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International Journal of Pavement Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/gpav20
Three-dimensional microstructural modelling of coupled moisture–mechanical response of asphalt concrete a
b
c
d
e
Maryam Shakiba , Masoud K. Darabi , Rashid K. Abu Al-Rub , Taesun You , Dallas N. Little & Eyad A. Masad
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Department of Civil and Environmental Engineering, University of Illinois at UbranaChampaign, Urbana, IL 61820, USA b
Department of Civil, Environmental and Architectural Engineering, University of Kansas, Lawrence, KS 66045, USA c
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Mechanical Engineering Program, Masdar Institute of Science and Technology, Abu Dhabi, UAE d
Department of Civil Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA
e
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA f
Mechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar Published online: 04 Feb 2015.
To cite this article: Maryam Shakiba, Masoud K. Darabi, Rashid K. Abu Al-Rub, Taesun You, Dallas N. Little & Eyad A. Masad (2015): Three-dimensional microstructural modelling of coupled moisture–mechanical response of asphalt concrete, International Journal of Pavement Engineering, DOI: 10.1080/10298436.2015.1007239 To link to this article: http://dx.doi.org/10.1080/10298436.2015.1007239
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International Journal of Pavement Engineering, 2015 http://dx.doi.org/10.1080/10298436.2015.1007239
Three-dimensional microstructural modelling of coupled moisture –mechanical response of asphalt concrete Maryam Shakibaa, Masoud K. Darabib*, Rashid K. Abu Al-Rubc, Taesun Youd, Dallas N. Littlee and Eyad A. Masade,f a
Department of Civil and Environmental Engineering, University of Illinois at Ubrana-Champaign, Urbana, IL 61820, USA; Department of Civil, Environmental and Architectural Engineering, University of Kansas, Lawrence, KS 66045, USA; cMechanical Engineering Program, Masdar Institute of Science and Technology, Abu Dhabi, UAE; dDepartment of Civil Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588, USA; eZachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA; fMechanical Engineering Program, Texas A&M University at Qatar, Doha, Qatar b
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(Received 12 December 2014; accepted 15 December 2014) Three-dimensional (3D) microstructural representation of asphalt concrete subjected to moisture diffusion and mechanical loading is simulated and analysed. The continuum moisture – mechanical damage mechanics framework and the moisture damage constitutive relationship developed by the authors are used in this study to couple the detrimental effects of the mechanical loading and moisture diffusion on the complex response of asphalt concrete. A 3D finite element (FE) microstructural representation of a typical asphalt concrete is used for these simulations. The 3D microstructure is reconstructed from slices of two-dimensional X-ray computed tomography images that consist of the matrix and the aggregates. Results show that the generated 3D FE microstructure along with the coupled moisture – mechanical constitutive relationship can be effectively used to simulate the overall thermo-hygro-mechanical response of asphalt concrete. The analyses provide insight into the impact of the microstructure on the overall response of asphalt concrete. Keywords: moisture-induced damage; microstructural simulations; moisture – mechanical coupling; asphalt concrete pavements
Introduction Asphalt concrete is a highly heterogeneous material composed of aggregate, mastic (i.e. mixture of asphalt binder and fine aggregates) and air voids. These materials are subjected to both mechanical and environmental loading conditions. Moisture has been long recognised as one of the most, if not the most, important environmental factors contributing to premature failure of asphalt concrete. Moisture infiltrates through the microstructure and degrades the adhesive and cohesive properties of asphalt concrete. Application of mechanical loading to the moisture-degraded material encourages the fast propagation of cracks, which subsequently leads to premature failure of asphalt concrete materials and pavements. The properties and arrangement of asphalt concrete constituents are amongst the crucial factors affecting the response of asphalt concrete subjected to moisture –mechanical loading conditions. The complex asphalt concrete microstructure makes it imperative to develop systematic microstructural approaches that can relate the properties of the constituents to the material response at the macroscopic scale. These modelling and analysis approaches should explicitly incorporate distinct properties of the microstructural components and ultimately render a more deterministic
*Corresponding author. Email:
[email protected] q 2015 Taylor & Francis
and accurate prediction of mechanical responses. Such analyses should determine (1) the relation between the macroscopic response of the material and its composition and (2) the distributions of stress, strain and damage within the microstructure, which in turn should provide insight into failure mechanisms. Although the characterisation of macro-scale behaviour of asphalt concrete under coupled moisture diffusion and mechanical loading is procurable through experimental testing, it is difficult to control multiple microstructural features (e.g. aggregate shape, size and gradation; asphalt binder type; and air void content) in order to identify the critical factors that influence the response. Therefore, accurate microstructural models that utilise proper constitutive relationships and realistic microstructural representations are required to account for the effects of material variations in predicting the response of asphalt concrete subjected to various combinations of mechanical loading and moisture effects. Several researchers have conducted two-dimensional (2D) microstructural analyses to evaluate the effect of moisture degradation on the mechanical response of asphalt concrete. Kringos et al. (2008a) simulated an idealised 2D asphalt concrete microstructure and analysed the moisture degradation by introducing a moisture damage variable as a function of moisture content.
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Graham (2009) applied a time-dependent moistureinduced damage constitutive relationship to simulate an idealised 2D microstructural representation of asphalt concrete to investigate the response of moisture-conditioned specimens subjected to mechanical loading. Caro et al. (2010a, 2010b) constructed a simple 2D finite element (FE) microstructural representation of asphalt concrete using X-ray computed tomography (CT) image technique and subjected it to cycles of moisture diffusion and mechanical loading. They embedded cohesive zone elements to simulate the effect of moisture on damage evolution at aggregate –matrix interfaces. However, the main limitation of their method was that the model was only able to predict adhesive failure and not cohesive failure. Although it is known that crack growth due to moisture damage occurs usually at the aggregate– matrix interface, cracks may also initiate at the matrix phase and cracks initiated at the interface may propagate through the matrix. Furthermore, there is no concrete experimental study confirming that crack propagation occurs only at the aggregate –matrix interface. Therefore, a comprehensive constitutive relationship that can consider both adhesive and cohesive degradation as well as the transition between them is needed to simulate and predict crack propagation within the asphalt microstructure more accurately. Obviously, careful experiments should be designed and conducted to characterise cohesive and adhesive moisture damage properties independently. A more realistic and less restrictive three-dimensional (3D) representation of the asphalt concrete microstructure is necessary to obtain insight into its response to mechanical loading coupled with moisture intrusion. Due to the high complexity and very expensive computational cost of 3D microstructural representation very few attempts have been made to simulate asphalt concrete in this manner even in a dry condition. Abu Al-Rub et al. (2011) and You et al. (2012) employed coupled constitutive relationships of asphalt concrete developed by Darabi et al. (2011) to simulate the thermo-mechanical response of 2D and 3D microstructural representations of asphalt concrete. The FE microstructural representations were obtained based on 2D X-ray CT images. Recently, Varveri et al. (2014) developed and implemented a 3D micromechanical moisture damage model of asphalt concrete. The developed 3D FE meshes, obtained by X-ray scans, were used to demonstrate the significance of the air voids structure in the development of moisture damage in asphalt concrete specimens. This article addresses 3D FE simulations of the asphalt concrete microstructure subjected to various mechanical and environmental loading conditions. A 3D microstructural representation of stone matrix asphalt mixture was used in this study for these simulations. The constructed asphalt concrete microstructure was assumed to have two phases: aggregates and the matrix that include air voids, asphalt binder and aggregates smaller than 2.34 mm.
