Viscoelastic Behavior Of Asphalt Mixture Research Articles

Characterization of viscoelastic behavior of basalt fiber asphalt mixtures based on discrete and continuous spectrum models.

In order to analyze the differences between the master curves of relaxation modulus E(t) and creep compliance J(t) obtained from discrete and continuous spectrum models, and to comprehensively evaluate the effect of basalt fiber content on the viscoelastic behavior of asphalt mixtures, complex modulus tests were conducted for asphalt mixtures with fiber content of 0%, 0.1%, 0.2% and 0.3%, respectively. Consequently, the master curves of Viscoelastic Parameters of asphalt mixtures were constructed according to the generalized Sigmoidal model(GSM) and the approximate Kramers-Kronig (K-K) relationship. Then, transformation of master curves using discrete and continuous spectrum models to obtain the models of E(t) and J(t) containing all viscoelastic information. Also, the accuracy of the models of E(t) and J(t) was evaluated. The results show that the addition of basalt fibers improves the strength, stress relaxation and deformation resistance of asphalt mixtures. It is worth noting that basalt fibers achieve the improvement of asphalt mixtures by changing their internal structure. Considering the different viscoelastic master curves at four dosages, the optimum fiber dosage was 0.2%. In addition, both discrete and continuous model conversion methods can obtain high accuracy conversion results.

Experimental and Numerical Studies of Viscoelastic Behavior of Bituminous Mixture with a High Rate of Reclaimed Asphalt Pavement, Dune Sand and Lime

Road construction is now a priority in the economic and social development policy of a country. The increased need to improve the infrastructure system and to counter the deficit in certain quarry gravels and non-renewable resources while saving increasingly expensive road investments, makes recourse to the use of abundant and inexpensive materials in order to reduce the use of non-renewable natural materials. The objective of this research is to predict the viscoelastic behavior of asphalt mixtures incorporating high Reclaimed Asphalt Pavement (RAP) content, allowing to reduce the consumption of new aggregates and bituminous binders, and other additives such as dune sand and lime. A new formula containing 3,7% of 35/50 penetration grade virgin bitumen, 40% of Reclaimed Asphalt, 10% of dune sand, and 1% of hydrate lime was tested and compared to the conventional formula containing 5,3% of the same virgin bitumen. To evaluate the impact of dune sand and lime addition on the mechanical behavior of bituminous mixtures containing high rates of RAP, complex modulus tests were conducted on the studied mixtures, at different temperatures and frequencies, using a two-point bending device that was developed at the National School of Engineers of Tunis. Their viscoelastic properties were determined using a Generalized Maxwell model which was calibrated by 2S2P1D model. The paper describes a three-dimensional Finite Element (FE) model developed using ABAQUS software, that is used to simulate 2-point bending tests on trapezoidal samples of the studied mixtures to determine their complex modulus and accurately predict their mechanical behavior under traffic loading at ranges of temperatures and frequencies that are not experimentally accessible. To validate the FE model, determined viscoelastic properties have then been introduced into through the Prony series and its outputs were validated by experimental measurements. Both experimental and numerical results show that the use of RAP, dune sand and lime greatly improves the rigidity of the mix at high temperatures. A suggested continuation of this work would be an investigation of the rutting resistance.

Pure mode I fracture resistance of hot mix asphalt (HMA) containing nano-SiO2 under freeze–thaw damage (FTD)

