Creep models for asphalt under static load

CREEP MODELS IN ASPHALT TABLE OF CONTENT INTRODUCTION 3 Creeps in asphalt 3 CREEP ANALYSIS 4 Creep models 4 Mathematical creep models for asphalt 5 Factors affecting creep formation 6 CREEP ANALYSIS 4 Creep test analysis of static load of asphalt 6 Observed Results 7 Micromechanical modeling of asphalt uniaxial creep by using discrete element method 7 Characteristics of Asphalt concrete microstructure 7 Discrete element approach for micromechanical modeling of uniaxial creep in asphalt 8 Axial creeps versus

CREEP MODELS IN
ASPHALT
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TABLE OF CONTENT
INTRODUCTION...........................................................................................................................3
Creeps in asphalt..............................................................................................................................3
CREEP ANALYSIS........................................................................................................................4
Creep models...............................................................................................................................4
Mathematical creep models for asphalt.......................................................................................5
Factors affecting creep formation................................................................................................6
CREEP DAMAGE PROPERTIES OF ASPHALT UNDER STATIC LOAD...............................6
Creep test analysis of static load of asphalt.................................................................................6
Observed Results.........................................................................................................................7
Micromechanical modeling of asphalt uniaxial creep by using discrete element method..............7
Characteristics of Asphalt concrete microstructure.....................................................................7
Discrete element approach for micromechanical modeling of uniaxial creep in asphalt............8
Axial creeps versus load time......................................................................................................8
Log loading duration versus creep compliance...........................................................................8
Finite element analysis of creep equation for high modulus asphalt...............................................9
Comparison of discrete and finite element models......................................................................9
Creep constitutive equation.........................................................................................................9
CONCLUSION..............................................................................................................................10
REFERENCES..............................................................................................................................11
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INTRODUCTION
Pavement engineering is defined as the branch of civil engineering which deals with the
rehabilitation and management of pavements. These structures are concerned with application of
man-made surfaces to ground so that objects are allowed to move across it. This branch
emphasizes on designing and maintenance of rigid and flexible pavements (Esfandiarpour,
Saman, and Ahmed, 2017). The report aims at evaluation of advance topic in pavement
engineering. It will critically evaluate the creep models in asphalt (flexible pavement). The
document will analyze the creep damage model of asphalt. It will describe the creep behavior
and stability analysis of this advance technique. The report will highlight the finite element
analysis on creep constituting high modulus asphalt concrete. Further the report will analyze the
results and advantages obtained from this advance technique. It will compare Burger’s model
and Vander Pool model along with their stability analysis.
Creeps in asphalt
In asphaltic concrete creep is also called rutting or deformation and is key failure
mechanism within infrastructure of road network. In many countries including Australia
construction authorities does not focus on minimizing creeps rather they have greater reliability
on empirical testing methods which rank material performance in testing laboratory. The
advancements in the creep models in asphalt are effective in predicting creeps and provide highly
efficient methods for simulation of temperature, stress and boundary parameters of pavement in
field. Asphalt is mainly used in urban environment and involves huge investment in
maintenance. Structural distresses in asphalt are in the form of creep deformation and fatigue
cracking. Creep refers to strain accumulation as a result of traffic loads and is dependent on time.
Due to heavy traffic on roads under the wheel paths permanent deformation occurs which is
known as rutting (Moghaddam and et.al., 2014). When load is removed then some deformations
can be easily recovered while some remains permanently in asphalt mixture. The factors like
temperature, stress, properties of material used, duration of load and mix design controls the
severity of deformation. Rutting generation is accomplished by following two mechanisms:
Shear deformation: It is defined as the lateral movement of material and is more significant than
densification approach. In this approach asphalt is pushed down under the pressure of tyre or
wheel load and is displaced in upward direction on either side of wheel path.
Densification: It is the result of inefficient compaction during the process of construction or in
early development stage of pavement. Traffic pressure encourages aggregates to pack more
closely which is known as post construction compaction. Thus it also reduces air voids.
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In the initial stages permanent deformation is result of traffic compaction or densification
whereas during entire life time of pavement shear deformation is the major case for developing
rutting.
