Pavements and Materials: Testing and Modeling in Multiple Length Scales

While the Superpave binder-specification system successfully introduced laboratory-measured performance parameters, the constitutive stress-strain relationship of asphalt binders should be described. The availability of a computationally efficient constitutive relationship would allow to improve the accuracy of predicting the response of asphalt binder to loading and to characterize its viscoelastic properties as well as its relationship to mix performance. To this end, the objective of this study was to provide a theoretical insight into the mechanical behavior of unmodified asphalt binder at low temperatures and to present a constitutive model that may be used to predict asphalt binder's response to loading. To achieve this objective, nine unmodified binders obtained from two asphalt suppliers were tested using the direct tensile test (DTT). A viscoelastic model was formulated and fitted to laboratory measurements obtained at different loading rates. Fitting parameters were then incorporated into a 2D FE model representation of the DTT sample and comparison was established between measured and calculated stress responses. This comparison indicated that the adopted Generalized Kelvin Model is adequate in describing the stress-strain relationship of asphalt binder at low temperatures.

Molecular dynamic simulation is employed to determine the thermodynamic properties of asphaltene before and after oxidative aging. The asphaltene structure used in MD simulation is a moderate size aromatic core with larger branches. For oxidative aging, the amount of oxygen considered are – 0.1%, 1%, 12%, 23% and 46.5% of total number of asphaltene atoms. Thermodynamic properties calculated from atomistic molecular simulations of asphaltene include density, glass-transition temperature and potential energy. It is shown that density increases with the increase in oxidation level up to 2.5%, and then it decreases. Density has an inverse relationship with temperature. At high temperature, density decreases as temperature increases because at high thermal energy the molecules are largely unassociated and mobilized. Glass transition temperature (T_g) is calculated from the characteristics of density vs. temperature plots. Unaged asphaltene shows a glass transition temperature of 273 K (0 °C). T_g of asphaltene decreases at highly oxidized state (> 20%). Variation of T_g as a function of oxidation can be useful in the study of hardness, brittleness, stiffness, viscosity of asphaltene. The kinetics of asphaltene aging is shown to be affected by oxidation rate and temperature. At low oxidation level, density-aging time relationship is hyperbolic and at the high oxidation level, it is nearly linear.

Computational models at varying length scales are currently being used to improve our understanding of the behavior and performance of asphalt mixtures. The accuracy of these computational models is highly dependent on the use of accurate constitutive relationships and material constants. Typical computational models at the mastic and mortar length scale comprise asphalt binder as the matrix and aggregates as the inclusion. For such models asphalt binder is typically modeled as a linear viscoelastic material with material constants that are typically obtained using a Dynamic Shear Rheometer (DSR). This paper presents a review of the tests methods and models that are used to characterize asphalt binders. This section also includes a review of the nonlinear viscoelastic response of asphalt binders. The second part of this paper investigates in more detail the potential sources for the nonlinear response of asphalt binders and models that can be used to represent this response. A DSR was used to measure the response of asphalt binders subjected to creep-recovery at multiple stress levels and sinusoidal loading at different stress amplitudes, using parallel plate and cone and plate geometries. In addition to the shear stress and strain, the normal stress was also recorded and used in the analysis of the test results. Preliminary results indicate that asphalt binders demonstrate a nonlinear viscoelastic response even at low stress levels due to the biaxial stress state. Test data is presented to demonstrate and verify this form of nonlinear response, which is also referred to as interaction nonlinearity.

Asphalt binder and mineral aggregates constitute the building blocks of asphalt concrete as pavement materials. An important trait of these materials is that they display highly characteristic hierarchical structures across multiple scales from nano to macro. Asphalt and aggregates are intriguing examples of materials that balance multiple tasks, representing some of the coarse/fine frame and stick solutions that integrate structure/function. This paper presents nanoscale modeling to investigate the mechanical properties of asphalt/mineral materials to investigate structure-property relations. The atomistic simulation provides a powerful approach in studying mechanical properties of asphalt concrete materials. The molecular origin of mechanical processes of two minerals and two asphalt mix models are demonstrated in this paper. Elastic constants of bulk quartz and calcite, as well as thermodynamic quantities of two asphalt molecular structures are all calculated. The simulation results indicate that the characteristics of bitumen are determined by both the constitution (chemical composition) and the structure (physical arrangement) of the molecules in the bitumen. Changes to the constitution, structure or both will result in a change to the thermodynamic and mechanical properties. In addition, viscosity and cohesive energy density of asphalt molecular models are both temperature dependent quantities. Furthermore, the highly anisotropic elastic properties of mineral structure appear at atomic scale. The elastic constants from atomistic simulation have both positive and negative values, as well as the non-diagonal components of mineral crystals can be non-zero at nanoscale. These mechanical properties are in correspondence with the two mineral crystals structures.

