Resonant frequency testing of cylindrical asphalt samples

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1 See discussions, stats, and author profiles for this publication at: Resonant frequency testing of cylindrical asphalt samples Article in European Journal of Environmental and Civil Engineering April 2011 Impact Factor: 0.51 DOI: / CITATIONS 12 READS author: Nils Ryden Lund University 75 PUBLICATIONS 509 CITATIONS SEE PROFILE Available from: Nils Ryden Retrieved on: 08 May 2016

2 Resonant frequency testing of cylindrical asphalt samples Nils Ryden Engineering Geology, Faculty of Engineering, Lund University Box 118, SE Lund Sweden ABSTRACT. There is a need to develop simple and quick non-destructive tests to measure the complex dynamic modulus of asphalt over a wide frequency and temperature range, i.e. mastercurve. In this study results from free-free resonant frequency measurements on cylindrical disk shaped asphalt samples are presented. The resulting mastercurve, obtained by resonant frequency testing at different temperatures, compares well with reference values within the high modulus range. The proposed method is simple and repeatable. RÉSUMÉ. On étudie ici la faisabilité d une méthode non destructive et rapide pour établir les courbes maîtresses du module dynamique complexe des matériaux bitumineux dans une large gamme de fréquences et de températures. La méthode utilise la mesure des premières fréquences propres de résonances en mode libre de tranches minces issues de carottages de matériaux bitumineux. Les courbes maîtresses calculées sont en bon accord avec les courbes de référence pour des modules élevés. La méthode est simple à mettre en œuvre et les résultats sont reproductibles. KEYWORDS: resonance, dynamic modulus, asphalt. MOTS-CLÉS : résonance, module complexe, fréquence propre, matériaux bitumineux. DOI: /EJECE Lavoisier, Paris EJECE 15/2011. Non destructive testing in civil engineering, pages 587 to 600

3 588 EJECE 15/2011. Non destructive testing in civil engineering 1. Introduction Modern pavement design is based on the use of a frequency and temperature dependent dynamic stiffness modulus (E*) of the asphalt material (AASHTO, 2002, Design Guide). Along with the asphalt thickness, E* is the most important asphalt property influencing the structural response of a pavement construction (Garcia and Thompson, 2007). The asphalt mastercurve depicts E* over a wide frequency range at one reference temperature (T ref ) and is needed to account for different temperatures and rate of loading in mechanistic pavement design. The complex dynamic stiffness modulus can be measured through traditional laboratory testing on cylindrical samples using steady state uniaxial or indirect tensile tests at different temperatures (T) and frequencies (f). The traditional procedure for obtaining the asphalt mastercurve, from laboratory prepared or cored samples, is a relatively complicated and expensive test. Resonant frequency (f r ) tests are widely used in many other fields of material characterization and can be used to measure the dynamic modulus of arbitrary sized elastic or viscoelastic samples. This study presents initial tests using f r measurements on cylindrical asphalt samples with arbitrary diameter (D) to length (L) ratios to obtain a low strain E* at different frequencies and temperatures. This paper is an extended version of the original conference proceeding from the international symposium on Non-Destructive Testing in Civil Engineering 2009 (Ryden, 2009). 2. Dynamic modulus mastercurve The complex dynamic modulus E* is defined as: E * * i φ = E ' + ie ' ' = E e [1] where the real part (E') is the storage modulus and the complex part (E'') is the loss modulus. The phase angle (φ) between the real and imaginary part is related to the damping factor (ξ) as: ( E ' ' / 2 E ') ξ = tan( φ ) / 2 = [2] E* can be measured on laboratory specimens using a cyclic uniaxial or indirect tensile test in a narrow frequency range ( Hz). The time temperature superposition principal is then used to extend this frequency range by repeated tests

