Top-Down Cracking of Hot-Mix Asphalt Layers: Models for Initiation and Propagation (2010) / Chapter Skim
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A-ii TABLE OF CONTENTS page TABLE OF CONTENTS ............................................................................................................
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A-1 CHAPTER 1 DEVELOPMENT OF THE VECD-BASED MODEL Top-down cracking has been proven to be one of the major distresses in hot-mix asphalt (HMA) pavements in the United States.
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A-2 into the public domain finite element code, FEP++. The resulting product, the so-called VECDFEP++, allows the accurate evaluation of boundary condition effects (e.g., layer thickness)
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A-3 have been performed since the test road was constructed and will be continued. Predictions made using the VECD-FEP++ for the KEC test road sections demonstrate field performance trends and also reveal a generally positive relationship between model predictions and field observations for all the sections.
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A-4 Prior to all testing, the steel end plates were glued to the specimen using DEVCON steel putty. Extreme care was taken to completely clean both the end plates and the specimen ends before each application to prevent failure at the glued area.
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A-5 (LVE) range.
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A-6 properties, along with the complex modulus, in LVE theory. Because these two properties are the responses for respective unit inputs, they are called unit response functions.
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A-7 The coefficients determined from this process are then used with Equation (A-37) to find the relaxation modulus.
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A-8 Once the coefficients, jD , are determined, they are substituted into Equation (A-39) to find the creep compliance.
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A-9 A.1.2.2 Viscoelastic continuum damage model (VECD) A.1.2.2.1 Continuum damage On the simplest level, continuum damage mechanics considers a damaged body with some stiffness as an undamaged body with a reduced stiffness.
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A-10 where RE is a particular reference modulus included for dimensional compatibility and typically taken as one. Using pseudo strain in place of physical strain, the constitutive relationship presented in Equation (A-33)
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A-11 The LVE relationship represented by the pseudo strain in Equation (A-45) can be modified to Equation (A-47)
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A-12 is a material property independent of temperature and test type. The simplified model formulations are shown in the following equations with descriptions of the variables (20)
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A-13 pp = peak-to-peak amplitude, and ta = tension amplitude. The transient portion of the loading history, i.e., the first half of the first cycle, is important because it is used to define the specimen-to-specimen correction factor, I , and because damage growth in this first loading path can be significant.
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A-14 the point after which the data cannot be used for VECD characterization. Figure 1-1 (b)
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A-15 nmSC e= (A-55)
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A-16 Figure 1-3. Typical bad pseudo stiffness prediction (I19C-10)
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A-17 Figure 1-4. Experimental observation of pseudo stiffness values at failure against reduced frequency It is found from Figure 1-4 that, in general, the pseudo stiffness at failure ( *
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A-18 a genetic algorithm technique is used. A commercial Excel-based macro language add-in, Evolver, is used for this purpose.
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A-19 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 Measured Nf Pr ed ic te d N f S9.5C S9.5B I19C B25B I19B RS12.5C RI19B RI19C RB25B LOE (a) R2=0.932805 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Measured Nf Pr ed ic te d N f S9.5C S9.5B I19C B25B I19B RS12.5C RI19B RI19C RB25B LOE (b)
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A-20 To validate the failure criterion, fatigue test results from mixtures not used in the calibration of Equations (A-58) through (A-60)
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A-21 for the CRTB experiments, it was found that the number of cycles to failure values for the two tests do not follow the expected trends. Specifically, the test with the higher input strain values produced a larger number of cycles to failure than the experiment with the lower input strain values.
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A-22 Equation (A-61) can be used directly to find the effect of strain amplitude, loading frequency and testing temperature on fatigue life.
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A-23 Controlled Stress Test Simulation The simplified VECD model is also applied to simulate the controlled stress direct tension fatigue test. The formulation of the stress-based model is not as straightforward as that of the strain-based model due to the complexity of the integration, as evident in Equation (A-62)
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A-24 1.E+02 1.E+03 1.E+04 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 Nf St re ss L ev el (k Pa ) 5C Simulation 19C Simulation 27C Simulation (a)
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A-25 bending test results from the SHRP project A-003A (13) and also consistent with findings from material level testing on the ALF mixtures (26)
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A-26 figures clearly shows that the test results, i.e., the means plus a single standard deviation, of the LTA specimens are higher overall than those from the STA specimens. Although this graphical technique led the research team to conclude that the differences between the STA and LTA samples are significant, a more comprehensive statistical analysis of these values using the step-down bootstrap method has also been performed.
