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44 Weather Data Hourly Solar Daily Wind Daily Air Emissivity Coefficient Radiation Speed Temperature Absorption Coefficient Albedo a d Hourly Wind Hourly Air Speed Temperature Daily Traffic Vehicle Pavement Temperature (T) Binder Properties Class Distribution 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 Each Vehicle Class (Axle and Tire Loads) Bending Stress Intensity Factor Layer Relaxation Modulus (SIF) (Artificial Neural Network Model) (Artificial Neural Network Model) Crack Growth Fracture Properties A,n C=A[J]n N Is C Overlay No. of Days Yes Thickness? NfB Figure 38. Flow chart of the bending crack growth computations. overlay types except one. The exception was the AC overlay the reflection cracking model were limited to those sets which with reinforcing over AC in the Dry-Freeze Zone. Bending were actually observed. was the principal crack growth mode up to Position I in this A separate calibration program was assembled to assist in the model. Shearing was the principal cracking mode from Posi- development of other regional computational model-to-field tion I to the overlay. An example of this latter model is in data calibration coefficients (a User's Guide to this Calibration Equation 43. Program is presented in Appendix P). The complete set of calibration coefficients for each of the types of pavement structures and overlays and the statistical Validation of the Calibration Coefficients measures of their fit to the observed data is provided in Appendix N. In some cases, no distress was observed at the In reviewing the detailed data for each of the test sections, high severity level and in other cases, only low severity distress it was determined that there were only 150 overlay sections was observed. In such cases, the calibration coefficients for with unique data. In some cases multiple sections were located

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45 Weather Data Hourly Solar Daily Wind Daily Air EmissivityCoefficient Radiation Speed Temperature Absorption Coefficient Albedo a d Hourly Wind Hourly Air Speed Temperature Daily Traffic Vehicle Pavement Temperature (T) Binder Properties Class Distribution 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 Each Vehicle Class (Axle and Tire Loads) Shear Stress Intensity Factor Layer Relaxation Modulus (SIF) (Artificial Neural Network Model) (Artificial Neural Network Model) Crack Growth Fracture Properties A,n C=A[J]n N Is C Overlay No. of Days Yes Thickness? NfS1, NfS2 Figure 39. Flow chart of shearing crack growth computations. on the same highway (i.e., each with the same traffic, climate, cients by regression analysis and comparing the set of coeffi- and pavement structure). Therefore, the calibration and vali- cients with the original field data. If the set of calibration coef- dation process was conducted in a different way than was ini- ficients reproduced the original observed scales, trends, and tially envisioned. It was planned to separate the overlay sections patterns of and values with a high coefficient of determi- of each type into two groups: one group would be used to nation (R2) and with an acceptable scatter pattern around the develop the calibration coefficients and the other group would line of equality, the set of coefficients were accepted as valid. If be used to verify that their distress accumulation could be sat- they did not produce an acceptable fit to all of the original isfactorily predicted. The small number of unique pavement- observed and values, then the calibration coefficients were overlay sections did not permit splitting the sections into two revised by trying a new model with bending or shearing as the such groups. Instead, it was necessary to use the observed data principal distress mode. The model with the highest coefficient of all of the sections in both developing the calibration coeffi- of determination (R2) was selected. No separate validation

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46 Figure 40. Example user input screen for the reflection cracking program. Position II NfS2 NfT2 Overlay Position I NfB1 NfS1 NfT1 C Bending Stress Shearing Stress Thermal Stress Figure 41. Definition of the number of days of crack growth. NfB1 = Number of days for crack growth due to bending to reach Position I. NfT1 = Number of days for thermal crack growth to reach Position I. NfS1 = Number of days for crack growth due to shearing stress to reach Position I. NfT2 = Number of days for thermal crack growth to go from Position I to Position II. NfS2 = Number of days for crack growth due to shearing stress to go from Position I to Position II.

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47 100 dicted using fracture mechanics concepts and material prop- % Total Length of Cracks erties which are based on tabulated asphalt mixture, pavement Low+Medium+High structure, traffic and climatic variables. Thus, there are likely to be errors in the independent variables as well as in the Medium+High dependent variables (i.e., the values of and which were fit- High severity ted to the observed distress). 36.8% A total of 33 possible sets of calibration coefficients could have been developed if low, medium, and high levels of crack- ing severity had been observed in all pavement types. Because 0 LMH MH H some of these severity levels were missing, a total of 24 sets of No. of Days calibration coefficients were developed (all of the sets of cali- bration coefficients are found in Appendix N). Figure 42. Illustration of amount and severity of reflection cracking distress curves. After arriving at a final set of calibration coefficients, a fur- ther quality control step was taken by graphically plotting the distress patterns for all of the test sections to make certain that process was pursued with the limited number of overlay test the predicted patterns of distress accumulation were both sections that was available. reasonable and realistic. Logical tests were programmed into The purpose of validation is to check if the equations the design program to make certain that the predicted distress derived by regression analysis correctly fit the observed scales, patterns will be correctly ordered from low to medium to trends, and patterns of the field data. Validation is required high levels of distress. Examples of the final predicted values because the regression analysis assumes that all of the error is of and plotted against the observed field values are pro- in the observed dependent values and not in the independent vided in the Chapter 3 (full set of such plots is provided in variables. In this case, the independent variables were pre- Appendix N).