4 Resonant frequency testing asphalt 589 at different temperatures. This procedure assumes a thermorheological simple material where measurements made within a narrow frequency range at several temperatures are equivalent to measurements made over a wide frequency range at a single temperature. Measurements at different temperatures are shifted along the frequency axis until all points fall on the same smooth continuous mastercurve. After shifting, the frequency is termed reduced frequency (f red ), and it is related to the original measured frequency by the shift factor (a T ): f red = at f [3] where a T can be expressed using the WLF (Williams Landel Ferry) equation: a = C ( T T ) 1 ref log( T ) [4] C2 + T Tref and the dynamic modulus mastercurve is represented by a sigmoidal function: log( E * ) a e 2 ( a a log 3 a = [5] 4 f red ) where the coefficients C 1 and C 2 and a 1 to a 4 are all unknown constants estimated by fitting both Equation [4] and [5] simultaneously to measured dynamic modulus values at different temperatures and frequencies. The conventional dynamic modulus test using uniaxial or indirect tensile tests is a rather complex test. Therefore, the pavement community has strived to develop predictive equations which can be used to estimate the mastercurve from properties of the asphalt mixture (Garcia and Thompson, 2007; Witczak, 2004). The so called Witczak equation (Witczak, 2004) is the most widely predictive equation used. Witczaks equation can be written on the same form as Equation [5] but E* is then given in the psi unit (1 psi = kpa) and a 1 -a 4 are related to the mixture properties as: 2 a 1 = ρ ( ρ 200 ) - ( ρ 4 ) - ( V a ) ( Vbeff V + V beff a ) [6]

5 590 EJECE 15/2011. Non destructive testing in civil engineering a 2 = ρ ρ ( ρ + ρ [7] 2 38 ) a 3 = log( η ) [8] a 4 = [9] where: η is viscosity at the temperature of interest, V a is air voids in percent, V beff is effective bitumen content percent by volume, ρ 200, ρ 4, ρ 38, and ρ 34 is the cumulative percent retained on the mm, 4.76 mm, 9.5 mm, and 19 mm sieve respectively. This version of the Witczak equation is simple to use, with respect to the input parameters, but does not account for polymer modified asphalt binders (Garcia and Thompson, 2007). However, the influence from polymer modified binders is usually most noticeable in the low modulus range which is not used in this study. 3. The free-free resonant frequency method Natural resonant frequencies of a solid are a function of the geometrical dimensions, mass, and elastic properties of the sample. Thus, by measuring the density, D, L, and f r of a cylindrical asphalt sample, E* can be calculated. This technique is widely used in other fields (Migliory and Sarrao, 1997; Ostrovsky et al., 2001) and is usually called the free-free resonant column method or impact resonant method in civil engineering applications. The resonant frequency method is especially practical and simple for geometries like long rods where theoretical resonant frequencies can be predicted based on a one-dimensional wave equation. Existing standards for cylindrical concrete samples are for example limited to one or two resonant frequencies (modes of vibration) and sample geometries with L/D > 2 (ASTM C 215) or L/D < 0.25 (ASTM E ). The concrete standard for long cylinders (L/D > 2) have been successfully tested on asphalt cylinders (Whitmoyer and Kim, 1994; Kweon and Kim, 2006). Kweon and Kim (2006) and La Croix et al. (2009) studied several different asphalt mixtures and concluded that the dynamic modulus from single mode resonance frequency testing compared well to the conventional dynamic modulus test for long cylinders (ASSHTO TP 62). Asphalt samples, taken from field cores or prepared in the laboratory, do usually not meet the desired L/D ratios used in the concrete standards. For asphalt applications it is desirable to measure E* at many different frequencies (modes of vibration in this case) and on any sample size (L/D ratio). This requires a more accurate three-dimensional numerical model to predict any number of modes for any cylindrical geometry. In this study the Rayleigh-Ritz method has been used for this purpose (So and Leissa, 1998; Ostrovsky et al., 2001). However, at this stage

