A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers (2018) / Chapter Skim
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16 CHAPTER 4. FINDINGS Introduction This chapter on the findings of the research project first reviews the methods to determine the complex modulus and modulus gradient of asphalt field cores with different aging times.
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17 mixtures become stiffer after a long-term aging period, which is similar to the laboratory-mixedlaboratory-compacted (LMLC) mixtures under long-term aging in the laboratory.
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18 (b) Measured Strain of Laboratory Fabricated Specimen Figure 4.1.
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19 3) Convert the functions of the measured loads, strains and modulus gradient parameters using the Laplace transform to calculate the corresponding viscoelastic property: complex modulus; 4)
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20 Figure 4.3. Modulus Gradients of 8 and 22 Months Aged Field Specimens at Three Temperatures and 0.1 Hz Time-Temperature-Aging-Depth Shift Functions for Dynamic Modulus Master Curves A single dynamic modulus master curve cannot be constructed including the effects of temperature and aging for both of the LMLC and field-aged asphalt mixtures.
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21 The effect of aging shifts (a)
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22 where gE and eE are the glassy modulus (i.e., modulus at infinite frequency) and equilibrium modulus (i.e., modulus at zero frequency)
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23 Figure 4.5. Dynamic Modulus LMLC Master Curves Constructed by CAM Model Determination of Aging Vertical Shift and Rotation The aging shift function is defined at the aging level for an asphalt mixture at a specific aging time compared to the same asphalt mixture at an unaged or reference aging level.
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24 horizontal aging shift factor. The power law equation is used to determine the change of the rheological index for the rotation: 0 0 Rn Ex x E R a R a (4.6)
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25 (B) Modified and Original 6 Months Master Curves (c)
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26 As shown before, the aging is mainly affected by two factors: aging time and aging temperature. Therefore, the horizontal aging shift factor has the following form which includes an Arrhenius relation: 0 0 1 1( )
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27 Construction of Dynamic Modulus Master Curve of Field Cores The process for constructing a final LMLC dynamic modulus master curve illustrated above is also used for constructing a final dynamic modulus master curve for field-aged mixtures but with several modifications, as follows.
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28 (a) Baseline Aging Master Curve of Field Asphalt Mixtures (b)
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29 is needed to quantify this non-uniform aging. The bottom of the asphalt layer is selected as the reference pavement depth of 38 mm.
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30 (b) Horizontal Depth Shift Figure 4.10.
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31 prediction models. For example, the reaction rate of CA in an asphalt binder is predicted using an Arrhenius equation for temperature variation and pressure dependence (127-128)
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32 Table 4.2 Laboratory Testing Results and Calculation Results for Field Condition Ty pe o f Fi el d Co re s Sa m pl e ID AV*
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33 Establishment of Aging Prediction Model for Field Modulus Gradient Based on the measured modulus gradient of field cores, the modulus gradient in an asphalt pavement can be idealized as illustrated in Figure 4.12. As aging time increases, the modulus within the top 1.5-inch increases and changes nonuniformly with depth.
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34 in which: afs field E RT fs fsk A e (4.14) acs field E RT cs csk A e (4.15)
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35 aging with depth below the surface, field cores always have modulus gradients. As the first step of developing the aging mixture modulus prediction model, the laboratory test condition must be converted to the field aging condition.
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36 With known rheological parameters, Equation 4.14 is then used to determine the modulus gradient of field cores in the field aging condition. The viscosity at the field aging temperature at the given age is calculated by substituting fieldT for labT and selecting the rheological parameters at the corresponding age.
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37 Figure 4.14. Fast-Rate Period and Constant-Rate Period of Field Core Modulus Gradient Third, following the same approach above, the slopes of the straight lines in the second and third portions are obtained for the baseline modulus, surface modulus, and aging exponent of the field cores.
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38 Figure 4.15. Examples of Arrhenius Plot of Constant-Rate Reaction Constant for Field Cores Aged at 28 and 16˚C Fourth, after using the second and third portions for the constant-rate period, the first portion is used to determine the aging activation energy and pre-exponential factor for the fastrate period.
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39 Figure 4.16. Goodness of Representation by Aging Prediction Model for Field Aging Gradient Figure 4.17.
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40 Table 4.3 Results of Aging Activation Energies and Pre-Exponential Factors of Field Cores Type of Field Cores Baseline Modulus AV<7% AV>7% afbE (kJ/ mol)
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41 moduli of asphalt mixtures at different ages. The FWD is a widely used technique for nondestructive evaluation of pavements.
