Models for Predicting Reflection Cracking of Hot-Mix Asphalt Overlays (2010) / Chapter Skim
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Available Reflection Cracking Models Concern about reflection cracking of asphalt overlays over existing pavements dates back to 1932, when Gary and Martin (10) studied this problem.
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Surface initiated cracking Thermal contraction Warping Crack growth Temperature gradient giving greater contraction at surface Thermally induced fatigue Crack growth Thermal expansion and contractionExisting layer Sub-base HMA overlay Traffic movement Traffic induced fatigue Crack growth Figure 3. Mechanisms of reflection cracking (8)
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and the mixture design data for the overlay. • Collect pavement distress data (including the total length of cracking in the old pavement surface prior to overlay and the lengths and levels of severity of reflection cracking)
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The layer moduli of the old pavement were backFigure 6. Flow chart of the process of constructing a calibrated reflection cracking model.
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AC = existing hot mix asphalt surface layer, JCP = jointed concrete pavement, CRC = continuously reinforced concrete surface layer, Mill = old surface layer was milled before the overlay was placed. SAMI = (Strain Absorbing Membrane Interlayer)
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Traffic Data Collection Traffic data is a key element for the design and analysis of a HMA overlay structure or a new pavement structure. For compatibility with the MEPDG, traffic was described by the actual load distribution (spectrum)
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within a given range of axle load. The axle load distribution factor is the percentage of the total axle applications in each load interval by an axle type for a specific vehicle class (classes 4 to 13)
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Axle Load (lb) Vehicle Class 4 5 6 7 3,000 0 53,818 183 11 4,000 10 54,606 558 52 5,000 42 39,113 993 139 6,000 175 20,289 1,099 168 7,000 988 24,555 2,426 252 8,000 10,687 22,491 5,617 298 9,000 9,713 13,719 8,154 365 10,000 10,156 12,839 12,423 879 11,000 6,011 7,127 8,945 1,516 12,000 5,875 6,413 7,725 2,913 13,000 3,409 3,511 3,257 2,464 14,000 2,947 3,128 2,289 2,710 15,000 1,640 1,756 975 1,740 16,000 1,239 1,513 725 1,419 17,000 679 834 285 664 18,000 446 800 235 423 19,000 212 424 104 159 20,000 181 360 73 111 21,000 106 261 44 70 22,000 51 131 22 46 23,000 41 135 6 26 24,000 21 85 4 9 25,000 24 90 3 12 26,000 11 43 1 7 27,000 4 33 1 2 28,000 1 12 3 1 29,000 4 25 0 1 30,000 3 13 0 0 31,000 1 16 2 0 32,000 2 8 0 0 33,000 0 5 0 0 34,000 0 2 1 0 35,000 0 0 0 0 36,000 0 0 0 0 37,000 0 2 0 0 38,000 0 0 0 0 39,000 0 0 0 0 40,000 0 0 0 0 Total 54,679 268,157 56,153 16,457 Table 6.
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Annual normalized single axle load distribution for vehicle class 4 to 7 (LTPP Section 180901 in 2004)
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. The one dimensional heat transfer model employs an unsteady-state heat flux boundary condition at the pavement surface, a depth-independent heat flux 3 m below the surface, and the ability to estimate site-specific model parameters using known measured pavement temperatures.
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over cracked asphalt surface; • Asphalt overlay with reinforcing geosynthetic layer over cracked asphalt surface; • Asphalt overlay over jointed concrete surface; • Asphalt overlay with reinforcing geosynthetic layer over jointed concrete surface; and • Asphalt overlay over cracked continuously reinforced concrete surface. The following three different loading conditions were used in the finite element calculations of the SIF at the tip of the crack: • Thermal stress; • Bending stress due to traffic; and • Shearing stress due to traffic.
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In the thermal stress cases, different levels of thermal expansion coefficient were used. With the jointed concrete pavement structures, different levels of load transfer efficiency were used.
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An example of the fit of an ANN model to the SIF data that was calculated by the finite element program is given in Figure 12 for the case of thermal stress in a HMA overlay over an old cracked asphalt pavement surface for which the R2 was 0.9982. Appendix F provides similar graphs for all of ANN models and describes the variations and ranges of overlay pavement structure and the material and interface properties used Model No Model Name Load Case 1 AC_over_AC_Interlayer_slip_L Thermal 2 AC_over_AC_Interlayer_slip_M Thermal 3 AC_over_AC_Interlayer_slip_H Thermal 4 AC_SC_AC Thermal 5 AC_over_AC Thermal 6 AC_over_PCC Thermal 7 Pure_Bending_AC_over_AC_Dual_Tire_Together Traffic 8 Pure_Bending_AC_over_AC_Dual_Tire_Together_Only_Positive Traffic 9 Pure_Bending_AC_over_AC_Single_Tire_Together Traffic 10 Pure_Bending_AC_over_AC_Single_Tire_Together_Only_Positive Traffic 11 Pure_Bending_AC_over_PCC_Single_Tire_Together Traffic 12 Pure_Bending_AC_over_PCC_Single_Tire_Together_Only_Positive Traffic 13 AC_Over_AC_Shearing_Bend_Part_Dual_Tire Traffic 14 AC_Over_AC_Shearing_Shear_Part_Dual_Tire Traffic 15 AC_Over_PCC_Shearing_Shear_Part_Dual_Tire Traffic 16 AC_Over_AC_Shearing_Bend_Part_Single_Tire Traffic 17 AC_Over_AC_Shearing_Shear_Part_Single_Tire Traffic 18 AC_Over_PCC_Shearing_Shear_Part_Single_Tire Traffic Table 10.
