Journal of Materials in Civil Engineering

A micromechanical model for the steady-state deformation of idealized asphalt mixes is presented. Triaxial compression tests were conducted on idealized asphalt mixes and the volumetric and deviatoric strains were measured. The specimens were observed to dilate under compressive stresses and the deformation behavior was seen to be dependent on the hydrostatic as well as the deviatoric stresses. A simple model for the nonlinear viscous steady-state behavior of idealized mixes is presented based on a “shear box” analogy. Predictions of the model are seen to agree well with experimental measurements for a wide range of conditions. An upper bound is calculated for the steady-state deformation rates within a plane strain half space comprising the idealized asphalt mix subject to a uniform pressure over a finite contact strip. The deformation rate varies nonlinearly with the applied load and is strongly dependent on the hydrostatic stress. Further, the deformation rate is seen to be a maximum at a position about half a contact length below the surface of the half space. These findings are in general agreement with wheel tracking experiments on these idealized mixes.

Asphalt concrete is a heterogeneous material composed of aggregates, binder cement, and air voids, and may be described as a cemented particulate system. The load carrying behavior of such a material is strongly related to the local load transfer between aggregate particles, and this is taken as the microstructural response. Simulation of this material behavior was accomplished using a finite element technique, which was constructed to simulate the micromechanical response of the aggregate/binder system. The model incorporated a network of special frame elements with a stiffness matrix developed to predict the load transfer between cemented particles. The stiffness matrix was created from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. A damage mechanics approach was then incorporated with this solution, and this lead to the construction of a softening model capable of predicting typical global inelastic behaviors found in asphalt materials. This theory was then implemented within the ABAQUS finite element analysis code to conduct simulations of particular laboratory specimens. Experimental verification of the elastic response has included tests on specially prepared cemented particulate systems, which allowed detailed measurement of aggregate displacements and rotations using video imaging and computer analysis. Model simulations compared favorably with these experimental results. Additional simulations including inelastic behavior of laboratory indirect tension tests have been conducted, and while preliminary in nature these results also compared well with experimental data.

This paper describes the use of the displacement discontinuity boundary element method to model the microstructure of asphalt mixtures. The problem of indirect tension test (IDT) was used to demonstrate the application of the method in the modeling of the cracking behavior of asphalt mixtures. An IDT sample was modeled by three sets of displacement discontinuity boundary elements based on location and function: (1) on the periphery of the specimen, (2) inside the specimen to represent the aggregate structure, and (3) internal fracture path elements inside the aggregate structure. The mastic was modeled by a nonlinear failure law. The simulation of the cracking behavior of the IDT test with this method showed a good agreement with laboratory observations. The predicted stress–strain curves matched the experimental results for both vertical compressive stress and horizontal tensile stress. Crack patterns from these simulations were also similar to the patterns observed visually in the laboratory. In summary, explicit fracture modeling has shown promise as a tool for studying the crack growth and localization of asphalt mixtures.

The dynamic shear rheometer (DSR) is used to characterize linear viscoelastic properties of asphalt cement and asphalt mastic (asphalt cement with a filler that is smaller than 75 μm in size). The study focuses on using micromechanical and rheology-based models to assess the effect of two fillers, limestone and hydrated lime, on the performance of the asphalt mastic. Two distinctly, compositionally different asphalt cements were selected to assess the filler effect. Micromechanical models were reviewed, and the most appropriate of these models were used to characterize the viscoelastic behavior of the asphalt mastic (composite). Since the micromechanical models are developed for elastic materials, it was necessary to use the elastic–viscoelastic correspondence principle in order to apply these models. The literature was also reviewed for the most appropriate rheology-based models to account for the effect of fillers in the mastic. The Nielsen model was selected since it employs two rheological parameters to explain the filler effect: the generalized Einstein coefficient and the maximum filler packing fraction. The micromechanical models show good agreement with testing data at low particle volume concentration. The rheological model can successfully predict the stiffening effect of limestone filler when added up to 25% by volume. However the effect of hydrated lime requires a more specific understanding of the substantial surface interactions, which are highly binder specific.

The paper at hand presents a methodology for analyzing the viscoelastic behavior of asphalt concretes, whose microstructure is captured through two-dimensional imaging techniques. The paper describes the viscoelastic behavior of the binder through mechanistic models fitted to rheological data obtained at different strain levels. The resulting binder stress–strain behavior is computed through a convolution integral approach and implemented into a subroutine defining material behavior in a commercially available finite element program. The use of a convolution integral approach is shown to facilitate incorporating the binder nonlinear viscoelatic behavior in the analysis of the asphalt concrete microstructure response. This is conducted by assigning the binder model constants as a function of strain level. The model is tested by comparing asphalt concrete shear modulus $G^{*}$ predictions to earlier predictions obtained with a generalized piecewise linear viscoelastic model, as well as measurements obtained with a simple shear tester. The model is used to explain some of the discrepancies observed between experimentally obtained axial and shear dynamic moduli.

