Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images

The objective of this study is to predict the dynamic modulus of asphalt mixture using both two-dimensional (2D) and three-dimensional (3D) Distinct Element Method (DEM) generated from the X-ray computed tomography (X-ray CT) images. The 3D internal microstructure of the asphalt mixtures (i.e., spatial distribution of aggregate, sand mastic and air voids) was obtained using the X-ray CT. The X-ray CT images provided exact locations of aggregate, sand mastic and air voids to develop 2D and 3D models. An experimental program was developed with a uniaxial compression test to measure the dynamic modulus of sand mastic and asphalt mixtures at different temperatures and loading frequencies. In the DEM simulation, the mastic dynamic modulus and aggregate elastic modulus were used as input parameters to predict the asphalt mixture dynamic modulus. Three replicates of a 3D DEM and six replicates of a 2D DEM were used in the simulation. The strain response of the asphalt concrete under a compressive load was monitored, and the dynamic modulus was computed. The moduli of the 3D DEM and 2D DEM were then compared with both the experimental measurements results. It was revealed that the 3D discrete element models successfully predicted the asphalt mixture dynamic modulus over a range of temperatures and loading frequencies. It was found that 2D discrete element models under predicted the asphalt mixture dynamic modulus.     

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Edge cracked semi‐circular shape specimen subjected to three point bend loading is a favourite test specimen for determining fracture toughness of asphalt mixtures. However, in the vast majority of previous experimental works, the homogeneous medium assumption has been considered for determining the stress intensity factor and geometry factors of asphalt mixtures tested with this test configuration. As a more realistic model and in order to consider the effects of heterogeneity on corresponding values of stress intensity factors, the asphalt mixture was modelled as a two‐phase aggregate/mastic heterogeneous mixture and its fracture behaviour was investigated using numerical models of asymmetric semi‐circular bend (ASCB) specimens. The generation and packing algorithm was employed to randomly distribute the aggregates with different shapes and sizes inside the mastic part. The effect of the mechanical properties of asphalt mixture (elastic modulus and the Poisson's ratios of aggregates and mastic), coarse aggregates distribution and crack length were studied on modes I and II geometry factors by means of extensive two‐dimensional finite element analyses. Moreover, the effect of the elastic modulus of asphalt mixture components was evaluated on the fracture path using the maximum tangential stress criterion. It was shown that crack tip location, elastic modulus of aggregates and mastic are the most important affecting parameters on the magnitude of modes I and II geometry factors. It was also shown that the geometry factors are not sensitive to the Poisson's ratios of aggregates and mastic. In addition, fracture cracking path is affected by the elastic modulus of the asphalt mixture components such that, depending on the difference between the stiffness of stiffer coarse aggregates and softer mastic part, the crack may propagate either through the aggregates, mastic or interface of aggregate/mastic.     

基于细观力学的沥青混合料动态模量预测

为了建立能够表征组分材料性能及细观结构特征的沥青混合料动态模量预测模型, 根据复合材料细观力学理论, 将沥青混合料视为由沥青胶浆包裹的集料颗粒嵌入于有效沥青混合料介质中的复合材料, 考虑集料尺寸、级配组成和空隙的影响, 建立了沥青混合料动态模量三相细观力学预测模型。结合组分材料性能研究, 应用该预测模型求解得到了动态模量, 其与试验值比较结果表明, 预测值较试验值小, 产生此差异的原因可归结为模型的适用条件与真实细观结构的差别;据此对预测模型进行了修正, 提出了考虑沥青膜厚度的动态模量细观力学分析方法;鉴于集料与沥青胶浆之间的力学特性差异, 简化了预测模型求解参数, 给出了参数值的范围。     

