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Publication Number: FHWA-HRT-10-065
Date: December 2010

Modeling of Hot-Mix Asphalt Compaction: A Thermodynamics-Based Compressible Viscoelastic Model


Asphalt concrete is a composite material made up of graded aggregate rocks bound together by an asphalt binder along with the presence of air voids. The nature of this mixture is dependent on the type of each of the constituents selected to prepare the mix. Asphalt concrete pavement, more commonly known as HMA pavement, consists of bound layers of a flexible pavement structure. For most applications, asphalt concrete is placed as HMA, which is a mixture of coarse and fine aggregate and asphalt binder. HMA derives its nomenclature from the fact that it is mixed, placed, and compacted at elevated temperatures. Asphalt concrete pavement can also be placed at ambient air temperatures, but HMA is the primary placement method for roads and interstates.

Because of its composition, asphalt concrete displays a nonlinear response even at small strain and exhibits a different response in tension and compression, particularly for long-duration loading. Also, the extreme temperature sensitivity of asphalt concrete causes a change in temperature to have a more significant impact on the mechanical behavior than changes in loading magnitude.(3) The deformation resistance of asphalt concrete is mainly derived from the aggregate matrix and the viscous asphalt binder matrix. Because of the change in microstructure, due to either mechanical changes such as reduction of air voids or chemical changes such as aging of the asphalt, the response of the aggregate matrix and the asphalt binder matrix to traffic loading changes over time. Also, the ability of the pavement to stress-relax upon load removal changes because of continual changes in the microstructure. This change in microstructure and changes in loading and environmental conditions cause phenomena such as ruts, fatigue cracking, low-temperature cracking, and moisture-induced damage. Distress due to rutting is caused by the accumulation of deformation under repeated traffic loading, which results in the development of longitudinal ruts along the pavement. This accumulation of deformation depends largely on the one-dimensional densification due to air-void reduction and the flow of the asphalt-mortar matrix. A thorough review of the nature and uses of asphalt concrete and the many attempts at modeling the material are presented by Krishnan and Rajagopal.(4)

The current approach to flexible pavement design relates the engineering properties of asphalt mixtures to pavement distress. Therefore, current models are mostly distress-prediction models and not constitutive models as usually understood in mechanics. In distress-prediction models, some measure of distress—for example, the number of cycles to failure and amount of permanent deformation—is related to material properties, assuming asphalt mixtures to be either linear viscoelastic or linear elastic. However, HMA behaves like a nonlinear fluidlike material at elevated temperatures and slowly transforms into a highly viscous nonlinear viscoelastic fluid toward the end of the construction process.


Proper construction of roadways requires that pavements be laid down according to certain specifications governing the desirable characteristics for the material. Construction of HMA pavements takes advantage of the direct and indirect compacting forces exerted by rollers passing over the loose mix to produce dense layers of structurally durable material. Compaction reduces the volume of a mixture of hot asphalt binder, aggregates, and filler materials to form the required dense, impervious mass. The motivation for compacting an asphalt pavement is a desire to achieve an optimum air-void content, to provide a smooth riding surface, and to increase the load-bearing capacity of the material under construction.(1) The densification of the mixture due to compaction causes an increase in the unit weight of the material and improves the aggregate interlock.(5,6) The literature notes extensively that improper compaction generally leads to poor performance from the asphalt pavement, in spite of all other desirable mixture-design characteristics being met. This can lead to premature irreparable damage to the built-in infrastructure, typically in the form of rutting, permanent deformation, cracking, and moisture damage.


The compaction process is influenced by many factors, including the properties of the materials in the mixture, environmental variables, conditions at the work site, and the method of compaction, as detailed by the U.S. Army Corps of Engineers and summarized in some detail by Kassem.(5,7) The required compaction effort increases with an increase in aggregate angularity, size, and hardness. The grade and amount of asphalt binder also influence the compaction process. A mixture produced with too little asphalt is stiff and usually requires more compaction effort than a mixture with high asphalt-binder content. The temperatures of the air, mixture, and base are also important factors that influence compaction, according to the U.S. Army Corps of Engineers.(5) In addition, the compaction effort increases with an increase in layer thickness.