Aggregates smaller than 2.34 mm were included as part of the matrix phase to reduce the computational cost associated with FE microstructural simulations. For simplicity, the interface zone between the aggregate and matrix and the effect of air voids were not considered in this study. The moisture damage constitutive relationship developed by Shakiba et al. (2013) was coupled with the thermo-mechanical constitutive relationships developed by Darabi et al. (2011) and implemented in the pavement analysis using nonlinear damage approach (PANDA) FE package. The coupled moisture – mechanical constitutive relationship was assigned to the matrix phase to analyse the moisture degradation effect on the complex environmental –mechanical response of asphalt concrete. The effect of moisture on the evolution of distresses within the asphalt concrete’s microstructure was demonstrated through several simulations. It should be noted that considering the effect of different microstructural configurations, air void content, air void structure and tortuosity and the interface between aggregate and binder phase are among important factors that will affect the 3D coupled moisture mechanical response of asphalt concrete materials. Including these factors in 3D microstructural analysis will be the subject of future studies by the authors and their collaborators.
3D Representation of asphalt concrete’s microstructure The non-destructive X-ray CT technique was used to capture images of the internal microstructure of asphalt concrete. You et al. (2012) used the X-ray CT device in the advanced characterisation of infrastructure materials lab at Texas A&M University, Figure 1(a), to obtain 2D images from a cylindrical asphalt concrete specimen as illustrated in Figure 1(b), (c). The planar images include aggregates, mastic and air voids. A 3D microstructural representation of asphalt concrete was constructed based on the planar images. This study does not explicitly distinguish among binder, fine aggregates and air voids in order to decrease the computational cost. The mixture of asphalt binder, fine aggregates and air voids is referred to as matrix in this study. To implicitly account for fine aggregates and air voids, the average diffusivity of the mixture of binder, fine aggregates and air voids was assigned to the matrix phase. The digitised images obtained to represent the asphalt sample consist of 512 by 512 pixels. Each pixel has a grey intensity ranging from 0 to 255, with the lowest value representing black and the highest value representing white. Lower grey intensities correspond to the denser materials. Threshold filtering (e.g. Shapiro and Stockman 2002, Wang et al. 2004) was used to obtain the grey-scale
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International Journal of Pavement Engineering
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Figure 1. (a) X-ray computer aided tomography for non-destructive internal characterisation of material specimen, (b) grey-scale image and (c) image with well-separated aggregates.
contour between white as aggregate with the upper limit intensity of 255 and black as matrix with the lower limit intensity of 0. While aggregates and matrix are distinguishable clearly, they are connected to each other, see Figure 1(a), which poses a challenge for FE simulations which treats connected media as a single particle. To overcome this issue, the threshold segmentation capability of the commercial visualisation software Avizo (2009) was used to carefully divide the connected aggregates as shown in Figure 1(c). This step was conducted carefully to make sure the aggregate percentage remained approximately the same before and after the segmentation. It should be noted that the thinnest layer of matrix separating the aggregates dictates the element size in the FE model. This is one of the main reasons for high computational cost of FE analysis of realistic 3D microstructural representations of asphalt concrete since the matrix can be very thin causing the total number of elements in a 50 mm £ 75 mm sample to be of the order of several millions. The processed 2D images were used to construct the 3D microstructure as shown in Figure 2 by stacking them
vertically with equivalent 1 mm spacing. The obtained microstructural representation is a cylindrical specimen with a 50 mm diameter and 75 mm height. For simplicity, the matrix phase was fully bonded to the aggregate phase. The resulting representative volume element illustrated in Figure 2 was used to investigate the effect of
Figure 2. Reconstructed 3D FE microstructural representation of asphalt concrete.
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moisture on the mechanical response of asphalt concrete. Figure 2 shows the FE representation of the asphalt concrete microstructure composed of more than 2 million elements. The resulting FE representation of asphalt concrete was used to represent samples on which virtual tests were performed and the asphalt concrete was subjected to different moisture-conditioning and mechanical loading scenarios at different temperatures. The bottom of the specimen was constrained in the vertical direction and the mechanical load was applied on the top of the specimen to represent the configuration of testing in the lab. The microstructural simulations were conducted using the supercomputer HYDRA in the supercomputer facility at Texas A&M University. HYDRA is an IBM p575 massive parallel supercomputer with cumulative capacity of 640 processors and 1632 GB of memory. The average CPU time to run a single simulation presented in this article was around 40 h.
Coupled continuum moisture– mechanical damage mechanics framework The well-known framework of classical continuum damage mechanics (CDM) (e.g. Kachanov 1958) was extended to the continuum moisture – mechanical damage mechanics (CMMDM) framework (e.g. Shakiba et al. 2013) to suit CDM theories to be applicable to moisture susceptible materials. Mechanical loading and moisture conditioning both contribute in degrading the material integrity. Mechanical loading causes evolution and propagation of micro-cracks and micro-voids through the material while moisture diffusion and presence simultaneously degrades adhesive and cohesive strength of the material. To simplify the numerical implementation and mathematical modelling of complex moisture –mechanical response of asphalt concrete, this article defines different configurations in the context of CDM theories. Therefore, the well-known concept of the effective stress in the effective (undamaged) configuration was extended to the concept of stress in the introduced wet-damaged, wet-undamaged and dry-undamaged configurations. The term ‘wet’ is referred to the configuration that includes the degraded area due to moisture presence. Wet-undamaged, for example, is the configuration that includes the degraded areas due to moisture presence while microcracks and micro-voids induced due to mechanical loading were removed from the material. The modified framework introduces three material representative configurations. (a) wet-damaged configuration, which is the actual configuration of the material and includes micro-cracks and micro-voids as well as the area degraded by moisture; (b) wet-undamaged configuration that is the moisture-degraded but mechanically undamaged configuration. This configuration is obtained by
removing the mechanical induced micro-cracks and micro-voids inside the material from the real wet-damaged configuration of the material and (c) dry-undamaged configuration includes only the intact portion of the material that is neither mechanically damaged nor moisture degraded and significantly facilitates the coupling between the moisture damage and mechanical damage constitutive relationships. Readers are referred to Shakiba et al. (2015) for detailed information on the introduced representative configurations. This extension allows one to relate stress tensors in the dry-undamaged (i.e. counterpart of the effective configuration in CDM) and wet-damaged (i.e. counterpart of the nominal or damaged configuration of CDM) configurations, such that: s ¼ sð1 2 feff Þ;
feff ¼ 1 2 ð1 2 vÞð1 2 fÞ;
ð1Þ
where s and s are the stress tensors in the effective and nominal (wet-damaged) configurations, respectively. The term feff is the effective damage density ranging from 0 # feff # 1. The term f is the classical mechanical damage density variable ranging from 0 # f # 1, which is interpreted as the micro-damage density. The term v is the moisture damage variable such that v ¼ 0 corresponds to the case when moisture damage has not contributed to the degradation of the material and v ¼ 1 corresponds to full degradation due to moisture. Any value between 0 and 1 (i.e. 0 , v , 1) corresponds to partial reduction in material integrity due to moisture. Equation (1) treats the moisture damage generally as the contribution of the moisture in degrading the properties of moisturesusceptible materials. However, it should be emphasised that the moisture damage constitutive relationship will be different depending on the mechanism of the moisture damage and type of the material. Therefore, feff ¼ 0 indicates that the material has neither been mechanically damaged nor degraded by moisture while feff ¼ 1 indicates failure either due to complete damage (or fracture), full degradation or a combination of both. Any value between 0 and 1 (i.e. 0 , feff , 1) states that the materials’ integrity is partially reduced due to combined effects of moisture presence and mechanical loading. The expanded configurations allow one to express the constitutive relationships in the dry-undamaged configuration and then couple them with mechanical and moisture damage mechanisms as demonstrated in Equation (1). The strain equivalence hypothesis (Lemaitre and Chaboche 1990) was used in this article to relate the strain tensors in different configurations.
