High frequency shear modulus of bitumen by ultrasonic measurements

Transcription

1 High frequency shear modulus of bitumen by ultrasonic measurements Nicolas Larcher Mokhfi Takarli Nicolas Angellier Christophe Petit Hamidou Sebbah Groupe d Etudes des Matériaux Hétérogènes Centre Universitaire de Génie Civil, Université de Limoges Boulevard Jacques Derche Egletons, FRANCE nicolas.larcher@etu.unilim.fr {mokhfi.takarli; nicolas.angellier; christophe.petit; hamidou.sebbah}@unilim.fr ABSTRACT. In this study, we will evaluate the high frequency shear modulus of bitumen using an ultrasonic method. This method is based on the measurement of both the velocity and attenuation of shear waves. The ultrasonic shear modulus is calculated by taking into account wave propagation in homogeneous viscoelastic media. The results are plotted in terms of master curve, Cole-Cole and Black spaces. The modulus magnitude evaluated by ultrasonic testing exhibits agreement with the results Dynamic Shear Rheometer test. A comparison between mechanical, rheological and ultrasonic approaches illustrates the importance quality velocity measuremen. In addition, each part of attenuation phenomenon (geometric spreading, viscous dissipation, and scattering) is evaluated and discussed. The work presented herein is a first step in preparation for future studies of biphasic media as Hot Mix Asphalt (HMA). KEYWORDS: Ultrasonic test, S-wave, velocity, attenuation, complex shear modulus, 2S2P1D EATA 2013, pages 1 to 17

2 2 EATA Introduction Nondestructive testing (NDT) is technical method to examine structures, materials or components in ways that to do not impair their future use and serviceability. In civil engineering, NDT is a valuable tool for structural diagnostics (in-service, in-situ or field NDT) and materials characterization (laboratory NDT). McCann and Forde (McCann et al., 2001) reported a state-of-the-art review on nondestructive testing (NDT) methods with respect to the civil engineering industry. Recently, an NCHRP report (Von Quintus et al., 2009) mentioned a number of NDT techniques that have been significantly improved. Ground penetrating radar, falling weight deflectometers, penetrometers, infrared and seismic technologies, are a few of those techniques which have shown promise for potential employment in quality control and acceptance of flexible pavement construction. The major advantages of NDT methods are their economy and efficiency. Seismic NDT, which is based on stress wave propagation, is a useful method for the structural evaluation of pavement, and asphalt materials characterization. These techniques can be divided into two approaches: the passive approach, and the active approach. Active techniques are those in which a material is investigated by the creation of a forced physical field with a specified orientation. The signal contents of the interrogating medium are changed through interaction with the material. In seismic NDT, the potential of active techniques (sonic/ultrasonic methods) in pavement applications has been clearly demonstrated in the literature review. The most commonly used seismic methods are: (i) Ultrasonic methods (Ultrasonic Pulse Velocity UPV with compressive and shear waves, Ultrasonic Echo UE ); (ii) Sonic method (Impact Echo IE ); (iii) Dynamic methods (Impulse Response IR, Spectral Analysis of Surface Wave SASW ). Several experimental laboratory studies have been described in the literature and demonstrate the potential of stress wave propagation techniques for measuring complex modulus of asphalt concrete which is a key parameter for pavement design. These techniques are: impulse echo method (Dos Reis et al., 1999); free-free resonant testing (Ryden, 2009); spectral analysis of surface wave and multichannel analysis of surface wave (Barnes et al., 2009); flexural wave propagation technique and forced longitudinal vibration technique (Hochuli et al., 2001); and ultrasonic body wave propagation techniques (compression (P) and shear (S) wave) (Di Bendetto et al., 2009) (Norambuena-Contreras et al., 2010) (Mounier et al., 2012). Testing temperature ranges from -19 to 42 C. More recently, Buannic et al., (Buannic et al., 2012) measured the shear high frequency modulus of bitumen G* under Annular Shear Rheometer (ASR) by using a shear wave propagation measurement. The efficiency of these laboratories applications to measure complex moduli (E* and G*) at high frequencies has been clearly demonstrated. However it should be