Current practices
Current standards of Australian use include quasi or full confining stress so that the better
replica of field conditions can be obtained. In quasi confinement smaller platen is kept on an
oversized sample of asphalt. The lack of proper confining of annulus of asphalt can result in
radial splitting (Ma and et.al., 2016). The purpose of this approach is to explore platen to effects
of sample diameter with the help of viscoelastic modeling. However this can be augmented by
using hoop stress which is applied through confining ring. This mechanism is similar to
geomechanism of soil consolidation test by odometer method. Performance of creep field in
asphalt can be predicted by calibrating viscoelastic model.
CREEP ANALYSIS
Creep strain in asphalt can be divided into four components by following equation.
ε (t) = ε (e) +ε (p) + ε (ve) + ε (vp)
Where, ε (t) is the creep strain
ε (e) is time dependent and recoverable elastic strain
ε (p) is called is time dependent and irrecoverable plastic strain
ε (ve) is known as viscoelastic strain. It can also recover with time and thus can be considered as
time dependent.
ε (vp) is unable to recover and is called viscoplatic strain.
 Small stresses can cause asphalt to behave elastically. When load or stress is removed
elastic strain is also disappeared.
 The creep behavior becomes plastic when high stress is applied. It leads to permanent
strain so even after stress is removed recovery is not possible.
 In viscoeleastic behavior loading first cause elastic action which is followed by gradual
increase of strain at declining rate.
Creep models
Asphalt concrete belongs to viscoelastic materials. The standard form of Hookean spring model
and Newtonian dashpots is used to explain the creep behavior but it cannot be used in case of
asphalt (Safi and et.al., 2018). Spring model is suitable for purely elastic material. To describe
the nature of these materials following models can be used.
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Kelvin model: It is also known as the Voigt model and it gives the characteristic of elastic delay.
It can be achieved by parallel combination of Newtonian dashpot and spring model. In unloaded
situation deformation is not observed. On application of load dashpot immediately accept load
and is deformed. With passage of time spring deformation also began.
ε = (σ /E)* [ 1-e^(-Et/ η) ]
This model does not show both permanent srain after unloading and time independent strain
during unloading and loading.
Maxwell model: In this model series connection of Newtonian dashpot and Hookean spring is
used. In this model total strain is expressed as the sum of elastic and viscous strain.
ε (t) = (σ/E) + (σ *t/ μ)
Where E is the Young’s modulus and σ is stress (Esra'a, Alrashydah, and Saad, 2018). The ratio
(σ/E) is called elastic strain and (σ *t/ μ) is viscous strain (Zhang and et.al., 2018).
Van der Poel model: It combines the Hookean spring with Kelvin model. The strain is given by
the expression:
ε = (σ/E1) + (σ/E2)* [ 1-e^(-E2t/ η) ] where η is viscosity coefficient
Burgers model: This model consists of Van der Poel model along with an additional connection
of Newtonian dashpot. Its equation is given by
ε (t) = = (σ/E1) + (σ/ η)*t + = (σ/E2) * [ 1-e^(-E2t/ η2) ]
Mathematical creep models for asphalt
The following models are mostly used for asphalt creep analysis.
Power model: It gives the relationship between load applications and permanent strain by
following equation.
ε (P) = a*(n)^b
ε (P) is permanent strain, n is the number of load application and a, b are constants.
Ohio state model: This model characterizes accumulation of permanent strain. It is also valid for
formation of ruts in all layers of pavement. The model equation is given by expression:
ε (P) /N = A(N)^(-M)
N is the number of permitted load applications
A and M are constant which depends upon stress and type of material
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Allen and Deen model: It is also one of the models which describe permanent deformation to
predict creeping in asphalt, sub bases and dense aggregate layers (Mounes and et.al., 2016).
log εp=C0+C1(log N)+C2(log N)2 +C3(log N)3
Where N is number of times stress repetitions occur and
C0, C1, C2, C3 are regression coefficients.
Factors affecting creep formation
The factors which influences creep formation are classified into asphalt related and
others. The non asphalt associated factors includes temperature, traffic load, frequency of
loading and unloading and moisture. Similarly asphalt related parameters include aggregate,
mixture properties and bitumen.
Impact of frequency: In repeated load asphalt test it is observed that short pulse duration results
in increased rate of permanent strain.
Load application: As the wheel load and tire pressure increases there is significant increment in
stress within asphalt. Gradually it leads to permanent strain and decline in failure duration.
Bitumen and mixture properties: The content, quality and its grade affect the creep behavior.
