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26 Reflection Cracking Amount Because the reflection cracking severity and amount model and Severity Model has a clear physical boundary condition (0 to 100 percent) and the parameters, and , have physical meanings, the The development of reflection crack amount and severity model was selected for the calibration with different field data versus time or number of load repetitions follows a sigmoidal sets. However, because the database used for model calibra- curve having a finite upper asymptote for three different sever- tion consisted of the length of observed transverse cracks ity levels, as shown in Figure 20. when the survey was performed before and after overlay, the Jayawickrama and Lytton (12) proposed an s-shaped empir- variables of the original reflection cracking model were mod- ical model to describe the amount and severity development of ified as follows: reflection cracking on an asphalt overlay. This model describes the reflection cracking versus the number of load repetition or - time relationship as follows: D ( N i )( % ) = e Ni (8) where - RFAS = 100 e i D Total (7) D(Ni) = percent of reflection crack length of maximum crack length at N; where i = ith crack observation; RFAS = reflection cracking amount and severity, ranging Ni = number of days after overlay. from 0 to 100%; The percent of reflection crack length, D(Ni), at each DTotal = total number of days since the overlay construc- observation was calculated by dividing the observed length tion was completed; and of transverse crack, after overlay construction, by the total and = calibration parameters for each severity level. length of transverse crack on an existing pavement surface The parameter is the scale factor for reflection cracking just before overlay construction. The total crack length on amount and severity. A large value indicates that much accu- an existing surface can be described as the likelihood of mulated damage must occur to reach a given level of reflection maximum reflection cracking length on an overlay surface. cracking amount; that is, the parameter describes the spread The number of days after overlay, Ni, is determined by of the rising portion of the curve, the parameter is always counting the days after overlay construction when a given equal to the total number of days to reach 36.8 percent (= 1/e) set of observations were made. Based on the field data of the total amount of expected reflection cracking. The param- obtained from test sections, the parameters and were eter is the shape factor that describes how steep the rising por- calibrated for different severity levels. Three sets of param- tion of the curve is as shown in Figure 21 (more details on this eters were calibrated when all three severity levels were amount and severity model are provided in Appendix K). available: 90 80 70 Crack Length or Area (%) 60 50 40 30 Low+Medium+High (L+M+H) Severity 20 Medium+High (M+H) Severity 10 High (H) Severity 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Time (Days) Figure 20. Typical development of reflection crack by severity levels.