Determining effects of moisture in mastic materials using nanoindentation

Asphalt concrete consists of coarse aggregates coated with asphalt binder, matrix, which is a mixture of binder and fine aggregates, and mastic, which is a mixture of asphalt binder and fines passing number 200 sieve (0.075 mm). In this study, nanoindentation tests were conducted on dry and wet mastic materials to determine the contact creep compliance, which is used to examine the effects of moisture in the mastic materials. Indentation creep data were fitted using viscoelastic mechanical models. Results show that the dry mastic materials exhibits viscoelastic behavior, while the wet mastic materials shows less viscoelastic behavior compared to the dry mastic materials. Moisture reduces retardation time significantly in the wet mastic materials. The dry mastic materials follow the linear Burgers viscoelastic model and the wet mastic materials follow the Maxwell viscoelastic model. Stiffness measured on the surface of the wet mastic materials is higher than that of the dry mastic materials. Due to moisture conditioning, mastic sample surface might have eroded that makes it less viscous or become exposed to mastic aggregate, and therefore exhibits high stiffness. Indentation results reveal that the wet mastic is softer below a certain depth from the surface. This study projects that the indenter needs to penetrate more than 4000 nm to reach softer wet mastic materials. Also indentation creep holding time needs be more than 1200 s to reach that target depth in wet mastic materials.     

Micromechanical modelling of bituminous materials’ complex modulus at different length scales

The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (?10 °C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.     

A multiscale model for predicting the viscoelastic properties of asphalt concrete

It is well known that the accurate prediction of long term performance of asphalt concrete pavement requires modeling to account for viscoelasticity within the mastic. However, accounting for viscoelasticity can be costly when the material properties are measured at the scale of asphalt concrete. This is due to the fact that the material testing protocols must be performed recursively for each mixture considered for use in the final design.In this paper, a four level multiscale computational micromechanics methodology is utilized to determine the accuracy of micromechanics versus directly measured viscoelastic properties of asphalt concrete pavement. This is accomplished by first measuring the viscoelastic dynamic modulus of asphalt binder, as well as the elastic properties of the constituents, and this comprised the first scale analysis. In the second scale analysis, the finite element method is utilized to predict the effect of mineral fillers on the dynamic modulus. In the third scale analysis, the finite element method is again utilized to predict the effect of fine aggregates on the dynamic modulus. In the fourth and final scale analysis, the finite element method is utilized to predict the effect of large aggregates on the dynamic modulus of asphalt concrete. This final predicted result is then compared to the experimentally measured dynamic modulus of two different asphalt concretes for various volume fractions of the constituents. Results reveal that the errors in predictions are on the order of 60 %, while the ranking of the mixtures was consistent with experimental results. It should be noted that differences between the “final predicted results” and the experimental results can provide fruitful ground for understanding the effect of interactions not considered in the multiscale approach, most importantly, chemical interactions.     

Modelling dilation in an idealised asphalt mixture using discrete element modelling

This paper investigates the use of discrete element modelling (DEM) to simulate the behaviour of a highly idealised bituminous mixture under uniaxial and triaxial compressive creep tests. The idealised mixture comprises single-sized spherical (sand-sized) particles mixed with bitumen and was chosen so that the packing characteristics are known (dense random packing) and the behaviour of the mixture will be dominated by the bitumen and complex aggregate interlock effects will be minimised. In this type of approach the effect of the bitumen is represented as shear and normal contact stiffnesses. A numerical sample preparation procedure has been developed to ensure that the final specimen is isotropic and has the correct volumetrics. Elastic contact properties have been used to investigate the effect of the shear and normal contact stiffnesses on bulk material properties. The bulk modulus was found to be linearly dependent on the normal contact stiffness and independent of the shear contact stiffness. Poisson’s ratio was found to be dependent on only the ratio of the shear contact stiffness to the normal contact stiffness. An elastic contact has been assumed for the compressive normal contact stiffness and a viscoelastic contact for shear and tensile normal contact stiffness to represent the contact behaviour in idealised mixture. The idealised mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on the rate of dilation with shear strain for the sand asphalt. The numerical results have been validated with experimental data.     

Mechanism and behavior of fiber-reinforced asphalt mastic at high temperature

Abstract

The rheological behaviour and reinforcement mechanism of asphalt mastic mixed with fibres at high temperature were investigated in this study. Fibres, including basalt, polyester and glass, were added to asphalt mastic. Repeated creep and multi-stress creep tests were conducted to characterise the high-temperature properties of the mastic, and numerical simulation was performed with ABAQUS software to analyse the reinforcement effect of fibres. Test results indicate that the fibres have excellent reinforced performance; for example, the accumulated strain and its change rate decrease, and its creep stiffness modulus increases after the fibres are mixed into the mastic. The creep recovery rate increases, and its creep residual value decreases at a high stress level. The creep stiffness modulus under different loading cycles can be expressed by a power function. Numerical simulation shows that the fibres effectively absorb mastic stress; hence, creep strain in the mastics decreases. The Burgers model was utilised to present the rheological behaviours of mastics with fibres; the model parameters were estimated.     

