Continuum Coupled Moisture-Mechanical Damage Model for Asphalt Concrete

72

Transportation Research Record: Journal of the Transportation Research Board, No. 2372, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp. 72–82.DOI: 10.3141/2372-09

M. Shakiba, R. K. Abu Al-Rub, T. You, E. A. Masad, and D. N. Little, Zachry Depart-ment of Civil Engineering, and M. K. Darabi, Texas A&M Transportation Institute, Texas A&M University System, College Station, TX 77843. Alternate affiliation for E. A. Masad, Mechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar. Corresponding author: M. K. Darabi, [email protected].

crete materials (4–6). The mathematical modeling of the physical– mechanical processes related to moisture damage has been investi-gated via two main approaches. The first is micromechanical modeling of asphalt concrete, which considers degradation of mastic and the aggregate–mastic interface by using cohesive elements (7, 8). The sec-ond approach, macromechanical modeling, considers the mixture as a continuum without modeling its individual constituents (9–11). Caro et al. used cohesive elements at the aggregate–mastic interface (8). They captured the effect of moisture through degrading the cohesive stiffness and strength. Kringos, Scarpas, and their collaborators studied asphalt concrete at the micro scale to predict the infiltration of mois-ture and proposed a simple moisture damage model as a function of moisture content (9, 10, 12). However, their model is time independent and allows for full moisture damage recovery (or reduction) on drying, which is a controversial assumption. Recently, Graham proposed a time-dependent continuum damage model for predicting the adhesive and cohesive moisture damage in asphalt concrete (11). However, this model does not account for moisture damage history, and it has not been verified against experimental measurements. It is, then, impera-tive to develop a robust and comprehensive physically based moisture damage model that can effectively predict the performance of asphalt pavements affected by moisture intrusion.

The moisture susceptibility of asphalt concrete can be easily char-acterized at the macro scale by performing experimental testing. However, moisture susceptibility of asphalt concrete may signifi-cantly change as a result of variations in the mineral composition of the aggregate portion, proportioning of the components (mix design), the physical–chemical properties of the constituents, and micro-structural features (e.g., air void content and aggregate size, dis-tribution, and shape). Considering the effects of such variations is a challenging and crucial task that demands the development of constitutive models and numerical techniques that can be used effectively to simulate the micromechanical behavior of asphalt concrete. However, because of the high complexity and expensive computational cost of such an approach, few attempts have been made to model the three-dimensional microstructure of asphalt concrete. Recently, You et al. and Abu Al-Rub et al. used two-dimensional (2-D) X-ray computed tomography (CT) images to create 2-D and three-dimensional (3-D) finite element representations of the micro-structure under dry conditions (13, 14). They used a thermomechanical constitutive approach to model the mechanical response of asphalt concrete under several loading conditions (15). Kringos et al. and Graham modeled the effect of moisture on mechanical response by using an idealized 2-D representation of asphalt concrete micro-structure (9, 11). Caro et al. presented 2-D micromechanical simula-tions of moisture-induced damage in asphalt concrete (8). However, no attempt has been recorded in the literature, to the best knowledge of

Continuum Coupled Moisture–Mechanical Damage Model for Asphalt Concrete

Maryam Shakiba, Rashid K. Abu Al-Rub, Masoud K. Darabi, Taesun You, Eyad A. Masad, and Dallas N. Little

Despite the detrimental effects of moisture damage in asphalt pavements, few macroscale models are capable of modeling this important phenom-enon. Existing models have limitations in accounting for the irrevers-ibility and time dependency of moisture-induced damage. This study presents a moisture damage model based on continuum damage mechan-ics. Adhesive and cohesive moisture damage phenomena are modeled independently; this procedure allows for the introduction of fundamental mechanical properties for each process and for modeling the transition between adhesive and cohesive damage. Two- and three-dimensional sim-ulations are performed, and the results of the simulations are presented to demonstrate the applicability and utility of these micromechanical com-putational models. It is shown that the proposed moisture damage model can simulate the effect of moisture damage on the mechanical response of asphalt concrete subjected to different loading conditions. The model also provides useful insight into the effect of mixture design and material properties on resistance to moisture damage.

