Verification of modulus and fatigue cracking models for hot-mix asphalt with asbuton in laboratory scale

. Design and analysis of flexible pavement structure using mechanistic approaches require, among other input data, the dynamic modulus of asphalt layer (E*) and it’s resistance to fatigue cracking (N f ). These material characteristics can be obtained from both laboratory test results and calibrated against field conditions and from mathematical models, such as the Asphalt Institute’s. The two values are to be compared for assessing the applicability of the models for mixes using petroleum bitumen (pen 60/70) and using modified asphalt (with 8% asbuton). The laboratory tests were conducted using Asphalt Mixture Performance Test (AMPT) and Four Point Loading equipment. It was found that the resulting curves are consistent with the Asphalt Institute’s model for both types of mixes. Meanwhile, fatigue life model curves show a similar trend to the Asphalt Institute’s model on the conservative side. This is explainable the laboratory model needs to be calibrated for variations of wheel track and loading time occuring on site.


Introduction
Design and analysis of flexible pavement structure using mechanistic approaches require the dynamic modulus of asphalt layer (E*) and it's resistance to fatigue crack (fatigue life) values.
The dynamic modulus is a stress-strain relationship for a linear viscoelastic material that accepts a sinusoidal load of a certain frequency (N. Suaryana, 2014).
Fatigue cracking is a phenomenon of cracking due to recurrent loads that occur due to repetition of strain still under the strength of the material (E.J Yoder and M.W Witczak, 1975).
The values mentioned above, in addition can be obtained from the test results in the laboratory, can also be obtained from mathematical model. Models of asphalt mixed modulus have been widely developed, among others modulus models by Witczak (2006), Asphalt Institute (1982), Bonnaure et.al (1977) and Nottingham (Brown, et al., 1984). In this research, the dynamic modulus model used is the Asphalt Institute (AI) model.
The fatigue life (Nf) models is derived based on different laboratory testing methods: a.

Dynamic modulus
The dynamic asphalt mixed modulus testing uses AMPT and making of the sample using a gyratory compactor. Dynamic modulus testing was performed with sinusoidal loading at 20°C, 35°C, 50°C, for each temperature tested at a frequency of 0.01 Hz; 0.1 Hz; 1 Hz; 10 Hz.
The summary of HMA with 8% asbuton, dynamic modulus test results is presented in Table 1, whereas the results for HMA without asbuton show the same behavior. Then for mathematical calculations the modulus model can be seen in Table 2.
To compare the results of the dynamic modulus testing of the AMPT test with the modulus of the Four Point Loading test and the modulus model according to the Asphalt Institute, the first step is to mathematically calculate the model based on equations 1 to 7.
Furthermore, to obtain the relationship between the Four Point Loading modulus test results with the AMPT test results need to adjust the loading frequency, because the Four Point Loading test is done at the frequency of 8.06 Hz, while the AMPT test at the frequency of 0.01; 0.1; 1; 10 Hz. The step taken is to perform a linear interpolation between the AMPT test results and the Four Point Loading test results.
All modulus values are then plotted into the graph of the temperature relation ( o C) with the modulus shown in Figure 2 and 3. To see the consistency between these values, a statistical test is performed, complete verification steps are presented in Figure 1. As for the other mixtures showing the same behavior.
In Figure 2 dan 3, shows of HMA without and with 8% asbuton, at temperature and all frequencies (0.01 Hz; 0.1 Hz; 1 Hz; 10 Hz) for the three variations of asphalt content (5%; 6%; 7%), the value of the test modulus is mostly above the model.
When observed on the graphs of the dynamic modulus, at a frequency of 0.01; 0.1;10 Hz, AI model line and the AMPT test line look consistent, where in the 0.01 Hz and 0.1 Hz frequencies the lines are both concave, as does the AMPT test line. Then for the 10 Hz frequency the AI convex model line, same as the AMPT test line. But somewhat distorted occurs in the frequency of 1 Hz (black line), where the model line tends to convex, while for the AMPT test line tends to be concave. This needs further research to find the cause of the phenomenon.
The dynamic modulus relationship of the AMPT test results and the AI model shown in Figure 4, most of the modulus values of the test results are greater than the model. This, if seen from its influence on flexible pavement design, that the model is safer to use in planning, because it produces a lower modulus, which in fact in the asphalt layers is built has a greater modulus value, indicated by the results of AMPT testing.  Figure  5.
The amount of stress is maintained by maintaining the load, the strain that occurs will be greater as the cycle increases. In this test the fatigue life is achieved when the flexural stiffness has been reduced by 50% of the initial value because at this point it is considered to be a shift of the crack, from microcrack to crack propagation / macrocrack (Rowe and Bouldin, 2000).
Summary of fatigue crack test results of HMA with 8% asbuton is presented in Table 3 and for the other mixtures showing the same behavior.
The result of fatigue crack test for asphalt mixture without and with 8% asbuton were then plotted into fatigue life correlation graph with flexural stiffness, shown in Figure 6 and 7 below this. As for the other asphalt mixture shows the same behavior. note: * discontinued, because if testing continues it will take a very long time, for it must be extrapolated  In this study, there were 3 (three) tests of unfinished fatigue life, all three for asphalt mixture 8% asbuton with 6% asphalt content. The tests were carried out at a stress of 2065 kPa, 2450 kPa and 2650 kPa with fatigue life when discontinued respectively were 312,600 cycles, 175,110 cycles and 124,920 cycles which can be seen in Table 3.
The predicted fatigue life can be performed by extrapolating the graph of the decrease in the flexural rigidity modulus to fatigue life to 50% of the initial flexural stiffness modulus (NCHRP, 2010 The relationship between test results using Four Point Loading and model, can be seen in Figure 8. Generally, from the results of the fatigue crack testing using Four Point Loading, it has been shown that asphalt mixture with 8% asbuton has a fatigue life (Nf) greater than asphalt mixture without asbuton. This illustrates that the asphalt mixture with 8% asbuton is more resistant to fatigue than the asphalt mixture without asbuton.
Verification based on the results of statistical analysis of the fatigue life using the four points loading test results with AI Model is good enough in predict fatigue life, with 95% confidence level and significance (error) 5%.
The relationship between the test results and the fatigue crack model is shown in Figures 9. From the analysis showed that the mixture was asphalt without and with 8% asbuton, most of fatigue life (Nf) from Four Point Loading test were lower than model. The laboratory model need to be calibrated for variations wheel track and loading time occuring on site. From the analysis showed that the mixture was asphalt without and with 8% asbuton, most of fatigue life (Nf) using Four Point Loading were lower than model. The laboratory model need to be calibrated for variations wheel tracks and loading time occuring on site. The calibration factor of this model is still to be subject for futher research.