基于细观力学的纤维沥青混凝土有效松弛模量

为了研究纤维沥青混凝土的本构模型,将其视为以沥青混合料为粘弹性基体,纤维为弹性夹杂的两相复合材料。对基于复合材料细观力学理论建立的有效模量表达式进行了修正,提出了纤维沥青混凝土的割线有效松弛模量。以聚酯纤维沥青混凝土为例进行了有效松弛模量的解析分析和模拟蠕变实验的有限元分析,分析结果与试验数据的比较表明,该文提出的割线有效松弛模量模型对于纤维沥青混凝土粘弹性力学行为具有很好的预测能力。应用该模型对路面弯沉变形进行了有限元分析,结果表明:纤维的加入有效的改善了沥青混凝土路面的粘弹性性能。     

Using the poker-chip test for determining the bulk modulus of asphalt binders

The properties of asphalt binders strongly influence the overall mechanical response of asphalt mixture composites. A thorough understanding of the mechanistic behavior of asphalt binders is important in order to fully and accurately characterize the behavior of the asphalt mixture. The mechanical properties of the asphalt binder, the matrix in the asphalt mixture composite, are time and temperature dependent and have a lower stiffness compared to the inclusions (aggregate particles). However, computational methods used to model the micromechanics of asphalt mixtures typically assume a constant bulk modulus or Poisson’s ratio for asphalt binders. This research investigates the time-dependence of the bulk modulus of asphalt binders. Several approaches for measuring the bulk modulus were explored and the poker-chip geometry was found to be the most suitable one. The boundary value problem for the poker-chip geometry was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research improve our understanding of the viscoelastic behavior of asphaltic materials, and also guide important assumptions that are typically made during computational modeling of asphaltic materials.     

老化对水泥乳化沥青胶结料动态力学性能的影响

基于分数导数修正Burgers模型,建立了水泥乳化沥青胶结料（简称复合胶结料）的本构方程。结合不同材料配比的复合胶结料的老化试验及频率扫描试验,分析了老化时间及材料配比等因素对复合胶结料黏弹性力学参数的影响。研究表明,复合胶结料的存储模量与损耗模量均随老化时间的增加而增大,在老化时间为0~8 h时,存储模量及损耗模量增加较快,当老化时间超过8 h后,其增长趋势减缓。对于乳化沥青与水泥的质量比（m_A/m_C）为1.2和1.4的复合胶结料,在不同的加载频率下,其相位角均随老化时间的增加而减小。对于m_A/m_C为1.0的复合胶结料,其相位角随着老化时间的增加呈现先增加后减小的变化规律。随着老化时间的增加,复合胶结料趋向于弹性材料的力学性质。分数导数修正Burgers模型可以较好的描述老化后复合胶结料的黏弹性动态力学行为,模型参数弹性模量E₁、黏度η₁和分数导数r可以描述老化情况下材料黏弹特性的变化规律。     

Analytical modeling and experimental study of tensile strength of asphalt concrete composite at low temperatures

In this study, analytical modeling of the tensile strength of hot-mix asphalt (HMA) mixtures at low temperatures was developed. To do this, HMA mixtures were treated as a two-phase composite material with aggregates (coarse and fine) dispersed in an asphalt mastic matrix. A two-phase composite model, which was similar to Papanicolaou and Bakos's [J. Reinforced Plast. Compos. 11 (1992) 104] model with a particle embedded in an infinite matrix, was proposed. Unlike Papanicolaou and Bakos's model, an axial stress was introduced to the fiber end to consider the load transferred from the asphalt mastic the aggregate. Efforts were also made to consider the effect of aggregate gradation, asphalt mastic degradation, and interfacial damage between the aggregates and asphalt mastic matrix on the tensile strength of the HMA mixtures. Experimental investigations were conducted to validate the developed theoretical relations. A reasonable agreement was found between the predicted tensile strength and the experimental results at low temperatures. Parameters affecting the tensile strength of asphalt mixtures were discussed based on the calculated results.     