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A-28 pavement. Modifications to these distributions may drastically alter the potential for bottom-up cracking because these structural viscoplastic effects have been shown to be the most drastic near the pavement base.
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A-29 hardening viscoplastic material model and pavement responses predicted using the FEP++ without damage for the pavement structure under evaluation. To model the viscoplastic behavior of AC under tensile loading Uzan (23)
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A-30 11 11 0 1 t pp q vp p dt Y ε σ ++ + = ∫ .
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A-31 by repeated, thermally-induced tensile stress at the pavement surface, which can gradually damage the pavement and contribute to surface-induced cracking; and (2) through acute thermal cracking, where very low temperatures cause sudden fracture of the pavement surface.
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A-32 slowest cooling rate. From a comparison of the predicted stresses among each other, it is evident that the VEPCD model yields the most accurate predictions, slightly better than the VECD model.
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A-34 0 2 4 6 8 10 12 14 -10 0 10 20 30 40 50 Temperature (°C)
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A-35 Comparisons of material type reveal that when the SBS materials are used, higher strain magnitudes result. If the temperatures shown in Figure 1-13 are combined with the data shown in Figure 3-35, i.e., the mastercurve, appropriate time temperature shift factors, and a quasiapproximate time-frequency conversion (27)
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A-36 case is greater than in the simulations. It is also observed that the approximate pavement shear center, as indicated by a bulb of radial strain extending near the loading edge, is relatively higher in the thick pavement (at 20% of total depth)
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A-37 Table 1-17. Tensile Stress and Strain Contours for Reasonableness Check: Thick Pavements - Florida Case Tensile Stress at t = 0.05 sec (kPa)
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A-38 Table 1-18. Tensile Stress and Strain Contours for Reasonableness Check: Thick Pavements - Wyoming Case Tensile Stress at t = 0.05 sec (kPa)
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A-39 Table 1-19. Tensile Stress and Strain Contours for Reasonableness Check: Thin Pavements – Full Depth 72°C Case Tensile Stress at t = 0.05 sec (kPa)
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A-40 support condition leads to an overall reduction in damage distribution. The effect is most significant for the top-down damage, but also affects the damage at the bottom of the pavement.
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A-41 A.2.2.2 Aging effect To investigate the effect of aging, FEP++ simulations were conducted, and the results are shown in Table 1-22. In the simulations a single year run was performed, but the input material properties correspond to either the un-aged properties (denoted as No Aging in Table 1-22)
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A-42 A.2.2.3 Thermal stress effect Thermal stress is the direct result of structural constraints on material expansion. When a material is heated or cooled it tends to expand or contract by an amount directly proportional to the change in temperature.
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A-43 result, the material is more likely to relax and absorb thermally-induced dimensional changes and, therefore, experience less damage. Because the overall effect of thermal damage is reduced, the apparent effect of the thermal coefficient is also reduced for Florida.
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A-44 one year with and without the DCF. As is clearly seen in Table 1-23, the DCF noticeably reduces the total damage growth for both the Wyoming and Florida regions.
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A-45 the asphalt layer and subgrade, respectively. As shown in Table 1-24, the two methods generate similar results.
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A-46 case of the thin pavement, the length of time was somewhat longer than a full year, but the thick pavement was simulated for the full ten years. Table 1-25 shows the contours for the months of October through July of the first simulation year for both the thick pavement and the thin pavement.
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A-47 Table 1-25. Damage Contours for Example Simulations Mon.
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A-48 7 (Jan)
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A-49 11 (May)
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A-50 Table 1-26. Parametric Study Simulations for Thin (t)
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A-51 Table 1-27. Parametric Study Simulations for Thick (T)
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A-52 Table 1-28. Parametric Study Simulations for Thick (T)
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A-53 Table 1-29. Parametric Study Simulations for Thick (T)
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A-54 Table 1-30. Damage Progression and Healing in SBS and Control Pavements Mon.
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A-55 A.4 List of References 1.
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A-56 12. Strategic Highway Research Program (SHRP)
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A-57 24. Schapery, R
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