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Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Page 10
Page 11
Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
×
Page 11
Page 12
Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
×
Page 12
Page 13
Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
×
Page 13
Page 14
Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
×
Page 14
Page 15
Suggested Citation:"Chapter 3: Research Plan." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
×
Page 15

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10 CHAPTER 3. RESEARCH PLAN The research plan requires the development and synthesis of eight components to cover the eleven submodels for top-down cracking as mentioned in the previous chapter. The relationship between the components used to develop the corresponding submodels is shown in Figure 3.1. The eight components are: (a) laboratory testing of asphalt field cores for complex modulus gradient and dynamic modulus master curve; (b) kinetics-based modeling of long-term field aging in asphalt pavements; (c) finite element computations of the J-integral at the 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 under thermal stresses; (f) development of a top-down crack initiation model and a micro-crack growth model under traffic loading; (g) generation of a cumulative damage model to predict top-down cracking; and (h) development and calibration of top-down cracking prediction model. Figure 3.1. Proposed Approach to Develop a Complete Mechanistic-Empirical Model for Top-Down Cracking

11 Laboratory Testing of Asphalt Field Cores The research team tests the asphalt field cores with modulus gradient at different aging times using the direct tension test. The purpose is to determine the complex modulus and modulus gradient, and construct the dynamic modulus master curve for field-aged asphalt mixtures. Due to the non-uniform aging nature of the field cores, the mechanical responses are measured at different depths of the specimens. It is found that the tensile strain is smaller on the stiffer side of the sample. The complex modulus is determined using the elastic-viscoelastic correspondence principle and Laplace transform. An inverse approach and iteration are then used to obtain the pseudo strain in order to accurately calculate the modulus gradient parameters. After obtaining the complex moduli of field cores at different temperatures, aging times, and pavement depths, time-temperature-aging-depth shift functions are developed to construct dynamic modulus master curves of field cores. The dynamic modulus master curves at different aging times and pavement depths are constructed using the modified Christensen-Anderson- Marasteanu (CAM) model with the time-temperature shift factor. The long-term aging shift function is determined as a function of activation energy, aging time, and aging temperature. The depth shift function is derived as a function of pavement depth. With the aid of these shift factors and functions, a single dynamic modulus master curve is formed by including the effects of temperature, long-term aging, and non-uniform aging below the pavement surface. Kinetics-Based Aging Modeling The research team makes use of the field core test data and field deflection data to develop kinetics-based aging models for asphalt mixtures. This allows predicting the change of the modulus gradient in the field and long-term field aging characteristics of asphalt mixtures. The proposed model consists of three components for baseline modulus at the standard depth of 1.5 inches (38 mm), the surface modulus, and the aging exponent respectively to define a changing modulus gradient with aging time. The model contains kinetic parameters for asphalt mixtures (e.g. aging activation energy) and combined the fast-rate and constant-rate periods. A number of asphalt field cores at different ages are tested for the modulus gradients, which are used to determine the kinetics-based aging model parameters. To extend the application of the proposed aging model, the research team examines the feasibility of using this model to analyze the field data from Falling Weight Deflectometer (FWD) measurements. The FWD data is the key element in the Long-Term Pavement Performance (LTPP) database. A total of eight pavement sections from the four different climate zones are selected from the LTPP database. For each pavement section, the rheological properties of the asphalt mixture are determined to characterize the temperature dependency of field asphalt mixtures, and the aging properties are determined to characterize and predict the aging of field asphalt mixtures. Finite Element Modeling of J-Integral The finite element program is used to determine the fracture parameter J-integral, which is a critical input to predict the crack growth rate for top-down cracking. The literature review