Development of a stress-mode sensitive viscoelastic constitutive relationship for asphalt concrete: experimental and numerical modeling

Asphalt binder is responsible for the thermo-viscoelastic mechanical behavior of asphalt concrete. Upon application of pure compressive stress to an asphalt concrete specimen, the stress is transferred by mechanisms such as aggregate interlock and the adhesion/cohesion properties of asphalt mastic. In the pure tensile stress mode, aggregate interlock plays a limited role in stress transfer, and the mastic phase plays the dominant role through its adhesive/cohesive and viscoelastic properties. Under actual combined loading patterns, any coordinate direction may experience different stress modes; therefore, the mechanical behavior is not the same in the different directions and the asphalt specimen behaves as an anisotropic material. The present study developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery’s nonlinear viscoelastic model. The proposed constitutive relationship was implemented in Abaqus using a user material (UMAT) subroutine in an implicit scheme. Uniaxial compression and indirect tension (IDT) testing were used to characterize the viscoelastic properties of the bituminous materials and to calibrate and validate the proposed constitutive relationship. Compressive and tensile creep compliances were calculated using uniaxial compression, as well as IDT test results, for different creep-recovery loading patterns at intermediate temperature. The results showed that both tensile creep compliance and its rate were greater than those of compression. The calculated deflections based on these IDT test simulations were compared with experimental measurements and were deemed acceptable. This suggests that the proposed viscoelastic constitutive relationship correctly demonstrates the viscoelastic response and is more accurate for analysis of asphalt concrete in the laboratory or in situ.     

沥青混合料黏弹性主曲线模拟及换算

基于时间-温度等效原理将不同温度下沥青混合料的储存模量和蠕变柔量进行平移形成主曲线,采用广义Maxwell和Kelvin模型分别模拟沥青混合料的松弛和蠕变特性,利用Prony级数表达式和Laplace变换实现黏弹性主曲线间的相互换算,并将换算结果与试验结果进行了比较。结果表明,广义Maxwell和Kelvin模型可以较好地模拟沥青混合料黏弹性主曲线,储存模量和蠕变柔量主曲线相互换算结果与试验结果规律基本一致,松弛模量实际结果应介于由储存模量和蠕变柔量换算的松弛模量主曲线之间,这可为沥青混合料黏弹性力学研究及黏弹性参数的获取提供有益参考。     

Performance comparative analysis of stone mastic asphalts with electric arc furnace steel slag: a laboratory evaluation

The paper presents the results of a laboratory study, aimed at verifying the possibility to use two particular typologies of electric arc furnace (EAF) steel slags, in substitution of the natural aggregates, in the composition of stone mastic asphalt (SMA) for flexible pavements. The research has been articulated in a preliminary study of the chemical, leaching, physical, and mechanical properties of the EAF steel slag, and in the following mix design and performance characterization of the bituminous concretes, through gyratory compaction tests, permanent deformations tests, stiffness modulus tests at various temperatures, fatigue tests and indirect tensile strength tests. All the mixtures with EAF slag have satisfied the requisites for acceptance in the road sector technical standards, thus resulting as suitable for use in the construction of road infrastructures, moreover presenting higher mechanical characteristics than those of the corresponding asphalts with full natural aggregate.     

Numerical analysis of moisture vapor diffusion in asphalt mixtures using digital images

The presence of moisture in asphalt mixtures is detrimental to their performance, e.g., softening the asphalt binder and weakening the aggregate-binder bond. One of the mechanisms of moisture transport, and the focus of this study, is molecular diffusion. Moisture diffusion occurs in response to a concentration gradient. The objective of this study was to estimate the diffusion coefficient of moisture vapor in asphalt mixtures by using finite element (FE) and finite difference (FD) numerical algorithms that employ digital images to discretize the composite. X-ray computed tomography was used to characterize the microstructure of laboratory-prepared specimens and provide the required three-dimensional digital images, which were segmented into three phases: air voids, a mixture of asphalt binder and the fine aggregate fraction, and coarse aggregates. Individual diffusion coefficients were assigned to each phase and the effective diffusion coefficient for the composite was computed using the numerical algorithms. The outcome was compared against experimental values. The effective diffusion coefficient for the asphalt mixtures obtained using the FD method showed closer agreement with the experimental data, while the FE results overestimated the experimental measurements in all cases.     

