Numerical implementation and validation of a nonlinear viscoelastic and viscoplastic model for asphalt mixes (original) (raw)
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A two-constituent nonlinear viscoelastic model for asphalt mixtures
Road Materials and Pavement Design, 2019
The goal of this study is to model the creep and recovery response of fine asphalt mixtures using a thermodynamically consistent nonlinear viscoelastic model. The model considers asphalt mixture to consist of two constituents: aggregate structure incorporating the asphaltaggregate interface and asphalt binder. The efficacy of the model is evaluated using the response of warm fine aggregate mixtures (WFAM). These materials were produced using a polymer-modified binder of PG 76-22 and three warm mix additives (Sasobit, Advera and Rediset). Unaged and aged samples were subjected to creep stress levels of 75 and 400 kPa followed by rest periods. The model was quite successful in capturing the material behaviour as a single set of parameters were derived from the prediction of shear and normal stress responses for both 75 and 400 kPa stress levels. The presented model offers a unique feature in modelling the energy storage and dissipation of each of the two constituents. As such, one can examine the effect of changes in individual material properties on the material response and performance.
A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials
2011
A temperature-dependent viscodamage model is proposed and coupled to the temperature-dependent Schapery's nonlinear viscoelasticity and the temperature-dependent Perzyna's viscoplasticity constitutive model presented in Abu Al-Rub et al. (2009) and Huang et al. (in press) in order to model the nonlinear constitutive behavior of asphalt mixes. The thermo-viscodamage model is formulated to be a function of temperature, total effective strain, and the damage driving force which is expressed in terms of the stress invariants of the effective stress in the undamaged configuration. This expression for the damage force allows for the distinction between the influence of compression and extension loading conditions on damage nucleation and growth. A systematic procedure for obtaining the thermo-viscodamage model parameters using creep test data at different stress levels and different temperatures is presented. The recursive-iterative and radial return algorithms are used for the numerical implementation of the nonlinear viscoelasticity and viscoplasticity models, respectively, whereas the viscodamage model is implemented using the effective (undamaged) configuration concept. Numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. The model is then calibrated and verified by comparing the model predictions with experimental data that include creep-recovery, creep, and uniaxial constant strain rate tests over a range of temperatures, stress levels, and strain rates. It is shown that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions.
International Journal for Numerical and Analytical Methods in Geomechanics, 2012
Based on the continuum damage mechanics, a general and comprehensive thermodynamic-based framework for coupling the temperature-dependent viscoelastic, viscoplastic, and viscodamage behaviors of bituminous materials is presented. This general framework derives systematically Schapery-type nonlinear viscoelasticity, Perzyna-type viscoplasticity, and a viscodamage model analogous to the Perzyna-type viscoplasticity. The resulting constitutive equations are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identifying the model parameters is discussed. Finally, the model is validated by comparing the model predictions with a comprehensive set of experimental data on hot mix asphalt that include creep-recovery, creep, uniaxial constant strain rate, and repeated creep-recovery tests in both tension and compression over a range of temperatures, stress levels, and strain rates. Comparisons between model predictions and experimental measurements show that the presented constitutive model is capable of predicting the nonlinear behavior of asphaltic mixes under different loading conditions. In terms of the viscoelastic behavior of materials, Biot [13] derived a formulation for linear viscoelastic materials. Schapery used the thermodynamics of irreversible processes and developed a single integral constitutive model for nonlinear viscoelastic materials such as polymers . Schapery's constitutive model has been applied to asphalt mixes by several researchers (e.g. ). Later, Touti and Cederbaum [22], Haj-Ali and Muliana [16], and Huang et al. [18] developed algorithms for numerical implementation of Schapery's viscoelastic constitutive model in finite element codes. Recently, Levesque et al. [12] extended Schapery's nonlinear viscoelastic model for 3D applications based on laws of thermodynamics. In terms of the viscoplastic behavior of asphalt mixes, Perzyna's theory [23] has been used by several researchers for predicting the permanent deformation in asphalt mixes. For example, Lu and Wright [24] and Masad et al. [25] used Perzyna's viscoplasticity for modeling mechanical response of hot mix asphalt (HMA). Saadeh et al. [26], Huang [27], and Abu Al-Rub et al. [20] coupled Schapery's nonlinear viscoelasticity model to Perzyna's viscoplasticity model to more accurately simulate the nonlinear mechanical response of HMA at high stress levels and high temperatures.
