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OCR for page 36
36
8
6
Daily Average Temperature (Degree C)
Temperature Flutuation Pattern Around
4
2
0
-2
-4 Texas (48-1000)
Texas (48-0800)
Texas (48-A800)
-6
South Dakota (46-0800)
Utah (49-0800)
-8 Nevada (32-0100)
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Hours
Figure 32. Predicted daily air temperatures at six different LTPP
test sites.
models is described. The tensile strength was determined by 0.68 and 0.98 for the 1999 Witczak model and the ANN algo-
Schapery (36, 37) to be an important variable in making real- rithm, respectively, when using the source input data
istic estimates of the Paris and Erdogan's Law fracture coeffi- The binder input data for the 2006 Witczak model is the
cient, A. Earlier studies reported tensile strengths obtained of magnitude of the shear modulus, G*, of the binder and its phase
field cores taken from pavement sections well distributed angle, c, in degrees, as shown in Table 21. Also shown in that
around the United States and Canada (4, 38) and were con- table are the other required input variables for the model, which
sidered to be representative of HMA mixtures. The calibra- include the same gradation and volumetric composition as in
tion coefficients from these studies (4) could be used to the 1999 model. The output is the magnitude of the Complex
predict both thermal and traffic related reflection cracking Modulus. A comparison of the behavior of the 2006 Witczak
and healing between traffic loads. model (3) and the corresponding ANN algorithm is shown in
Figure 34. The R2 values are 0.77 and 0.96 for the 2006 Witczak
model and the corresponding ANN algorithm, respectively.
Artificial Neural Network Algorithms
The user input to the ANN mixture modulus model is the
for Witczak's Complex Modulus Models
gradation and volumetric parts of the mix design and the
The binder input data required for the 1999 Witczak model binder data. In keeping with the MEPDG format, the binder
(2) are the viscosity, , and frequency of loading in Hertz, as data can be input at any of three levels. The binder data are
shown in Table 20. Figure 33 shows a graphic comparison the six properties of the CAM model (i.e., Gg, the glassy mod-
between the data obtained using Witczak's 1999 model and ulus in Gpa; R, the Rheological Index; rm, the cross-over fre-
those developed using the ANN algorithm (35) (statistical quency in rad/sec; Td, the defining temperature in °C; and the
comparisons are provided in Appendix G). The R2 values are two time-temperature shift parameters, C1 and C2) (39). The
Table 20. Data input for 1999 Witczak model (viscosity, , and
frequency of loading in Hertz).
Input R2
Output
Gradation Volumetric Binder Data Witczak ANN
3/4 3/8 #4 #200 Vbeff
Va (%) fc Hz E* psi 0.68 0.98
(%) (%) (%) (%) (%) 106 poise
OCR for page 37
37
Figure 33. Comparison of Witczak 1999 model with
ANN algorithm.
Table 21. Input data for the 2006 Witczak model (magnitude of the shear
modulus of the binder and its phase angle in degrees).
Input R2
Output
Gradation Volumetric Binder Data Witczak ANN
3/4 3/8 #4 #200 Va Vbeff Log|G*| 106 c
E* psi 0.77 0.96
(%) (%) (%) (%) (%) (%) psi deg
Figure 34. Comparison of Witczak 2006 model with
ANN algorithm.