3 High frequency shear modulus of bitumen by ultrasonic measurements 3 noted that the group velocity and elastic wave propagation hypotheses are most frequently used. The viscoelastic approach is used less frequently and requires combination with a rheological model to identify viscous parameters, such as phase angle or viscous attenuation. In this work, an ultrasonic S-wave propagation technique is used to measure the shear complex modulus of bitumen at high frequency. Thus two parameters of wave propagation (group velocity and attenuation) are determined for temperatures of - 18 C. It is worth mentioning that the combination of these parameters allows the calculation of real (instantaneous or elastic response), and imaginary (viscous response) parts of the shear complex modulus by considering wave propagation in viscoelastic material. The results indicated that the value for the shear complex modulus from the ultrasonic method compares well with the reference master curve. In addition, the results compare well with those obtained with the 2S2P1D rheological model that predicts the behaviour of bituminous materials. 2. Theoritical and experimental methods 2.1. S-Wave motion in viscoelastic media Using the general wave equation [1] (Ryden, 2004) with a viscoelastic solution [2] (Zinzer et al., 1967), the parameters of wave propagation (velocity and attenuation) can be expressed. Shear velocity V! [3] and viscous attenuation α!,! [4] are determined according to the shear complex modulus and its real part, taking into account the viscoelastic behavior of the bituminous material. ρ!!!! = λ + μ! +! +! + μ! u!!!! [1]! u! x, t = u! exp!,!!!!! exp!!!! [2] V! =!!!!!! [3] α!,! = ω!!!!!!! [4] By combining previous equations [3,4], the shear complex modulus is expressed [5]. Therefore, the both components of the complex modulus, real and imaginary parts are respectively determined with equations [6,7].

4 4 EATA 2013 G = G! =!!,!!!!!!!!!!,!!!!! [5] [6] G! = (!!! )!,!!!!! [7] 2.2. Ultrasonic test The ultrasonic test device is composed of an arbitrary waveform generation card (sinus, dirac, sweep ) with frequency modulation; shear piezoelectric transducers with resonant frequencies from 10 to 160 khz; a 40 db analog pre-amplifier; a 40 Ms/s acquisition and sampling card; and software for treatment and analysis of the waveforms. For this study, impulse sinus was chosen with a frequency of 100 khz. The sampling rate was 10 Ms/s. Recorded waveforms can be analyzed with respect to time and frequency. When conducting a temporal analysis, group velocity is obtained by measuring the time of travel for a given wave from the emitter to the receiver, and adjustments must be made to account for lag created by the acquisition system. For the measurement of the attenuation parameter, simply taking into account the impulse signal as a reference is not sufficient. This is due to the effects of wave reflection on the interface between emitter and sample. Therefore, this signal does not represent a material response. In this study, velocity and wave attenuation are computed with signals obtained for two different propagation distances. In bitumen, transmission mode is more appropriate than reflection mode, because attenuation is very important and increases with temperature and frequency. Thus, our experimental protocol is realized according transmission configuration, (figure 1) when considering two samples with two different lengths (L1 and L2). Length L2 is regarded as the more disadvantageous for signal acquisition, i.e, when the amplitude of the signal decreases strongly. For length L1, near-field phenomenon of wave propagation must be considered. Here, the lengths L1 and L2 are 40 and 90 mm respectively. An ultrasonic pulse velocity test enables the determination of group velocity, which is the velocity of the wave packet. Many methods of calculation are available such as temporal difference (i) the first exceeding of zero for two different signals (this method is highly dependent on the signal to noise ratio) (ii) between the peaks (positive or negative) of two different signals. In this experiment, group

5 High frequency shear modulus of bitumen by ultrasonic measurements 5 velocity is computed using the difference of time between the positive peaks of two different signals (figure 1). Similar results have been found using negative peaks. Figure 1. Schematic principle of ultrasonic test and velocity determination Wave attenuation can also be measured with an ultrasonic test. Several methods exist for the calculation of this parameter. In temporal analysis: ratio of peaks (positive or negative), ratio of the difference between the positive and negative peaks. In frequency analysis: ratio of FFT magnitude for each frequency and ratio of spectral density. Here, attenuation is computed with respect to temporal analysis, using the ratio of positive peaks. All methods were compared and gave similar result. The experimental attenuation is computed with the following formula [8]. α!" Np m =!"!"#$%"&!"#$%&'()!"!"#$%!!"#$%"&!"#$%&'()!"!"#$%& [8] To plot the ultrasonic value of shear modulus, on the master curve, it s necessary to identify the dominant frequency of the recorded signals. Then, a Fast Fourier Transformation (FFT) is used. The spectral analysis shows that the maximum magnitude decreases with the distance of propagation. However the two signals, L1 and L2 samples, have the same frequency peak (figure 2).