Several studies have attempted to examine the relationship between field compaction methods, laboratory compaction methods, and mechanical properties. Consuegra et al. and Harvey and Monismith evaluated several laboratory compaction methods based on the relationship between the mechanical properties of laboratory specimens and field cores.(8,9) These studies provided recommendations concerning devices that produce laboratory-compacted specimens with properties that better relate to those of field cores. Peterson et al. evaluated the influence of changing the compaction parameters in the SGC on the mixture's mechanical properties and their correlation with the mechanical properties of field cores.(10) The control parameters that were varied in the study were the angle of gyration, specimen height, gyratory compaction pressure, and temperature of the compaction mold. Peterson et al. found the angle of gyration to be the most important parameter influencing mechanical properties.(10)

Masad et al. used image-analysis techniques to study the air-void distribution in the SGC.(11) The results showed that the air-void distribution in SGC specimens is not uniform and that the top and bottom layers have a higher air-void content than the middle layer. Tashman et al. compared the air void distribution and mechanical properties of SGC-compacted specimens to field cores compacted using different compaction patterns.(12) That study showed that the compaction parameters in the SGC can be changed in order to improve the relationship between the internal structure (including air-void distribution) and mechanical properties of SGC specimens and field cores.

More detailed descriptions of the various factors influencing compaction and compaction methods/techniques and a summary evaluation of various studies into the compaction of HMA are presented in Huerne and Kassem.(13,7)


The motivation for most studies of asphalt concrete behavior is to develop models to understand the distress an asphalt concrete pavement is subjected to and to determine experimental variables based on the analysis of such distress models. Unlike asphalt, for which models that describe the behavior of viscoelastic fluids have been developed, asphalt concrete has constitutive specifications that are mostly related to empirical correlations for different types of distress. However, studies assuming asphalt concrete to be a viscoelastic material also assume that the macroscopic mechanical behavior of asphalt concrete is viscoelastic. These studies use either a spring-dashpot analogy in the form of a Burger's model or some simple form of viscoelastic constitutive equation. (See references 13–28.)

As noted by Krishnan and Rajagopal, the deformation resistance of asphalt concrete is mainly derived from the aggregate matrix and the viscous asphalt mastic.(4) Because of the change in the microstructure (either due to mechanical changes such as reduction of air voids or chemical changes such as aging of asphalt), the response of the aggregate matrix and the asphalt mastic to traffic loading changes with time. Also, the ability of the pavement to stress-relax upon load removal changes as the microstructure is continuously modified. This change in microstructure and changes in loading and environmental conditions cause phenomena such as rutting, fatigue cracking, low-temperature cracking, and moisture-induced damage. For instance, distress due to rutting is caused by the accumulation of deformation under repeated traffic loading, resulting in the development of longitudinal ruts along the pavement. While most studies have not considered the mechanism of densification (assuming that the pavement will be compacted well during construction), the plastic flow of the asphalt concrete has been assumed to be dependent on the temperature, loading rate, and loading time interval.(29,30)

