Nonlinear Weighted Directed Acyclic Graph and A Priori Estimates for Neural Networks

In an attempt to better understand structural benefits and generalization power of deep neural networks, we firstly present a novel graph theoretical formulation of neural network models, including fully connected, residual network (ResNet) and densely connected networks (DenseNet). Secondly, we extend the error analysis of the population risk for two layer network \cite{ew2019prioriTwo} and ResNet \cite{e2019prioriRes} to DenseNet, and show further that for neural networks satisfying certain mild conditions, similar estimates can be obtained. These estimates are a priori in nature since they depend sorely on the information prior to the training process, in particular, the bounds for the estimation errors are independent of the input dimension

Crack initiation in asphalt mixtures under external compressive loads

Crack initiation was studied for asphalt mixtures under external compressive loads. High tensile localized stresses e direction of the external loads. A quantitative crack initiation criterion the edges of compressed air voids lead to the growth of wing cracks in thon was derived using pseudostrain energy balance principle. Bond energy is determined and it increases with aging and loading rate while decreases with temperature. Cohesive and adhesive cracking occur simultaneously and a method was proposed to determine the individual percentage. The crack initiation criterion is simplified and validated through comparing the predicted and measured compressive strength of the asphalt mixtures

Implementation of pseudo J-integral based Paris’ law for fatigue cracking in asphalt mixtures and pavements

Pavement analysis and design for fatigue cracking involves a number of practical problems like material assessment/screening and performance prediction. A mechanics-aided method can answer these questions with satisfactory accuracy in a convenient way when it is appropriately implemented. This paper presents two techniques to implement the pseudo J-integral based Paris’ law to evaluate and predict fatigue cracking in asphalt mixtures and pavements. 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. The physical significance of the quasi-elastic simulation is clarified. Introduction of this technique facilitates the implementation of the fracture mechanics models as well as continuum damage mechanics models to characterize fatigue cracking 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 and the R2 values are around 0.9. The presented case studies serve as examples to illustrate how the pseudo J-integral based Paris’ law predicts fatigue resistance of asphalt mixtures and assesses fatigue performance of asphalt pavements. Future applications include the estimation of fatigue life of asphalt mixtures/pavements through a distinct criterion that defines fatigue failure by its physical significance

Prediction of geogrid-reinforced flexible pavement performance using artificial neural network approach

This study aimed to develop a methodology to incorporate geogrid material into the Pavement ME Design software for predicting the geogrid-reinforced flexible pavement performance. A large database of pavement responses and corresponding material and structure properties were generated based on numerous runs of the developed geogrid-reinforced and unreinforced pavement models. The artificial neural network (ANN) models were developed from the generated database to predict the geogrid-reinforced pavement responses. The developed ANN models were sensitive to the change of base and subgrade moduli, and the variation of geogrid sheet stiffness and geogrid location. The ANN model-predicted geogrid-reinforced pavement responses were then used to determine the modified material properties due to geogrid reinforcement. The modified material properties were finally input into the Pavement ME Design software to predict geogrid-reinforced pavement performance. The ANN approach was rapid and efficient to predict geogrid-reinforced pavement performance, which was compatible with the Pavement ME Design software

Kinetics-based aging evaluation of in-service recycled asphalt pavement

Reclaimed asphalt pavement (RAP) is a type of material that already suffers long-term aging in the field, so its aging characteristics become prominent since they are closely related to premature distresses and longevity of recycled pavements. While most of investigations of RAP mixtures are carried out in the laboratory, this study focuses on in situ aging of asphalt pavements with RAP overlays. A kinetics-based aging modeling approach is proposed to analyze and quantify long-term field aging of RAP overlays using the Falling Weight Deflectometer (FWD) data and climate data. The kinetics-based approach contains a modulus aging model with kinetic parameters (e.g. aging activation energy) for asphalt mixtures. Eight asphalt overlays are selected with different mixtures (RAP and virgin), thickness (50 mm and 125 mm), and surface preparation (milling and no milling). An asphalt pavement with an overlay has a composite aging process since the aging speeds of different asphalt layers are different. Thus an approach to separate the FWD modulus is developed in order to obtain the actual aging behaviors and properties of the overlay. By applying the kinetics-based modeling to the separated FWD moduli, the aging activation energies of both the overlays and old asphalt layers are determined. It is found that the RAP overlay has the highest aging activation energies and slowest aging rates among the RAP overlay, virgin overlay, and old asphalt layer for the selected pavements. It also reveals through the aging activation energy that the thick overlays age slower than thin ones, and the overlays on milled pavements age slower than those placed without milling. The findings in terms of the aging activation energy can be used to explain the difference in the field performance of overlay pavement sections

Mechanistic-empirical models for better consideration of subgrade and unbound layers influence on pavement performance

It has been reported that the pavement performance predicted by the current mechanistic-empirical pavement design shows low or no sensitivity to subgrade and unbound layers. This issue has raised wide attention. Targeting this problem, this paper summarizes the process used by the authors to find better models of the influence of subgrade and unbound base course layers on the performance of flexible and rigid pavements. A comprehensive literature review is first conducted and the findings are categorized. It is found that the resilient modulus, permanent deformation, shear strength, and erosion are key factors. In particular, the properties that provide greater sensitivity are 1) the moisture-dependency of the modulus, shear strength, and permanent deformation; 2) stress-dependency of the modulus and permanent deformation; and 3) cross-anisotropy of the modulus. A number of unbound layer/subgrade models have been located and categorized. Three criteria are developed to identify the candidate models in terms of the degree of susceptibility, degree of accuracy, and ease of development. The first two criteria are used to evaluate the collected unbound layer/subgrade models, while associated development and implementation issues are planned as subsequent work. Two models that the authors previously developed are selected as examples to illustrate the improvement of the performance prediction, including the moisture-sensitive, stress-dependent, and cross-anisotropic modulus model for unbound layers and stress-dependent mechanistic-empirical permanent deformation model for unbound base layers. These two models are verified through laboratory tests and numerical simulations. Moreover, they are compared to their counterparts in the AASHTOWare Pavement ME Design. The advantages of accuracy and sensitivity to the operational conditions (e.g. moisture, traffic stress, and load-induced/particle-induced anisotropy) are obvious. In addition to these two models, the development of the shear strength model and erosion model are sketched. The candidate models need further development and implementation, which address issues such as hierarchical inputs, calibration/validation, and implementation. These are the on-going and planned work on this topic to better incorporate the influence of subgrade and unbound layers so as to contribute to the improvement of pavement designs