The temperature for mixing, nature and type of compaction, aggregate also influences the asphalt
creep. The temperature factor is responsible for stiffness in asphalt. As temperature is increased
it reduces the stiffness. Temperature variations also have significant impact on bitumen content
and can dramatically change permanent strain (Grishchenko, Alexey and Artem, 2016).
CREEP DAMAGE PROPERTIES OF ASPHALT UNDER STATIC LOAD
Viscosity deformation of asphalt does not increase in an uncontrolled mechanism with
loading time. With time rate of deformation flow gradually decreases with time. In order to
explain the creep deformation analysis of asphalt non linear viscoelastic creep model and
damage model for creeps are used for analysis of permanent deformation. The static creep
deformation is divided into three stages.
 Migration period: In this phase strain is rapidly increased but strain rate decreases
gradually with increasing time period.
 Stability period: Though strain is increased gradually with steady growth but strain rate
remains constant.
 Destruction period: In this period with the time increment strain and strain rate both
factors increases until failure occurs.
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Creep test analysis of static load of asphalt
At lower stress level in asphalt mixture value of creep curve slope stabilizes from high to
low value. It shows that deformation resistance is increased and makes further process of
deformation quite difficult. Viscous flow with the load variation does not influence the time
extension with load and increases infinitely. Gradually the increment process decreases a nd
reaches to stability. This process is known as the consolidation effect. At the same temperature
with higher extent of stress, asphalt is not able to produce viscous flow and this flow decreases
with time. Temperature has great impact on ability of deformation resistance (Saboo, Nikhil, and
Praveen, 2015). With the increase in temperature values of resistance quickly decreases at just
double rate. Asphalt mixtures are typical viscoelastic thus their deformation properties are
temperature dependent.
Observed Results
From the above mentioned damage properties following conclusions can be drawn:
 Viscous flow deformation is stable after long duration of loading with low stress level.
This phenomenon is called consolidation effect.
 When stress is high and same temperature is maintained then with passage of time strain
rate remains stable and distortion is accelerated. It is also observed that temperature and
deformation resistance are inversely proportional to each other.
 An ideal and more stable creep model is developed on the basis of asphalt mixture
characteristics. This model can explain consolidation effect, permanent deformation after
unloading and rheological features such as instantaneous elastic deformation.
Micromechanical modeling of asphalt uniaxial creep by using discrete element
method
Asphalt mixtures are heterogeneous mixtures which consist of mastic, air voids and
aggregates. The interaction and distribution of these elements defines the properties of asphalt
concrete. It also has significant impact on durability, capacity of bearing load and creep
resistance potential. Plastic deformation in asphalt is the function of aggregate properties like its
shape, texture and performance of asphalt pavement. On the other hand mastic properties depend
upon temperature, asphalt binder and loading rate (Zhu and et.al., 2014). There are mainly two
simulation techniques which can be used for modeling of asphalt concrete Theses methods are
finite element method (FEM) and discrete element method (DEM). The discrete method is based
on micromechanical approach.
Characteristics of Asphalt concrete microstructure
In the microstructure analysis of asphalt its cores are scanned in a direction perpendicular
to the vertical axis at regular intervals around 1mm. The images of asphalt concrete are captured
by threshold algorithm called Volumetric based global minima (VGM). This is an automated and
one of the highly efficient techniques of digital image processing. VGM can also process
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horizontally slice X-ray cathode tube images. This approach is based upon identification of gray
level boundaries which is threshold between mastic, air and aggregate phases related to
volumetric knowledge. VGM has following three stages.
 Initially image is processed for enhancement and eliminating noise.
 In the second phase key action of accepting threshold route is performed. It is accepted as
enhanced image for first phase and as volumetric information for asphalt. Thus this stage
consists of two elements: Thresholding driven by volume and 3 dimensional sectioning.
 In final stage image segmentation and edge detection techniques are used for more
detailed enhancement of particle separation.
Discrete element approach for micromechanical modeling of uniaxial creep in asphalt
Discrete element model (DEM) is most widely used two dimensional models. In this
model testing is performed on the principle of coulomb frictional components and assumption
that particles are circular disk which interact through shear and normal springs. To calculate the
displacement and contact forces movement of each particle is traced. The interaction of each
particle with its neighbor particle provides the effective force. For simulation purpose discrete
element model uses Newton’s second law and force displacement law. The first scheme
evaluates the mobility of every particle due to body forces which acts on it whereas the second
scheme updates the forces resulting from relative motion (Micromechanical Modeling of Asphalt
Concrete Uniaxial Creep Using the Discrete Element Method, 2010). Thus DEM model of
asphalt concrete involves following stages.