Asphalt concrete pavements are constantly exposed to environ-mental conditions such as oxygen and moisture. The combined effects of dynamic traffic loading and environmental conditions gradually degrade the mechanical properties of asphalt concrete pavements. Moisture is among the important environmental factors that cause the most concern in maintaining asphalt concrete pave-ments. Moisture damage affects both safety and serviceability over the performance life of asphalt pavements. Moisture at the surface of asphalt pavements in the form of water or vapor disperses into the mixture, fully or partially fills the air voids, and diffuses through the components (binder, mastic, and aggregate). The infiltrated mois-ture aggravates the time-dependent stiffness and strength of asphalt concrete as part of chemical, physical, and mechanical processes. This detrimental effect is referred to as moisture damage and is one of the main causes of early failure.

Investigations of the detrimental effects of moisture from mechan-ical, physical, chemical, and thermodynamic processes have been ongoing since 1932 (1–3). Moisture damage affects both mechani-cal response and surface bonding characteristics, leading to the degradation of the adhesive–cohesive bond strength in asphalt con-

Shakiba, Abu Al-Rub, Darabi, You, Masad, and Little 73

the authors, to model the effect of moisture damage on the mechanical response of asphalt concrete by using realistic 3-D representations of asphalt concrete. In this paper, a moisture damage constitutive model is proposed and coupled with the thermoviscoelastic, thermovisco-plastic, and thermoviscodamage models. The proposed model is used to conduct 2-D and 3-D realistic micro mechanical simulations to investigate the effect of moisture damage on the complex mechanical responses of asphalt concrete.

ExpErimEntal Work

Several experimental studies have characterized the effect of moisture on aggregate–mastic bond strength (16–18). In this study, the test results reported by Kringos et al. were used to calibrate and validate the moisture damage model (16). They performed pull-off tests on six mastic–stone combinations to measure the moisture susceptibility of the aggregate–mastic bond strength. The experi-ments included two types of aggregate (sandstone and granite) and four types of mastic to form six combinations, two of which are used in this paper. Granite aggregate with a diffusion coefficient of 0.72 mm2/h was used with two mastic types with diffusion coefficients of 0.47 × 10−3 and 1.31 × 10−3 mm2/h. Additional information on experimental setup and testing procedures are available elsewhere (16). In the pull-off test, a thin layer of mastic was bonded between an aggregate substrate and a metal pull stub. The specimen was con-ditioned in a water bath for three conditioning times. The moisture was constrained to diffuse via the aggregate to avoid the occurrence of mixed weakening of both the mastic and the aggregate–mastic interface. The specimen was then pulled apart to determine the mastic–stone bond strength. The bond strength was measured in uniaxial direct tension at a constant displacement rate and temperature. Kringos et al. recorded the bond strength of different samples and the associated conditioning times (16).

Continuum moisturE–mEChaniCal DamagE mEChaniCs FramEWork

Stress tensors in the damaged (nominal) and effective (undamaged) configurations can be related as a function of mechanical damage density (ϕ) by using the concept of continuum damage mechanics (CDM), as shown by Equation 1 (19, 20):