6 Resonant frequency testing asphalt 591 measurements have been limited to the fundamental anti-symmetric flexural mode (f 1 ) and the fundamental symmetric longitudinal mode (f 2 ), for simplicity. If a limited number of modes and a limited range of L/D ratios are used, a straightforward alternative to the computationally more demanding Rayleigh-Ritz method is to use pre-computed look-up tables from the literature. Look-up tables were extensively used in the past when computational power was more limited. Precomputed look-up tables for the geometries and modes of vibration used in this study has for example been presented by Martincek (1965). The measurement set-up on a typical asphalt sample is shown in Figure 1 along with the impact locations relative to the accelerometer. The sample is placed on a soft support (soft foam) to mimic free boundary conditions. Figure 2 shows the mode shapes of the two different resonance frequencies used in this study. a) b) Figure 1. a) experimental test set-up for resonant frequency measurements on asphalt samples; b) position relative to the accelerometer for exciting the two modes f 1 and f 2 f 1 f 2 Figure 2. Mode shapes for the fundamental anti-symmetric flexural mode (f 1 ) and the fundamental symmetric longitudinal mode (f 2 )

7 592 EJECE 15/2011. Non destructive testing in civil engineering Using this measurement set-up f 1 and f 2 can be easily identified as the peaks with the lowest frequencies in the amplitude spectrum from the two impact locations. These measured frequency peaks correspond to a damped resonant frequency (f d ). The damping factor at each resonant frequency is evaluated by using Equation [10] below (the half-power bandwidth method): ξ = f / 2 f d [10] where f is the bandwidth over the resonant peak at of the maximum peak amplitude. f d is always slightly lower than f n and related as: 2 f d = f n 1 ξ [11] By using these equations f n and ξ are automatically calculated from the amplitude spectrum of each mode of vibration. The corresponding real part of the dynamic modulus (E') is then calculated from each mode of vibration (f n ) using the Rayleigh-Ritz method. The complex part of the dynamic modulus (E'') is finally calculated from E' and ξ (Equation [2]). Poisson s ratio (ν) is not directly measured in this process but needs to be assumed or estimated when E' is calculated from the resonant frequency. In elastic materials without any significant frequency dependent modulus, ν can be calculated from the ratio between different resonant frequencies (Martincek, 1965; Subramaniam et al., 2000). However, in viscoelastic materials where E* is a function of frequency, this approach is only applicable at very low temperatures where the frequency dependency can be neglected. At higher temperatures both E* and ν are frequency dependent (Lee and Kim, 2009; Nguyen et al., 2009). In this study a slightly modified version of the equation from (AASHTO, 2002, Design Guide) has been used to estimate ν as a function of E* : * ( ( 2.291*log( abs ( E )))) ( 0.35 /( 1 + e ) ν = [12] This equation is used iteratively along with the Rayleigh-Ritz method to calculate E* from each measured resonant frequency. Three iterations were usually enough to use a value of ν in the Rayleigh-Ritz calculation which also satisfies Equation [12] above. The first constant in the exponential term (-14.0) has been slightly increased compared to the value (-12.0) recommended in (AASHTO, 2002 Design Guide). This modification results in a slightly higher ν which was necessary to always obtain an increasing dynamic modulus with increasing frequency. Figure 3 shows the empirical relationship between E* and ν calculated from Equation [12] and used in this study. This relationship is in general agreement with values from

8 Resonant frequency testing asphalt 593 other studies (Aouad, 1993; Kim et al., 2004; In et al., 2009; Nguyen et al., 2009) but should be further investigated in future studies and possibly expanded to a complex value (Nguyen et al., 2009). In this study Equation [12] is considered to be a better approximation compared to using a fixed ν value over the complete range of modulus values. Figure 3. Empirical relationship between E* and ν used to estimate ν at each measured resonant frequency (Equation [12]) The complete measurement procedure can be summarized in four steps. (1) Measure f d and ξ for one resonance mode along with the geometry and mass of the sample. (2) calculate f n using Equation [11]. (3) calculate E' from f n, ν, geometry, and mass using the Rayleigh-Ritz method or a suitable look-up table. (4) calculate E'' and E* using Equation [2]. The last two steps may have to be repeated iteratively to satisfy the assumed relationship between E* and ν (Equation [12]). The procedure described above can be repeated for different modes of vibration (frequencies) and different temperatures to obtain as many data points, E*(f,T), as possible for the final construction of the mastercurve. In this study measurements were performed with a computer based data acquisition system (Measurement Computing model PC-CARD DAS 16/16-AO) and a small high frequency accelerometer (PCB model 352B10). A small steel bolt attached to plastic strip was used as a manual impact source, Figure signals (10 ms) were recorded at each impact point using a sample rate of 200 ks/s. These measurements can be performed in less than 1 minute for each sample and temperature using an automatic trigger and save function.