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18 Pavement Model Thermal Cases Traffic Load Cases AC Inter Layer LevelingCourse AC AC Over PCC AC Over AC and AC Mill AC AC InterLayer LevelingCourse AC-H AC InterLayer LevelingCourse AC-M AC InterLayer LevelingCourse AC-L AC Over SC Over AC Shearing Load Cases Pure Bending Load Cases Pure_Bending_ACoverAC_DualTire_Together Pure_Bending_ACoverAC_DualTire_Together (Only Positive) Pure_Bending_ACoverAC_SingleTire_Together Pure_Bending_ACoverAC_SingleTire_Together (Only Positive)
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2 ⎛⎝⎜ ⎞⎠⎟ × ( ) 3 Determination of the Effect of Cumulative Axle Load Distribution on Tire Length Because of the difficulty of employing each tire length for axle load intervals to evaluate traffic load effects on propagation of reflection cracking, the effect of the axle load distribution on the tire patch length for each category was used for the evaluation of traffic load.
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Determination of Hourly Number of Axles In order to analyze reflection cracking propagation caused by bending or shearing, the hourly number of axles should be considered in each of the tire length increments within each traffic category. The number of axles can be calculated from the probability density which is determined based on the cumulative axle load distribution of tire lengths in each category (details of the process of determining the hourly traffic distribution are provided in Appendix E)
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The number of traffic loads for each 1-hour time period in each day for eight traffic categories and tire length increments is used to calculate the bending or shearing stress intensity factor. The probability density of tire patch lengths for each traffic category can be determined from the cumulative axle load distribution function as follows: P L dC L dL j j j ( )
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= Cumulative Axle Load Distribution on Tire Length Tire Length Cumulative Axle Load Distribution = = Figure 14. Determination of cumulative axle load distribution on tire patch length.
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Cumulative axle load distribution versus tire length (Category 1 of LTPP Section 180901 in 2004)
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Default cumulative axle load distribution for each traffic category.
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Number represents the tire patch length increment listed in Table 12. Table 17.
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The total crack length on an existing surface can be described as the likelihood of maximum reflection cracking length on an overlay surface. The number of days after overlay, Ni, is determined by counting the days after overlay construction when a given set of observations were made.
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. These sections included HMA overlays over cracked asphalt surface layers in Amarillo and HMA overlays over jointed concrete pavements in Marlin.
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Low severity reflection cracking amount data in Amarillo, Texas.
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= sensitivity matrix = m, n = number of output data and model parameters, respectively; fk = mathematical model; pi = model parameters; {αi} = change vector (relative change of parameters)
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The coefficients by which the different modes of crack propagation relate to these field derived model parameters are the "calibration coefficients" which define a particular application (pavement structure, climatic zone, region) of the reflection cracking model.
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Overlay Type Model Parameters (L+M+H)
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32 0 10 20 30 40 50 60 70 80 90 100 0 1000 2000 3000 4000 5000 No. of Days % C ra ck L en gt h Measured Data Model Figure 27.
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that is used in the MEPDG. A comparison of the temperatures in a pavement surface as measured and as calculated by the EICM model is shown in Figure 8.
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The incoming and outgoing long-wave radiation (in W m-2) are calculated by: where a = absorption coefficient of pavement; = emission coefficient of pavement; Ts = pavement surface temperature, k; Ta = air temperature, k; and σ = 5.68 × 10−8W m−2K−4 is Stefan-Boltzman constant Q Tr s= σ 4 17( )
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In order to estimate hourly wind speed data, a method was developed to estimate hourly air temperatures from daily maximum and minimum air temperatures. Recorded daily maximum and minimum air temperatures can be obtained easily from the Virtual Weather Stations in the LTPP database or NCDC.
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Figure 32. Predicted daily air temperatures at six different LTPP test sites.
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37 Figure 33. Comparison of Witczak 1999 model with ANN algorithm.
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The form of the equations for both A and n were taken from viscoelastic crack growth theory by Schapery (36, 37) (some details on developing these formulas using a Systems Identification method are presented in Appendix J)
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The healing coefficients were used only with the traffic crack growth equations. Stress Wave Pattern Correction for Viscoelastic Crack Growth Schapery's theory of crack growth in viscoelastic materials takes into account the loading time and the shape of the stress pulse during the time that the material is being loaded (30, 31)
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34 lengths above this point, bending stresses no longer contribute to the growth of cracks and crack growth is due only to thermal and shearing stresses. The number of days that are required for cracks caused by each type of stress to reach Position 1 are recorded.
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. As with the growth of cracks due to traffic stresses, the incremental crack growth each day is accumulated until Position 1 is reached.
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These five numbers of days can be combined in several ways to model the value of ρ, the scale parameter of the amount, and severity of the observed reflection cracking distress. One way of modeling the ρ-value is to assume that the principal cause of reflection cracking is bending stress and another way is to assume that shearing stress is the principal cause of reflection cracking.
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of Days NfT1, NfT2 Yes No Fracture Properties A,n Weather Data Collocation E inverse Figure 37. Flow chart of the thermal crack growth computations.
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In some cases multiple sections were located 44 Hourly Solar Radiation Hourly Wind Speed Daily Wind Speed Emissivity Coefficient Absorption Coefficient Albedo a d Daily Air Temperature Hourly Air Temperature Pavement Temperature (ΔT) Each Vehicle Class (Axle and Tire Loads)
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No separate validation 45 Hourly Solar Radiation Hourly Wind Speed Daily Wind Speed EmissivityCoefficient Absorption Coefficient Albedo a d Daily Air Temperature Hourly Air Temperature Pavement Temperature (ΔT) Each Vehicle Class (Axle and Tire Loads)
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• NfS2 = Number of days for crack growth due to shearing stress to go from Position I to Position II.
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Illustration of amount and severity of reflection cracking distress curves.
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