1 (1)( )σ = − φ σij ij

where σ̃ij and σij are the stress tensors in the effective and dam-aged configurations, respectively. Equation 1 was originally devel-oped to capture the effect of mechanically induced microdamage (i.e., micro cracks and microvoids) on true stress measures in the effective configuration. In this study, the well-known CDM framework was modified by introducing wet damaged, wet, and dry un damaged natural configurations. The proposed configurations enhance the CDM framework to model the moisture degradation in materials and couple it to the mechanical responses. These modifications enabled the stress tensors in the wet damaged and dry undamaged configurations to be related as a function of a physically based moisture damage variable (φ), as shown by Equation 2:

ij ij( )( )σ = − ϕ − φ σ1 1 (2)

where – (overbar) designates the dry undamaged configuration. The moisture damage variable in Equation 2 ranges from 0 to 1. The case in which moisture damage has not contributed to the degradation of the material is denoted by φ = 0, and φ = 1 shows that the material has been fully degraded as a result of moisture. Any value between zero and one (i.e., 0 < φ < 1) corresponds to the case in which the material’s integrity is only partially reduced as a result of moisture.

Comparing Equations 1 and 2 enabled the authors to define an effec-tive damage density (ϕeff) that considers the combined contribution of moisture and mechanical damage, as shown by Equation 3:

1 1 1 (3)eff( ) ( )( )− φ = − ϕ − φ

It can be argued that once the material degrades under mechanical and moisture loading conditions, further loading can be sustained only by the intact portion of the material that is neither damaged mechani-cally nor degraded due to moisture (i.e., dry undamaged configura-tion). Therefore, the constitutive models can be expressed in the dry undamaged configuration. The mechanical and moisture damage com-ponents can then be coupled to the rest of the constitutive models by using Equation 2. The proposed framework for modeling the moisture damage mechanism naturally inherits the simplicity and robustness of the CDM framework.

moisturE DamagE moDEl

The effect of moisture in degrading the mechanical properties is observed in two physical mechanisms. The first is adhesive moisture damage (φa), which is the degradation of bond strength between the aggregate and the asphalt mastic as a result of diffusion of mois-ture through the thin films surrounding the aggregate particles. The second mechanism is cohesive moisture damage (φc), which is the degradation of the cohesive strength of the asphalt mastic (21, 22). In this study, these phenomena were modeled independently such that the fundamental physics associated with each mechanism can be modeled separately by assuming proper evolution functions for adhesive and cohesive moisture damage. The combined effect of adhesive and cohesive damage, as well as the transition between them, can also be modeled by defining the total moisture damage, as shown by Equation 4:

1 1 1 (4)( )( )( )− ϕ = − ϕ − ϕa c

Similar evolution functions were assumed for the adhesive and cohesive moisture damage as a function of the normalized moisture content (θ), as shown by Equation 5:

t t i a ci i [ ]( )( )ϕ = ϕ θ = , (5)

where the superimposed dot designates the time derivative. The term φi(t) is the aggregate–mastic adhesive damage variable for i = a (adhesive) and the mastic cohesive damage variable for i = c (cohesive) at time t, and φ

. i(θ[t]) is the rate of decay of the adhesive or cohesive strength for θ at time t.

A linear function of θ(t) is assumed as the first approximation for the evolution of the moisture damage variable [i.e., φ

. i(θ)] (11). How-ever, experimental results show that φ

. i(θ) decreases as the level of damage increases. In order to be able to consider the effect of damage history on the bond strength of the material and also to consider the

74 Transportation Research Record 2372

coupling between the mechanical and moisture damage mechanisms, the following evolution function (Equation 6) is proposed:

t k t i a ci i

q

[ ]( ) ( )ϕ θ = θ −φφ

=1 , (6)eff

cr

where

ka and kc = material properties describing the rate of degrada-tion of the adhesive and cohesive damage variables, respectively;

ϕeff = effective damage variable as defined in Equation 3; q = damage history exponent parameter; ϕcr = critical damage; and k l = Macaulay brackets defined by kξl = (ξ + |ξ|)/2.

