Top-Down Cracking of Hot-Mix Asphalt Layers: Models for Initiation and Propagation (2010) / Chapter Skim
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12 3. FINDINGS: THE VECD-BASED MODEL The primary feature of the VECD-based crack initiation model was to account for effects of damage zones on response prior to cracking.
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13 Figure 3-1. VECD-based model framework 3.1.1 Inputs Module Preprocessors have been developed to facilitate easy and rapid analysis of pavement systems using the FEP++.
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14 Table 3-1. Inputs Required for the VECD-based Model Input Quantity of Interest Test Method LVE Material coefficients ( E∞ , iE , iρ )
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15 3.1.2 Material Property Sub-models A brief review of the concepts of the LVE model and the VECD model and their most important formulations are given in Appendixes A.1.2.1 and A.1.2.2, respectively; a review of both the viscoplastic and thermal stress models is given in Appendix A.1.2.5 and A.1.2.6. However, because the aging, healing, and failure criteria sub-models were developed in this project, the details of each are given below.
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16 to account for variables such as field-aging conditions and mix properties (16)
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17 single Gmm value for the STA mixture was used for all the aged specimens. Therefore, it was concluded that no apparent damage occurred due to aging.
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18 0 20 40 60 80 100 Sieve Size (mm) % P as si ng A mix AL mix Control Points 0.
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19 the effect of the asphalt binder properties on the total mixture behavior may become more noticeable. Similar trends can also be seen in the phase angle master curve graph, shown in Figure 3-3 (c)
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20 0 5000 10000 15000 20000 25000 30000 1E-08 1E-05 1E-02 1E+01 1E+04 Reduced Frequency (Hz)
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21 0 5000 10000 15000 20000 25000 1.E-08 1.E-05 1.E-02 1.E+01 1.E+04 Reduced Frequency (Hz)
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22 0 5 10 15 20 25 30 35 40 45 1.E-08 1.E-05 1.E-02 1.E+01 1.E+04 Reduced Frequency (Hz)
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23 include the effects of aging in the formulation of the current constitutive model using another time variable that accounts for the aging time, as shown in Equations 3-1 and 3-2. The major advantage of this approach is that the interaction between loading and aging can be modeled realistically, thus allowing a more accurate evaluation of the effects of aged binders on mixture properties and the performance of the mixtures.
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24 effects of aging. Moreover, solving Equation 3-1 with the two-dimensional relaxation modulus (Equation 3-2)
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25 nmSC e= (3-4) where C is normalized pseudo secant modulus, and S is damage parameter.
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26 However, a more thorough investigation into the correlation between the oven aging and field aging times for damage characteristics is beyond the scope of the current research. 0.996 1.000 1.004 1.008 1.012 1.016 1.020 0 5 10 15 20 Aging Time (yrs)
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27 0.996 0.997 0.998 0.999 1.000 1.001 0 5 10 15 20 Aging Time (yrs)
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28 temperature. This subsection compares the fatigue performance for mixtures aged at different levels, then presents a new method to analyze cyclic fatigue tests, and finally, presents the failure criteria used to interpret the FEP++ results.
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29 Using the cyclic test results, comparisons can be made with regard to four conditions: (1) magnitude of the input, (2)
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30 Table 3-2. Cyclic Fatigue Test Summary (Frequency of 10 Hz)
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31 some trials were conducted, and the resultant damage characteristic curves collapsed reasonably using two options taken from the originally suggested analysis method: (1) the function is defined as (1/u + 1)
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32 0.0 0.2 0.4 0.6 0.8 1.0 0E+00 1E+05 2E+05 3E+05 4E+05 5E+05 S (Method D)
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33 In Figure 3-13, the pseudo stiffness (C) values at failure are plotted against the test temperatures for the CX tests for all aged mixtures.