9 594 EJECE 15/2011. Non destructive testing in civil engineering 4. Results Three different laboratory prepared samples (1A, 1B, and 1C) from the same asphalt mixture have been tested with the proposed resonance frequency method. Table 1 shows the properties of each sample. Each sample was compacted using laboratory marshal compaction, and then cut parallel to the final length as given in Table 1. It should be noted that the accuracy of the measured geometry is equally important as the measured resonance frequency and it should therefore be measured as precisely as possible. Table 1. Tested asphalt samples Sample 1A 1B 1C Bulk density (kg/m 3 ) Diameter, D (m) Length, L (m) Air voids content, V a (%) Effective binder content, V beff (%) Repeatability test A repeatability test was first conducted to estimate the repeatability of the measured resonant frequencies. Figure 4 shows an example from 50 individual measurements on sample 1C at 20 C. Figure 4a shows the automatically extracted peak frequencies from all impacts at the edge of the sample, i.e. mode f 1. Measured resonant frequencies are very repeatable with a variance of 0.1%. It is also interesting to see that there is actually a trend in the data showing a decreasing resonant frequency as a function of impact number. This could possibly be explained from an increasing temperature within the sample and/or hysteresis effects in the material. Figure 4b shows the corresponding E* values as a function of impact number. The mean value, standard deviation, and variance are MPa, MPa, 0.18% respectively. Using the mastercurve evaluated in the next section, a -140 MPa drop in E* corresponds to a temperature rise of +0.3 C. All measurements were carried out in room temperature at C which was slightly higher than the temperature of the sample (20 C), further motivating a possible small increase in temperature during this repeatability test (~ 3 minutes). Regardless of the true origin of the observed trend in Figure 4 it should be pointed out that the repeatability is high, making this test suitable for observations of very small changes of E* in asphalt samples. These results also show the importance of keeping the temperature in the sample as constant as possible during testing.

10 Resonant frequency testing asphalt 595 (a) (b) Figure 4. (a) measured damped resonant frequency f 1 as a function of impact number from a repeatability test on sample 1C. (b) corresponding E* calculated from each measured resonant frequency and damping factor 4.2. Mastercurve test Resonance frequency measurements were performed at 11 different temperatures ranging from -10 C to 55 C. Figure 5 shows the measured damped resonant frequencies and damping factor at each sample and temperature. As expected f d decreases and ξ increases with temperature. (a) (b) Figure 5. Measured (a) damped resonant frequencies and (b) damping factor at the different testing temperatures and samples Figure 6a shows the corresponding calculated E* from both resonant frequencies f 1 and f 2 (resulting in E1* and E2* ) at the different testing temperatures. E* increases with increasing frequency at all temperatures except at

11 596 EJECE 15/2011. Non destructive testing in civil engineering 55 C indicating that this temperature may be too high for these measurements. In Figure 6b a mastercurve have been fitted to the measured data points by finding the best match of the 6 unknown constants in Equation [3]-[5]. A reference temperature of 25 C has been chosen and the measured frequencies at all other temperatures have been shifted horizontally to obtain the best possible match to Equation [3]-[5]. It should be noted that the lowest measured dynamic modulus (8 185 MPa) is relatively high compared to the lowest modulus values usually used for the construction of the mastercurve (~500 MPa). This is due to the inherent limitation of the method that f d is in the khz range even at the highest temperature. Modulus values outside the measured range (8-33 GPa) should be treated with caution. a) b) Figure 6. a) dynamic modulus from both resonant frequencies f 1 and f 2 (f 1 < f 2 ) at the different testing temperatures on sample 1A; b) resulting mastercurve obtained by fitting the measured values from Figure 5a to Equation [3]-[5] Mastercurves from all three samples have been constructed following the same procedure as for sample 1A above. Figure 7 shows all three measured mastercurves compared to predicted mastercurves from Witczaks predictive equation (Witczak, 2004). The following input parameters for Equation [6]-[9] were obtained from a mixture analysis on all three samples: η = Poise a 25ºC, ρ 3 = 0.0%, ρ 38 = 10.0%, ρ 4 = 31.5%, ρ 200 = 6.5%. Individual measures of V a and V beff are presented in Table 1. The measured and predictive mastercurves agree reasonably well within the measured range (8-33 GPa) but deviate more and more at lower modulus values (Figure 7). Estimated mastercurves from resonance frequency measurements are also compared to results from conventional Indirect Tensile Tests (IDT) using the CEN (Annex C) standard test method. Figure 8 shows the measured stiffness modulus from IDT at different test temperatures compared to estimated mastercurves from resonance testing plotted at a fixed frequency of 2 Hz (using Equation [3]-[5] and the fitted constants). Again results compares reasonably well within the 8-33 GPa