The evolution equation proposed in this paper has several advan-tages over previously proposed moisture damage models (9, 11). First, the model proposed in Equation 6 is time dependent, such that the material can gradually degrade, at a fixed moisture content, as a function of time. Second, it accounts for the irreversibility of moisture damage, such that stiffness and strength lost because of the presence of moisture cannot be recovered on drying. Third, the model describes the damage process as a function of the damage history and not only the current moisture state. Finally, unlike the models based on the cohesive zone elements, it can predict crack propaga-tion both in the matrix and at the interface without prescribing a predefined crack path. The proposed framework and the moisture damage model can be used to relate the wet bond strength at the current time (t) to the initial dry bond strength of the material, as shown by Equation 7 (11):

X X i a ci i i( )= − ϕ =1 , (7)0

Equation 7 shows that for the dry state of the material (φi = 0), the adhesive or cohesive strength (or both) are equal to the initial dry strength [Xi(t) = Xi

0]. When the material is completely degraded (φi = 1), all adhesive or cohesive strength is lost [Xi(t) = 0]. The model parameters associated with the moisture damage model are identified in the subsequent sections.

Moisture diffusion within the microstructure of the asphalt concrete is assumed to follow Fick’s second law, as shown by Equation 8:

(8)2∂θ∂

= ∇ θt

D

where D is a moisture diffusion coefficient, and ∇2 is a Laplace opera-tor. The built-in algorithms in the Abaqus finite element package were used to obtain the evolution of θ inside the model. Abaqus solves Equation 8 according to the imposed moisture content boundary condition to calculate the moisture content at each time step.

The modeling approach presented in Equations 1 to 8 essentially extends the well-known concepts of CDM to continuum mois-ture–mechanical damage mechanics theories. These modifications are made in two stages. First, a physically based moisture damage parameter is introduced that evolves as a function of moisture con-tent (Equation 6). The moisture damage variable can be considered as an internal state variable responsible for considering the moisture effect. Second, the degradation effect of moisture is modeled by

making stress a function of the moisture damage state variable (Equa-tion 2). These modifications make the implementation very simple and avoid the complexities associated with the direct couplings between moisture damage and the rest of the constitutive model. Therefore, a complex phenomenon such as moisture damage can be coupled to complex viscoelastic–viscoplastic–viscodamage constitutive models through the introduced framework by using the introduced moisture damage variable. The authors believe that this is one of the simplest ways to capture the complex effect of moisture on the mechanical response of asphalt concrete. More accurate moisture damage mod-els can be proposed only by modifying the evolution function of the moisture damage variable.

The numerical algorithm for the proposed moisture damage model was implemented in the pavement analysis by using the non-linear damage approach (PANDA) program to model the effect of moisture damage on the complex mechanical response of asphalt concrete at macro and micro scales. PANDA, which was developed and continues to be refined by the authors and their collaborators, includes Schapery’s nonlinear viscoelasticity (23), Perzyna-type viscoplasticity (24), and the viscodamage model proposed by Darabi et al. (15). Some details of PANDA are presented below, and readers are referred to previous publications by the authors for more details regarding PANDA and the procedures required for the identification of the model parameters (15, 25, 26).

iDEntiFiCation oF moisturE DamagE moDEl paramEtErs

The pull-off test of the moisture-conditioned specimens conducted by Kringos et al. was modeled numerically to calibrate the moisture damage model (16). In this test, moisture was allowed to diffuse from the sides and bottom of the aggregate and gradually reach the interface and mastic. The pull-off test was then performed to measure the bond strength between the aggregate and the mastic for different conditioning times.

Figure 1a shows the finite element mesh for this model. An axisymmetric coupled diffusion–mechanical analysis model was used to simulate moisture diffusion within the aggregate and at the binder–aggregate interface. The PANDA model was also used to model the evolution of the moisture damage during the condition-ing time. Figure 1b shows moisture diffusion through the model. Figure 2, a and b, shows the experimental results compared with the predicted bond strength at different conditioning times. Figure 2, c and d, shows the adhesive moisture damage that occurred at the aggregate–mastic interface for two combinations. The predictions presented in this figure show that the proposed moisture damage model is capable of predicting the degradation in bond strength as a function of conditioning time. Figure 2, a and b, confirms the historical effect on the rate of degradation of bond strength, such that the rate of decay of bond strength decreases as the conditioning time increases.