• Pure mode I fracture resistance of Nano-SiO2-modified asphalt mixture under FTD was evaluated. • The semi-circular bending and edge notched disc bend tests were performed on samples at ± 15 °C. • Nano-SiO 2 improved the behavior of LTC and ITC asphalt mixtures under mode I loading and FTD conditions. • Nano-SiO 2 improved the fracture energy and fracture toughness of asphalt mixture under FTD. • SCB geometry with an angle of 35°was critical due to lower average fracture toughness. In cold climates, increased traffic load has increased the damage caused by low-temperature cracks (LTCs) in asphalt mixes. Due to the viscoelastic behavior of asphalt mixtures, cracks caused by intermediate temperatures (ITCs) have led researchers to think more about improving the technical properties of asphalt mixtures with additives. On the other hand, asphalt pavements are affected by freeze–thaw cycles during their service life, a process that intensifies distress and reduces crack resistance. However, despite the effect of freeze–thaw cycles on the fracture behavior of LTCs and ITCs, this process has received less attention from researchers. Hence, in this study, the effect of Nano-SiO 2 on the occurrence of low and intermediate temperature cracks under freeze–thaw damage (FTD) conditions in asphalt mixtures has been investigated experimentally. For this purpose, Semi-Circular Bending (SCB) and Edge Notched Disc Bend (ENDB) tests were used under mode I loading to investigate the effect of Nano-SiO 2 on the crack resistance of the asphalt mixture (i.e., vertical and angular cracks) at temperatures of ± 15 °C. Before the fracture test, the samples were subjected to 0 and 3 FTD cycles to investigate the effect of these conditions on the long-term fracture resistance of the samples. The results showed that adding Nano-SiO 2 increased the brittleness of the mixtures, fracture energy, and fracture toughness of asphalt mixtures containing vertical and angular cracks in both 0 and 3 FTD cycles. Also, it was concluded that Nano-SiO 2 could recover a large part of the resistance reduced by the 3 FTD cycles; therefore, using Nano-SiO 2 additive improved the long-term behavior of LTC and ITC asphalt mixtures under mode I loading and FTD conditions. Finally, by comparing all the geometries used in this research, it was concluded that from the point of view of fracture energy, the ENDB geometry, and from the point of fracture toughness, the SCB geometry with an angle of 35°was critical due to lower average fracture energy and lower average fracture toughness, respectively (temperatures of ± 15 °C under 0 and 3 FTD cycles).

Numerical Simulation of Viscoelastic Behavior of Asphalt Mixture Using Fractional Constitutive Model

An innovative procedure was proposed to simulate the viscoelastic mechanical behavior of asphalt mixture. The existing fractional viscoelastic models were quantitatively analyzed, and the fractional Zener model was adopted. The model parameters were obtained by fitting the storage modulus and loss modulus simultaneously. The relaxation modulus of the fractional Zener model in the time domain was deduced using the Mittag-Leffler function. The numerical algorithm of the fractional Zener model was proposed and implemented into finite-element (FE) software ABAQUS version 6.9. Simulations of the relaxation test were conducted to verify the effectiveness of the numerical algorithm and the FE implementation. Then dynamic modulus tests were simulated, and the master curve of the storage and loss modulus was calculated. The simulation results indicated that the fractional Zener model can be effectively applied to FE analysis and accurately predict the storage modulus and loss modulus master curve of asphalt mixture in a wide frequency or temperature range.

Study on Dynamic Modulus Dependence Model for Asphalt Mixture Based on Temperature and Strain Parameters

In order to objectively characterize the nonlinear viscoelastic behavior of asphalt mixture and its dependence on temperature and load, the two-point dynamic flexural tensile modulus test of asphalt mixture at different strain levels, temperatures and loading frequencies is carried out by using French trapezoidal beam tester. By introducing the method of nonlinear operator, the dynamic modulus dependency modeling method for asphalt mixture based on temperature and strain parameters is put forward, the expression of dynamic modulus principal surface of asphalt mixture is established, and the reliability of the dynamic modulus dependent model is evaluated by correlation coefficient test and variance analysis method. The result shows that (1) for the two-point flexural tensile test of trapezoidal beam based on asphalt mixture of full-scale test track, the mean values of dynamic modulus variation coefficient at 0℃ and 45℃ are about 2.5% and 6.2% respectively, the mean values of dynamic modulus variation coefficient at 10 test temperatures is about 4%, the variation level of the test method is low, the error is small, which has a very good parallelism and reliability; (2) for the established dynamic modulus dependent model expression based on temperature and strain parameters, the decision coefficient R2 can reach more than 0.99, the P value of F test is 0, the fitting effect of the model on the test result is good, and there is a significant correlation of dynamic modulus with temperature and strain level; (3) the model can be used to describe the dynamic flexural tensile modulus of asphalt mixture, and the description model of the dynamic modulus can be transformed from principal curve to principal surface. In pavement structure analysis, this model can reflect the nonlinear response phenomenon in actual pavement more objectively, and can avoid the problems such as distortion of the calculation result caused by unreasonable modulus value in structural analysis effectively.