 Input the asphalt microstructure.
 Defining initial and boundary values
 Determining properties of material
Axial creeps versus load time
Discrete element model predicts the axial strain or creeps similar to creeps which are
measured experimentally. The axial strain and time response curve has three regions namely
primary, secondary and tertiary region. In primary region strain rate undergoes into declination.
The secondary stage is also known as the steady state in which strain rate remains constant.
Usually the tertiary stage in which strain rate is increased is rarely observed in experiments. It is
also observed that in primary phase experimental strain for simulated asphalt mixture are higher
than predicted value of strain. Contrary to this, in secondary phase axial strain value give
satisfactory agreement in relation to experimental value. The regression models can be used to
measure the permanent deformation of asphalt concrete (Falchetto, Augusto and Ki Hoon Moon,
2015). However it is observed that for tertiary region experimental observations cannot
characterize asphalt behavior distinctly. The major cause for this evaluation is that laboratory
creep tests are not conducted for long duration and thus tertiary zone is not materialized to show
these results.
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Log loading duration versus creep compliance
Creep compliance is also known as the inverse of stiffness. The benefit of plotting load
duration and creep compliance is that this approach allows identification of various creep stages
at the earliest. Creep compliance can also be expressed as the ratio of axial strain and time
dependent stress. In the initial stage discrete element measurements have lower values of creep
compliances as compare to experimental one. While for steady state they give satisfactory
results. The maximum absolute error for steady state intercept and slope is less than 2.5%. Also
the models cannot provide comparison of flow time parameters and measurements which are
provided in experimental measurements.
Finite element analysis of creep equation for high modulus asphalt
High modulus asphalt concrete (HMAC) mixture is agitated by grading stones and
additives which are called hard asphalt. At 15 degree Celsius their dynamic modulus can posses
value around 14000 MPa which encourages the high rutting resistance and low temperature and
thermal fatigue cracking. Viscoelastic theory can give suitable method to analyze the mechanical
properties of HMAC. Creep test methods are simple and controllable thus many engineers and
researchers consider the laboratory test for evaluation of road stress by using strain and stress
relationship of asphalt (Finite Element Analysis on the Creep Constitutive Equation of High
Modulus Asphalt Concrete, 2015). It is very difficult to simulate mechanical properties when
viscoelastic data is obtained from stress-strain parameters of asphalt. Thus to accomplish better
analysis for high modulus asphalt creep models can be analyzed in ABAQUS.
Comparison of discrete and finite element models
From the experimental results it is observed that predictions for finite element (FE)
method are higher than the discrete element method (DEM). The aggregates are rigid in FE
whereas in DE aggregate stiffness is used. In stiffness analysis it is observed that FE over predict
the value. However in DEM stiffness is under predicted at high temperature and long duration of
loading time. Thus both models can give suitable prediction for measurement of stiffness.
Creep constitutive equation
Plastic deformations are not recoverable it is not possible to determine the inelastic
deformation and stress by using current deformation state or route history. To address this
situation finite element analysis use incremental constitutive equation. Creep effect is considered
as time dependent. Finite element analysis can evaluate the steady creep phase (Zhang and et.al.,
2016). However in order to evaluate the transient phase of creep stages incremental FE is
employed along with the thermal elastic and plastic creep analysis. The strain parameters of
asphalt are expressed by the equation:
ε (t) = ε (e) +ε (p) + ε (ve) + ε (vp)
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On simplifying this equation by using Bailey Norton creep law creep rate can be obtained as
follow:
ε (Cr) = [ C1 * (σ ^C2)* (t^C3+1) ] / (C3+1)
The above equation is known as the creep rate in converted ABAQUS. The parameters C1, C2
and C3 are temperature dependent parameters and can be determined by material testing. At
constant temperature C1 has the highest amplitude of variation and C3 is always negative with
its values always less than 1. At variable temperature creep coefficient C1 shows increment in
series and the partial stress index C2 undergoes into declination at an extent of around 4 times
(Zhang and et.al., 2017).
CONCLUSION
From the report it can be concluded that creep models for asphalt concrete can be used to
analyze the behavior and characteristics of creep formations and permanent deformations in
asphalt. The study will help to develop and construct roads and pavements with higher strength
and load handling capacity. The report has explained the creep behavior in asphalt concrete and
the factors which affects the creep formation. It has described the creep damage properties under
stationary load. The document has analyzed the finite element analysis for high modulus asphalt
concrete.