miCromEChaniCal moisturE–mEChaniCal DamagE simulations

The calibrated moisture damage model, which was implemented in PANDA, was used to conduct the micromechanical simulations. The continuum-based moisture damage model has the merits of simulat-ing the effect of moisture damage on the mechanical response of


NT11+1,0003+00+9,167e-01+8,333e-01+7,500e-01+6,667e-01+5,833e-01+5,000e-01+4,167e-01+3,333e-01+2,500e-01+1,677e-01+8,333e-02+2,070e-11

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FIGURE 1 PANDA model: (a) finite element mesh and (b) moisture diffusion profile after 4 weeks.

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FIGURE 2 Comparison between bond strength measurements for (a) Combination 1 and current model prediction with k = 0.236 1/week and q = 8 and (b) Combination 2 and current model prediction with k = 0.638 1/week and q = 8, and adhesive moisture damage versus moisture-conditioning time for (c) Combination 1 and (d) Combination 2 (16).


engineering structures for minimum computational cost. However, simulations at the macroscale level are incapable of illustrating the phenomena and mechanisms that occur at the microstructural level. In fact, the properties observed at macro scale stem from the microstructure configuration, as well as the properties of the constitu-ents. To demonstrate the model’s capabilities in performing micro-mechanical simulations, 2-D and 3-D simulations were performed. X-ray CT images were used to create 2-D and 3-D finite element rep-resentations of the microstructure of a typical dense-graded asphalt concrete (13, 14). The 3-D representation of the microstructure was constructed by using sets of 2-D CT scan images (Figure 3).

This study did not consider the air void phase and assumed the mix-ture to be a two-phase material consisting of matrix and aggregate.

Considering air voids as a separate phase in the model would have significantly increased the computational cost. Instead, air voids were assumed as part of the matrix. A threshold filtering was used to convert the grayscale images to two phases: white as an aggregate and black as matrix, which also includes the air voids. Investigating the effect of air voids on moisture diffusion and moisture-induced damage will be the subject of future work by the authors.

For the 2-D simulations, finite element meshes were constructed considering two phases (i.e., aggregates and asphalt matrix). Inter-face transition zones (ITZs) were defined in the 2-D models at the aggregate–mastic interfaces to investigate the adhesive bond strength at the interfaces. However, ITZ and adhesive failure were not included in the 3-D models for the sake of simplicity and to reduce the com-

(a) (b)

(d)

(c)

FIGURE 3 X-ray CT: (a) grayscale image, (b) contrasted image, (c) image with well-separated aggregates, and (d) slices of processed image (13).


putational time. The 3-D simulation results show only the results of cohesive moisture damage.

In these simulations, aggregates were assumed as isotropic linear elastic materials with Young’s modulus of Eagg = 1 GPa and Poisson’s ratio of νagg = 0.16, and the mastic phase was assumed as a viscoelastic–viscoplastic–viscodamage material with the model parameters reported by Darabi et al. (15). The ITZ properties in the 2-D model were assumed to be the same as the mastic properties with different moisture damage model parameters. The moisture damage model parameters for the mastic represent the susceptibility of the cohesive bond strength to moisture, and those associated with ITZ resemble the susceptibility of the adhesive bond strength to moisture. Mastic and aggregate diffusivity were selected as 5.56 × 10−6 mm2/s and 2.44 × 10−4mm2/s, respectively (7). The analysis assumed that moisture diffused through both matrix and aggregate phases. The diffusion rate through each phase depends on their associated diffu-sion coefficients. Therefore, moisture diffused through the matrix at a slower rate than through the aggregate. This study also assumed that the aggregates were fully coated with the matrix. That is, moisture had to diffuse first through the matrix in order to move from one aggregate particle to another.