New Model for Visco-Elastic Behavior of Asphalt Mixture with Combined Effect of Stress and Temperature

The analysis of pavements and their ingredients has always been important due to a good understanding of their behavior under different conditions; that leads to more accurate relations. Due to the extent of asphalt mixture application in the world, the assessment of different behaviors of this mix is very important from various aspects of performance and safety. Given that the asphalt mixtures are inherently very sensitive to temperature changes due to bitumen content, identification and analysis of the viscoelastic and visco-elasto-plastic behavior of the mixture is of particular importance. The scope of present research is to provide new model of viscoelastic behavior of asphalt concrete pavements with a combined effect of stress and temperature using genetic programming techniques. For this purpose, a number of dynamic creep tests under various temperatures and different stress levels were done. Beside, in this study a comparison is made between the generalized model and proposed model in estimating the visco elastic response of asphalt samples. Performance of the genetic programming model is quite satisfactory. The new proposed model will also help further researchers willing to perform similar studies, without carrying out destructive tests.

An Image-Based Finite Element Approach for Simulating Viscoelastic Response of Asphalt Mixture

This paper presents an image-based micromechanical modeling approach to predict the viscoelastic behavior of asphalt mixture. An improved image analysis technique based on the OTSU thresholding operation was employed to reduce the beam hardening effect in X-ray CT images. We developed a voxel-based 3D digital reconstruction model of asphalt mixture with the CT images after being processed. In this 3D model, the aggregate phase and air void were considered as elastic materials while the asphalt mastic phase was considered as linear viscoelastic material. The viscoelastic constitutive model of asphalt mastic was implemented in a finite element code using the ABAQUS user material subroutine (UMAT). An experimental procedure for determining the parameters of the viscoelastic constitutive model at a given temperature was proposed. To examine the capability of the model and the accuracy of the parameter, comparisons between the numerical predictions and the observed laboratory results of bending and compression tests were conducted. Finally, the verified digital sample of asphalt mixture was used to predict the asphalt mixture viscoelastic behavior under dynamic loading and creep-recovery loading. Simulation results showed that the presented image-based digital sample may be appropriate for predicting the mechanical behavior of asphalt mixture when all the mechanical properties for different phases became available.

Study of normal and shear material properties for viscoelastic model of asphalt mixture by discrete element method

In this paper, the viscoelastic behavior of asphalt mixture was studied by using discrete element method. The dynamic properties of asphalt mixture were captured by implementing Burger’s contact model. Different ways of taking into account of the normal and shear material properties of asphalt mixtures have been reviewed. Two models, Model I and Model II, with different design parameters were developed and compared. For Model I, Burger’s model parameters in normal and shear direction were calibrated by using laboratory test results from Frequency Sweep Test performed in both normal and shear direction, respectively; while for Model II, the same calibrated parameters in the normal direction were used, but the values for the shear direction were chosen to be equal with the normal direction. The complex modulus of asphalt mixtures were predicted for both optimized models by conducting DE simulation under dynamic strain control loading. A sensitivity study was carried out, where the effects of different design parameters on the dynamic properties of asphalt mixture has been investigated, including the eight parameters of Burger’s model and the friction coefficient.

Characterizing the low-temperature viscoelastic behavior of asphalt mixtures: A comparative study

Thermal cracking is a critical pavement issues in the cold regions and has been of a major concern in asphalt pavements. The paper presents a viscoelastic modeling work using pure power law, generalized power law, and Prony series functions to characterize low temperature performance of asphalt mixtures. The bending beam rheometer (BBR) using asphalt mixture beams was employed to obtain creep compliance and further viscoelastic analyses were performed to determine relaxation moduli and thermal stresses of asphalt mixtures. The objective of this paper is to provide a better understanding on low temperature viscoelastic behavior of asphalt mixtures by quantifying creep compliance errors and differences among these representation models (pure power law, generalized power law, and Prony series functions) in the predictions of relaxation moduli and thermal stresses. Based on the comparison of viscoelastic analyses at low temperatures, the generalized power law function shows a better agreement with the experimental data and has the least creep compliance error as compared with other two representation functions.

Study of the internal mechanical response of an asphalt mixture by 3-D discrete element modeling

In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties for all the distinct elements. The dynamic modulus and phase angle from uniaxial complex modulus tests of the asphalt mixtures in the laboratory have been collected. A macro-scale Burger’s model was first established and the input parameters of Burger’s contact model were calibrated by fitting with the lab test data of the complex modulus of the asphalt mixture. The Burger’s contact model parameters are usually calibrated for each frequency. While in this research a constant set of Burger’s parameters has been calibrated and used for all the test frequencies, the calibration procedure and the reliability of which have been validated. The dynamic modulus of asphalt mixtures were predicted by conducting Discrete Element simulation under dynamic strain control loading. In order to reduce the calculation time, a method based on frequency–temperature superposition principle has been implemented. The ball density effect on the internal stress distribution of the asphalt mixture model has been studied when using this method. Furthermore, the internal stresses under dynamic loading have been studied. The agreement between the predicted and the laboratory test results of the complex modulus shows the reliability of DEM for capturing the viscoelastic properties of asphalt mixtures.

