A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers (2018)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

I-1 APPENDIX I. PREDICTION OF TOP-DOWN CRACK INITIATION TIME AND DETERMINATION OF CALIBRATION COEFFICIENTS FOR DIFFERENT CLIMATE ZONES In order to account for the effect of four different climatic zones, four regression equations are developed to predict the top-down crack initiation time t0 using the observed t0 and material properties of the asphalt layer, energy parameter and traffic load. Table I-1 lists the calibration parameters for the wet no-freeze (WNF) zone, wet-freeze (WF) zone, dry no-freeze (DNF) zone, and dry-freeze (DF) zone, respectively.  0 0 0 100 log 21 aB C HT D LT E AADTT A At e              (I-1) where A , B , C , D and E are calibration coefficients; HT is the average annual number of high temperature (above 32°C) and LT is the average annual number of low temperature (below 0°C). Table I-1. Calibration Confidents for Top-Down Cracking Initiation Time Climatic Zone A B C D E WNF 28941264.02 0.494784812 0.006244585 0.01502521 2.103057482 WF 67229707.38 0.567536488 0.000757411 0.002708574 2.292690006 DNF 16770183.48 0.4239992 9.9949E-06 8.12072E-05 2.311665472 DF 28941264.02 0.440246595 0.006241042 0.013906837 1.890063314 The measured t0 versus predicted t0 in the four climatic zones are shown in Figure I-1 (a) to (d), respectively. As can be seen, the R2 values are within a reasonable range, which indicate the goodness of fit. (a) Prediction of t0 in WNF Zone R² = 0.8103 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 M ea su re d  Cr ac k  In iti at io n  Ti m e  (d ay ) Predicted crack initiation time (day)

I-2 (b) Prediction of t0 in WF Zone (c) Prediction of t0 in DNF Zone R² = 0.9427 0 1000 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 M ea su re d  In iti at io n  Ti m e  (d ay ) Predicted Initiation Time (day) R² = 0.8397 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 M ea su re d  Cr ac k  In iti at io n  Ti m e  (d ay ) Predicted Crack Initiation Time (day)

I-3 (d) Prediction of t0 in DF Zone Figure I-1. Prediction of t0 in Four Climatic Zones The observed coefficients  and  are determined from the LTPP database using Equation H-1 in Appendix H. The number of days NTR to reach the critical crack depth is computed following the mechanistic approach presented in the text. After obtaining the associated  and  as well as NTR for each pavement section, linear regression analysis is used to determine the calibration coefficients. For the pavement sections without significant thermally-induced longitudinal cracking, the following calibration equations are developed in Equations I-2 and I-3: 2 3i TRiN    (I-2)   21 logi TRiN   (I-3) where NTR is the number of days to reach the critical crack depth due to traffic load only; α1 and α2 are calibration coefficients for ρ; and γ1 and γ2 are calibration coefficients for β. Only four pavement sections in the wet-freeze zone showed crack growth due to thermal stresses, which may, for the most part, not be considered as a factor in top-down cracking. Two sets of calibration coefficients (αi and γi) are developed: one for the wet zone and one for the dry zone, which takes into account the geographical difference in the climate. The summary of the results is shown in Table I-2. Figures I-2 (a) through (c) show the results of the linear regression in terms of the predicted number of days NTR and β versus the observed ρ and the observed versus the predicted β for each climatic zone. R² = 0.8908 0 1000 2000 3000 0 500 1000 1500 2000 2500 3000 M ea su re d  Cr ac k  In iti at io n  Ti m e  (d ay ) Predicted Crack Initiation Time (day)

I-4 Table I-2. Summary of Modeling Coefficients for ρ and β in Different Climate Zones Climatic Zone 1 2 1 2 Wet 631. 04 2269.8 0.4201 -1.097 Dry 1617.6 -1705.3 0.4201 -1.097 (a) ρ in Wet Zone (b) ρ in Dry Zone R² = 0.8409 N=16 Standard error=1496 0 2000 4000 6000 8000 10000 12000 14000 16000 0 5 10 15 20 25 Ca lc ul at ed  ρ (d ay ) Pre fatigue life (month) R² = 0.896 N=13 Standard error=1972 0 5000 10000 15000 20000 25000 0 2 4 6 8 10 12 14 16 Ca lc ul at ed  ρ (d ay ) Pre fatigue life (month)

I-5 (c) β in all zones Figure I-2. Prediction of Calibration Coefficients R² = 0.5527 N=22 Standard error=0.583 0 0.5 1 1.5 2 2.5 3 3.5 0 0.2 0.4 0.6 0.8 1 Be ta log (N)