Moisture damage constitutive relationship The moisture damage constitutive relationship developed by Shakiba et al. (2013) was used in this study to simulate the effect of moisture degradation on the multi-mode
International Journal of Pavement Engineering response of asphalt concrete. The simplified form of the moisture damage constitutive relationship is recalled here, such that (Shakiba et al. 2013):
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v_ i ½uðtÞ ¼ k i uðtÞð1 2 feff Þq ;
i ¼ a; c;
ð2Þ
where u is the normalised moisture content defined as the ratio of the volume of air voids occupied by moisture over the total volume of air voids. The superimposed ‘i’ can be either ‘a’ for adhesive moisture-induced damage or ‘c’ for cohesive moisture-induced damage. The material properties k a and k c are adhesive and cohesive moisture damage fluidity parameters. The term q is the damage history exponent parameter. These parameters, k i and q, capture specific mechanisms occurring during moisture degradation and are bonded to the underlying physics of moisture degradation. In fact, 1/k has the unit of second and captures the time dependency of the moisture susceptibility of the material. In other words, this measure is an indication of the rate of loss in the strength and stiffness of asphalt concrete when subjected to moisture loading. The term ð1 feff Þq is referred to as the moisture damage history term. The history term captures three mechanisms implicitly. First, it captures the concentration-dependent moisture diffusivity. Experimental data show that moisture diffusivity is concentrationdependent and decreases as the level of moisture content
5
increases (Gandhi et al. 1987). The history term takes this effect into account such that the moisture diffusivity is implicitly decreased as the moisture content and subsequently the moisture damage level increases. Second, it defines the relative amount of material subjected to both adhesive and cohesive modes of damage and where cohesive and adhesive strengths have not yet been compromised by moisture damage, such that the more the cohesive and adhesive strengths are compromised the lower the rate of the moisture damage variable. Experimental results show that the rate of moisture damage variable decreases as the level of damage increases (Youtcheff and Aurilio 1997). Therefore, the history term, at a constant moisture content level, captures the availability of the intact material at the adhesive and cohesive modes, which are not moisturedegraded yet. The surface at the aggregate – matrix interface available for moisture substitution decreases with time as moisture gradually occupies the aggregate – matrix interface. Similarly, the rate at which matrix continues to absorb the moisture gradually decreases as the concentration of moisture within the matrix increases. Therefore, the evolution of both adhesive and cohesive moisture damage variables decreases with time, which is implicitly modelled through the history term. Finally, during concurrent moisture conditioning and mechanical loading, moisture damage encourages faster nucleation and propagation of micro-cracks and micro-voids until
Figure 3. (a) Schematic illustration of the pull-off experiment test set up, (b) FE mesh, and (c) moisture content contour after 24 h of moisture conditioning.
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2.5
(b) 2.5 AAG/Ceramic experiment results
2
2
Bond Strength (MPa)
Bond Strength (MPa)
AAM/Ceramic experiment results
1.5 AAM/Ceramic k=9.0×10–3 1/min & q=3
1
AAD/Brick experiment results 1.5 AAD/Brick k=1.8×10–4 1/min & q=3
1 AAG/Ceramic k=5.1×10–2 1/min & q=4
AAD/Ceramic experiment results 0.5
0.5 AAD/Ceramic k=9.5×10–1 1/min & q=5
0
0 0
5
10
15
20
0
25
5
10
(c)
15
20
25
Time (hrs)
0.9 Adhesive Moisture Damage, ωa
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Time (hrs)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
5
10
15
20
25
30
Time (hrs)
Figure 4. (a) and (b) Comparison of the proposed model predictions of the uniaxial bond strength with experimental measurements conducted by Youtcheff and Aurilio (1997) at different moisture-conditioning periods, (c) Model prediction of moisture damage evolution.
damage reaches a high enough level after which moisture can dissipate through flow and pressure gradients. At this stage, the rate of moisture damage evolution decreases as damage level increases. Based on the moisture damage framework presented herein, the moisture damage variable can physically be related to the adhesive and cohesive strengths at dry and moisture-conditioned states, such that (Graham 2009): X iðtÞ ¼ X i0 ð1 2 v i Þ i ¼ a; c:
ð3Þ
Equation (3) states that the adhesive/cohesive bond strength is equal to the initial dry bond strength when v i ¼ 0 (i.e. X iðtÞ ¼ X i0 ). However, when the material is completely degraded (i.e. v i ¼ 1), all strength is lost (i.e. X iðtÞ ¼ 0).
Equation (2) defines the evolution of the moisture damage variable in terms of normalised moisture content u. However, u should be known prior to solving for the moisture damage variable. Fick’s second law is used to simulate moisture transport phenomenon, such that:
u_ðx;tÞ ¼ 72 ðD uÞ;
ð4Þ
where D is the moisture diffusivity and 72 is the Laplace operator. The built-in algorithms of Abaqus FE software were used to obtain the evolution of normalised moisture content. It should be emphasised that the reduction of the moisture diffusivity as the moisture concentration increase is captured implicitly through the history term ð1 feff Þq . The presented moisture damage constitutive relationship has several advantages over the previously developed moisture damage relationships (Kringos et al. 2008a,
International Journal of Pavement Engineering Table 1.
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Viscoelastic, viscoplastic and mechanical damage parameters at the reference temperature T ¼ 208C, (Darabi et al. 2011).
n
1
2
3
4
5
0.01 1.43 £ 1023
0.001 2.47 £ 1023
k1 (MPa) 610 £ 1023
k2 215
Viscoelastic parameters
ln (s21) Dn (MPa21) D0 (MPa21)
10 1.98 £ 1024
1 1.48 £ 1023
0.1 6.56 £ 1024 3.5 £ 1023 Viscoplastic parameters
a 0.3
b 0.15
s0y (kPa) 100
Gvp (s21) 5 £ 1024
N 3.63
k0 (MPa) 35 £ 1023
Viscodamage parameters
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Gvd 4 £ 1026
Y 0 (MPa) 0.7
p 5
r 30
Time-temperature shift factors (T 0 ¼ 20o C) T ðo C Þ aT
10 7
Graham 2009). Equation (2) is time-dependent and considers the gradual degradation of the bond strength at a fixed moisture content. It accounts for the moisture damage irreversibility, such that lost stiffness and strength due to the moisture presence cannot be recovered upon drying. While partial recovery may occur upon drying, moisture may cause debonding between aggregate and matrix phases which is an irreversible phenomenon. In fact, one of the advantages of modelling the moisture damage phenomenon in the context of CDM is that it provides the flexibility to consider such recovery. However, addressing partial damage recovery upon drying is out of scope of this study. Equation (2) describes the damage process as a function of the damage history and not only based on the
20 1
40 0.008
current moisture state. Unlike the models based on cohesive zone elements, it can predict crack propagation both within the matrix and at the interface without prescribing a predefined crack path. Equation (2) provides the ability to simulate the evolution of adhesive and cohesive moisture degradation at the interface and the matrix simultaneously by assigning proper adhesive and cohesive moisture damage material parameters.