Choice of an Advanced Rheological Model for Modeling the Viscoelastic Behavior of Hot Mixtures Asphalt (HMA) from Sénégal (West Africa)

The main purpose of this article is to choose among advanced rheological models used in the French rational design, one that best represents the viscoelastic behavior of asphalt mixtures mixed with aggregates of Senegal. The model chosen will be the basis for the development of computational tools for stress and strain for Senegal. However, the calibration of these models needs complex modulus test results. In opposition to mechanical models the complex modulus can directly characterize the viscoelastic behavior of bituminous materials. Here determination is performed in the laboratory by using several types of tests divided into two groups: homogeneous tests and non-homogeneous tests. The choice of model will be carried out by statistical analysis through the least squares method. To this end, a study was carried out to “Laboratory of Pavement and Bituminous Materials” (LCMB) with asphalt concrete mixed with aggregate from Senegal named basalt of Diack and quartzite of Bakel. In this study, the test used to measure the complex modulus is the Canadian test method LC 26-700 (Determination of the complex modulus by tension-compression). There mainly exist two viewing complex modulus planes for laboratory test results: the Cole and Cole plane and the Black space. The uniqueness of the data points in these two areas means that studied asphalt concretes are thermorheologically simple and that the principle of time-temperature superposition can be applied. This means that the master curve may be drawn and that the same modulus value can be obtained for different pairs (frequency-temperature). These master curves are fitted during the calibration process by the advanced rheological models. One of the most used software in the French rational design for the visualization of complex modulus test results and calibration of rheological models developed tools is named Visco-analysis. In this study, its use in interpreting the complex modulus test results and calibration models shows that, the studied asphalt concretes are thermorheologically simple, because they present good uniqueness of their Black and Cole and Cole and Black diagrams. They allow a good application of the principle of time temperature superposition. The statistical analysis of calibration models by the least squares method has shown that the three studied models are suitable for modeling the linear viscoelastic behavior of asphalt mixtures formulated with the basalt of Diack and the quartzite of Bakel. Indeed their calibration has very similar precision values of “Sum of Squared Deviation” (SSD) about 0.185. However, the lower precision value (0.169) is obtained with the 2S2P1D model.

Approach for Quantifying the Effect of Binder Oxidative Aging on the Viscoelastic Properties of Asphalt Mixtures

Because of the noted influence of oxidative aging on mixture properties and pavement performance, it is becoming imperative to have a more complete understanding of the influence of asphalt binder aging on the viscoelastic behavior of asphalt mixtures. This study proposes a new approach to correlating the oxidative aging of asphalt binder for carbonyl functional groups with the viscoelastic behavior of asphalt mixtures for a continuous relaxation spectrum. The asphalt mixture complex modulus and the carbonyl area for the recovered asphalt binder were measured for mixtures subjected to varying durations of long-term aging in the laboratory. The continuous relaxation spectrum was obtained analytically from the 2S2P1D model of complex modulus of asphalt mixture through the inverse Fourier–Laplace transform approach. A consistent horizontal shift in the continuous relaxation spectrum was observed for all mixtures with the increase in aging duration. However, the shape and the amount of shifting of the spectra were mixture dependent. In particular, mixtures with higher asphalt binder absorption exhibited the greatest shift in the continuous spectra for both unmodified and polymer-modified asphalt mixtures. Good correlations were observed between the carbonyl in asphalt binder and the continuous relaxation spectrum parameters of the asphalt mixture. Such relationships should permit the incorporation of long-term oxidative aging directly into the constitutive equation used in pavement response analyses.