There are quite a few models for asphalt concrete that consider the microstructure, but as with most of the phenomenological models, they neglect the evolution of the microstructure during the lifetime of the pavement or consider it, for instance, by means of some shift factors. Nijboer conducted microstructural modeling of asphalt concrete using the analogy of soil mechanics, postulating that the entire deformation resistance of bituminous mixes can be explained in terms of initial resistance, internal friction, and viscous resistance.(31) Huschek used a three-phase system consisting of regions characterized by viscosity, modulus of elasticity, and modulus of plasticity.(23) Van der Poel modeled the behavior of asphalt mixes by calculating the rigidity of concentrated solutions of elastic spheres in an elastic medium, using a method developed for dilute dispersions by Frolich and Sack.(32,33) Hills developed models for the long-term creep behavior of asphalt mixes by characterizing the internal structure of the mix by means of the asphalt film thickness.(34) Cheung et al. and Deshpande and Cebon have developed models for asphalt-concrete mixes using isolated contact models and shear box models.(35–37) Boutin and Auriault used the analogy of a porous medium saturated by a viscoelastic fluid to classify the macroscopic behavior of asphalt concrete as biphasic, elastic, or viscoelastic depending upon the ratio of the dimension of the pores to the macroscopic wave length.(38) Florea used the viscoplastic potential to develop an elastic/viscoplastic model for bituminous concrete.(39,40)

Recently, Krishnan and Rao attempted to model the air-void reduction in asphalt concrete using the continuum theory of mixtures and the theory of linear elastic material with voids.(41,42) A thermodynamic framework has recently been put into place and can be used for the constitutive description of asphalt concrete. This framework has a reasonably general structure within which a host of dissipative processes can be described. This framework to model asphalt concrete recognizes the change in the microstructure of the material through the changes in the natural configurations of the body. For the purpose of this study, a natural configuration is a stress-free configuration, with further details of the framework presented by Rajagopal and later adopted by Rajagopal and coworkers. (See references 4 and 43–46.)


Very little research has been directed toward modeling HMA compaction and the material properties that influence compactability. Guler et al. proposed the use of a porous elastoplastic compaction model using a modified Gurson-Tvergaard yield function.(47) An incremental constitutive relation for the porous material was formulated for this purpose. Researchers focused on obtaining statistically significant parameters for this constitutive relation and a correlation between the model parameters and mixture variables (i.e., volumetric properties and particle size). Simple linear models were built to predict the model parameters. The displacement field used to represent three-dimensional compaction was an approximation of the actual motion in an SGC. Also, the model was formulated assuming the small-strain theory, was time independent, and assumed isothermal conditions (no changes in temperature).

Huerne used a modified form of soil critical-state theory in modeling asphalt-mixture compaction.(13) The critical-state theory describes granular material behavior by means of a closed yield locus, which gives a boundary between stress states that cause elastic (recoverable) deformations and plastic (irrecoverable) deformations. Huerne's implementation simulated void reduction by means of plastic volume changes. The Hveem device was used for determining the model's parameters. The model was developed assuming small strain deformation and, consequently, is limited in modeling the high strains involved in the compaction process. Also, the model has many parameters that are not directly linked to mixture properties.

Krishnan and Rao developed a constitutive model for asphalt mixes using mixture theory to model the one-dimensional compaction of asphalt mixtures under a static load.(41) This model utilizes the fundamental balance laws to obtain mathematical relations to describe the performance and characteristics of asphalt mixes. While their work places the modeling within a general framework that takes into account the balance laws of mechanics, it ignores certain critical issues concerning the material response, such as the evolution of the microstructure of the material being compacted during the process. Also, such an approach to modeling compaction of HMA is limited by the restrictive experimental techniques available to measure the various mixture properties involved in the model.

In summary, previous attempts to model HMA compaction were limited in the following ways:

Recently, efforts have been made to develop material models to describe asphalt concrete behavior based on a thermodynamically consistent methodology by employing the framework of multiple natural configurations formalized by Rajagopal.(48,49,43)


An important motivation for developing a material model to be used in simulations is the concept of IC. Moore defines IC as a system that applies to a vibratory roller and that automatically adjusts the energy output of the roller to neither undercompact nor overcompact the materials.(50) IC of soil and asphalt layers is a relatively new technology introduced in the United States for compaction control.(51) IC for HMA compaction is in an even earlier stage of development. This new compaction concept is, however, gaining attention from the asphalt-paving industry. The application of the model developed here can be extended to obtain correlations between pavement designs and model characteristics. This will enable the decision process in an IC control system.


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