The main objective of this study is to predict and interpret the stiffness ratios of sand mastics to asphalt binder at a broad range of temperatures. Both fine and coarse sand mastics were studied using discrete element (DE) method. Twelve samples were prepared in this study, including six fine sand mastics, and six coarse sand mastics. The six fine sand mastics were prepared by blending fine sands (diameters ranging from 0.075mm to 0.3mm) with the 42.15%, 52.4%, 61.8%, 70.8%, 80.3%, 90% of asphalt binders by volume. The six coarse sand mastics were fabricated by blending coarse sands (diameters ranging from 0.3mm to 2.36mm) with the 42.15%, 52.4%, 61.8%, 70.8%, 80.3%, 90% of asphalt binders by volume. The previously developed DE model was employed to consider the interactions in the digital specimens of the 12 sand mastics. The DE simulations were conducted by varying the asphalt binder stiffness values with the constant stiffness value of sands. The stiffness ratios of mineral aggregates to asphalt binders were varied from 1 to 1 x 10¹⁰. The outputs of the simulations were the predicted stiffness of the sand mastics. Finally, the outputs were analyzed to evaluate the impacts of asphalt binder stiffness values and volumetric fractions on the stiffness values of the asphalt sand mastics. Through this study, it was observed that 1) the DE simulation results agreed well with the micromechanical models; 2) the stiffness ratios of sand mastics to asphalt binders ranged from 1 to 1.18 x 10⁹ for fine sand mastics and from 1 to 3.76 x 10⁸ for coarse sand mastics.

Packing model of aggregate is a very important issue in gradation design and research on asphalt mixture. The packing characteristics of coarse aggregate and fine aggregate can affect the skeleton and volumetric parameters, such as VMA (Void in Mineral Aggregate), of asphalt mixture respectively. In this study, based on the ideal packing model of aggregate, the 2-D packing model which is a random distribution and compacted contact of different size aggregates is built, and the mathematic solution to this model is figured out by using the geometric theory of space topology. The model has been programmed and visualized by using Visual Basic language. The impact of gradation on the skeleton and VCA (Void in Coarse Aggregate), and the effect of fine aggregate packing on VMA can be analyzed by using this model and algorithm. The model is helpful to the gradation design, analysis and evaluation for asphalt mixture.

This study presents a multiscale computational model and its potential applications to mechanical behavior predictions of bituminous materials, mixtures, and pavement structures. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element (RVE). With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, inelasticity, and damage accumulation in the small scale on the overall performance of larger scale mixtures or structures. This paper is not to provide any realistic predictions yet but to briefly introduce the model framework and demonstrate the potential applicability of the model in the field of bituminous materials and mixtures through an example simulation of asphalt concrete mixtures.

Long-term performance of hot mix asphalt (HMA) pavements is significantly influenced by the internal structure characteristics related to the aggregate skeleton. The type and degree of compaction is very important for internal packing and generation of the aggregate skeleton in HMA pavements. However, direct quantification of aggregate packing in HMA in 3D has not been successfully accomplished. One method to quantify 3D microstructures is through experimental and imaging techniques (e.g. X-ray Computed Tomography), which is usually very costly and time consuming. On the other hand, generating digital specimens through 3D numerical packing/compaction simulations using the real aggregate shapes may be an efficient and economical alternative. This paper presents a realistic 3D packing/compaction model that utilizes real 3D shapes of aggregates. The model is based on one of the most efficient particle-based simulation techniques called "Dissipative Particle Dynamics (DPD)". The primary advantage of DPD is that the movement of arbitrarily shaped aggregates (during compaction) can be simulated realistically. In this paper, a modified version of DPD model (called MDPD) was developed to better represent the micromechanical behavior of HMA. The model was compared against laboratory tests, and a very good agreement was observed.