12 has demonstrated that top-down cracking is affected by various factors, including the complex state of high tensile or shear stresses induced by the traffic loading, material properties such as the modulus gradient in the asphalt layer, moduli of the base and subgrade layers, and pavement structures. Therefore, the finite element modeling to simulate the propagation of top-down cracking should consider different combinations of these essential factors and calculate the J- integral for each case. A three-dimensional finite element model is developed for this purpose. The model contains a user-defined material subroutine (UMAT) to model the modulus gradient. The contact stresses in the model are decomposed into vertical stress, longitudinal stress and transverse stress, which are nonuniformly distributed. Based on the different combinations of all of the variables in the finite element modeling, there are 194,400 cases needed to be determined. Because of the large number of calculations, the technology from SA-CrackPro is utilized to change the values of all the variables in the finite element model automatically. Artificial Neural Network Modeling of J-Integral Based on the database generated from the finite element modeling, six backpropagation ANN models including one input layer, two hidden layers and one output layer are developed using the same input variables and output variable as those used in the finite element model. As a widely used supervised learning algorithm, the backpropagation ANN is chosen in this project, which means that once the network is trained the signal will come back to update the initial weights and bias to reduce the calculation errors. Based on comprehensive comparisons, the gradient descent weight/bias learning function is employed as the learning function in the ANN model. To ensure the convergence and performance of the ANN model, several other model parameters are also considered in the training. Based on the literature and trial and error, the following parameters including the epochs between displays, learning rate, the maximum number of epochs for training, and the performance goal are determined as 0.05, 0.9, 400, 1e-4, respectively. 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 finite element model. Top-Down Cracking Modeling Due to Thermal Loading The mechanistic-empirical approach to predict the top-down cracking under thermal loading is based on the modeling of pavement temperature, thermal stress and ANN of thermal- induced J-integral and thermal crack growth. The climate data used in the model including hourly solar radiation, daily air temperature, and wind speed are collected from the LTPP database and National Climate Data Center (NCDC) database for development of the pavement temperature model. The viscoelastic thermal stress model is developed by the finite difference solution to the viscoelastic constitutive equation based on Boltzmann’s Superposition Principle using the Prony series representation of relaxation modulus. The prediction of top-down cracking propagation under thermal loading in asphalt pavement layer is established by using Paris’ law and computed by programming in the C# language. The fracture coefficients are determined by

13 pavement materials and the thermal J-integral is determined using the ANN model. Aging of asphalt mixture is taken into consideration for prediction of the thermal J-integral. Top-Down Crack Initiation and Growth Modeling Due to Traffic Loading The top-down crack initiation is defined as the stage for microcracks initiate and coalesce into a visible macro-crack at pavement surface. With the aid of J-integral, micro-fracture mechanics and Miner’s hypothesis are first used as the fundamental mechanistic approaches to calculate the numbers of loading cycles at different load spectrum levels and the corresponding cumulative damage in the initiation phase. A prediction model for air void distribution within asphalt layer is developed based on the X-ray Computed Tomography (X-ray CT) measurement since the air voids are initial flaws in asphalt mixtures especially for the pavement surface. The LTPP data including traffic loads, pavement distresses, material properties, pavement structures and environmental effects are collected and analyzed for 60 pavement sections distributed in different climatic zones. Traffic load is characterized using the load spectra model and the top- down crack initiation time is predicted from historical distress observations for each pavement section. The collected LTPP data are utilized to develop the prediction models for the energy parameter and top-down crack initiation time. The Annual average daily truck traffic (AADTT), unaged modulus, environmental effects and pavement structure are the key factors for the energy parameter. Unaged modulus, AADTT, energy parameter and air void content are critical to the top-down crack initiation time. The research team uses the pseudo J-integral based Paris’ law to predict crack propagation of top-down cracking. To facilitate the application and implementation of the pseudo J-integral based Paris’ law, two techniques have been developed. The first technique, quasi-elastic simulation, provides a rational and appropriate reference modulus for the pseudo analysis (i.e., viscoelastic-to-elastic conversion) by making use of the widely used material property: dynamic modulus. Introduction of this technique facilitates the implementation of the fracture mechanics models as well as continuum damage mechanics models to characterize fracture in asphalt pavements. The second technique about modeling fracture coefficients of the pseudo J-integral based Paris’ law simplifies the prediction of fatigue cracking without performing fatigue tests. The developed prediction models for the fracture coefficients rely on readily available mixture design properties that directly affect the fatigue performance, including the relaxation modulus, air void content, asphalt binder content, and aggregate gradation. Sufficient data are collected to develop such prediction models. Cumulative Damage Modeling for Top-Down Crack Growth The candidate cumulative damage models utilizes the observed crack initiation time and the observed crack length data to calibrate the calculated crack depth and downward crack propagation data for the fracture mechanisms. The general shape of the field top-down cracking data with different severity levels and crack initiation time is obtained from the LTPP database. It is found from the LTPP database that much less data on the length of medium and high severity top-down cracking is available. This is probably because when top-down cracks