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34 Figure 3-13. Variation of C at failure from cyclic fatigue tests 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 Temperature (°C)
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35 where 0 et t λ λ = *
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36 increase in pseudo stiffness during the rest periods, C2(S2) , and the reduction in pseudo stiffness as the healed material is redamaged, C3(S3)
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37 Ps eu do S tif fn es s (k Pa )
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38 Table 3-3. Healing Model Formulation Coefficients (21)
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39 pseudo stiffness healing with a single function because, as shown in Figure 3-15, the healed material is more sensitive to loading than the virgin material (i.e., the damage rate of the healed material is greater than that of the virgin material in Region I, while it is the same for the healed and virgin materials in Region II)
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40 to point 1; from point 1 to point 3 (second cycle) ; and finally from point 3 to point 5 (third cycle)
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41 between the pseudo stiffness values at point 1 and point 2. In order to apply the outcomes universally, the damage level, S, and energy input, ∆S, were normalized to the damage level at failure, Sf, and the change in pseudo stiffness was normalized to the pseudo stiffness level.
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43 Table 3-4. Simplified Healing Model Coefficients Coefficient AAM Value AAD Value Function Κ a 0.1679 0.1657 b 2.2695 2.8865 c 0.0548 0.0261 d 0.2572 0.2379 Function β f 27.3913 1.5144 g -1.5887 -4.7659 h 30.1058 5.0763 i -5.8228 -3.3953 j 0.5070 0.5290 k -8.1700 -3.0063 Function γ y 1.4707 1.2448 z -1.6387 -1.6425 Function δ n -0.3593 1.0526 o 30.1626 7.2289 p 2.8853 1.7666 q -0.2850 -2.0453 δ2 -0.0843 -0.1597
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44 0.E+00 1.E+00 2.E+00 3.E+00 4.E+00 0.E+00 1.E+00 2.E+00 3.E+00 4.E+00 Observed dC/C Pr ed ic te d dC /C (a) 1.E-09 1.E-06 1.E-03 1.E+00 1.E-09 1.E-06 1.E-03 1.E+00 Observed dC/C Pr ed ic te d dC /C (b)
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45 Figure 3-19, but was not encountered during the development of the more robust healing model because the earlier work (21) did not include experiments in which the subsequent healing and redamaging occurred in Region I of the previous healing cycle.
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46 P se ud o S tif fn es s (k P a)
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47 is positive, the healing potential should nonetheless decrease as the damage grows. This situation is believed to be related to the fact that high damage levels represent both an increase in crack density and an increase in the average size of the cracks.
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48 1E-02 1E-01 1E+00 1.E-01 1.E+01 1.E+03 1.E+05 Total "S" Healed *
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49 structural aging model, (2) a damage correction factor (DCF)
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50 A & VTS, MAAT Viscosity (η)
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51 As the GAS model is a function of the MAAT, the effective time varies for different climatic regions. To represent the wide range of conditions encountered in the United States, five regions are included in the study.
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52 The viscoplasticity of a given material and structure is considered by applying the damage correction factor (DCF)
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53 femε = the strain computed by an FEP++ simulation, dmg veε = the strain contributing to damage, and β = a factor that is 0 for control strain and 1 for control stress. Thus, the problem of significant damage due to total strain can be handled by using the DCF to scale the strain used in the damage calculation.
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54 iρ = the relaxation time (fitting coefficient)
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55 3.1.3.3 Temperature variation The variation of temperature in a pavement has two effects: a change in stiffness of the AC and a change in the thermal stress due to thermal expansion of the material. Thermal stress is generated in the pavement depending on the boundary conditions.
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56 the same time segments and will be input for the simulation. Further, these segments generally follow daily traffic distributions.
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57 -4 -3 -2 -1 0 1 2 3 4 5 0 5 10 15 20 25 Time (hr)
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59 where { }σ = the stress vector, [ ] D = the stiffness matrix that is a function of damage, and { }Rmε = the ve ctor of mechanical ps eudo s train, c omputed us ing t he s tate variable solution to pseudo strain (26)
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60 phenomenon to be captured. The FEM implementation is also useful in studying the effects of layers with different stiffness values.