Constitutive Modeling of Asphalt-Aggregate Mixes with Damage and Healing
Research Thesis, 2006
Asphalt-aggregate mixes are being used throughout the world as a prime construction material for pavements. An asphalt mix is a multiphase heterogeneous material; it is a composite blend of air-voids, asphalt-cement (bitumen) and aggregates of a range of sizes. These materials exhibit extremely complex mechanical behavior that is very difficult to capture and model. Mainly for this reason available pavement-performance models are empirical, as no rigorous constitutive models were yet formulated for asphalt mixes. The motivation underlying this research work was to improve material modeling and characterization techniques for asphalt-aggregate mixes. An up-to-date review of literature revealed that current characterization efforts are limited principally because they deal with material behavior in uniaxial tests and provide essentially one-dimensional models. This dissertation presents the development of a triaxial viscoelastic-viscoplastic constitutive model for asphalt mixes including the effects of damage and healing. The model is confined to the description of pre-peak load response under isothermal conditions. It is based on additive separation of the total strain into viscoelastic and viscoplastic components and provides individual constitutive treatment to each part. The viscoelastic formulation is nonlinear, cross-anisotropic, and characterized by one unique (scalar) time-function. Three nonlinear isotopic effects are modeled: i) damage, i.e. loss of stiffness under load; ii) stiffening, i.e. increase of stiffness under compression conditions, and iii) healing, i.e., a decrease in the level of damage during rest periods. The viscoplastic equations resemble the kinematic-hardening formulations used to describe creep of metals. Internal stress-like variables are used to produce hardening (or softening) in each direction. Neither damage nor healing is included in the viscoplastic model. It should be noted that coupling is introduced between the individual formulations, making the viscoelastic response dependent also on the viscoplastic component. In order to support the development of the constitutive formulation, new experimental procedures were designed and executed using the triaxial apparatus. Creep and recovery test results are presented and analyzed, providing means (also) to calibrate and validate the model for biaxial stress-conditions and one test temperature. Good reproducibility and forecast-ability were obtained in the analyses of versatile test-data for both small and large strain load-cycles; indicating that the model is suitable for simulating the 3D load-response of asphalt-aggregate mixes. The constitutive development in this study constitutes the first attempt to describe the triaxial (viscoelastic-viscoplastic) load-response of asphalt materials including damage and healing. Several aspects of this development were found limited - specifically the ability to rigorously describe the viscoplastic behavior after large rest periods. Further research is needed to try and resolve this limitation and remove some of the other formulation restrictions.
Computational Materials Science, 2007
ABSTRACT The study and development of recycling techniques for pavements is an increasing activity in engineering nowadays. This research line demands a more realistic characterization of the material properties with the aim of simulate the asphalt mixture’s response placed into a multilayered system over granular bases, under dynamic loads, considering also temperature variation or strength reduction for cyclic loads.In order to improve the current formulations, a new viscoplastic model has been developed assuming the strain rate dependency of the material’s response observed in the experimental tests. The strain rate variable affects in a significant way the Young modulus and the viscosity parameter of the model. According to this hypothesis a constitutive equations have been formulated. The mechanical variables involved have been calibrated according to experimental results, developing new expressions for the strain rate dependent parameters. The new viscoplastic model permits us to characterize the material’s response with a few mechanical values, easily obtained from standard laboratory tests. The results obtained show a good approximation to experimental laboratory curves for different rates of loading and temperatures.The model has been applied to simulate the response of a real flexible pavement structure conformed by two asphalt layers over two granular bases, that’s materials with different constitutive behaviors. Experimental tests in the recycled track have been made obtaining the horizontal strain evolution under dynamic load. Different loading rates and temperatures, as well as cracked and continuum pavement responses have been considered in the study. Strains were measured in the interface between the two asphalt layers and simulated using the here proposed model offering a fairly good approximation of the real response observed in the track, although the degree of variation even in the experimental curves is quite high.The results of this study represent a proper base for further developments in structural analysis of pavement layers, considering more complex phenomena, determinant in the long term material’s response, to develop a numerical tool for pavements’ design and lifetime prediction.
Linear viscoelasticity was strictly differentiated from the nonlinearity. Material properties in linear viscoelastic stage were the reference properties. Viscoelastic stress, reference modulus & pseudostrain were rigorously established. The sole linear viscoelastic effect was eliminated to determine pseudostrains. Dissipated pseudostrain energies were determined for representative loading cycle. a b s t r a c t It has been demonstrated that asphalt mixtures experienced linear viscoelastic stage, nonlinear viscoelas-tic stage and damage stage when subjected to controlled-strain repeated direct-tension (RDT) tests with increasing strain levels. However, the linear viscoelastic properties of asphalt mixtures are usually muddled up with their nonlinear viscoelastic properties. These confusions directly lead to the incorrect determination of the pseudostrains and dissipated pseudostrain energies (DPSEs) in the nonlinear viscoelastic stage and damage stage. This study investigated the material properties of fine aggregate mixture (FAM) specimens in all three stages. These three stages were differentiated and characterized in terms of the viscoelastic stress, pseudostrain and DPSE. The definitions of viscoelastic stress, reference modulus and pseudostrain were rigorously established to assure that the material properties in the linear viscoelastic stage were the reference properties and that the sole linear viscoelastic effect was eliminated when determining the pseudostrain and DPSE in the three stages. The characteristics of the DPSE in the three stages were found to be: (1) the DPSE of any loading cycle was zero in the linear viscoelastic stage; (2) in the nonlinear viscoelastic stage, the DPSE of each loading cycle remained approximately the same with the growth of the number of loading cycles, and the DPSE increased to a larger value when the strain level of the RDT test increased to a higher level; (3) in the damage stage, the DPSE of the loading cycle increased as the number of loading cycles increased. This study strictly distinguished the linear viscoelas-ticity from the nonlinear viscoelasticity of the asphalt mixtures, which is critical for the accurate determination of the DPSE spent in overcoming the nonlinear viscoelasticity and in developing damages, such as cracking and permanent deformation, in the asphalt mixtures.