14 progress beyond the low severity stage, they become connected with small transverse cracks and identified with alligator cracking. The developed top-down cracking model predicts the development of a crack downward from the pavement surface. The predictions are calibrated to the observed field distress data to develop the calibration coefficients. The field distress data have different severity levels, depending on the width of a surface longitudinal crack. As a result, the following relationships are developed in the project for the purpose of the calibration: surface crack width versus crack depth, distress severity versus surface crack width, and crack shape versus crack depth. These relationships are documented in Appendix J, an example of the crack width versus crack depth given in Figure 3.2. Such a relationship is used to determine the transitions between low, medium and high severity distresses. Figure 3.2. Plot of Crack Shape versus Crack Depth of a Top-Down Crack Data Collection for Model Development and Calibration The research team has assembled the known descriptions of top-down cracking from the technical literature, field observations, accelerated test sections, and test tracks to determine those pavement conditions and structures that promote top-down cracking. From a synthesis of this work (Appendix E), a set of criteria are developed in the search for top-down cracking data:  Distress criterion;  Thickness criterion;  Climate criterion; and  Stabilization criterion. The distress criterion identifies which type of pavement distress forms top-down cracking. It is widely accepted that top-down cracking is the longitudinal wheel path cracking. There are also researchers believing that top-down cracking starts as longitudinal cracks, and eventually deteriorates into an extensive network of longitudinal cracks connected by short transverse cracks. The thickness criterion identifies which type of pavement structure that most likely 0 20 40 60 80 100 120 ‐6 ‐1 4 9 Cr ac k  De pt h  (m m ) Crack Width (mm) 1 mm 3 mm 6 mm 10.6 mm 1 mm crack shape 3 mm crack shape 6 mm crack shape 10.6 mm crack shape

15 suffers top-down cracking. The literature review conducted identifies the pavement structure that most likely suffers top-down cracking. It indicates that top-down cracking is observed in both thin and thick asphalt layers. The climate criterion is used to ensure that the collected top-down cracking data covers nationwide geographic and climatic conditions. The climatic conditions of each pavement section needs to be taken into account to develop pavement temperature submodels for the final top-down cracking model. The U.S. is split into the characteristic four climatic zones: 1) wet-freeze (WF); 2) dry-freeze (DF); 3) wet no-freeze (WNF); and 4) dry no- freeze (DNF). The stabilization criterion is used to discriminate top-down cracking from other surface cracking based on the type of base course. Distinction needs to be made between lime or cement stabilized base courses and bituminous stabilized base courses. Two types of pavement surface distresses are generated due to over-stabilization: block cracking and Y-cracking, which should be excluded from top-down cracking. Therefore, even though longitudinal cracks or a network of longitudinal cracks with transverse cracks are recorded in the database, the data should be discarded if the base course is over-stabilized by the lime or cement.

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TRB's National Cooperative Highway Research Program (NCHRP) Web-Only Document 257: A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers develops a calibrated mechanistic-empirical (ME) model for predicting the load-related top-down cracking in the asphalt layer of flexible pavements. Recent studies have determined that some load-related fatigue cracks in asphalt pavement layers can be initiated at the pavement surface and propagate downward through the asphalt layer. However, this form of distress cannot entirely be explained by fatigue mechanisms used to explain cracking that initiates at the bottom of the pavement. This research explores top-down cracking to develop a calibrated, validated mechanistic-empirical model for incorporation into pavement design procedures.

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