6 6 EATA ,15 Magnitude FFT 0,1 0,05 FFT Signal L1 FFT Signal L2 Effective bandwith 0 0,0E+00 5,0E+04 1,0E+05 1,5E+05 2,0E+05 Frequency (Hz) Figure 2. Spectral analysis using FFT 2.3. Mechanical test The material tested is a 35/50 bitumen. A Dynamic Shear Rheometer (DSR) test is performed by EIFFAGE TP (Lyon, France) for temperatures and frequencies ranging respectively from 70 C to -30 C and 0.01 Hz to 30Hz. Results of the mechanical test allow the isotherms (figure 3) of the shear complex modulus to be plotted. Then, with the shift factor a T the master curve is constructed at the reference temperature of -18 C (figure 3). Moreover, representation of these results the use of the 2S2P1D rheological model (figure 4) and predicts shear complex modulus for ultrasonic frequencies (figure 3). 3. Results and discussion 3.1. Mechanical results Consideration of both frequency and the temperature dependent dynamic moduli of bituminous materials are very important for model pavement design. The master curve is a graphic representation of this viscoelastic behaviour. The master curve of the bitumen, at the reference temperature of -18 C, was plotted (figure 3) using the Time Temperature Superposition Principles (TTSP). This principle is based on the fact that a given modulus value, in the isotherm curve, can be obtained by different pairings of frequency and temperature. TTSP allows the expression of G*(ω,T) as G*(ω,f(T)). The master curve was obtained by a translation using the shift factor called a T, which is computed either by a type of Arrhenius equation, or the WLF formula. After determining the master curve, the 2S2P1D rheological model (Olard et al., 2003) is fitted (figure 4), which allows the prediction of the shear complex modulus at frequencies not reached by the experimental master curve.

7 High frequency shear modulus of bitumen by ultrasonic measurements 7 8,0E+08 6,0E+08 Shear modulusg* (Pa) 4,0E+08 Isotherms Mechanical data 2S2P1D rheological model US modulus 2,0E+08 Mechanical frequencies range Potential US frequencies range 0,0E+00 1,0E-10 1,0E-06 1,0E-02 1,0E+02 1,0E+06 1,0E+10 1,0E+14 Equivalent frequency (Hz) Figure 3. Isotherms, experimental and analytical master curves, ultrasonic shear modulus Figure 4. Principle of 2S2P1D rheological model 3.2. Ultrasonic results The velocity and attenuation of the shear wave at the reference temperature of - 18 C were determined by both experimental measurement and rheological modelling associated to wave motion in a viscoelastic media [6,7]. Figure 5.a illustrates the evolution of the theoretical value of S-wave velocity with respect to equivalent frequency. We can observe that the predicted velocities, (in the ultrasonic range from 20 khz to 600 khz), slightly increase according the frequency. This result shows that bitumen, at -18 C, exhibits again a minor viscoelastic behaviour and don t reach its embrittlement temperature. Thus, ultrasonic measurements should be able to point out this behaviour, especially through the viscous attenuation parameter α!. The ultrasonic experimental value of S-wave velocity, reported in the same figure, is compared to the modelled result at the frequency of 92 khz. This comparison shows that the theoretical approach

8 8 EATA 2013 slightly underestimates the shear wave velocity about 4,8% or 39m/s. The standard deviation of the ultrasonic measurement is estimated at 32 m/s (a) S-wave velocity (m/s) S2P1D shear velocity Experimental velocity Mechanical frequencies range Potential US frequencies range 100 1,0E-03 1,0E+00 1,0E+03 1,0E+06 1,0E+09 Frequency (Hz) 1,0E+06 (b) 1,0E+04 S-wave attenuation (Np/m) 1,0E+02 1,0E+00 1,0E-02 1,0E-04 1,0E-06 2S2P1D attenuation Total attenuation Viscous attenuation Mechanical frequencies range Potential US frequencies range 1,0E-08 1,0E-03 1,0E-01 1,0E+01 1,0E+03 1,0E+05 1,0E+07 1,0E+09 Frequency (Hz) Figure 5. S-wave parameters (a) velocity; (b) attenuation Figure 5.b compares theoretical and experimental values of S-wave attenuation. Attenuation has several causes; it can be due to thermal dissipation (viscous effect), and/or scattering (interaction with the heterogeneities), and/or geometric spreading. The attenuation determined by ultrasonic testing is likely caused by the combination of different phenomena and it can be written as: α!" = α!"#$%&# + α!"#$!"#$%& + α!"#$%&'() [9] For a bitumen specimen, that can be considered as a homogeneous material, scattering attenuation α!"#$$%&'() should not exist. In fact, spectral analysis plotted in