Coupled moisture –mechanical constitutive relationship The moisture damage constitutive relationship presented in this article was implemented in the PANDA that
Figure 5. (a) Moisture diffusion, (b) moisture damage contour through the 3D microstructural representation of asphalt concrete after 10 days moisture-conditioning.
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Cross sectional area A
3 dry 5hrs moisture conditioning
2.5
24hrs moisture conditioning
Average stress (MPa)
36hrs moisture conditioning
L
δ F
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Average stress = F/A Average strain = δ/L
2
1.5
1
0.5
0 0
0.005
0.01 0.015 Average strain (mm/mm)
0.02
Figure 6. Average stress– strain diagram for different conditioning period under compressive loading (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
dry
5hrs
24hrs
36hrs
Moisture damage
Mechanical damage at 0.67% strain
Mechanical damage at 1.0 % strain
Figure 7. Damage distribution due to moisture conditioning and compressive loading at different strain level (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
International Journal of Pavement Engineering for 3D problems can be written as:
1.4
dry 5hrs moisture conditioing 24hrs moisture conditioing 36hrs moisture conditioing
Average tensile stress (MPa)
1.2
1nve;t ij
1
d
¼
g0 ðstij ; T t ÞD0 stij
g2 ðstij ; T t Þstij
0.8
ct ¼
0 0
0.002
0.004
0.006
0.008
0.01
ðt
DD ðc
t
2c t Þ
0
dj ; aT
ð5Þ
0
0.6 0.4
þ
g1 ðstij ; T t Þ ðt
dt ;
dt
0.2
where t and t designate the response at a specific time; g0 , g1 and g2 are nonlinear viscoelastic parameters, s t is the stress tensor, T is temperature, c t is the reduced-time, aT is the time-temperature shift factor, D0 is the instantaneous compliance and DD is the transient compliance defined as a Prony series:
Average Strain (mm/mm)
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9
t
DD c ¼
Figure 8. Average stress – strain diagram for different conditioning period under tensile loading (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
N X
Dn 1 2 exp ð2ln c t Þ ;
ð6Þ
n¼1
where N is the number of terms, Dn is the nth coefficient of Prony series associated with the nth retardation time ln . includes constitutive relationships for the mechanical response of asphalt concrete. PANDA was developed and continues to be refined by the authors and their collaborators to predict the asphalt concrete response under environmental and mechanical loading. PANDA includes Schapery’s (1969) nonlinear viscoelasticity, Perzyna’s (1971) viscoplasticity and Darabi et al.’s (2011) viscodamage constitutive relationship. The key equations of the thermo-mechanical constitutive relationships implemented in PANDA are recalled in this section. Readers are referred to the previous publications by the authors and their collaborators for more details regarding PANDA and the methods used for the identification of PANDA model parameters (Abu AlRub et al. 2010, Darabi et al. 2011, Huang et al. 2011, Abu Al-Rub and Darabi 2012, Darabi et al. 2012a, 2012b).
Total strain additive decomposition The total deformation of asphalt concrete is influenced by time, temperature and loading rate and can be decomposed into recoverable and irrecoverable components. PANDA additively decomposes the total strain tensor, 1, into the nonlinear viscoelastic (recoverable), 1nve , and viscoplastic (irrecoverable), 1vp , strain tensors (i.e. 1 ¼ 1 nve þ 1 vp ).
Thermo-viscoplastic constitutive relationship PANDA uses Perzyna-type (1971) hardening viscoplastic constitutive relationship to account for permanent deformation (i.e. viscoplastic strain) of asphalt concrete materials, such that: * 1_vp ij
¼G
vp
f s0y
+N
›g ; ›sij
f ¼ t 2 aI 1 2 kðpÞ ;
ð7Þ
g ¼t 2 bI 1 ; where Gvp is the viscoplastic fluidity parameter, N is the viscoplastic rate sensitivity component, kl is Macaulay brackets, g is the viscoplastic potential function, f is the yield function and s0y is a yield stress quantity used to normalised the yield function and can be assumed to be a unity quantity. The terms a and b are the pressure sensitivity parameters, I 1 is the first stress invariant and t is the deviatoric effective shear stress. kð pÞ is the isotropic hardening function which is a function ofqthe effective ffiffiffiffiffiffiffiffiffiffiffiffi ffi vp (equivalent) viscoplastic strain p (i.e. p_ ¼ 1_vp ij 1_ij ) and defined as: kðpÞ ¼ k0 þ k1 1 2 exp ðk2 pÞ ; ð8Þ where k0 , k1 and k2 are material parameters.
Thermo-viscodamage constitutive relationship Nonlinear thermo-viscoelastic constitutive relationship PANDA uses Schapery’s (1969) nonlinear viscoelasticity to simulate the nonlinear viscoelastic response of asphalt concrete. The nonlinear viscoelastic strain, 1 nve;t , at time t
PANDA uses the viscodamage constitutive relationship proposed by Darabi et al. (2011). They postulated that the mechanical damage evolution in asphalt concrete, f_ , is a function of effective stress, s, hydrostatic effective stress,
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M. Shakiba et al. dry
5hours
24hours
36hours
dry
5hours
24hours
36hours
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Moisure damage
Mechanical damage at 0.2% strain
Mechanical damage at 0.4% strain
Figure 9. Damage distribution due to moisture conditioning and tensile loading at different strain level (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
skk , strain, 1, strain rate, 1, _ temperature, T, and mechanical damage history, f, such that (Darabi et al. 2011):
viscoplastic parts, T is the temperature and T 0 is the reference temperature.
2 p T f Yð1 2 fÞ Tot _ f ¼ G0 exp ðr1eff Þ exp 2d 1 2 ; To Y0 ð9Þ
Identification of moisture damage material properties
where Gf0 and Y 0 are the reference damage viscosity parameter and the reference damage force obtained at a reference stress for a creep test, Y is the damage force in the effective (undamaged) configuration, f is the mechanical damage density variable, which allows one to include damage history effects, p, r and d are material pffiffiffiffiffiffiffi Tot parameters, 1Tot eff is the effective total strain, 1eff ¼ 1:1, where 1 is 1 ¼ 1 nve þ 1 vp including both viscoelastic and
This section analyses pull-off test results performed by Youtcheff and Aurilio (1997) on different aggregate– binder combinations to identify the material properties associated with the presented moisture damage constitutive relationship. In these tests, a thin layer of binder was bound between an aggregate substrate and a metal pullstub. The metal pull-stub was pulled in uniaxial tension at a constant displacement rate to determine the aggregate– binder bond strength. Prior to testing, the sample was conditioned in a water bath for varying conditioning periods and moisture was forced to diffuse through the
International Journal of Pavement Engineering Θ = 1 on top
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3.5 teta=1, top teta=1, bottom teta=1, side diffusion
Average compressive stress (MPa)
3
Θ = 1 on the bottom of specimen
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(b)
0.005
Θ = 1 on lateral sides
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0.45 Average tensile stress (MPa)
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0
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.002
0.004 0.006 Average strain (mm/mm)
0.008
0.01
Figure 10. Stress – strain diagram for a normalised moisture content of 1, u ¼ 1, on top, bottom, and lateral surfaces after 3 days moisture-conditioning period and under (a) compressive (b) tensile loading (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
aggregate (Figure 3(a)). Displacement was then applied to the metal stub at a constant rate until the binder and the aggregate were separated. The bond strength (i.e. the ultimate tensile stress) was recorded for each moistureconditioning period. Visual observations confirmed that the failure was mostly in the adhesive mode. It should be mentioned that pull-off test results may change if the film thickness changes. Film thickness should be selected in a way to represent the actual thickness of the film coating the aggregates in asphalt concrete. In fact, in a recent study, Birgisson et al. (2005) investigated the concept of asphalt binder film thickness experimentally on the basis of measurements obtained by image analysis techniques, reflective light microscopy and scanning electron microscopy. Experimental results indicated that asphalt binder films coating large aggregates
do not actually exist in asphalt concrete. Instead, what are referred to as asphalt binder films surrounding large aggregates are actually asphalt mastic films referred to as asphalt matrix in this study. These films are highly irregular in shape and have a thickness greater than 100 mm in the asphalt concrete in their study. Furthermore, Marek and Herrin (1968) observed an inverse relationship between tensile strength and log of film thickness. Film as thick as 200 mm exhibited both brittle and intermediate ductile types of failure. Thicker films possess low tensile properties and could fail via flow failure. Therefore, thicker films would require some modification of the pulloff tester to accommodate excessive ductility during testing. The thinner films would lead to a decreased screening sensitivity. In this study, the pull-off test results with the film thickness of 200 mm were selected as an
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M. Shakiba et al. Diffusion from bottom
Diffusion from top
Diffusion from lateral side
Moisture damage
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Mechanical damage at 0.2% strain in compression
Mechanical damage at 0.2% in tension
Figure 11. Damage distribution at two different strain levels due to compressive and tensile loadings and three different moistureconditioning boundary condition (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C, 3 days moisture-conditioning period).