12 Resonant frequency testing asphalt 597 modulus range measured from resonance frequency testing, but deviate considerably at lower modulus values. However, it should be noted that the loading frequency cannot be controlled in this type of IDT test since the sample is loaded by repeated pulses containing a wide range of frequencies which also change with temperature. The rise time of the load pulse (124 ms) is fixed but the length of the unloading part, which is used to calculate the stiffness modulus, increases with increasing temperature. It is therefore difficult to estimate a fixed representative frequency although 2 Hz is sometimes used for this comparison (Pasetto and Baldo, 2007). Measured mastercurves from the proposed resonance frequency method should ultimately and in future studies be compared with measured mastercurves from true frequency sweep measurements (Kim et al., 2004). Figure 7. Estimated mastercurves from resonant frequency measurements (solid lines) and Witczaks predictive equation (dash dotted lines) Figure 8. Estimated mastercurves from resonant frequency measurements at a fixed frequency (2 Hz) and variable temperature (solid lines) compared to stiffness modulus from the conventional Indirect Tensile Test (CEN ) at different temperatures

13 598 EJECE 15/2011. Non destructive testing in civil engineering 5. Conclusions In this feasibility study results from free-free resonant frequency measurements on cylindrical disk shaped asphalt samples with arbitrary size are presented. Two modes of vibration are measured at each testing temperature and used to calculate E* at each damped natural frequency. Results from different temperatures and frequencies are then used to construct a high frequency asphalt mastercurve within the measured modulus range (here 8-33 GPa). Within this high frequency range, measured mastercurves compare reasonably well with predicted values from Witczaks equation and measured stiffness values using the Indirect Tensile Test (CEN ). The observed deviation at lower modulus values may possibly be explained from the very low strain level used in resonance testing compared to conventional methods. The low frequency part of the asphalt mastercurve cannot be measured using resonant frequency testing because of the inherent limitation to use the natural resonant frequencies of the specimen. Measured frequencies can be somewhat reduced by using larger samples but will still be higher compared to the frequency range used in the conventional uniaxial frequency sweep test. The proposed method is however simple and repeatable and may therefore provide an alternative for the high frequency part of the asphalt mastercurve which is important for low temperature cracking. Future research is needed to study the influence of the very low strain level, Poisson s ratio, and the optimal test protocol regarding stabilization time and test temperatures. Acknowledgements Laboratory work by Cathrine Johansson at Peab is gratefully acknowledged. The financial support from the Swedish construction industry's organisation for research and development (SBUF) and the Swedish road administration (Vägverket) is greatly appreciated. 6. References AASHTO TP 62-07, Standard Method of Test for Determining Dynamic Modulus of Hot- Mix Asphalt (HMA), American Association of State Highway and Transportation Officials (AASHTO). ASTM C 215, Standard test method for fundamental transverse longitudinal and torsional resonant frequencies of concrete specimens, American Society for Testing and Materials (ASTM). ASTM E , Standard test method for dynamic Young s modulus, shear modulus, and Poisson s ratio by impulse excitation of vibration, American Society for Testing and Materials (ASTM).

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