CHAPTER 6 TESTING SETUP
6.2 Testing Parameters – Phase II
6.2.4 Predicting Dynamic Modulus
Numerous models have been developed to predict dynamic modulus values of HMA by using measurable variables like aggregate and asphalt characteristics, as well as the loading regimen. An extensive study was undertaken by Akhter and Witczak (1985) in an effort to identify variables that were relevant to a dynamic modulus predictive equation. These variables apply to the mix design process because they have a direct influence on the stiffness of the pavement layer. Over 130 mix designs were evaluated under this study with
data contributions being made by The Asphalt Institute. From an analysis of the mix designs, it was determined that the mixture temperature was the most significant variable in a
dynamic modulus predictive equation. This was in addition to the already identified
variables that were controllable in terms of material properties, which include the amount and type of asphalt (asphalt content and viscosity) and the gradation of the aggregate (percent retained on the 3/4in, 3/8in, and #4 sieves and percent passing the #200), and air voids in the mix. The frequency of loading also played a significant role in a dynamic modulus
predictive equation. Equation 6.5 shows the latest dynamic modulus equation developed by Witczak et al. (2002). 2 200 200 4 2 4 3/8 3/8 3/ 4 ( 0.603313 0.313351 log( ) 0.393532 log * 1.249937 0.029232( ) 0.001767( ) 0.002841( ) 0.058097( ) 0.802208( ) 3.871977 0.0021( ) 0.003958( ) 0.000017( ) 0.005470( ) 1 a beff f beff a E V V V V e ρ ρ ρ ρ ρ ρ ρ − − × − = − + − − − − + − + − + + + ×log( ))η (equation 6.5) where:
E* = dynamic modulus (105psi),
η = bitumen viscosity (106psi),
f = loading frequency (Hz), Va = air void content (%),
Vbeff = effective bitumen content (% by volume),
ρ3/4 = cumulative percent retained on 19mm sieve,
ρ3/8 = cumulative percent retained on 9.5mm sieve,
ρ4 = cumulative percent retained on 4.75mm sieve, and
ρ200 = percent passing 0.075mm sieve.
The gradation inputs and effective binder content are determined from the job mix formula (JMF) supplied by the contractor. The loading frequencies have been predetermined and were previously stated in Table 4.2. The air void content has been determined from the bulk specific gravity testing. Bitumen viscosity was the only property that needed to be measured.
The bitumen viscosity was determined by three different methods. The first method was the viscosity of the original binder, rolling thin film oven (RTFO) aged binder viscosity, and finally a calculated binder viscosity (Mirza and Witzcak 1995) to simulate mix/laydown conditions. The RTFO aging simulates the aging of the asphalt binder during production and construction of an HMA pavement. The forthcoming AASHTO Mechanistic Empirical Pavement Design Guide (M-E PDG) specifies the test temperatures at which the bitumen viscosities are to be performed at as shown in Table 6.3 (NCHRP 1-37A, 2004).
Table 6.3 Conventional Binder Tests and Corresponding Test Temperatures
Test Temperature, °C Penetration 15 Penetration 25 Rotational Viscosity 80 Rotational Viscosity 100 Rotational Viscosity 121 Rotational Viscosity 135 Rotational Viscosity 176
Considering the temperature specification of 176°C it was realized that this test temperature was unreasonably high and aging of the binder may occur at this high test temperature even at the asphalt plant, so 165°C was selected because this is the high end temperature when conducting AASHTO TP48 in order to determine the mixing and compaction temperatures. In some cases with the RTFO aged binder a bitumen viscosity reading at 80°C could not be obtained due to the stiffness and lack of fluidity of the binder.
Penetration testing was conducted in accordance with ASTM D5. Penetration testing measures the consistency of asphalt binder by applying a weighted needle to the sample over a given period of time. The penetration results were then converted to an equivalent
viscosity (cP) in order to determine the temperature susceptibility of the binder; the conversion equation follows (NCHRP 1-37A, 2004).
log η = 10.5012 - 2.2601 log(Pen) + 0.00389 log(Pen)2 (equation 6.6) where:
η = viscosity, Poise, and Pen = penetration, mm/10.
Rotational viscosity testing was conducted in accordance with AASHTO TP48. Viscosity is a fundamental measurement unit of an asphalt binder and it measures the
workability of a binder. A vessel was filled with a 10.5gram sample and a standard spindle is submerged in the binder. The viscometer was typically set to 20rpm and three measurements are made at the above outlined temperatures. Every asphalt binder for this research has been tested in the outlined manner.
