A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers (2018)

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109 CHAPTER 6. CONCLUSIONS AND SUGGESTED RESEARCH Summary A mechanistic-empirical top-down cracking model is developed in this project. The model consists of seven developments that cover mixture material properties, mixture aging, traffic traction stress, traffic load spectrum, pavement temperature, thermal stress, crack initiation, crack propagation, finite element analysis, Artificial Neural Network models, and cumulative damage. The seven developments used in this project are: (a) laboratory testing of asphalt field cores for complex modulus gradient and master curve; (b) kinetics-based modeling of long-term field aging in asphalt pavements; (c) finite element computations of the J-integral at crack tip; (d) use of the finite element program to develop full factorial sets of pavement data to construct Artificial Neural Network (ANN) models for the J-integral at the crack tip; (e) prediction of top-down cracking due to thermal loading based on the J-integral; (f) development of a top-down crack initiation model and a crack propagation model under traffic loading; and (g) calibration of the top-down cracking propagation model. These developments resulted in a total of 11 submodels that have been integrated into the final top-down cracking subprogram. The major findings drawn from these approaches are summarized as follows. Laboratory Testing of Asphalt Field Cores 1. Modulus gradient is a key input for modeling top-down cracking. An inverse approach with an iteration process for field cores is used to determine the modulus gradient of asphalt field cores using the pseudo strain concept. The relaxation modulus and reference modulus are determined to calculate the pseudo strain. The pseudo strain is calculated by iteration to determine the accurate results of n and k, and dynamic modulus. 2. Dynamic modulus master curve is constructed using the modified Christensen-Anderson- Marasteanu (CAM) model. The two CAM model parameters (i.e., glassy modulus and rheological index) are found to be functions of aging time, both of which are used as the aging parameters; 3. Construction of a single dynamic modulus master curve which includes the effects of aging requires the following shifts:  Horizontal time-temperature shift  Vertical shift of the glassy modulus with age  Rotation of the master curve by modifying the rheological index with age  Horizontal aging time-aging shift  Vertical aging-depth shift 4. After the determination of the vertical shift and rotation of the master curve with aging, the modified dynamic modulus master curves at other aging times can be shifted horizontally to the master curve at the reference aging time using the horizontal aging shift factor. The horizontal aging shift factor is similar to and as effective as the time- temperature shift factor; 5. The horizontal aging shift factor is found to be a function of aging time, activation energy, and aging temperature. The aging time effect is modeled as a power law function

110 and the aging temperature effect is determined based on the Arrhenius equation. The acceleration factor A is a measure of the laboratory accelerated aging relative to field aging. An A-value of 5.6 was measured in this project, indicating that laboratory aging had the effect of 5.6 such times aging in the field. 6. The depth shift factor is developed as a function of pavement depth to account for the non-uniform aging for the field-aged asphalt mixtures. With the aid of the depth shift factor, the dynamic modulus master curve at a given depth can be obtained when the dynamic modulus master curve at the reference depth is known; and 7. A final master curve is constructed considering the effects of temperature, long-term aging and non-uniform aging for the field-aged asphalt mixtures. This model can be used for design computations as well as for forensic investigation of an in-situ asphalt pavement. Kinetics-Based Modeling of Long-Term Field Aging  A complete kinetics-based aging prediction model for the field aging gradient is composed of three submodels: baseline modulus aging submodel, surface modulus aging submodel, and aging exponent submodel. They define how the modulus changes with age and with the depth in an asphalt pavement.  The proposed kinetics-based aging prediction model makes use of parameters such as aging activation energy and the pre-exponential factor of asphalt mixtures for the baseline modulus, surface modulus, and aging exponent, respectively.  Laboratory measured modulus gradients of 29 field cores are used to determine the aging parameters of the proposed model. The predictions match well with the measurements, and the calculated aging parameters are verified.  Asphalt mixtures have aging activation energies that are somewhat lower than the activation energies of their constituent binders because of the interaction between the binder and aggregates and the impact of air voids.  Field aging of asphalt mixtures consists of a fast-rate period and a constant-rate period. The end of the fast-rate period, or the beginning of the constant-rate period must be accurately identified in order to model these two periods and determine the associated aging parameters separately. The fast-rate period for asphalt mixtures in the field occurs during mixing.  Field aging of the modulus gradient of asphalt mixtures must consider the effects of temperature and age at the same time. The temperature dependence of an asphalt mixture at a given age is quantified by the rheological activation energy in the form of an Arrhenius equation. The rheological activation energy varies with the type of asphalt binder, and it significantly increases as the aging time increases.  The LTPP database is a comprehensive and convenient source to obtain the field moduli over a long aging period. When the backcalculated FWD moduli data are used in the modeling, the rationale and variations of the data should be taken into account.  The speed of field aging of an asphalt pavement depends on the binder type, aggregate type, air void content, pavement depth, aging temperature, and aging time, which are all considered in the aging prediction model.