The microfabric discrete element modeling (MDEM) approach is used herein to predict the asphalt mixture complex modulus in extension/compression across a range of test temperatures and load frequencies. The method allows various constitutive models to be employed to describe particle and interface properties, such as normal and shear stiffness and strength. An uncalibrated two-dimensional (2-D) model was developed, and complex modulus predictions were compared to theoretical bounds on moduli. As expected, the uncalibrated 2-D model underestimates the significant stiffening effects of the coarse aggregate skeletal structure and predictions are found to be near the lower theoretical bounds, well below experimentally determined moduli. A technique was developed to calibrate the MDEM model to experimental results by dilating aggregates to create additional aggregate contact, which is believed to be more representative of the actual three-dimensional behavior. This method is shown to provide better modulus estimates across a range of test temperatures and load frequencies compared to more traditional calibration methods. As future modeling efforts are extended to three dimensions, the degree of model calibration required should be greatly reduced.

Asphalt mixtures exhibit both temperature and rate dependencies. Most current constitutive models used in design and prediction of the performance of asphalt pavements do not incorporate both characteristics into their equations. Therefore, they do not effectively reflect the actual pavement responses under traffic loads and environmental conditions. This paper presents a temperature dependent viscoplastic model that incorporated temperature and loading rate into the Hierarchical Single Surface plasticity based model. The model presented in this paper was able to reflect the nonlinear plasticity, as well as the temperature and loading rate dependencies of the asphalt mixtures. Triaxial compression, triaxial extension, and axial creep tests at three temperatures (28, 40 and 60°C) were performed to calibrate the material properties. A comparison of numerical analysis obtained from the proposed model and experimental results was conducted based on the algorithm proposed by the writers. A reasonable agreement was observed from the back calculation and the experimental results. Further studies of the applicability of this model in predicting pavement performance were recommended.

The response of an asphalt concrete pavement to external loading depends on its internal structure. Using a recent framework that associates different natural configurations (for example, stress-free configurations) with distinct internal structures of the body, we model asphalt concrete. We assume asphalt concrete to be a mixture of an aggregate matrix and an asphalt mortar matrix with evolving natural configurations. The evolution of the natural configuration is determined using a thermodynamic criterion, namely, the maximization of the rate of dissipation. Appropriate choices for the Helmholtz potential, the rate of dissipation and the other thermodynamic criteria are assumed to describe how energy is stored, the manner of the rate of dissipation, etc. As an example, we choose a specific form for the Helmholtz potential and the rate of dissipation function that leads to a generalized “upper convected Burgers’s model,” its linearized version being the viscoelastic model that is usually used for modeling asphalt concrete. This model is just an example of how a class of thermodynamically consistent models can be generated to describe the nonlinear behavior of materials such as asphalt concrete. We model the uniaxial compressive and tensile creep of asphalt concrete for two different types of specimens and test methods. We provide details of the numerical scheme we use to solve the initial value problem and we compare the experimental data of Monismith and Secor in 1962 with predictions of the model.

Asphalt concrete is a heterogeneous mixture of three constituents of asphalt binder, aggregate, and air void. The local volume fractions of these constituents vary spatially and therefore result in the spatial gradients of the local volume fractions. The local volume fractions and their spatial gradients are important field variables in mixture theory that predicts the mixture behavior out of the structure of the mixture and the properties of the constituents. In this paper, the fundamentals of mixture theory and a general method for solving boundary value problems using mixture theories were presented. A simplified mixture theory for two-constituent mixtures of solids and air voids was proposed to model the initial stress distribution of asphalt concrete under static loading. The analytical solutions of simple two-dimensional (2D) and one-dimensional (1D) cases using the simplified theory were obtained to illustrate how this theory predicts the effective stress distribution of a heterogeneous mixture. Methods to quantify the two field variables of the mixture theory, namely the local void volume fraction and its gradient, are developed using x-ray tomography imaging. The quantified void local volume fraction and its gradient for the specimens of mixes with known performance indicated a promising perspective for using mixture theory to evaluate the mechanical properties of asphalt concrete.

Pavement cracking can be considered to be an irreversible step-by-step fracturing process induced by cyclic truck load applications. Hence, pavement crack propagation depends primarily on the accumulated axle loads (ESALs) and also on asphalt mixture stiffness and fatigue characteristics as well as pavement support conditions. This paper presents a model which can predict the distribution of longitudinal surface initiated wheel path crack depths in a family of in-service pavements based on cumulative ESALs. To formulate the primary model, the crack depth versus cumulative ESAL relationship throughout any construction cycle of a given pavement is analytically represented. Pavement failure is tracked by terminal crack indices on record in the Florida Dept. of Transportation’s pavement management database. The random variation of ESALs needed for any given pavement family to reach a specified crack depth is determined based on the variation of life spans of its members and the above analytical relationship. Then, a Markov model is utilized to predict the probability distribution of crack depths at any given cumulative ESAL count. The transitional probabilities associated with specific crack stages are evaluated from the above determined ESAL statistics. A stochastic relationship is also developed between the crack width/depth ratio and cumulative ESALs based on measurements obtained from a large number of core samples. The secondary model can be used to further refine the initial crack depth predictions by utilizing crack width measurements and Bayesian estimation. Model predictions are validated using measured data from field core samples. Finally, it is illustrated how the above models can be used to improve estimation of pavement milling depths prior to rehabilitation.