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42 Mixture properties, including the air void content of the mixture, asphalt binder content, and the aggregate gradation. When the information of the air void content is not available, the bulk specific gravity and maximum specific gravity are collected instead to calculate the air void content.
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43 Table 4.5 Information of LTPP Pavement Sections LTPP Sections Date when FWD Data Collected Age of Aging (Days) Type of Asphalt Binder*
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44 Table 4.6 Examples of Modulus and Mixture Property Data Collected from the LTPP Database (a) Modulus Data ID Test date FWD Pass Average Modulus*
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45 (a) Climate Zones WF and WNF (b)
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46 2) Absorption of atmospheric downwelling long-wave radiation and emission of long-wave radiation; and 3)
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47 (a) Hourly Pavement Temperature for Entire Aging Time (b)
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48 (b) One Summer Day (8/18/2000)
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49 5. Use the starting point of Segment 2 as the end of Segment 1.
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50 Figure 4.22. Fitted FWD Backcalculated Modulus Curve Figure 4.23.
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51 Figure 4.24. Calculated Aging Activation Energy from FWD Data and Climate Data in Different Climate Zones Validation of Aging Prediction Model After determining all of the coefficients in the aging prediction model, this model can be used to predict the modulus at any age.
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52 (b) Extrapolated Moduli of All LTPP Sections at Last Test Date Figure 4.25.
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53 determining a rational and appropriate reference modulus for the use in both fracture mechanics and continuum damage mechanics models by making use of the widely used material property (i.e., dynamic modulus)
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54 Modified Paris' Law with Application of Quasi-Elastic Simulation The modified Paris' law is early proposed as follows (103)
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55 2 2 2 21 1 R I II III R R J K K K E E (4.29) in which RE is determined as the representative elastic modulus; is the Poisson's ratio; IK is the Mode I (opening)
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56 between the modified Paris' law coefficients. Once one of them is known, the other coefficient can be estimated by: 1 .2 46 3 .61510 nA (4.33)
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57 Aggregate gradation characteristics: the particle size distribution, or gradation, of aggregates affects almost every important property of asphalt mixtures, such as stiffness, durability, permeability, fatigue resistance, frictional resistance and moisture susceptibility (144)
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58 Table 4.8. Examples of Values of Fracture Coefficients and Performance-Related Material Properties Segment Data Source and Test Type Fracture Coefficients Performance-Related Material Properties A n 1E (MPa)
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59 parameter, , from the aggregate gradation model in Equation 4.35. This is because when both and are used to perform the multiple regression analysis, the p-value of is larger than 0.05, so the aggregate gradation scale parameter is not a significant variable and excluded from the prediction model.
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60 (b) A' Figure 4.28.
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61 in-place asphalt pavement are the initial damages which cause the local stress concentrations to allow microcracks to grow so that asphalt pavements suffer fatigue from the first loading cycle. Development of Crack Initiation Model Derivation of Crack Initiation Model for a Load Level The pseudo J-integral based Paris' law is used to derive the number of loading cycles for top-down crack initiation.
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62 value of bi is determined to be 0.12. Since WRi is proportional to 2 iP s , ai can be related to the load levels as follows: 2 0 0 i i Pa a P (4.40)
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63 As can be seen, a higher binder content and percentage of passing # 200 sieve with a smaller air void content produces a higher volume of asphalt mastic, which improves the crack resistance in Equation 4.43. It is noted that for different load levels, Ni are different.
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64 2max minmin min max20 0 1 1 2 12 3 3 z h z h z z a aa a z dz a h z dz a a h h h (4.46) Based on the X-ray CT measurement, maxa is about two times as large as mina , the following relationship can be achieved: min 3 4 a a , max 3 2 a a (4.47)
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65 only. The load distribution with the AADTT should be estimated.
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66 For some cases that the WIM data is not available, the AADTT is used to predict the traffic load distribution as the level two input. The default distribution of a major multi-trailer truck route in the Pavement ME Design shown in Table 4.11 is adopted to calculate the number of vehicles in each truck class distribution.
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67 distress data points. To determine the initiation time t0, only the data of the low severity level is used.
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68 where ( ) Et is the relaxation modulus of asphalt mixtures; and E1 and m are the relaxation modulus parameters.
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70 DF Zone WNF Zone R² = 0.8594 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Pr ed ic te d In iti at io n En er gy P ar am et er (N /m ) Calculated Initation Energy Parameter (N/m)
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71 WF Zone Figure 4.32. Comparison of Predicted and Calculated Energy Coefficient 0 02 a A Prediction of Top-Down Crack Initiation Time and Model Validation Once 0 02 a A is determined with the known variables in Equation 4.53, the result can be inserted back to Equations 4.43 to 4.48 to back-calculate the crack initiation time t0.