In this paper, a methodology for modeling creep behavior of asphalt concretes (AC) under uniaxial static loading is presented. Three AC mixtures were produced using Coarse Matrix High Binder type C (CMHB-C) mixture type. Three different aggregate sources, namely a Hard Limestone (HL), a Soft Limestone (SL), and a Granite (G) and a PG 76-22 binder were used to prepare the mixes. The microstructure of AC was captured using X-Ray computed tomography (CT) and the Discrete Element Method (DEM) was utilized to describe the microstructure. An automated digital image processing technique called Volumetric-based Global Minima (VGM) thresholding algorithm was utilized to process the X-Ray CT images of AC cores. The viscoelastic properties of asphalt binders and their mastics were characterized by fitting the Burger models to Dynamic Shear Rheometer (DSR) mastic data. The DEM simulations results were compared favorably to experimental uniaxial creep data. It was found that the models underestimated the creep compliance of the mixtures in the primary creep stage and predicted quite accurately in the secondary creep stage.

Asphalt concrete (AC) is a granular composite material stabilized by the presence of asphalt binder. In continuum modeling for AC, the macroscopic response has been lacking the ability to explicitly account for the effect of the microstructure distribution. In this study, an elasto-viscoplastic continuum model is developed to predict AC response and performance. The model incorporates a Drucker-Prager yield surface modified to capture the influence of stress path direction on the material response. Parameters that reflect the directional distribution of aggregates and damage density in the microstructure are included in the model. The elasto-viscoplastic model is converted into a numerical formulation and implemented in finite element (FE) using user-defined material subroutine (UMAT). A fully implicit algorithm in time-step control is used to enhance the efficiency in the FE analysis. The FE model is used in this study to simulate experimental measurements with three mixes design under different confining pressures and strain rates.

Rheological properties of asphalt matrix, which is asphalt coated fine aggregate that passes through a No. 4 sieve, can play a significant role in the damage and cracking behavior of asphalt concrete. It is important to understand what factors affect the rheological behavior of matrix materials. In this study, a dynamic shear rheometer (DSR) is used to determine rheological properties of matrix materials of varying strain rate, gradation, overall grain size, and moisture conditions. Matrix behaves linear viscoelastically at about 0.007% strain amplitude. The complex shear modulus (G*) value of a matrix depends on the entire mix gradation, not on an individual sieve or grain size. Overall, dry matrix samples show high G* values compared to the wet matrix samples.

Indirect tensile creep test has been extensively employed to characterize the creep compliance of viscoelastic materials, especially asphalt concrete. Two-dimensional elastic stress solution developed by Hondros (1959) could be used to derive the viscoelastic solution of creep compliance in indirect tensile testing mode. The plane stress assumption of the two-dimensional solution, however, warrants the use of specimen with small thickness/diameter ratio. In this study, a three-dimensional elastic solution was derived, on the basis of Wijk's methodology (Wijk 1978). The elastic-viscoelastic correspondence principle was used to convert the three-dimensional elastic solution into viscoelastic solution of creep compliance. To verify the derivations, three-dimensional finite element viscoelastic analysis was performed using ABAQUS. The results demonstrated that the viscoelastic solution, based upon three-dimensional elastic solution, is accurate, which allows the selection of dimension of indirect tensile test specimen without the restriction of specimen geometry to approximate the plane stress assumption.

Motivated by the ultimate goal of linking the binder and aggregate properties to the cracking performance of asphalt concrete, a multiscale virtual testing methodology is developed in this paper. The main components of the proposed methodology are: (a) a virtual fabrication technique that generates the microstructure of asphalt concrete specimens without the need for physical fabrication, (b) a lattice modeling approach that simulates the micromechanical behavior of cracked asphalt concrete specimens, and (c) a multiscale methodology that incorporates the effects of aggregates of widely varying sizes. The resulting methodology is calibrated to simulate the load-deformation behavior of real uniaxial tension test specimens. A comparison of the predicted response against the measured response indicates that the proposed method shows promise, but requires further work aimed at the fundamental understanding of the micromechanical behavior.