appropriate thickness to calculate adhesive failure material properties since first, the constructed microstructure has aggregate and matrix phases and the thickness of 200 mm is in the range of the results observed by Birgisson et al. (2005) for film thickness coating the aggregates, and second, Marek and Herrin (1968) showed that 200 mm film thickness represents the failure mechanism more accurately. FE simulations of the Pull-off experiments were performed using Abaqus (2008) to identify material properties associated with the moisture damage constitutive relationship. Figure 3(b) shows the FE mesh consisting of the aggregate substrate, asphalt binder and interfacial transition zone (ITZ) between the aggregate and binder to simulate aggregate– binder interface. A thin row of elements was inserted at the aggregate surface without embedding the cohesive zone elements to represent the ITZ. To calibrate the moisture damage constitutive relationship based on pull-off experiments, moisture content must be known at the asphalt phase. Coupled diffusion – displacement analysis was made to calculate
the moisture content at the aggregate– binder interface by solving Fick’s second law, which is an input for PANDA to obtain the value of moisture damage variable. Figure 3 (c) illustrates a typical regime of moisture diffusion through the structure after 24 h of moisture conditioning. The moisture damage variable for each conditioning period was calculated from the ultimate uniaxial tensile strength using Equation (5). Since moisture was the sole reason for degradation of the bond strength, the effective damage density and the moisture damage variable were assumed to be the same (i.e. feff ¼ v). Integrating the evolution function over the conditioning period implies: ðv 0
dh i q ¼ 1 2 hi
ðt
k i uðtÞdt;
i ¼ a; c:
ð10Þ
0
The moisture damage variable at the end of the pull-off test was obtained using Equation (3). Knowing the moisture content u at the binder – aggregate interface along with the ultimate value of the moisture damage variable, Equation (10) was solved for moisture damage variable,
International Journal of Pavement Engineering
Average compressive stress (MPa)
(a)
3 k=5e–4 /s k=5e–5 /s k=5e–6 /s k=5e–7 /s
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2
1.5
1
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0 0
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Average tension stress (MPa)
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1.4
k=5e–4 /s k=5e–5 /s k=5e–6 /s k=5e–7/s
1.2 1 0.8 0.6 0.4 0.2
13
As shown in Figure (4), both experimental measurements and model predictions show a sudden drop in the bond strength at early stages of moisture conditioning. As the moisture conditioning continues, the rate of decrease in the bond strength decreases. As shown in Figure (4), the moisture damage constitutive relationship is capable of capturing the experimentally observed trend for the drop in the bond strength as the conditioning time increases. Figure 4(c) demonstrates a typical evolution of the moisture damage variable as the condition time increases. As shown in Figure 4(c), the moisture damage variable increases at high rates at the beginning and then its rate decreases as the moisture-conditioning time increases. It is evident from Figure 4 that the moisture damage constitutive relationship is capable of predicting the time- and history-dependent decrease of the bond strength. It should be emphasised that these data were used for calibration purposes only to show that the moisture damage constitutive relationship is capable of capturing the trends observed in these experiments. The pull-off tests cannot be used for validation purposes because different materials were used in different sets of pull-off test experiments. The moisture damage constitutive relationship developed by Shakiba et al. (2013) was also calibrated against other pull-off tests result available in the literature (Kringos et al. 2008b, Pinto et al. 2009).
0 0
0.01
0.02
0.03
0.04
Average strain (mm/mm)
Figure 12. Stress – strain diagram for three different moisture damage model parameter, k, after 3 days moisture-conditioning period under (a) compressive, (b) tensile loading (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
Equation (11). Then, the moisture damage material parameters, k a and q, may be obtained by solving Equation (11) numerically.
1=ð12qÞ vaðtÞ ¼ 1 2 k a uðtÞ q 2 1 þ 1 :
ð11Þ
This procedure was repeated to identify the moisture damage material properties for different material combinations using the outlined procedure. Youtcheff and Aurilio (1997) conducted pull-off tests for different aggregate – binder combinations and measured bond strength at different moisture-conditioning periods. The procedure outlined earlier was used to identify the moisture damage material properties associated with the moisture damage constitutive relationship. Figure 4(a), (b) compares model predictions of the bond strength with the experimental data reported by Youtcheff and Aurilio (1997).
Micromechanical simulations To scrutinise the effect of moisture on the rate-dependent mechanical response of asphalt concrete, virtual constant displacement rate tests on specimens subjected to different moisture-conditioning periods were simulated at different temperatures. FE model was composed of aggregates and matrix phases. Aggregates were assumed as linear elastic with Young’s modulus of Eagg ¼ 25 GPa, Poisson’s ratio of n agg ¼ 0.16 and moisture diffusivity of 2.44 £ 1024 mm2/s while matrix was assumed to be moisture susceptible with thermo-viscoelastic-viscoplastic-viscodamage mechanical behaviour (e.g. Darabi et al. 2011, Shakiba et al. 2013) and moisture diffusivity of 5.56 £ 1026 mm2/s (Caro et al. 2010b). Material properties associated with the mechanical response of matrix phase are listed in Table 1. Moisture was allowed to diffuse through both matrix and aggregate phases. Since aggregate has higher diffusivity coefficient, moisture diffuses through matrix at a slower pace. To reduce the computational cost, aggregates were assumed to be fully coated by the matrix. It is noteworthy to mention that the proposed moisture damage constitutive relationship and the coupling framework were developed on the basis of CDM. This framework was developed for general cases and allows
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M. Shakiba et al. kc = 5×10–4/s
kc = 5×10–5/s
kc = 5×10–6/s
kc = 5×10–7/s
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Moisture damage
Mechanical damage at 0.67% strain
Mechanical damage at 2% strain
Figure 13. Damage distribution at different strain levels due to compressive loading after 3 days moisture-conditioning period for different moisture damage model parameters (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
one to simulate adhesive and cohesive moisture damage as well as the transition between them independently. To model both adhesive and cohesive moisture damage in a microstructure, the ITZ should be defined at the interface of aggregate and matrix. The adhesive properties should be assigned to the ITZ and the cohesive properties should be assigned to the matrix to distinguish between adhesive and cohesive moisture damage. In 3D FE representation of asphalt concrete, the number of aggregate faces were substantial such that considering the ITZ around each aggregate resulted in significant increase in the computational cost. Furthermore, adhesive and cohesive material properties should be extracted based on the pull-off tests that show distinct adhesive and cohesive failure regimes, respectively. However, most of the available experimental data show adhesive-type failure and proper experimental data to identify the cohesive moisture damage material properties were not available.