9 High frequency shear modulus of bitumen by ultrasonic measurements 9 figure 3 shows no significant preferential (selective) variation in the attenuation of the effective bandwidth of the signals. Spreading attenuation can be modelled using the equation of the relative overpressure of the ultrasonic wave ( δp δp! ) [10] (Chekroun, 2008). The result is reported in figure 6 and showns two distinct fields of wave propagation (near-field or Fresnel field, and far-field or Fraunhofer field). The near-field is characterized by wave disturbances which do not allow for a clear determination of wave propagation parameters. Moreover between 4 cm and 9 cm, the relative pressure of the ultrasonic wave can be fitted by an exponential law. This law can be assimilated to the Beer- Lambert attenuation law [11]. Thus considering this approach, the geometric attenuation spreading α!"#$%&'() is evaluated at approximately 15 Np/m. Moreover, this modelling allows separating two different fields of wave propagation: the nearfield and the far-field obtained respectively by the Fresnel diffraction equation and the Fraunhofer diffraction equation.!" = 2!!!! A(x) = A!. e!"#$%&'()! [10] [11] In these equation, a is the diameter of the transducer (m), λ is the wavelength (m) and x is the distance from the transducer (m), A is the amplitude of the wave (V). 2,5 Fresnel field 2 Fraunhofer field Relative overpressure Attenuation law Relative overpressure 1,5 1 0,5 y = 1,24e -15,41x R² = 0, ,02 0,04 0,06 0,08 0,1 Distance from the transducer(m) Figure 6. Modelling of geometric spreading From the ultrasonic experiment, and assuming that the material is homogeneous, viscous attenuation can be evaluated by subtracting the previously calculated

10 10 EATA 2013 geometric spreading from the total ultrasonic attenuation. The ultrasonic viscous attenuation reported in figure 5.b agrees with the value predicted by the theoretical approach, and the absolute variation is about 3 Np/m High frequency shear modulus The results reported in the previous paragraphs show that shear wave propagation parameters (group velocity and attenuation) are in agreement with the mechanical results fitted by the 2S2P1D rheological model. A viscoelastic hypothesis of wave propagation was necessary to determine the theoretical velocity and attenuation from the rheological model. Now, we propose to compare the results in terms of shear complex modulus. In figure 3, which represents the master curve, the ultrasonic method seems to overestimate the high frequency (92 khz) shear modulus at about 12%. This overestimation is due to the difference observed in velocity parameters (about 4,8%, 39 m/s). This result highlights the importance of an accurate velocity measurement. Concerning the attenuation parameter, bitumen (at high frequency) is stiffer and attenuation induced by viscosity is quite small. Thus, in equation [5] used for computing the ultrasonic modulus, the term α²/ω² converges to zero. In conclusion, the eventual error in attenuation measurement will have a negligible effect on the determination of ultrasonic shear modulus. Cole-Cole representation enables fitting the rheological models by determining the following parameters h, k, G 0 and G 00. The determination of parameter G 0 needs an extrapolation of mechanical data. The real and imaginary parts of the shear complex modulus obtained by the ultrasonic test are represented in Cole-Cole space (figure 7.a). The result indicates an agreement with the extrapolation of mechanical results from the 2S2P1D rheological model. G 0 identified with the rheological model (620 MPa) is close to the ultrasonic value (634 MPa). The margin of error if 2,40%. The value of G 0 can also be identified in Black space representation as shown in figure 7.b. In this case, the phase angle is close to zero, and the value of shear complex modulus is near to the glassy shear modulus.