This study developed an eXtended Finite Element model (XFEM) to investigate the concrete micro-crack properties and morphology by simulating the Compact Tension (CT) tests on the idealized specimens. The complex concrete microstructure includes the hydrated cement paste with pores, aggregates and interfacial transition zones. The XFEM was recently developed to overcome the continuity nature of traditional finite element (FE) analysis with defined enrichment functions and level set approach. The XFEM was implemented within MATLAB codes. In the cracked domain, the Heaviside jump and the linear elastic asymptotic crack-tip enrichment functions were used to account for the discontinuity across the crack surface and around the crack tip. For the interfacial transition zones, the stress gradation and debonding behavior were represented with the inclusion enrichment functions. The XFEM model simulation was firstly verified with the analysis results of CT tests. The developed XFEM models were then applied to the idealized concrete specimens with varied microstructures. The simulation results indicated that the developed XFEM model can be applied to characterize the micro-crack properties and morphology of heterogeneous concrete specimens.

This paper presents the results of a comprehensive simulation study that investigated the effects of infinite elements in pavement models, eigenvalue analysis, and damping. The results provide useful insight into pavement structural responses. This is not possible from traditional static linear elastic analysis and two dimensional-finite element models developed for pavement analysis and design. A three dimensional finite element half model of an asphalt highway pavement-subgrade system was created with optimum size and boundary conditions. The model was used for simulations of the load-time history of a falling weight deflectometer impact test. The half model was validated by the results of the Green's function and showed the limitation of the use of infinite elements for pavement models. The fundamental natural frequency of 8 Hz for the an asphalt highway pavement was determined by the eigenvalue analysis using the implicit finite element code. The results of a parametric study are presented to evaluate the effects of both system damping and Rayleigh damping on pavement deflection response and backcalculated modulus values.

In this study, Sasobit was used as an additive into asphalt. Different ratios of Sasobit (2%, 3%, 4% and 5% by mass of asphalt) were blended into base asphalt Pen. 60/80. The conventional tests, such as penetration test, softening point test, viscosity test, and constituent test, were carried out on asphalt mixed with different additive contents. Attempts to approach the influence of Sasobit on the asphalt micro-structure, the molecular weight distribution and the functional groups of asphalt blended with different additive content were also tested by using GPC and IR methods. The analyses of test results show that properties and micro-structure of Sasobit modified asphalt change dramatically when compared to those of the base asphalt. These changes are related not only with additive content but also with temperature. It is also found that some chemical reactions happen when Sasobit is added into asphalt. With these chemical reactions, the colloid structures, molecular weight distributions, functional groups, and wax crystals of Sasobit modified asphalt will be changed significantly.

The Projects NCHRP9-19 and 9–29 in the USA have researched and developed SPT (Simple Performance Test), which can be used to test asphalt mixture's dynamic modulus, static creep and permanent deformation under repeated loading and analyze the visco-elasticity of asphalt mixture. This article, based on the modified Burgers model and Boltzmann superposition principle, figures out visco-elasticity model parameters using the data observed from permanent deformation under repeated loading in SPT. A prediction model is established between the modified Burgers model and the permanent deformation in wheel tracking test. The test shows that the estimated value from the established predicting model is very close to the measured value through wheel tracking test, which means, to some extent, the predicting model illuminates the inherent relation between the two methods to evaluate permanent deformation of asphalt mixture.

Tire/pavement interaction has been an important research topic in pavement engineering for many years. This paper presents a finite element model for dynamic tire/pavement interaction, which can effectively include the dynamic tire rolling effect to predict the pavement response. The model represents a 4-tire vehicle. The tire is modeled as a finite strain hyperelastic material and pavement structure is modeled as elastic materials. The finite strain hyperelasticity model was implemented as user subroutine in ABAQUS. The numerical results show that tire contact area is neither circular nor rectangular. Also the contact pressure is not uniformly distributed, which provides some insight to justify why the conventional contact area assumption is inaccurate. Representative simulations are provided to demonstrate how the finite element model of tire/pavement interaction can be used to predict pavement response and pavement damage due to fatigue cracking and rutting in the field of pavement engineering.