Modification of Dynamic Modulus Predictive Models for Asphalt ...

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of the 1999 Witczak model. The p-values of the g 2 coefficients except for Cg2 4% are greater than 0.05. There is not an obvious trend in the p-values. Although the standard error is very small, Cg2 5% is still not a significant factor. This indicates that the RAS content may not have an effect on the parameter g 2 . The conclusions need to be verified by a larger sample space. Table 23: Regression Results of RAS-Effect Calibration Parameters for the 2006 Witczak Model Parameter Estimation Standard Error P-value Cδ 3% 1.56497 0.540942 0.0041 Cδ 4% 0.60657 1.63964 0.7120 Cδ 5% 0.83865 1.093461 0.4434 Cδ 6% 2.182726 0.907241 0.0175 Cα 3% -1.95661 0.618857 0.0017 Cα 4% -0.63047 1.672241 0.7068 Cα 5% -0.8366 1.116441 0.4539 Cα 6% -0.82806 0.230407 0.0005 Cb 3% -0.52857 1.046937 0.6141 Cb 4% -1.81861 1.567145 0.2479 Cb 5% 0.574334 0.99932 0.5657 Cb 6% 5.866697 1.676873 0.0006 Cg1 3% -0.17666 0.094207 0.0618 Cg1 4% -0.00774 0.970961 0.9937 Cg1 5% -0.06169 0.250851 0.8058 Cg1 6% -0.07247 1.35486 0.9574 Cg2 3% 0.848671 0.509028 0.0966 Cg2 4% 1.1913 0.97377 0.2233 Cg2 5% -0.01117 0.373595 0.9762 Cg2 6% -2.5251 0.569046 0.1099 Statistics in Table 23 show that the coefficients having a p-value greater than 0.05 include Cδ 3% , Cδ 6% , Cα 3% , Cα 6% , and Cb 6% . The general p-value trend for the δ, α, and b coefficients are 87
decreasing with increasing RAS content. There are no distinct trends for the p-values of the g 1 and g 2 coefficients. This indicates that RAS content less than 5% may not result in significant decrease in the prediction accuracy of the 2006 Witczak Model. Adding shingles to HMA may not change the g 1 and g 2 parameters in the model. Hirsch Model The Hirsch model is developed from the Hirsch’s law of mixture. The basic equation is Equation 28 The model contains four empirical constants, E a , p 0 , p 1 , and p 2 . The values of the four constants determined by Christensen (2003) are 4,200,000, 20, 0.58, and 650 for E a , p 0 , p 1 , and p 2 , respectively. Dummy variables which are used to simulate different projects are added to the four constants in order to match the lab testing results. The 0%-RAS-effect calibration equations for E a , p 0 , p 1 , and p 2 are shown in Equation 29 through Equation 32 Lab tested E* values for mixes containing 0% RAS are used to determine the value of each coefficient. The regression results are shown in Table 24. Figure 49 shows the prediction accuracies of the calibrated Hirsch Model. There are no distinct linear trend lines for different projects. Variables are added to the calibrated E a , p 0 , p 1 , and p 2 to account for the effects of the RAS. The modified predicted E* values are calculated by Equation 28 with modified E a , p 0 , p 1 , and p 2 as shown in Equation 33 to Equation 36 Lab E* values for each RAS content are used for regression of the modified Hirsch function. The coefficients of the dummy variables are determined and summarized in Table 25. Figure 50 shows the lab tested E* vs. the predicted E* from the modified Hirsch model. Data points on Figure 50 are concentrated along the line of equality. The R 2 of the modified Hirsch model is 0.97 and the Se/Sy value is 0.19 on a normal scale. On a logarithm scale, the model achieves R 2 value of 0.51 and Se/Sy value of 0.76. According to Table 10, the goodness-of-fit for the modified Hirsch model is excellent on normal scale and fair on logarithm scale. Equation 28 88
Page 1 and 2:
Modification of Dynamic Modulus Pre
Page 3 and 4:
CHAPTER 5: CONCLUSIONS AND RECOMMEN
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Table 36: Project Effect Calibratio
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Figure 38: G* Master Curve for Asph
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ACKNOLEDGEMENTS I would like to exp