Practical Methodology of Determining the In Situ Dynamic (Complex) Moduli for Engineering Analysis

The viscoelastic behavior of asphalt mixtures can be conveniently presented in the form of a stiffness master curve in various engineering applications. However, the methods to obtain the in-service mixture stiffness are limited to the falling weight deflectometer (FWD) testing and back-calculation procedure because the pavement layer thicknesses in many cases are too thin to allow laboratory testing. The test protocol to measure the axial dynamic modulus requires cylindrical specimens with a height-to-diameter ratio higher than 2, while the cores need to be at least 38 mm thick for measuring shear stiffness. This technical note describes and compares the methods for constructing asphalt mixture master curves utilizing stiffness predictive equations for asphalt binders and mixtures, in addition to using laboratory measurements, as an alternative to FWD backcalculation analysis. This technical note also recommends constraining the low and high mixture stiffness values measured from simple shear testing to obtain stiffness comparable to the uniaxial dynamic modulus testing.

Prediction of Creep Stiffness of Asphalt Mixture with Micromechanical Finite-Element and Discrete-Element Models

This study presents micromechanical finite-element (FE) and discrete-element (DE) models for the prediction of viscoelastic creep stiffness of asphalt mixture. Asphalt mixture is composed of graded aggregates bound with mastic (asphalt mixed with fines and fine aggregates) and air voids. The two-dimensional (2D) microstructure of asphalt mixture was obtained by optically scanning the smoothly sawn surface of superpave gyratory compacted asphalt mixture specimens. For the FE method, the micromechanical model of asphalt mixture uses an equivalent lattice network structure whereby interparticle load transfer is simulated through an effective asphalt mastic zone. The ABAQUS FE model integrates a user material subroutine that combines continuum elements with viscoelastic properties for the effective asphalt mastic and rigid body elements for each aggregate. An incremental FE algorithm was employed in an ABAQUS user material model for the asphalt mastic to predict global viscoelastic behavior of asphalt mixture. In regard to the DE model, the outlines of aggregates were converted into polygons based on a 2D scanned mixture microstructure. The polygons were then mapped onto a sheet of uniformly sized disks, and the intrinsic and interface properties of the aggregates and mastic were assigned for the simulation. An experimental program was developed to measure the properties of sand mastic for simulation inputs. The laboratory measurements of the mixture creep stiffness were compared with FE and DE model predictions over a reduced time. The results indicated both methods were applicable for mixture creep stiffness prediction.

A Viscoelastic Displacement Discontinuity Method for Analysis of Pavements with Cracks

This paper presents a development of the displacement discontinuity boundary element method for modeling the linear viscoelastic behavior of asphalt mixtures and simulating crack propagation in asp ...

A Viscoelastic Displacement Discontinuity Method for Analysis of Pavements with Cracks

ABSTRACT This paper presents a development of the displacement discontinuity boundary element method for modeling the linear viscoelastic behavior of asphalt mixtures and simulating crack propagation in asphalt pavements. The viscoelastic formulation is based on the correspondence principle, involving Laplace transformation of the constitutive equations and the associated boundary conditions. The time-dependent behavior of the asphalt mixtures is characterized by the Burger's or power law model. The associated transformed problem is solved in an analogous way to using the linear-elasticity-based displacement discontinuity method. The corresponding time-dependent viscoelastic solution is obtained using an efficient and robust algorithm for numerical Laplace inversion. A substructuring approach is employed to construct the layered formulation and higher-order elements are used to capture the bending effect in the pavement structure. With incorporation of the hot mix asphalt (HMA) fracture mechanics, which is based on the concept that there is a dissipated creep strain energy (DCSE) threshold to cracking, the numerical framework can efficiently simulate crack onset and growth in asphalt pavements. Several examples are presented to verify the accuracy and efficiency of the numerical method and to demonstrate its application in modeling pavement cracking.

FOUNDMENTAL STUDY ON APPLICABILITY OF DISTINCT ELEMENT METHOD TO DEFFORMATION ANALYSIS OF ASPHALT MIXTURE

In this paper, simulation approach based on distinct element method (DEM) was applied to deformation analysis of asphalt mixture, and the applicability and mechanical property of the distinct element assembly were probed. Since a mechanical element model used in ordinary DEM was not suitable for simulating a deformation of asphalt mixture, different element model was reconsidered in accordance with real material property. The applicability was evaluated in comparing simulation results with real behavior of asphalt mixture. As a result of comparisons, it was found out that the proposed element model could represent viscoelastic behavior of asphalt mixture on the whole and this simulation method was applicable to deformation analysis of asphalt layer. In addition, mechanical relations between element model and the assembly were also studied by the parametric simulations in which physical properties of mechanical element were changed.