(f) versus wavelength or frequency is called a dispersion curve.
III. EXPERIMENTAL SET-UP
A typical TOFD experimental measurement is shown in fig. An experimental slab of concrete withW/C= 0.5 is used as specimen under test. A pair of Panametrics longitudinal wave transducers with central frequency 1 MHz is used. The coupling with the specimen under test is made through a Panametrics silicone gel, here, the wedge angle is fixed at 45°.
A Panametrics pulser-receiver is used to excite the emitter and to amplify the received signal. The receiver signal is fed into a
digital oscilloscope (TektronicsTDS 2001) and transmitted to a PC through a serial bus for further processing. In order to perform the SAWS method, the receiver was increased by 1.5 cm from its initial position while the transmitter remaining stationary.
Figure 2 : Schematic diagram of the experiment IV. RESULTS AND DISCUSSION
Several ultrasonic signals were obtained for the concrete slab over a length of 9 cm using the TOFD technique with defined scan spacing of 1 cm and with different position of the receiver transducer. A typical receiver signal with 1 cm offset is shown in Fig.3
Figure 3 : Receiver signal at position 1.5 cm offset As shown in Fig.3, the received signal is composed of surface wave, diffracted waves, reflected waves and mode conversion waves. Hence, the MP algorithm was used to separate the surface wave from the others waves. Fig. 4 shows the separated surface waves at different position of the receiver from 1.5 cm to 9 cm.
P u ls e r
R e c e i ve r D i g i t a l
O s c il l o s c o p e
C o m p u t e r S p ec im e n u n d er te s t
T r a n sm i tt e r R e c e i v e r
Figure 4 : Surface waves at position of receiver from 1.5 cm to 9 cm
The results presented in Fig. 5 show the variation of ultrasonic velocity versus frequency up to 2 MHz. The frequency dependence of the velocity is relatively slight within the frequency range used. These results are in agreement with those of other works [1].
Figure 5: Measurement of velocity surface wave dispersion for a distance between the receiver positions of 1.5 cm.
V. CONCLUSION
This study is an attempt to perform spectral analysis of surface waves in concrete structures. The method developed consists in using of time of flight diffraction technique to record two waves for two different positions of the receiver with a given position of the transmitter. The surface wave is separated from the received signal using the matching pursuit algorithm. Then the travel time and so the velocity of the surface wave between two receiver positions can be estimated for each frequency. This processing allows the velocity dispersion within the material to be examined.
For a more complete validation of the method, some further studies are being implemented on laboratory specimens for different water to cement ratio in order to verify its effect on the dispersion velocity curve.
References
[1] M. Goueygou, M. Goueygou, B. Piwakowski, “NDE of two-layered mortar samples using high-frequency Rayleigh waves,” Ultrasonics, vol.
42, pp. 889–895, 2004
[2] S. Mallat and Z. Zhang, “Matching Pursuit with Time-Frequency Dictionaries,” IEEE Trans. Signal Proc., 1993, vol. 41, pp. 3397-3415.
[3] YS. Cho, “Non-destructive testing of high strength concrete using spectral analysis of surface waves,” NDT&E Int, pp. 1-7, 2003.