Investigation of asphalt concrete rutting mechanisms by X-ray computed tomography imaging and micromechanical finite element modeling

This paper systematically investigates the changes in asphalt concrete (AC) microstructure caused by full-scale accelerated pavement testing with a heavy vehicle simulator (HVS), using X-ray computed tomography images taken before and after HVS rutting tests. A viscoelastic micromechanical finite element modeling was also used to investigate effects of bitumen mastic and aggregate skeleton properties on shear resistance. The primary purpose was to determine the reasons behind the earlier failure of the rubberized gap graded AC mix used in the test compared to the polymer modified dense graded mix also included in the experiment. Shear related deformation appears to control the long term rutting performance of the test sections while densification was primarily an initial contributor at the very early stages of trafficking. A high concentration of aggregate interlock in the polymer modified mix, as a result of the dense gradation and larger aggregate sizes, appears to have resulted in greater dissipation of shear stresses and therefore greater shear resistance. The lack of this interlocking effect for the rubberized gap graded mix is proposed to have caused the earlier failure on HVS test sections.     

Fatigue resistance investigation of warm‐mix recycled asphalt binder,mastic, and fine aggregate matrix

Fatigue cracking is one of the primary distresses in warm‐mix recycled asphalt pavements. This paper evaluates the fatigue resistance evolution of warm‐mix recycled asphalt materials in different scales during the service period. The strain sweep test and time sweep test were performed, respectively, by dynamic shear rheometer to determine the linear viscoelastic limits and to characterize the fatigue behavior of warm‐mix recycled asphalt binder, mastic, and fine aggregate matrix with different ageing levels and recycling plans. The dissipated energy method was used to define the failure criterion and to construct the fatigue model. Effects of ageing levels and recycling plans on stiffness and fatigue resistance were investigated. Performance correlations among warm‐mix recycled asphalt binder, mastic, and fine aggregate matrix were developed, respectively, by the statistical method to determine the critical material scale for stiffness and fatigue resistance.     

Nanoindentation investigation of asphalt binder and mastic viscoelasticity

An exploratory nanoindentation technique for creep testing of two neat asphalt binders and one mastic at room temperature is developed, tested and verified. This work presents a new approach to obtain viscoelastic properties from low-load spherical (blunt) nanoindentation. Interconverted shear relaxation modulus mastercurves are determined from nanoindentation data. The magnitudes and trends of these mastercurves are found to be in reasonable agreement with Dynamic Shear Rheometer (DSR) results in a stiffness range associated with the range of time and temperature used in nanoindentation testing. Nanoindentation creep data is transformed to develop a mastercurve of dynamic modulus. The portion of this mastercurve corresponding to the frequency and temperature range included in nanoindentation testing demonstrates reasonable agreement with DSR results. These initial results suggest the potential to expand nanoindentation testing to forensic investigations involving testing of preserved asphalt binder and mastic components within field-extracted asphalt concrete composites.     

基于Eshelby等效夹杂理论的沥青混合料有效粘弹性质分析

利用Eshelby 等效夹杂理论研究了沥青混合料的单轴压缩蠕变行为。通过时间域内的Laplace 变换将问题线性化, 得到了沥青混合料的蠕变本构关系。开展了不同温度、应力水平条件下沥青砂的单轴压缩蠕变实验, 根据数据拟合了沥青砂四参量流变模型的模型参数。在此基础上, 预测了沥青混合料在不同温度、应力水平下的蠕变曲线, 分析了温度、应力水平对沥青混合料蠕变行为的影响。结果表明:在相同的应力水平下, 沥青混合料的应变和应变率都随温度的升高而增大, 并且在沥青软化点附近发生明显突变;在相同的温度下, 沥青混合料的应变和应变率都随加载应力的增加而增大。