Determining temperature and time dependent Poisson’s ratio of asphalt concrete using indirect tension test
Introduction
Poisson’s ratio (ν) is a fundamental material property and an essential input parameter to many finite element and constitutive models of Asphalt Concrete (AC). The ν-value of AC is usually considered not to be dependent on temperature, loading time and frequency of loading due to lack of sufficient test evidence [1], [2]. This assumption may not be reasonable for AC; because AC is well known for its temperature, time and frequency dependency. The elastic ν-value can be applied to a material when temperature, time or frequency dependency of its mechanical properties can be neglected. This may be the case for certain materials. However for AC, the inherent loading time or frequency dependency cannot be disregarded in many applications. Upon applying load, the deformational energy in AC is not only stored elastically, but part of it is invariably dissipated by viscous action. Therefore, the ν-value of AC must be determined considering temperature, time and frequency of loading.
Accurate measurement of the ν-value is essential for pavement design. Because, change in ν-value can result in different predictions of structural responses and distresses. To prove this, a preliminary analysis has been performed in the present study using the AASHTOWare Pavement Mechanistic-Empirical (ME) Design software (previously known as Mechanistic-Empirical Pavement Design Guide (MEPDG)). The geometry, material properties and all other design inputs were kept the same except the ν-value in different simulation runs by the AASHTOWare Pavement ME design software. The input parameters are considered based on typical highway pavement in New Mexico. The parameters are listed as follows: AC thickness = 200 mm, base aggregate (crushed stone) = 200 mm, subgrade = AASHTO A-4 soil [3], initial two-way annual average daily traffic = 1500, number of lanes in design direction = 2, percentage of trucks in design direction = 50, percentage of trucks in design lane = 95, operational speed = 60 mph (97 kmph), climate: New Mexico (Albuquerque International Airport), ν-value = varied from 0.1 to 0.45 including the AASHTOWare Pavement ME Design default value [4].
The analysis was run for 20 years of design life and the two major distresses, rutting and top–down cracking (longitudinal cracking) are recorded and shown in Fig. 1. These two distresses were considered arbitrary. The other distresses such as alligator cracking may be affected. However, discussing the effect of ν-value on all distresses may be too much discussion for showing the importance of ν-value. It can be seen from Fig. 1 that both the rutting and top–down cracking increase with a decrease in ν-value, which is much expected. Vertical stress increases with the decrease in ν-value. Consequently, rutting and top–down cracking increase with a decrease in ν-value. The total rutting is 27 mm for ν-value = 0.1 and 14 mm for ν-value = 0.45. Similarly, the top-down cracking is 354 m per km for ν-value = 0.1 and 36 m per km for ν-value = 0.45. There is almost 10-fold difference in top down cracking due change in ν-value from 0.1 to 0.45. At any rate, on the point being made by this example calculation is that the ν-value is very important for accurate prediction of the distresses in asphalt pavement.
Past studies intensively explored ν-value using relaxation tests in uniaxial mode [5], [6]. In addition, frequency and temperature dependency of ν-value has been investigated by applying cyclic load on uniaxial sample [7], [8], [9], [10]. However, not a significant amount works were conducted on ν-value using Indirect Tensile (IDT) mode. Note that IDT test is very popular in asphalt society for its simplicity in AC’s performance evaluation. Therefore, research on ν-value using IDT samples may be praiseworthy for permanent literature.
Lee and Kim [11] determined the complex ν-value with respect to angular frequency and time by a creep test up to 100 s using IDT mode. The researchers used only a single temperature (10 °C). However, temperature varies a lot in real pavement. ν-value at other temperature is also an interesting research topic. Therefore, temperature dependency of ν-value using IDT test is still an unsolved issue. Frequency and temperature dependency of ν-value using IDT test has been conducted by Kim et al. [12]. The researchers evaluated the dynamic ν-values at different temperatures and frequencies of loading using IDT test. The ν-value is reported to be about 0.15 and 0.25 at −10 °C and 10 °C, respectively. This means the effect of temperature on dynamic ν-value is quite large. However, the effect of loading frequency was not very clear from their study. In addition, ν-value was observed by them so high, around 0.8 at 35 °C. Therefore, further investigations are needed to examine the effects of temperature and loading frequency on ν-value using IDT test.
From the above discussion, it is evident that ν-value of AC has been determined for single temperature, so far, by relaxation test using IDT samples. The effects of various temperatures on ν-values have not been studied. In addition, the effects of loading frequency and temperature on the dynamic ν-values using IDT test are still unsolved issues. Moreover, the correlation between ν-value and |E∗| can be beneficial for designing pavement using the Pavement ME Design software. All these effects and correlation are studied herein.
Section snippets
Objectives
The specific objectives of this study are to:
- (a)
Determine the temperature- and time-dependent ν-values of AC material by relaxation tests using IDT samples.
- (b)
Determining ν-values at different temperatures and frequencies of loading by cyclic loading tests on IDT samples.
- (c)
Examine the correlation between the measured ν-value with the |E∗| of AC.
Backgrounds
The horizontal stress along the horizontal direction, σx and the vertical compressive stress along the vertical direction, σy in IDT sample, as shown in Fig. 2, can be written as follows [13]:where
P = amplitude of the
Sample collection and preparation
A number of cylindrical samples of 150 mm diameter were collected from a pavement section of Interstate 40 (I-40) at the mile post 141 near the city of Albuquerque, New Mexico in collaboration with the New Mexico Department of Transportation (NMDOT). The surface layer of the section is 263 mm paved in three lifts of 87–90 mm thickness. The samples were cored from the second lift while construction. The reason for using field sample is that field compacted sample is more realistic compared to
Results and discussion
The ν-values from the relaxation tests are presented in Fig. 5. It shows that the ν-values at −15 °C, 0 °C, 20 °C, 37 °C and 54 °C start around 0.10, 0.12, 0.17, 0.30 and 0.38 respectively. On an average the starting increases by 0.004 for 1 °C increase in temperature. All of these values increase with temperature and time of loading. This behavior is due to the viscoelastic behavior of asphalt concrete. The fluidity (decrease in viscosity) of the material increases at higher temperature, which
Measured versus predicted Poisson’s ratio
In the AASHTOWare Pavement ME Design software, ν-value is predicted from the |E∗| (in psi) of AC by Eq. (10) [4]:where the coefficients, a and b are −1.63 and 3.84 × 10−6 respectively. An attempt is made to correlate the measured |E∗| in psi with ν-value. |E∗| is calculated using Eq. (8) using the vertical and horizontal displacements while applying the cyclic loading. Fig. 7 presents the measured ν-value, best fit curve of the measured ν-value and the AASHTOWare Pavement ME
Conclusions
The study investigates the effects of loading time and temperature on the ν-value of AC by the relaxation tests in IDT mode. In addition, the ν-values with frequency of loading and temperature are also examined by applying dynamic cyclic load on IDT samples. Finally, the measured ν-values are correlated with the prediction of the AASHTOWare Pavement ME Design Guide. In the reminder of this study, only field collected cored sample prepared using a single mixture has been used. Based on the
Acknowledgements
This study was funded by the New Mexico Department of Transportation (NMDOT). The authors would like to express their sincere gratitude and appreciation to Mr. Jeff Mann, Pavement Design and Management Bureau Chief at NMDOT, for being the advocate of this project and his regular support, sponsorship, and suggestions. The authors appreciate the valuable service and time of Mr. Virgil Valdez, who is the Project Manager. Special thanks go to several Project Panel members namely, James Gallegos,
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