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72 To validate Equation 4.54, a total of 10 pavement sections in different states for a variety of traffic levels, pavement structures and material properties are selected as the validation pavement sections, which are not used in the model development procedure. The predicted topdown crack initiation time and observed top-down crack initiation time are presented in Figure 4.34.
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73 Numerical Modeling and Artificial Neural Network (ANN) for Predicting J-Integral In this project, the fracture parameter J-integral for the top-down cracking propagation at the crack tips for different crack depths, material properties and pavement structures is determined using numerical model.
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74 (a) Aging Effect (b)
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75 Figure 4.36. Simplified Patterns of 3D Vertical, Longitudinal and Transverse Contact Stresses Table 4.13.
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76 L I Pl P w (4.56) where w is the tire width and l is the tire length.
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77 (a) Vertical Contact Stress (b)
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78 sides of the 3D model are fixed in the x and z directions and the bottom side is fully fixed. Sliding is not allowed between layers.
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79 (a) 3D FE Pavement Model (b)
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80 depth are shown in Figures 4.40 (a)
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81 (a) Different n Values (b)
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82 Artificial Neural Network Modeling of J-Integral Background and Preparation of ANN The task after the finite element modeling is to construct the ANN models for accurately predicting the J-integral of top-down cracks. The ANN models are developed using the commercial program MATLAB.
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83 1 1hk x A e (4.60) where i , j and k are the subscripts for the input layer, first hidden layer and second hidden layer, respectively; m, n and q are the numbers of inputs (i.e., 8)
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84 Figure 4.41. Structure of Artificial Neural Network Figure 4.42.
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85 Figure 4.43. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Dual Tire Loadings with Dual Tire Length of 185 mm Figure 4.44.
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86 Figure 4.45. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Single Tire Loadings with Single Tire Length of 64 mm Figure 4.46.
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87 Figure 4.47. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Single Tire Loadings with Single Tire Length of 406 mm Prediction of Crack Growth under Thermal Loading On the basis of the existing models on pavement temperature, thermal stress, aging, and crack propagation, a top-down cracking propagation model due to thermal loading is developed.
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88 pavement surface, the fraction of reflected solar radiation; Qa is the downwelling long-wave radiation heat flux from the atmosphere; Qr is the outgoing long-wave radiation heat flux from the pavement surface; Qc is the convective heat flux between the surface and the air; and Qf is the heat flux within the pavement at the pavement surface. Prediction of Viscoelastic Thermal Stress The thermal stress in the pavement structure is the result of temperature variation.
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89 where σ (ξ) is the thermal stress at reduced time ξ; E(ξ- ξ')
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90 hidden layer and one output layer. On the basis of the converged mean square error and computation time, 40 neurons are used in the hidden layer.
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91 Prediction of Aged Modulus of Asphalt Mixtures The reference modulus is used as one input of the asphalt concrete layer to the ANN model in Equation 4.68. This reference modulus is the representative elastic modulus (109)
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92 1. Climate data at a specific pavement section.
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93 4) Obtain the material properties data from the LTPP database, including the dynamic modulus data, air void content, binder content, and aggregate gradation.
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94 Figure 4.50. Pavement Temperature versus Time (29-1005, 27-1003, 19-102, and 2-1002 are 4 LTPP pavement sections as listed in Table 4.16)
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95 Figure 4.51. Longitudinal Thermal Stress versus Time Results of Thermal-Related Top-Down Cracking Prior to computing the thermally related top-down crack growth with time, the fracture parameters are determined using the given material properties.
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96 The other two parameters used to compute the fracture parameters are E1 and m in the power law function for the relaxation modulus. The fracture parameters A and n are calculated using the regression functions in Equations 4.33 and 4.36, as presented in Table 4.17.
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97 Figure 4.52. Aged Modulus versus Time After obtaining the pavement temperature and thermal stress, the J-integral is determined using the ANN model.
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98 Computation of Top-Down Cracking Calibration Coefficients In the top-down crack propagation calculation, there are two numbers of days calculated including the number of days for traffic load solely and number of days for thermal load solely to reach a standard depth within an asphalt pavement layer. The standard depth is 15 mm, which is the boundary line between low and medium severity.
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99 Table 4.18 Summary of Calibration Coefficients for Four Climatic Zones Climatic Zone 1 2 1 2 Wet 631.
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