Asphalt concrete is a rate- and temperature-dependent material. To investigate the effect of moisture on the rate-dependent mechanical response of asphalt concrete, uniaxial constant displacement rate tests were conducted for different moisture-conditioning times. This sec-tion reports the effect of different moisture-conditioning periods on the overall 2-D and 3-D thermomechanical response of the asphalt concrete.

The effects of different types of binder and aggregate and the distribution of air voids on the overall thermomechanical response of asphalt concrete were beyond the scope of this study and will be the subject of a future study by the authors.

The effect of moisture-conditioning level on the ultimate strength of the asphalt pavements under compressive loading conditions was

investigated. Figure 4 shows the finite element mesh for irregular-shaped aggregates with different size distribution. The aggregates were surrounded by a very thin ITZ layer to represent the aggregate–mastic interface. The aggregates and their associated ITZ were submerged in the mastic. Plane strain coupled diffusion–displacement elements were used for these simulations. The load was applied to the top edge of the model at a constant displacement rate. The left side of the model was constrained horizontally, and the bottom edge of the model was constrained vertically. Figure 5a shows the nor-malized moisture content contours when the model was exposed for 10 days to the normalized moisture content of one on the top and 0.5 on the lateral sides. The boundary condition assumed in this paper aimed to represent an asphalt pavement that has moisture at the surface and is dry at the base. In this case, the normalized moisture content on the surface of the asphalt pavement was equal to one. The moisture content changed linearly from one on the surface to zero at the base (i.e., dry base). For simplicity, the average value of the moisture content (0.5) was assumed for the sides. The moisture content inside the mixture was determined by solving Fick’s second law equation in the Abaqus finite element package using the pre-scribed boundary conditions. Figure 5, b and c, shows the cohesive and adhesive moisture damage, respectively, after 10 days of mois-ture conditioning. These figures show the capability of the proposed moisture damage model to model the concurrent evolution of both adhesive and cohesive damage.

Figure 6 shows an average stress–strain diagram for uniaxial compressive loading for the dry case and different conditioning times. It shows that the stiffness modulus and ultimate strength of the sample were reduced with increasing the time of exposure to mois-ture. These model predictions of the behavior of asphalt concrete in response to moisture degradation were qualitatively in good agreement with experimental results. Kringos et al. showed that ultimate strength and stiffness modulus decreased in response to more conditioning time in different combinations (16). Figure 7 shows

(a) (b)

FIGURE 4 2-D model: (a) geometry and (b) finite element mesh.


the induced mechanical damage density distribution for different moisture-conditioning times. This figure illustrates that the damage density gradually concentrated near the edges, where the material was already degraded by the moisture, as the exposure time increased.

The effect of the moisture-conditioning level on the ultimate strength of the asphalt concrete subjected to compressive loading was investigated via 3-D micromechanical simulations. Figure 8, a and b, shows the moisture diffusion through the 3-D model while it was exposed for 10 days to a normalized moisture content of one on the top of the sample. Figure 8c shows the moisture damage distribution at the end of the conditioning time.

Figure 9 shows the average stress–strain diagram in compressive mode of loading for dry and moisture-conditioned samples with different moisture-conditioning periods. This figure shows that the stiffness, ultimate strength, and failure strain of the material dimin-ished as the time of exposure to moisture increased. Figure 10 shows the moisture and mechanical damage distribution at different strain levels. As the moisture-conditioning time increased, the mechanical damage localized in the regions that had already experienced mois-ture damage. This effect can cause the local failure of a pavement section under traffic loading after a long wet season.

FIGURE 5 Proposed moisture damage model: (a) moisture diffusion when model was exposed to a moisture content of one on top and 0.5 on the lateral sides and (b) cohesive and (c) adhesive moisture damage (SDV 5 solution dependent variable; avg 5 average).