11 High frequency shear modulus of bitumen by ultrasonic measurements 11 Imaginary part G2 (Pa) 1,0E+08 5,0E+07 (a) Mechanical data 2S2P1D rheological model US data 0,0E+00 0,0E+00 2,0E+08 4,0E+08 6,0E+08 8,0E+08 Real part G1 (Pa) 100 (b) 80 Phase angle ( ) Mechanical data 2S2P1D rheological model US data 0 1,0E+02 1,0E+04 1,0E+06 1,0E+08 1,0E+10 Shear Modulus G* (Pa) Figure 7. (a) Cole-Cole space (b) Black space 4. Conclusion In this study, we showed that the considered ultrasonic method is an efficient tool for determining the mechanical parameters of bitumen at high frequency. Wave propagation parameters (group velocity and attenuation) of shear wave have been measured at a low temperature (-18 C) and allowing the computation of the shear complex modulus with a viscoelastic hypothesis of wave propagation. With these results, the following conclusions can be assumed: When the objective is to evaluate the shear complex modulus at high frequency, analysis of ultrasonic data shows that wave velocity is the major parameter in the calculation of the modulus. In fact at high frequency, the measured attenuation of shear wave is less than 10 Np/m and its contribution become negligible. This result highlights the importance of accurate velocity measurement.

12 12 EATA 2013 Rheological models are commonly used to understand phenomena in the origin of the viscoelastic behaviour of materials. In this study, the 2S2P1D model was used and compares well with mechanical results. G 0 was determined by the mechanical test and is an important input parameter for the model. However, an extrapolation of data is required which can be source of error in the final assessment. The measurement of viscous attenuation by the ultrasonic method, combined with the velocity parameter, allows a direct evaluation of G 0. The viscoelastic behaviour of asphalt concrete is attributed to the bitumen. The proposed ultrasonic method is an attractive method for the characterization of bitumen which is a homogenous thermo viscoelastic material. In further applications this method on heterogeneous material, special attention must be accorded to the interaction between waves and aggregates. Indeed, aggregates cause wave dispersion. Acknowledgements The authors acknowledge the technical support provided by the EIFFAGE Travaux Public society. Special acknowledgements are due to François Olard and Simon Pouget for providing specimens, and performing the mechanical test. This work will be continued with further applications on innovative asphalt mixes developed by EIFFAGE Travaux Public. 5. Bibliography Barnes C.L., Trottier J.F., Evaluating high-frequency viscoelastic moduli in asphalt concrete, Research in Nondestructive Evaluation, Vol. 20, 2009, p Buannic M., Di Benedetto H., Ruot C., Gallet T., Sauzéat C., Fatigue investigation of mastics and bitumens using annular shear rheometer prototype equipped with wave propagation system, 7 th RILEM International Conference on Cracking in Pavements, 2012 Chekroun M., Caractérisation mécanique des premiers centimètres de béton avec des ondes de surface, Ph. D thesis, 2008 Di Benedetto H., Sauzéat C., Sohm J., Stiffness of bituminous mixtures using ultrasonic wave propagation, Road Materials and Pavement Design, Vol. 10, No. 4, 2009, p Dos Reis H.L.M, Habboub A.L., Carpentier S.H., Nondestructive evaluation of complex moduli in asphalt concrete with an energy approach, Transportation Research Report, 1999 Hochuli A.S., Sayir M.B., Poulikakos L.D., Partl M.N., Measuring the complex modulus of asphalt mixtures by structural wave propagation, 26 th annual meeting of the association of asphalt paving cracking technologists AAPT, March 19-21, 2001

13 High frequency shear modulus of bitumen by ultrasonic measurements 13 McCann D.M., Forde M.C, Review of NDT methods in the assessment of concrete and masonry structures, NDT&E International, Vol. 34, 2001, p Mounier D., Di Benedetto H., Sauzéat C., Determination of bituminous mixtures linear properties using ultrasonic wave propagation, Construction and Building Materials, Vol. 36, 2012, p Norambuena-Contreras J., Castro-Fresno D., Vega-Zamanillo A., Celay M., Lombillo- Vozmediano I., «Dynamic modulus of asphalt mixture by ultrasonic direct test, NDT&E International, Vol. 43, 2010, p Olard F., Di Benedetto H., General 2S2P1D model and relation between the linear viscoleastic behaviours of bituminous binders and mixes, Road Materials and Pavement Design, Vol. 4, 2003, p Ryden N., Determining the asphalt master curve from free-free resonant testing on cylindrical samples, NDTCE 09, Nantes, France, June 30 th Julu 3 rd, 2009 Ryden N., Surface wave testing of pavements, Doctoral Thesis, 2004 Von Quintus H.L., Rao C., Minchin R.E. Jr., Nazarian S., Maser K.R., Prowell B., NCHRP report 626: NDT technology for quality assurance of HMA pavement construction, Transportation research board, 2009 Zinzer B., Bourbié T., Coussy O., Acoustique des milieux poreux, Paris, Technip, 1986