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61 various vehicle loadings and their accompanying load level distributions is an imprecise science at best, and predicting the order of the loadings is impossible. Furthermore, predicting the sequential effects of different loading configurations becomes computationally time consuming.
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62 and analyze a single side of the tire load. Currently, the effect of wheel wander is not considered in the simulations.
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64 13,000, but predicting this many cycles without extrapolation would require a significant amount of time. Instead, the simulation was carried out for only about 1,300 cycles, and comparisons were made at this number of cycles.
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65 The results of two different cases, (a) a healing-dominant case and (b)
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66 thermal damage results because it effectively smoothes some of the more extreme events. The thermal stress-related damage calculations are much more sensitive to changes in temperature because these damage calculations are directly proportional to the temperature raised to the VECD damage power, α .
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68 results of this simulation are shown in Figure 3-31. In this figure, the x-axis shows the damage calculated via the arithmetic average temperature, and the y-axis shows the damage calculated via the weighted average temperature.
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69 1E-06 1E-05 1E-04 1E-03 1E-02 1E-06 1E-05 1E-04 1E-03 1E-02 Reduction of C - Arithmetic Average R ed uc tio n of C - W ei gh te d A ve ra ge Figure 3-31. Arithmetic versus weighted average temperature and temperature rate for WY-Dec 3.1.5 Output Module The output module consists of the tools and techniques necessary to view and interpret the VECD-FEP++ performance predictions.
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70 entire structure. The contour plots in Figure 3-32 show the grids that represent the elements that build the AC layers in the pavement structure.
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71 3.1.5.3 Output in the form of a stacked bar graph Examining the damage contours has some advantages, but it is not the most efficient analytical method for evaluating the many cases that are simulated in this work. To better quantify the simulation results, a quantity termed the condition index area is employed.
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72 3.1.6 Model Integration Reasonableness and sensitivity studies were carried out by a series of FEP++ simulations to show whether or not the framework development and integration into the VECD-FEP++ were performed correctly. First, a reasonableness check was performed to verify the proper implementation of the VECD model, and hence, the analytical sub-models (healing, aging, thermal damage, etc.)
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73 Results from the material characterization show large differences in the material responses (see Figure 3-35)
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74 Table 3-5. Volumetric Properties of Laboratory Mixtures for ALF Pavements Mix Designation Control SBS Binder Type Unmodified Styrene Butadiene Styrene Binder Grade PG 70-22 PG 70-28 Binder Content 5.30% NMSA*
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75 Table 3-6. Elastic Modulus of Unbound Layers Layer Elastic Modulus, MPa (ksi)
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76 Table 3-7. Simulation Details for Example Simulation Item Number of Cases Details Region 1 DC Structure 2 Thin (127 mm or 5 in.)
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77 healing is more effective near the pavement surface of a thin pavement than that of a thick pavement (i.e., the thick pavement appears to heal better at the bottom of the pavement than does the thin pavement)
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78 summarized in Table 3-8. The most important factors identified, for which all the necessary inputs were available, are material type (modified versus unmodified)
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79 the major trends do not change substantially, and that these trends are observed most clearly in March.
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80 CI<0.2 0.2 |
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81 frictional resistance that can develop between the HMA surface and base layers The SBS material tends to soften the regional differences slightly as does the use of a strong support condition. The support condition effect is more prevalent for the thin pavement.
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82 3.3.5 Effect of Asphalt Mixture Properties From the thin pavement simulation, it appears that the SBS material results in improved performance with regard to damage at the bottom of the pavement but slightly poorer performance in terms of damage at the top of the pavement for the one month considered. The damage progression from October through June is shown in Figure 3-40.
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83 0 20 40 60 80 100 4 (O ct )
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84 A systematic evaluation using the VECD-FEP++ was carried out to gain insight into the parameters most responsible for the development and/or dominance of top-down cracking. In general, more damage at both the top and bottom of the pavement was observed in the case of a cold climate, thin structure, weak support layer, and the use of the Control mixture.
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