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CHAPTER 1: INTRODUCTION BACKGROUND
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well-known procedures among them. T
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and Hirsch Models (Chapter 4), and
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Table 1. The percentages in Table 1
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The binder grading results showed b
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maximum stress, and maximum strain
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Gyratory Compactor (SGC) is used to
Page 25 and 26:
Figure 3: Master Curve Construction
Page 27 and 28:
The penetration viscosities were us
Page 29 and 30:
V 1S V 2S Va ’ Vc Vv V m V 1P V 2
Page 31 and 32:
Previous Evaluation of the Witczak
Page 33 and 34:
Figure 6: Master Curve Comparison f
Page 35 and 36:
Figure 9: Summary of Percent Error
Page 37 and 38: Figure 12: Measured Values vs. Pred
Page 39 and 40: Figure 15: Comparison of Values Usi
Page 41 and 42: Effects of Fibers on Asphalt Concre
Page 43 and 44: Project Mix Number Table 5: Experim
Page 45 and 46: 500' 500' 500' 500' 500' 500' 500'
Page 47 and 48: Iowa DOT Demonstration Project The
Page 49 and 50: Percent Passing, % Table 7: Iowa De
Page 51 and 52: Percent Passing, % 100.0 90.0 80.0
Page 53 and 54: Percent Passing, % Table 9: Indiana
Page 55 and 56: Figure 28: Universal Testing Machin
Page 57 and 58: shear stress to achieve a preset st
Page 59 and 60: ORIGINAL MODEL EVALUATION A total n
Page 61 and 62: Witczak 2006 Model Predicted Dynami
Page 63 and 64: Hirsch Model Predicted Dynamic Modu
Page 65 and 66: Table 13: ANOVA Table for Hirsch Mo
Page 67 and 68: MN vs. MO Yes 0% vs. 4% Yes MN vs.
Page 69 and 70: Table 16: Volumetric Properties of
Page 71 and 72: | | where η = viscosity (Poise), |
Page 73 and 74: G*, Pa G*, Pa temperatures. As show
Page 75 and 76: Phase Angle 75 65 55 45 35 25 15 37
Page 77 and 78: (| | ) ( ( )) where | | = dynamic s
Page 79 and 80: calibration variable D IN, D IA , D
Page 81 and 82: Table 21: Regression Results of 0%-
Page 83 and 84: Modified Witczak Model Predicted Dy
Page 85 and 86: Modified Witczak Model Predicted Dy
Page 87: Table 22: Regression Results of RAS
Page 91 and 92: CP1 IN , CP1 IA , CP1 MN , CP1 MO =
Page 93 and 94: Equation 34. where P 1 c = modified
Page 95 and 96: MODIFIED MODEL EVALUATION The afore
Page 97 and 98: Dynamic modulus E*, psi Dynamic mod
Page 101 and 102: Model Predicted E*, psi Model Predi
Page 107 and 108: are larger than the variability of
Page 111 and 112: Dynamic modulus E*, psi 10000000 10
Page 115 and 116: 5%, and 6% RAS contents. The δ cal
Page 117 and 118: 0.1 0.05 3% RAS 5% RAS 6% RAS 0 -0.
Page 119 and 120: Table 29: Coefficient Correlation C
Page 121 and 122: 1.5 1 0.5 0 -0.5 -1 -1.5 6% RAS -2
Page 123 and 124: Table 31: 2006 Witczak Modification
Page 125 and 126: 10000 8000 6000 4000 3% RAS 4% RAS
Page 127 and 128: dummy variables. A statistical anal
Page 129 and 130: Table 32: Project Effect Calibratio
Page 131 and 132: Table 36: Project Effect Calibratio
Page 133 and 134: REFERENCES [1] New Hampshire Depart
Page 135 and 136: [26] D. W. Christen and D. A. Ander
Page 137 and 138: Table 39: Dynamic Modulus Test Resu
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Table 41: Dynamic Modulus Test Resu
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Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
APPENDIX B: DSR TEST RESULTS Table
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APPENDIX C: DSR FREQUENCY SWEEP TES
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Mix Temp. Freq. BC-21 BC-23 BC-24 B
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Mix Temp. Freq. BC-27 BC-28 BC-29 B
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29 1.585 2773000 52.32 4360000 47.8
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