To reduce the computational cost and due to unavailability of experimental data on cohesive moisture damage, this study did not consider ITZ. Therefore, the material properties identified from the experiments conducted by Youtcheff and Aurilio (1997), i.e. k ¼ 5 £ 1024/s and q ¼ 5, were assigned to the matrix phase without explicitly distinguishing between adhesive and cohesive moisture damage. Therefore, in this study the analysis results are referred to as moisture damage without differentiating between adhesive and cohesive moisture damage. It should be noted that once the mechanical load is applied, the matrix at the interface of aggregate were severely damaged, in most cases, due to stress and strain localisation showing that even without differentiating between adhesive and cohesive moisture damage, the aggregate– matrix interface is more prone to cracking when the material is subjected to concurrent moisture conditioning and mechanical loading.
International Journal of Pavement Engineering kc = 5×10–4 /s
kc = 5×10–5 /s
kc = 5×10–6 /s
15 kc = 5×10–7 /s
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Moisture damage
Mechanical damage at 0.2% strain
Mechanical damage at 0.4% strain
Figure 14. Damage distribution at different strain levels due to tensile loading after 3 days moisture-conditioning period for different moisture damage model parameters (strain rate ¼ 6.66 £ 1024 1/s, temperature 208C).
Figure 5(a) illustrates moisture content contours after 10 days of moisture diffusion from the top surface of the specimen. The commercial software Abaqus (2008) was used to solve Fick’s second law to computationally determine the moisture content within the asphalt concrete. Figure 5(b) illustrates the evolution of the moisture damage variable. Figure 5(b) shows that the region close to the top of the specimen is significantly damaged due to the presence of moisture since the region close to top surface was exposed to a higher moisture level for longer period. Therefore, severe stripping may occur at the top surface once the mechanical load was applied as the integrity of asphalt matrix was significantly degraded prior to the application of the mechanical load. These results illustrate the capability of the constitutive relationship to predict the tendency of striping in asphalt concrete due to the susceptibility of the matrix to moisture.
The effect of moisture-conditioning period Specimens were computationally exposed to a normalised moisture content of 1 on the top surface for 5, 24 and 36 h to investigate the effect of moisture-conditioning time. Compressive and tensile mechanical loading was then applied to the moisture-conditioned specimens at a constant strain rate of 6.66 £ 1024 1/s. As shown in Figures 6– 8, the initial stiffness, the ultimate strength and the strain to failure are reduced as the period of exposure to moisture increases. The average stress presented in Figures 6 and 8 measured as the total of nodal reactions at the bottom of the specimen divided by the specimen area, and the average strain is the applied displacement divided by the length of the specimen. The damage contours at different average compressive and tensile strain levels are demonstrated in Figures 7 and 9, respectively. Figures 7 and 9 show that mechanical
M. Shakiba et al.
(a)
4
Average compressive stress (MPa)
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dry-strain rate=1.33e–3/s 10days-strain rate=1.3e–3/s dry-strain rate=6.66e–4/s
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qualitatively in good agreement with experimental results. Experimental work by Kringos et al. (2008b) showed that ultimate strength and stiffness modulus decreases upon moisture conditioning.
10days-Strain rate=1.33e–3/s
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1 0.8 0.6 0.4 0.2 0 0
0.005
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0.025
0.03
Figure 15. Stress – strain diagrams for two different strain rates at dry and 3 days moisture-conditioning period under (a) compressive and (b) tensile loading (temperature 208C).
damage initiates and propagates within the specimen as the strain level increases. For dry condition, damage initiates and propagates through the whole specimen almost evenly. As the moisture-conditioning time increases, damage starts to localise more near the top surface. The reason is that the area near the top surface degrade more due to moisture as the moisture-conditioning time increases. This is due to the fact that the subsequent applied mechanical load can induce higher level of damage at the region degraded by the moisture. Damage distribution and propagation differ slightly between tensile and compressive loadings especially at dry condition while the general trend for the response remains the same, i.e. as moisture-conditioning period increases, damage localises near the surface of the specimen where moisture has the greatest impact on degrading the material. However, the reduction of maximum strength in compressive loading is greater than its equivalent reduction under tensile loading with increase in moisture-conditioning period. These predictions of the behaviour of asphalt concrete due to moisture degradation are
The effect of different moisture boundary condition To establish the effects of different boundary conditions for moisture diffusion, simulations were repeated by allowing moisture to diffuse from (a) top, (b) bottom and (c) sides of the specimen. Then, compressive and tensile uniaxial loads at a constant average strain rate of 6.66 £ 1024 1/s at 208C was applied to the specimens. Figure 10(a), (b) illustrates the average stress – strain diagram for compressive and tensile loading for different moisture boundary conditions. The corresponding moisture and mechanical damage density distributions in compression and tension are presented in Figure 11. Figure 10(a) demonstrates that material fails in compressive mode of loading much faster when moisture was allowed to diffuse from the top surface, where the load was applied, compared to the case when moisture was allowed to diffuse from the bottom surface. Under the tensile mode of loading, the total strength did not differ by changing the diffusion from the top or bottom of the specimen. This behaviour can be explained based on the difference in the load transfer mechanisms within the microstructure in tensile and compressive loading modes. In compressive mode of loading, stress and load transfer is mainly due to the contact amongst the aggregate skeleton. Therefore, aggregate skeleton is the main factor affecting the maximum tolerable compressive load. When moisture is diffused from the top surface, the top surface is highly degraded which prevents the applied compressive load to be transferred properly leading to the local failure of the material at that region. However, when moisture diffuses from the bottom of the specimen, the force applied at the top surface, that is not degraded due to moisture, can still be distributed through the aggregate skeleton and be transferred to the bottom surface. Therefore, the local failure in the matrix at the bottom of the specimen due to moisture does not significantly affect the failure of the specimen since the aggregate skeleton can still redistribute the load. Furthermore, tensile stress and force is mainly distributed through the matrix phase, such that failure occurs at the region where the matrix is degraded the most whether it is at the top or bottom of the specimen. Therefore, moisture diffusion from top or bottom surface have similar effects on the tensile strength and the ultimate tensile strength do not vary significantly when moisture diffuses either through the top or bottom of the specimen. According to Figure 10, side diffusion of moisture significantly degraded the material integrity due to a greater area over which
International Journal of Pavement Engineering Dry 1.33×10–3
Dry 1.33×10–3
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6.66×10–4
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Moisture damage
Mechanical damage at 0.3% strain in compression
Mechanical damage at 0.3% strain in tension
Figure 16. Damage distribution at two different strain levels due to compressive and tensile loading at dry and 3 days moistureconditioning period for two different strain rates (temperature 208C).
moisture was allowed to diffuse and to induce high moisture damage levels in the specimen. Damage distribution contours in Figure 11 confirm this phenomenon. These figures illustrate how the moisture damage and degradation pattern cause and change the concentration of mechanical damage.