The Mirza and Witczak (1995) equation was developed to convert the original binder viscosities to mix/laydown conditions (similar to RTFO aged material).
log log ηt=0 = a0 + a1 log log(ηorig ) (equation 6.7)
a0 = (0.054405 + 0.004082 code)
a1 = (0.972035 + 0.010886 code)
where:
ηt=0 = mix/laydown viscosity (cp) at temperature TR (Rankine),
ηorig = original viscosity (cp) at temperature TR (Rankine), and
Code = hardening resistance (code = 0 for average).
The value of zero was used for the code value. Research by Birgisson et al. (2005) found that rotational viscosity testing on RTFO aged material and the derived mix/laydown equation above yielded similar results.
The temperature susceptibility of each asphalt binder was determined by statistically regressing the logarithm of the logarithm of the mix/laydown bitumen viscosity against the logarithm of the test temperature in Rankine. The regression equation is as follows.
log log ηt=0 = A + VTS log TR (equation 6.8)
where:
A = regression intercept,
VTS = regression slope of the viscosity temperature susceptibility, and TR = temperature, Rankine.
Each binder has a unique intercept and slope. An equivalent bitumen viscosity was determined using the effective test temperatures at each location. This bitumen viscosity was then used in the dynamic modulus predictive equation. Results for the penetration and viscosity testing can be found in Appendix C: Bitumen Temperature Susceptibility.
Witczak et al. (2002) found that dynamic modulus testing has a strong relationship with field performance data from WesTrack (a full-scale test track), the FHWA’s
Accelerated Loading Facility (ALF), and MnRoad (an experimental test road) for permanent deformation. 100mm diameter by 150mm high cylindrical specimens were procured from materials from the individual test sites and tested under confined and unconfined loads. Various frequencies and temperatures were tested and the strains induced by a dynamic load were recorded. Different models for measuring dynamic modulus values were employed and statistically analyzed for goodness-of-fit. The strongest relationship to field rutting
performance was shown to be E*/sinφ, where the specimen is tested unconfined and modeled linearly. Tests that were conducted with a confining stress exhibited a poor relationship when compared to field measured rutting. In addition to testing dynamic modulus to
correlate to rut performance, dynamic modulus was run at low and intermediate temperatures by Witczak et al, (2002) to determine its relationship with that of thermal and fatigue
cracking from materials procured from the ALF, MnROAD, and WesTrack test sites. Recently, Christensen et al, (2003) developed an effective approach to estimating the HMA modulus using the Hirsch model, a variation of the Burger model. The Hirsch model
is based upon the law of mixtures which combines series and parallel elements of phases. The HMA complex modulus can be estimated by knowing the volumetric properties of the HMA along with the binder complex modulus. The binder complex modulus was obtained from conducting frequency sweep tests using a dynamic shear rheometer at the same frequencies as the dynamic modulus test for the mixtures. A 25mm parallel plate is used at high temperatures while an 8mm parallel plate is used for intermediate temperatures. The Hirsch model for the complex extensional modulus for an HMA mixture are as follows:
(
)
1 * 4, 200,000 1 3 * 100 10,000 1 100 1 4, 200,000 3 * mix binder binderVMA VFA VMA
E Pc G VMA VMA Pc VFA G − ⎡ ⎛ ⎞ ⎛ × ⎞⎤ = ⎢ ⎜ − ⎟+ ⎜ ⎟⎥ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎡ − ⎤ ⎢ ⎥ + − ⎢ + ⎥ ⎢ ⎥ ⎣ ⎦ (equation 6.9) where
E* = dynamic modulus (105psi), 0.58 0.58 3 * 20 3 * 650 binder binder VFA G VMA Pc VFA G VMA ⎛ × ⎞ + ⎜ ⎟ ⎝ ⎠ = ⎛ × ⎞ + ⎜ ⎟ ⎝ ⎠ (equation6.10)
where Pc is a contact factor,
VMA = voids in mineral aggregate (%), G* = dynamic shear modulus (105 psi), and VFA = voids filled with asphalt (%).
Christensen et al. (2003) found that there was very good agreement between the measured and predicted complex modulus values when using the Hirsch model. Also, there is good agreement between the Hirsch and Witczak models.