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J-1 APPENDIX J. RELATIONSHIP BETWEEN CRACK DEPTH AND CRACK WIDTH FOR A SURFACE CRACK The developed top-down cracking model predicts the development of a crack downward from the pavement surface. The predictions are calibrated to the observed field distress data to develop the calibration coefficients. The field distress data have different severity levels, depending on the width of a surface longitudinal crack. As a result, the following relationships are developed in the project for the purpose of the calibration: ï· Surface crack width versus crack depth; ï· Distress severity versus surface crack width; and ï· Crack shape versus crack depth. Surface Crack Width and Crack Depth The data extracted from Kumara et al. (1) is used to develop the surface crack width versus crack depth model, as shown in Table J-1. The best fitting function to the data in Table J-1 is as follows: 0.4871.461 0.049c c w d d ïï½ ï´ ï (J-1) where w is the width of the crack; and cd is the depth of the crack in mm. This equation can be used to predict the depth of the crack according to the surface width of the same crack. Table J-1. Crack Width to Crack Depth Ratio (1) Crack Depth (mm) w/d Ratio 0.5 2 5 0.6 17.1 0.32 90 0.115 100 0.106 Distress Severity and Surface Crack Width The data extracted from the distress identification manual (2) is used to develop distress severity â surface crack width model, as shown in Table J-2. A power function is fitted to the data in Table J-2 as the expression of this model: 0.5635.744 4.094s wïï½ ï ï« (J-2) where s is the severity of the distress; and w is the width of the crack in mm. Table J-2 Surface Crack Width versus Distress Severity (2) Crack Width (mm) Severity 3 1 (low) 6 2 (medium) 19 3 (high)
J-2 Crack Shape and Crack Depth The shape of the crack and the depth of the crack have the following relationship, as shown in Figure J-1: ,max 0 ,max cn c c c d d w w d ï¦ ï¶ï ï½ ï´ ï§ ï· ï¨ ï¸ (J-3) where 0w is the width of the crack at the surface in mm; ,maxcd is the maximum depth of the crack in mm, cd is the depth of the crack; and cn is the crack depth exponent. The model of cn is as follows: 0.0838 ,max2.907 2.259c cn dï½ ï´ ï (J-4) Given the value of ,maxcd , the value of cn can be obtained from Equation J-4, so the shape of the crack can be determined. Figure J-4. Plot of Crack Shape versus Crack Depth of a Top-Down Crack References: 1. Kumara, M. W., Gunaratne, M., Lu, J. J., and Dietrich, B. (2014) Methodology for random surface-initiated crack growth prediction in asphalt pavements. Journal of materials in civil engineering, 16(2), 2004, 175-185. 2. Miller, J. S., and Bellinger, W. Y. (2003) Distress identification manual for the long-term pavement performance program, Report FHWA-RD-03-031, Federal Highway Administration, McLean, VA, 2003. 0 20 40 60 80 100 120 â6 â1 4 9 Cr ac k De pt h (m m ) Crack Width (mm) 1 mm 3 mm 6 mm 10.6 mm 1 mm crack shape 3 mm crack shape 6 mm crack shape 10.6 mm crack shape