111 Finite Element Computation and ANN Modeling of J-Integral  The J-integral is not uniformly distributed within the depth of an asphalt layer. Specifically, there is a peak value at approximately one third of the layer thickness, after which it decreases. This means that a top-down crack can propagate fast near the pavement surface until reaching the peak point, after which it will slow down.  A UMAT subroutine is developed in the ABAQUS computer system to characterize the modulus gradient in an asphalt layer. The calculation results indicate that the modulus gradient is an important factor contributing to the propagation of a top-down crack. The modulus gradient induced by aging and temperature should always be included in the pavement analysis.  The developed ANN models have been proven to be efficient tools and the prediction accuracy is remarkably high. Once the ANN models are developed, users can input the parameters of the pavement structures and material properties to predict the J-integral without reconstructing the 3D FEM model. Prediction of Crack Propagation by Pseudo J-Integral Based Paris’ Law  The quasi-elastic simulation provides a way to conduct correspondence principle analysis (i.e., elastic to viscoelastic conversion) for damage using the basic viscoelastic property: dynamic modulus or relaxation modulus. The representative elastic modulus formulated by the dynamic modulus and relaxation modulus is assigned as the reference modulus when calculating the pseudo strain or pseudo energy. The physical significance of using the representative elastic modulus is that pseudo strains are real strains.  The prediction of top-down fatigue cracking makes it possible to estimate the damage density or crack size through the modified Paris’ law without performing simulative fatigue tests. The modified Paris’ law replaces the conventional stress intensity factor/J- integral with the pseudo J-integral, which is easily obtained via the quasi-elastic simulation. The modified Paris’ law coefficients, normally determined from cyclic load tests, are estimated using the prediction models formulated with the performance-related material properties, including the relaxation modulus, air void content, asphalt binder content, and aggregate gradation. Sufficient data are collected to develop such prediction models and the R-squared values are around 0.9. Prediction of Crack Initiation by Pseudo J-Integral Based Paris’ Law  The top-down crack initiation phase is defined as multiple microcracks which initiate in the air voids and coalesce into a visible macro-crack at the surface. Damage density instead of a single crack is used in the initiation phase.  Air voids distribution and air void content at the pavement surface are predicted using a parabolic model and is one of the most important factors in the top-down crack initiation.  The load spectra model is used to account for different load levels, which is critical in the Miner’s hypothesis and calculation of cumulative damage. The top-down crack initiation time is predicted using the field observations.  The AADTT, unaged modulus, environmental factors including annual number of days above 32°C (i.e., aging and high temperature effect) and annual number of days below 0°C (i.e., thermal effects), and pavement structures are the key factors to the energy

112 parameter in the crack initiation model. The unaged modulus, AADTT, energy parameter and air void content are critical to predict the top-down crack initiation time.  The prediction models are validated and agree generally well with the field observations, and a similar approach can be directly applied for local top-down crack calibration. Prediction of Crack Growth under Thermal Loading  The mechanistic-empirical top-down crack prediction model under thermal loads is implemented into computer program using Visual Studio C# language and is applicable to a wide range of pavement sections in a variety of climates.  The developed ANN model for predicting the thermal J-integral is a computationally efficient tool and has remarkably high prediction accuracy. The thermal J-integral can be calculated directly by the developed ANN model with inputs including pavement structure and material properties instead of being calculated with a FEM model.  Top-down cracking is not strongly influenced by thermal loads, but some pavement sections in the wet-freeze climate zone received substantial damage from thermal loading.  Once thermal loads become a dominant factor in the growth of top-down cracking, the crack can grow rapidly due to a large temperature change. Prediction of Calibration Coefficients and Distress Curve  The pre-fatigue life which is defined as number of months to reach the boundary line between low and medium severity levels after initiation is computed for each LTPP section using a computer program developed with the C# language, and the scale factor  and shape factor  are calculated based on the historical data for each LTPP section;  Regression analyses are applied to relate the pre-fatigue life to the scale factor and the shape factor, respectively;  The prediction models for top-down crack initiation time, scale factor and shape factor can be used to plot the top-down cracking length distress curve if the material properties, pavement structures, climatic data and traffic information are available. Suggested Research In composing the models developed in this study into the top-down cracking program, the fracture and aging properties of asphalt mixtures have been included. The fracture properties were divided into two parts: one is the simultaneous growth of a large number of microcracks that leads to the initiation of a single crack, and the other is the growth of that single crack downward into the pavement structure. The fracture properties that have been used are from several sources and test methods. It is found that the formation of the fracture properties was able to generate a good consistency in these fracture properties and the fracture properties for macrocracks are slightly different. The effect of aging into both sets of fracture properties has been incorporated but did not consider the effect of healing. Healing is adversely affected by aging of asphalt mixtures. The principle contribution occurs in the microcracking stage and the

113 model of the crack initiation time achieved an R-squared value above 0.8. This can still be increased further by including the effect of healing of asphalt mixtures. In all of the investigations that have been conducted in this project, it is realized that there is a direct connection between the appearance and growth of low severity top-down cracking and appearance and growth of medium severity alligator cracking. The observations of the LTPP data indicate that the low severity top-down cracking diminishes, which is replaced by the accumulation of medium severity alligator cracking. Future work in this regard should confirm and establish the connection of low severity top-down cracking as the precursor of the medium severity alligator cracking. The transverse thermal stress does not play a significant role in the development of top- down cracking. The program for calculating the transverse thermal stress included the effect of aging in downward crack propagation due to thermal stresses. As such this program may be proven to be useful in predicting longitudinal thermal stress and transverse thermal cracks. In the future, the traffic load spectrum used in the Pavement ME Design should follow the form that has been incorporated into this program. It includes the results of South African tire contact pressure research. The load spectrum model used in this program used a standard tire. Future work should construct the load spectrum using other tire types that were investigated in the South African study. Continued collection of the field data from the LTPP program is highly desirable. The calibration models used in this program would be materially improved with a greater number of data points on the pavement sections used in this study as well as many others.