From the report it is also observed that discrete element methods can be effectively used
for micromechanical modeling of asphalts having uniaxial creeps. Thus it is also concluded from
the report that study and advancements in creep models can prove to be effective and give highly
qualitative results to achieve goals and principles of pavement engineering. Creep models of
asphalt will help pavement engineering to construct designs which have will be able to cope up
with the increasing traffic loads without leading to deformation or creeps.
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REFERENCES
Books and Journals
Zhu, Xing-yi, Xinfei Wang, and Ying Yu. "Micromechanical creep models for asphalt-based
multi-phase particle-reinforced composites with viscoelastic imperfect interface." International
Journal of Engineering Science 76 (2014): 34-46.
Esfandiarpour, Saman, and Ahmed Shalaby. "Local calibration of creep compliance models of
asphalt concrete." Construction and Building Materials 132 (2017): 313-322.
Moghaddam, Taher Baghaee, Mehrtash Soltani, and Mohamed Rehan Karim. "Evaluation of
permanent deformation characteristics of unmodified and Polyethylene Terephthalate modified
asphalt mixtures using dynamic creep test." Materials & Design 53 (2014): 317-324.
Ma, Tao, Deyu Zhang, Yao Zhang, Yongli Zhao, and Xiaoming Huang. "Effect of air voids on
the high-temperature creep behavior of asphalt mixture based on three-dimensional discrete
element modeling." Materials & Design 89 (2016): 304-313.
Safi, Fazal R., Kamal Hossain, Shenghua Wu, Imad L. Al-Qadi, and Hasan Ozer. A Model to
Predict Creep Compliance of Asphalt Mixtures. No. 18-04715. 2018.
Esra'a, I. Alrashydah, and Saad A. Abo-Qudais. "Modeling of creep compliance behavior in
asphalt mixes using multiple regression and artificial neural networks." Construction and
Building Materials 159 (2018): 635-641.
Zhang, J. B., B. J. Lu, S. F. Gong, and S. P. Zhao. "Comparative Analyses of Creep Models of a
Solid Propellant." In IOP Conference Series: Materials Science and Engineering, vol. 359, no. 1,
p. 012050. IOP Publishing, 2018.
Zhang, Deyu, Lijin He, Youxin Wei, and Ling Cong. "Micromechanics-based Analysis of Effect
of Internal Structure on Creep Anisotropy of Asphalt Concrete." DEStech Transactions on
Materials Science and Engineering ictim (2017).
Mounes, Sina Mirzapour, Mohamed Rehan Karim, Ali Khodaii, and Mohamad Hadi Almasi.
"Evaluation of permanent deformation of geogrid reinforced asphalt concrete using dynamic
creep test." Geotextiles and Geomembranes 44, no. 1 (2016): 109-116.
Grishchenko, Alexey I., and Artem S. Semenov. "Effective methods of parameter identification
for creep models with account of III stage." In MATEC Web of Conferences, vol. 53, p. 01041.
EDP Sciences, 2016.
Saboo, Nikhil, and Praveen Kumar. "A study on creep and recovery behavior of asphalt
binders." Construction and Building Materials 96 (2015): 632-640.
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Falchetto, Augusto Cannone, and Ki Hoon Moon. "Micromechanical–analogical modelling of
asphalt binder and asphalt mixture creep stiffness properties at low temperature." Road Materials
and Pavement Design 16, no. sup1 (2015): 111-137.
Zhang, Jiupeng, Zepeng Fan, Kai Fang, Jianzhong Pei, and Li Xu. "Development and validation
of nonlinear viscoelastic damage (NLVED) model for three-stage permanent deformation of
asphalt concrete." Construction and Building Materials 102 (2016): 384-392.
Online
Finite Element Analysis on the Creep Constitutive Equation of High Modulus Asphalt Concrete,
2015. [Online] Accessed through < https://www.hindawi.com/journals/amse/2015/860454/>
Micromechanical Modeling of Asphalt Concrete Uniaxial Creep Using the Discrete Element
Method, 2010. [Online] Accessed through <
https://www.researchgate.net/publication/232891205_Micromechanical_Modeling_of_Asphalt_
Concrete_Uniaxial_Creep_Using_the_Discrete_Element_Method >
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