Uniqueness of the Viscoelastic Time-Function for Asphalt-Aggregate Mixes
International Conference on Advanced Characterisation of Pavement and Soil Engineering Materials, 2007
In general mechanical terms asphalt-aggregate mixes are both viscoelastic and viscoplastic at service temperatures and loading conditions. The focus of this paper is on the viscoelastic component-response under small-strains. This research is part of an ongoing effort by the authors to develop a 3-D constitutive model for asphalt mixes. The paper presents laboratory tests consisting of creep and recovery cycles under uniaxial and isotropic stress conditions. Using a special load-transfer device and employing advanced triaxial testing procedures it was possible to obtain fast unloading after each creep period and insure true zero-stress during recovery times. These features enabled a reliable and straightforward isolation of the viscoelastic response from the total deformation. Analysis of the test data shows that one unique creep-compliance function may be used to describe the viscoelastic response of the material under multiaxial stress conditions. This finding will greatly simplify any future development and calibration of a 3-D material-model.
Determining burger's model parameters of asphalt materials using creep-recovery testing data
Proceedings of the Symposium on Pavement Mechanics and Materials at the Inaugural International Conference of the Engineering Mechanics Institute - Pavements and Materials 2008: Modeling, Testing, and, 2008
this paper proposes a method for determining Burger's model parameters using creep-recovery data. With the determined Burger's model parameters, the viscoelastic behaviors of an asphalt binder (PG64-28) and its two mastics (a binder PG64-28 blended with mineral fines passing the ASTM 100# sieve and 200# sieve, respectively) are investigated. The total deformation of the mastics was separated into three parts: the instantaneous elasticity, delayed elasticity, and viscous flow. The ratios of the viscous flow to the elasticity were calculated and analyzed. It was found the proposed method is promising where the average errors of the creep section are 3.53%, 5.28% and 8.02% for the three materials, and the errors in the recovery section are 0.69%, 1.286% and 1.80%, , respectively.
On Viscoelastic Properties of Asphalt Mixtures
2017
Dragan T. Spasić 1, UDK: 691.16:539.3:517.965 DOI:10.14415/konferencijaGFS2017.039 Summary: This paper comprises the fractional Kelvin-Zener model of viscoelastic body, the Laplace transform and a least squares method, all applied in creep/recovery testing of asphalt mixtures for the purpose of parameter identification. The parameters describing viscoelastic properties of these mixtures are: the order of the fractional derivative, modulus of elasticity, as well as two relaxation constants that obey restrictions that follow from the second law of thermodynamics. Knowing these four parameters one may predict the behavior of an asphalt mixture for different loads. Besides, the pattern of change of these parameters may be related to alterations of the viscoelastic properties of an asphalt mixture due to either aging or different environmental conditions.
A framework for linear viscoelastic characterization of asphalt mixtures
Materials and Structures
The master curve of a viscoelastic variable is of significance due to its capability of characterizing the linear viscoelastic (LVE) property in an extended time or frequency range. However, the master curves constructed using the traditional approach fail to strictly comply with the LVE theory, leading to inaccurate predictions in the extended range. In order to address this issue, a framework was developed for the LVE characterization of asphalt mixtures. The generalized logistic sigmoidal model was adopted as the master curve model of storage modulus. A numerical model of loss modulus was established in relation to the continuous relaxation spectrum, whose mathematical model was derived in light of its relationship with the storage modulus. The model parameters determined using the storage modulus and loss modulus test data were employed to construct the master curves of storage modulus, loss modulus, dynamic modulus and phase angle. Then the relaxation modulus master curve was generated by establishing a numerical model. Afterwards, the continuous retardation spectrum was solved numerically based on its relationship with the continuous relaxation spectrum. The master curves of storage compliance, loss compliance and creep compliance were obtained using the corresponding numerical models that were established with respect to the continuous retardation spectrum. The interrelationship among the viscoelastic variables was then employed to obtain the dynamic compliance and phase angle master curves. It was demonstrated that the developed framework ensured the master curves of all viscoelastic variables complied with the LVE theory.