The effect of moisture damage model parameters In this section, a parametric study on the effect of moisture damage fluidity parameter (i.e. k in Equation (2)) is conducted. The moisture damage fluidity parameter captures the moisture susceptibility of asphalt matrix and consequently asphalt concrete and the rate at which
material degrades due to moisture presence. The constant compressive and tensile displacement controlled loading with the average strain rate of 6.66 £ 1024 1/s was applied on top of the specimen after 3 days of moisture conditioning. Figure 12(a), (b) illustrate the stress –strain diagram for different values of the fluidity parameter. It affirms that the maximum strength of material decreases as this parameter increases. Figures 13 and 14 demonstrate corresponding moisture and mechanical damage distribution at different strain levels in compression and tension, respectively. As the fluidity parameter decreases, the material becomes less susceptible to moisture presence and hence the contribution of the mechanical loading to failure increases.
M. Shakiba et al.
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does not have enough time to relax. The accumulation of more stress in the material encourages fast propagation of micro-cracks within the microstructure leading to lower ultimate strength. This is the main reason for the wellknown fact that viscous materials such as asphalt concrete behave more brittle at high rates of loading and become more prone to cracking. Similar trends were observed for both dry and moisture-conditioned specimens both in tension and compression. To confirm these arguments, damage density contours are plotted for compressive and tensile modes of loading in Figure 16. Figure 16 confirms that at the same strain level, more damage accumulates within the microstructure as the strain rate increases. The constitutive relationship used in this study can predict the impact of loading rate on the initial stiffness, ultimate strength, strain to failure and the coupling effect of moisture damage and strain rate.
dry, T=10°C
2.5
The effect of temperature
2 1.5
3days, T=10°C
1
3days, T=20°C dry, T=40°C
0.5
dry, T=20°C
3days, T=40°C
0 0
0.002
0.004 0.006 0.008 0.01 Average strain (mm/mm)
0.012
0.014
Figure 17. Stress – strain diagrams at three different temperatures for dry and 3 days moisture-conditioned specimens under a (a) compressive, (b) tensile loading (strain rate ¼ 6.66 £ 1024 1/s).
The effect of strain rate Rate of loading has a considerable impact on the response of asphalt concrete because of its time-dependent and viscous nature. To investigate the rate effect on the coupled moisture –mechanical response, simulations were repeated by applying displacement-controlled load at two different strain rates to dry and 3 days moistureconditioned specimens. Loading was applied at average strain rates of 6.66 £ 1024 1/s and 1.33 £ 1023 1/s both in compressive and tensile loading modes. Figure 15(a), (b) demonstrates the simulation results for average stress –strain responses in compression and tension, respectively. As shown in Figure 15(a), (b), for both dry and moisture-conditioned cases, the ultimate tensile and compressive strengths increase as the applied strain rate increases. The reason is that at lower strain rates, load is applied to the specimen slower, such that the induced stresses have more time to relax and does not cause rapid propagation of micro-cracks within the specimen. However, at high strain rates, the load is applied to the material very fast, such that induced stress
Simulations were repeated by applying a constant displacement rate loading with average rate of 6.66 £ 1024/s on dry and 3 days moisture-conditioned specimens at three different temperatures of 10, 20 and 408C. Figure 17 illustrates the significant effect of temperature on the response of asphalt concrete. Figure 17 shows that the initial stiffness and the ultimate strength of asphalt concrete significantly decrease as the temperature increases. For asphalt concrete materials, the effect of temperature and loading rate can be explained in a similar manner, such that material behaves more brittle at fast loading rates and low temperatures and more ductile at slow loading rates and high temperatures. The reason is that the asphalt binder and matrix govern the viscous behaviour of asphalt concrete. As temperature increases, asphalt binder and as a result asphalt concrete behave less viscous, such that induced stresses can relax faster and cause less damage. This trend is also confirmed in Figures 18 and 19 showing damage contours at different temperatures and strain levels for dry and moistureconditioned specimens. As shown in Figure 18, mechanical damage is greater at lower temperature as the material becomes more brittle. Figure 19 shows that for moistureconditioned specimens failure was mostly due to the moisture degradation and damage localised at the top surface where material integrity was lost due to the moisture presence. These figures depict damage distribution contours under tensile loading at dry and 3 days moisture-conditioned cases at three different temperatures. The mechanical damage concentrates on top of the specimen because of the moisture degradation effect and decreases as temperature increases. It can be concluded from these results that the coupled moisture –mechanical constitutive relationship is well
International Journal of Pavement Engineering T=10
T=20
19 T=40
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Mechanical damage at 0.13% strain in compression
Mechanical damage at 0.13% strain in tension
Mechanical damage at 0.3% strain in compression
Mechanical damage at 0.3% strain in tension
Figure 18. Damage distribution due to compressive and tensile loadings at three different temperatures at dry condition (strain rate ¼ 6.66 £ 1024 1/s).
suited to simulate the response of microstructure of asphalt concrete as a function of the effects of moisture and mechanical loading and can predict damage propagation within the matrix. Although these simulation results have not been validated against experimental data, the trends are compatible with experimental observations and can be used to obtain insight into the complicated microstructural behaviour of asphalt concrete. It should be emphasised that validation is an essential component of any modelling
effort. In a recent study, Shakiba et al. (2015) calibrated and validated the presented moisture damage constitutive relationship against lab experiments conducted on dry and moisture-conditioned specimens, as part of the asphalt research consortium (ARC) project sponsored by FHWA, to investigate the efficiency of the developed constitutive relationship in capturing the response of asphalt concrete subjected to mechanical and environmental loading conditions. Moreover, the microstructure representation
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M. Shakiba et al. T=10
T=20
T=40
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Moisture damage
Mechanical damage at 0.2% strain in compression
Mechanical damage at 0.2% in tension
Figure 19. Damage distribution due to compressive and tensile loadings at three different temperatures after 3 days moistureconditioning period (strain rate ¼ 6.66 £ 1024 1/s).
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 diffusion.
Conclusions In this article, the coupling framework and the moisture damage constitutive relationship of Shakiba et al. (2013) were applied to simulate the 3D microstructural representation of a typical asphalt concrete. The microstructural simulations conducted in this study show that: . The coupled moisture – mechanical framework and
constitutive relationships can be used effectively to simulate the evolution of damage as well as the region for damage localisation within the 3D
microstructural representation of asphalt concrete. . Microstructural simulations show that the moisture
damage constitutive relationship yield expected trends for the effect of moisture levels, moisture boundary conditions, moisture-damage material properties, applied strain rates and testing temperatures on the response of asphalt concrete. . The moisture – mechanical damage coupling framework can predict the change in damage propagation and localisation, which can lead to local and premature failure of the pavement structures, effectively. . The moisture damage constitutive relationship presented in this article is capable of predicting the coupled effect of mechanical and moisture damage. The moisture damage constitutive relationship coupled with the mechanical damage constitutive relationship implemented in PANDA is capable
International Journal of Pavement Engineering
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.
