Probabilistic Modeling of the Inherent Variability in the Dynamic Modulus Master Curve of Asphalt Concrete

Abstract

Pavement engineers and practitioners have come to recognize the urgent need to quantify the variability in dynamic modulus, | E*|, because of its influence on the predicted performance of asphalt pavements and to adopt realistic quality assurance or quality control measures associated with pavement construction. The objective of this study was to characterize the inherent variability in | E*| across the full spectrum of the | E*| master curve (fitted with a sigmoidal function for various reduced frequencies). The study analyzed | E*| data from six mixes that included at least eight replicates within a robust probabilistic framework that allowed for a preliminary quantification of uncertainty caused by the inherent variability in | E*|. Monte Carlo simulations were used to propagate the uncertainties of the sigmoidal model coefficients to determine the mean, coefficient of variation, and probability distribution of | E*| as a function of reduced frequency. In addition, the inherent uncertainty in | E*| was propagated through forward modeling to characterize the resulting uncertainty in the predicted rut depth in the asphalt layer for a set of pavement structures. The findings show that the values of the inherent uncertainty of | E*| are relatively small for cases with reduced frequencies that are high but increase dramatically for reduced frequencies that are in the medium to low range. This uncertainty increases as the nominal maximum aggregate size (NMAS) of the mix under investigation increases. It was found that the uncertainty significantly affects the probability distribution of rut depth and implies higher variability for cases of hot weather, slow traffic, or large NMAS.

Development of Probabilistic Viscoelastic Continuum Damage Model for Asphalt Concrete

“…Monte Carlo simulations of each parameter in the sigmoidal function are conducted to provide realistic estimates of the mean and COV of |E*| at specified values of reduced frequencies ranging from 10 −6 to 10 6 Hz. More details about modeling of the uncertainty in |E*| can be found in other references ( 11 , 14 ).…”

“…Quantifying and modeling the uncertainties of the materials’ properties are becoming of high interest to practitioners in the pavement industry ( 7 – 9 ). Recently, some researchers initiated incorporation of reliability in linear viscoelastic (LVE) characterization of asphalt as a precursor to its incorporation in the viscoelastic continuum damage (VECD) model, the focus of the paper at hand ( 10 , 11 ). Basically, through uncertainty quantification, reliability principles provide a set of tools to characterize and account for the precision and consistency of the measurements of inputs required for the VECD modeling.…”

Effect of Asphalt Mixture Components on the Uncertainty in Dynamic Modulus Mastercurves

“…The objective of this paper is to investigate the effect of various factors on the inherent uncertainty quantified for |E*| over the temperature and frequency domain of its mastercurve. The methodology here builds on the framework developed in earlier works (2,6,11) in which the inherent uncertainty was modeled using two probabilistic tools: first order approximation and Monte Carlo simulations. The factors to be assessed in this study include Mixture components, including aggregate gradation, represented by nominal maximum aggregate size (NMAS), usage of additives and what is basically wax as a warm mix asphalt (WMA) additive, and binder type (unmodified binder versus modified binder); Use of deterministic versus probabilistic timetemperature shift factors; and Machine loading and data acquisition.…”

“…The objective of this paper is to investigate the effect of various factors on the inherent uncertainty quantified for | E *| over the temperature and frequency domain of its mastercurve. The methodology here builds on the framework developed in earlier works ( 2, 6, 11 ) in which the inherent uncertainty was modeled using two probabilistic tools: first order approximation and Monte Carlo simulations. The factors to be assessed in this study include…”

“…Even though the asphalt binder constitutes only about 3–7% by weight of the AC mixture, its sensitivity to temperature and loading rate renders the analytical and numerical characterization of AC complex and necessitates experimental testing be done at a wide range of loading rate–temperature combinations. Such conditions can be considered as factors that might affect the inherent uncertainty in various AC properties ( 2 ). In addition, its testing is carried out within protocols that exhibit high variability in instrumentation and equipment from one lab to another ( 3 ).…”