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OCR for page 42
42 Table 24. Level 3 thermal coefficients. medium and low levels of severity (details of the various options for input and output are given in Appendix O). Climate Zone Thermal Coeff. Absorption Emissivity Albedo Wet-Freeze 0.0000248 0.7468 0.6628 0.3027 Wet-No Freeze 2.287E-05 0.7381 0.6571 0.1988 Computation-to-Field Dry-Freeze 0.00002298 0.7357 0.6071 0.2429 Dry-No Freeze 2.468E-05 0.7000 0.5750 0.2000 Calibration Coefficients At the end of the computations, there are five calculated numbers of days for a crack to reach a designated point used in the earlier research for each of the four climatic zones within an overlay (Position I) where the bending stresses (4). In addition, the absorption, emissivity, and albedo coef- become compressive and no longer cause crack growth (Posi- ficients for the same climatic zones may be input at Level 1 tion II, the surface of the overlay). These five numbers of days and Level 3. Table 24 gives the mean values for these coeffi- are illustrated in Figure 41. cients. Absorption, emissivity, and albedo coefficients vary These five numbers of days can be combined in several throughout the United States and with the seasons (detailed ways to model the value of , the scale parameter of the values are given in Appendix B). amount, and severity of the observed reflection cracking distress. One way of modeling the -value is to assume that the principal cause of reflection cracking is bending stress Supervisory Program to Compute and another way is to assume that shearing stress is the prin- Crack Growth cipal cause of reflection cracking. In both cases, it becomes The supervisory program for the separate analysis of the necessary to find how many days of each of the other types growing reflection cracks by each of the three mechanisms of cracking are the equivalent of the number of days of the (bending, shearing, and thermal stress) takes into account all principal cause of the distress. This concept is illustrated in of the identified details and produces five numbers of days to Figure 42 which shows all three -values (i.e., LMH, MH, and H). The linear regression form of the model for the LMH- reach a defining point in the growth of a reflection crack up value assuming that bending stress is the principal cause of through an overlay. One defining point is Position 1, at which the reflection cracking up to Position I and shearing is the point bending produces no additional crack growth. The principal cracking mechanism from Position I up to the sur- other defining point is the surface of the overlay. The five face of the overlay, is presented in Equations 40 through 42. numbers of days are the number of days to reach Position 1 The thermal calibration model for the low+medium+high by bending, shearing, and thermal stress and the number of distress curve is given by Equation 40. days for the crack to grow from Position 1 to the surface of the overlay because of shearing and thermal stress. N f B1 N f B1 LMH = N f B1 0 - 1 - 2 The supervisory program handles each of the crack growth N f T1 N f S1 processes separately and combines them after the calculations N f T 2 for each of the three separate mechanisms have been completed. + N f T2 3 - 4 (40) N fS2 Figures 37, 38, and 39 illustrate the calculation processes for thermal stress, bending, and shearing, respectively. In all cases, Calibration Coefficcients: 0 , 1 , 2 , 3 , 4 , LMH the initial crack length was taken to be the depth of the old pave- The thermal calibration models for the Medium + High ment surface layer. In all crack growth calculations, the initial and High distress curves are given by Equations 41 and 42, crack size, co, is assumed to be the thickness of the overlaid pave- respectively. ment surface layer. This value enters into the calculation of the SIF at the tip of the crack each day. N f B1 N f B1 MH = N f B1 5 - 6 - 7 N f T1 N f S1 User Interface Program for Input N fT2 + N f T2 8 - 9 (41) and Output Data N fS2 Calibration Coeffici ients: 5 , 6 , 7 , 8 , 9 , MH The input and output user interface for this program has been designed to have the same appearance as the user interface N f B1 N f B1 for the MEPDG software. An example of an input screen show- H = N f B1 10 - 11 - 12 ing the input of a pavement layered structure is given in Figure N f T1 N f S1 40. The user output is a graphic plot of the three severity level N f T 2 + N f T 2 13 - 14 (42) distress curves for reflection cracking, if the original field data N fS2 had a sufficient amount of observed data to include high, Calibration Coef fficients: 10 , 11 , 12 , 13 , 14 , H
OCR for page 43
43 Weather Data Hourly Solar Daily Wind Daily Air Emissivity Coefficient Radiation Speed Temperature Absorption Coefficient Albedo a d Hourly Wind Hourly Air Speed Temperature Pavement Temperature (T) Binder Properties 1999 Model? 2006 Model? 1999 Model 2006 Model Gradation Gradation Volumetric Composition Volumetric Composition Frequency (fc) Phase Angle (b) Viscosity () Shear Modulus of Asphalt (G*) No Collocation Relaxation Modulus at Crack Tip Viscoelastic Thermal Stress (T) E inverse (Artificial Neural Network Model) Thermal Stress Intensity Factor (SIF) Fracture Properties A,n (Artificial Neural Network Model) Crack Growth C=A[J]n N Is C Overlay No. of Days Yes Thickness NfT1, NfT2 Figure 37. Flow chart of the thermal crack growth computations. A similar set of coefficients can be derived by linear regres- The calibration coefficients are, as in the first form of this sion analysis, assuming that bending is the principal mode of model, 0, 1, 2, 3 and 4. Similar models are assumed for reflection cracking until it reaches Position I and then shear- the scale parameters MH and H; similar linear regression ing stress is the principal mode of reflection cracking from models were used to model the shape parameter, . Position I to the surface of the overlay. An example of this In performing the calibration analysis, the thermal, bend- assumed calibration form is shown in Equation 43. ing, and shearing forms of equation were tried and the one which proved to have the highest coefficient of determina- N f B1 N f B1 tion, R2, was selected. In general, the model with bending as LMH = N f B1 0 - 1 - 2 N f T1 N f S1 the principal cracking mechanism up to Position I and ther- N fS2 mal stress as the principal cracking mechanism from there to + N f S2 3 - 4 (43) N f T2 the surface of the overlay had the highest R2-value with all