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of predicting magnitudes and trends of responses prior to and following various moisture regime histories. Calibration of the model prior to simulations provides realistic magnitude of the responses. Simulation results illustrate the ability of the coupled the moisture – mechanical constitutive relationship to capture the temperature and strain rate effects on changes in the strength and brittleness of asphalt concrete. The framework presented herein can be used to provide insight into the influence of the asphalt concrete microstructure on the response at the macro scale. Therefore, it can provide an effective tool to design the asphalt concrete. The micromechanical simulations can be used to compare the moisture susceptibility of different asphalt concrete mixtures. These simulations can help in selecting materials in order to construct more sustainable pavement structures. Based on this research, the characteristics of each asphalt concrete mixtures that make mixtures susceptible to mechanical damage when coupled with moisture effects can be recognised, identified and adjustments can be made to mix design strategies to correct damage susceptibility. To fully achieve this goal, the presented constitutive relationship should be validated against extensive experimental data and should be applied to asphalt concrete with different microstructural properties. This is the subject of a future work by the authors and their collaborators.
Acknowledgements The authors acknowledge the financial support provided by Federal Highway Administration through the Asphalt Research Consortium (ARC). Moreover, the authors acknowledge the Texas A&M Supercomputing Facility for providing computing resources useful in conducting the research reported in this article.
References Abaqus, 2008. Version 6.8. Providence, RI: Habbit, Karlsson and Sorensen, Inc. Abu Al-Rub, R., et al., 2011. Mesomechanical modeling of the thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamage response of asphalt concrete. International Journal of Advances in Engineering Sciences and Applied Mathematics, 3 (1 –4), 14 – 33. doi:10.1007/s12572-011-0028-9. Abu Al-Rub, R.K. and Darabi, M.K., 2012. A thermodynamic framework for constitutive modeling of time- and ratedependent materials. Part i: theory. International Journal Plasticity, 34, 61 –92. doi:10.1016/j.ijplas.2012.01.002. Abu Al-Rub, R.K., et al., 2010. A micro-damage healing model that improves prediction of fatigue life in asphalt mixes.
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International Journal Engineering Science, 48 (11), 966– 990. doi:10.1016/j.ijengsci.2010.09.016. Avizo, 2012, FEI Visualization Sciences Group, Inc. Birgisson, B., et al., 2005. Development and evaluation of test methods to evaluate water damage and effectiveness of antistripping agents. Report, Florida Department of Transportation, Tallahassee, FL. Caro, S., et al., 2010a. Micromechanical modeling of the influence of material properties on moisture-induced damage in asphalt mixtures. Construction and Building Materials, 24 (7), 1184– 1192. doi:10.1016/j.conbuildmat.2009.12.022. Caro, S., et al., 2010b. Coupled micromechanical model of moisture-induced damage in asphalt mixtures. Journal of Materials in Civil Engineering, 22 (4), 380– 388. doi:10. 1061/(ASCE)MT.1943-5533.0000031. Darabi, M.K., et al., 2011. A thermo-viscoelastic-viscoplasticviscodamage constitutive model for asphaltic materials. International Journal of Solids and Structures, 48 (1), 191– 207. doi:10.1016/j.ijsolstr.2010.09.019. Darabi, M.K., et al., 2012a. A modified viscoplastic model to predict the permanent deformation of asphaltic materials under cyclic-compression loading at high temperatures. International Journal Plasticity, 35, 100– 134. doi:10.1016/j. ijplas.2012.03.001. Darabi, M.K., et al., 2012b. A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part ii: numerical aspects and application to asphalt concrete. International Journal Plasticity, 35, 67 – 99. doi:10.1016/j. ijplas.2012.02.003. Gandhi, M.V., Rajagopal, K.R., and Wineman, A.S., 1987. Some nonlinear diffusion problems within the context of the theory of interacting continua. International Journal of Engineering Science, 25 (11-12), 1441 –1457. doi:10.1016/0020-7225 (87)90022-X. Graham, M.A., 2009. Damaged viscoelastic – viscoplastic model for asphalt mixes, Civil Engineering. College Station, TX: Texas A&M University. Huang, C.W., et al., 2011. Numerical implementation and validation of a nonlinear viscoelastic and viscoplastic model for asphalt mixes. International Journal Pavement Engineering, 12 (4), 433–447. doi:10.1080/10298436.2011.574137. Kachanov, L.M., 1958. On time to rupture in creep conditions. Izviestia Akademii Nauk USSR, Otdelenie Tekhnicheskikh Nauk 8, 26 – 31 (in Russian). Kringos, N., et al., 2008a. Modelling of combined physical – mechanical moisture-induced damage in asphaltic mixes, part 2: moisture susceptibility parameters. International Journal of Pavement Engineering, 9 (2), 129– 151. doi:10. 1080/10298430701792227. Kringos, N., Scarpas, A., and deBondt, A, 2008b. Determination of moisture susceptibility of mastic – stone bond strength and comparison to thermodynamical properties. Journal of the Association of Asphalt Paving Technologists (AAPT), 77, 475– 478. Lemaitre, J. and Chaboche, J.L., 1990. Mechanics of solid materials. Cambridge, UK: Cambridge University Press. Marek, C.R. and Herrin, M., 1968. Tensile behavior and failure characteristics of asphalt cements in thin films. Assoc Asphalt Paving Technol Proc, Lino Lakes, MN, USA. Perzyna, P., 1971. Thermodynamic theory of viscoelasticity. Advances in Applied Mechanics, 11, 313– 354. Pinto, I., Kim, Y., and Ban, G., 2009. Moisture sensitivity of hot mix asphalt (HMA) mixtures in Nebreska – phase II. Lincoln: University of Nebraska-Lincoln (Department of Civil Engineering).
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M. Shakiba et al.
Downloaded by [Rashid Abu Al-Rub] at 09:51 10 February 2015
Schapery, R.A., 1969. On the characterization of nonlinear viscoelastic materials. Polymer Engineering and Science, 9 (4), 295– 310. doi:10.1002/pen.760090410. Shakiba, M., et al., 2013. Continuum coupled moisture – mechanical damage model for asphalt concrete. Transportation Research Record: Journal of the Transportation Research Board, 2372 (1), 72 – 82. doi:10.3141/2372-09. Shakiba, M., et al., 2015. Constitutive modeling of coupled moisture– mechanical response of particulate composite materials with application to asphalt concrete. ASCE Journal of Engineering Mechanics, 141 (2), 1 – 16. doi:10.1061/ (ASCE)EM.1943-7889.0000841. Shapiro, L.G. and Stockman, G.C., 2002. Computer vision. Upper Saddle River, NJ: Prentice Hall PTR. Varveri, A., et al., 2014. The influence of air void content on moisture damage susceptibility of asphalt mixtures:
A computational study. Transportation Research Board 93rd Annual Meeting, Washington, DC, USA. Wang, L.B., Frost, J.D., and Lai, J.S., 2004. Three-dimensional digital representation of granular material microstructure from X-ray tomography imaging. Journal of Computing in Civil Engineering, 18 (1), 28 – 35. doi:10.1061/(ASCE)08873801(2004)18:1(28). You, T., et al., 2012. Three-dimensional microstructural modeling of asphalt concrete using a unified viscoelastic – viscoplastic – viscodamage model. Construction and Building Materials, 28 (1), 531– 548. doi:10.1016/j.conbuildmat. 2011.08.061. Youtcheff, J. and Aurilio, V., 1997. Moisture sensitivity of asphalt binder: Evaluation and modeling of the pneumatic adhesion test results. 42nd Annual Conference of Canadian Technical Asphalt Association, Ottawa, Canada.