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FIGURE 6 Average stress–strain diagram for compressive loading at a strain rate of 5 3 10−5 1/s and temperature of 20°C.

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FIGURE 7 Mechanical damage distribution caused by compressive loading at (a) dry condition and (b) 3, (c) 10, and (d) 30 days’ moisture-conditioning time.

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FIGURE 8 Through 3-D model: (a) moisture diffusion contour, (b) moisture diffusion, and (c) cohesive moisture damage contour after 10 days’ moisture-conditioning time.

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FIGURE 9 Average stress–strain diagram for compressive loading at strain rate of 6.66 3 1024 1/s and temperature of 20°C (hrs 5 hours).

(Cohesive) Moisture damage

Mechanical damage at ε = 0.33%

dry 5 hrs 24 hrs 36 hrs

FIGURE 10 Damage distribution caused by compressive loading.(continued)


ConClusions

This paper proposes a moisture damage constitutive model coupled with a thermomechanical constitutive model to predict the complex responses of asphalt concrete subjected to mechanical loading and moisture. The model was used to conduct micromechanical simula-tions of 2-D and 3-D microstructural models. The theoretical devel-opments, experimental data, model predictions, and micromechanical simulations conducted in this study show the following:

• The proposed continuum moisture–mechanical damage mechan-ics framework provides a simple approach for constitutive modeling of the coupled moisture–mechanical phenomena.

• The proposed moisture damage model offers improvements over existing models in several aspects: the evolution function is time dependent, and it can consider the effect of damage history and the irreversibility of this phenomenon.

• The moisture damage model can model adhesive and cohesive moisture damage separately. It can also take into account the com-bined effect of adhesive and cohesive damage, as well as the transition between them.

• The proposed moisture–mechanical damage model along with the micromechanical simulations can be used effectively to simulate crack propagation within asphalt concrete materials.

• Moisture damage can alter the mechanical damage paradigm. Simulation results showed that mechanical damage localized within regions that were already degraded as a result of moisture. This localization phenomenon can lead to the local and premature failure (in the form of stripping) of pavement structures.

• Model simulations showed that the ultimate strength, stiffness moduli, and failure strain during the monotonic test decreased as the level of moisture damage increased.

• The model is capable of simulating the effect of moisture on the mechanical response of asphalt concrete materials.

The microstructure model used in this study did not include air voids as a separate phase. Future work will focus on including air voids and accounting for the effects of their interconnectivity on moisture diffu-sion. In addition, this study assumed constant diffusion coefficients that remain constants during the damage process. However, mechani-cal damage and moisture damage (in the form of stripping) probably affect the rate of moisture diffusion. This process can be modeled in future work by allowing the diffusion coefficient to change as a function of moisture damage and the evolution of mechanical damage.

Extensive experimentation continues to be conducted as part of the Asphalt Research Consortium project supported by FHWA to iden-tify the thermomechanical properties of asphalt binders and aggre-gates. As these properties continue to be identified, micromechanical



dry 5 hrs 24 hrs 36 hrs

FIGURE 10 (continued) Damage distribution caused by compressive loading.


simulations will be performed to validate the simulation results and to investigate the effect of different constituents on the moisture susceptibility of asphalt concrete. The authors believe that such studies will provide useful insights and practical recommendations to the pavement industry.

aCknoWlEDgmEnts

The authors acknowledge the financial support provided by FHWA through the Asphalt Research Consortium. Moreover, the authors acknowledge the Texas A&M Supercomputing Facility for providing computing resources useful in conducting the research reported in this paper. The authors acknowledge the assistance of Emad Kassem of the advanced characterization of infrastructure materials labora-tory at Texas A&M University in capturing and processing the X-ray CT images.

rEFErEnCEs

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The Characteristics of Asphalt–Aggregate Combinations to Meet Surface Requirements Committee peer-reviewed this paper.

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Continuum Coupled Moisture-Mechanical Damage Model for Asphalt Concrete