Viscoelastic Model for Discrete Element Simulation of Asphalt Mixtures

This paper presents a viscoelastic model of asphalt mixtures with the discrete element method, where the viscoelastic behaviors of asphalt mastics (fine aggregates, fines, and asphalt binder) are represented by a Burger’s model. Aggregates are simulated with irregular shape particles consisting of balls bonded together by elastic contact models, and the interplaces between aggregates are filled with balls bonded with viscoelastic Burger’s model to represent asphalt mastic. Digital samples were prepared with the image analysis technique. The micromechanical model was developed with four constitutive laws to represent the interactions at contacts of discrete elements (balls) within an aggregate, within mastic, between an aggregate and mastic, and between two adjacent aggregates. Each of these constitutive laws consists of three parts: a stiffness model, a slip model, and a bonding model in order to provide a relationship between the contact force and relative displacement and also in order to describe slipping and tensile strength at a particular contact. The relationship between the microscale model input and macroscale material properties was derived, and an iterative procedure was developed to fit the dynamic modulus test data of asphalt mastic with Burger’s model. The favorable agreement between the discrete element prediction and the lab results on dynamic moduli and phase angles indicates that the viscoelastic discrete element model developed in this study is very capable of simulating constitutive behavior of asphalt mixtures.     

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.     

基于细观结构有限元模型的环氧沥青混合料间接拉伸试验研究

运用有限元方法建立环氧沥青混合料细观结构模型,对其间接拉伸试验(IDT)进行数值模拟.首先借助图像处理技术得到由集料和沥青砂浆组成的环氧沥青混合料二相细观结构,并通过蠕变试验获取沥青砂浆常温下的黏弹性材料参数,最后结合有限元手段建立包含集料、砂浆等在内的混合料细观结构有限元模型.数值模拟结果表明,有限元计算的混合料劲度模量与实际IDT试验结果吻合较好,通过改变加载方向、加载速率等参数,发现对混合料细观结构的劲度模量以及局部点位应力均造成一定影响,分析主要原因可能是由沥青混合料的内部结构分布不均匀性以及沥青砂浆的黏弹性特点所造成.研究成果可为微观有限元方法进一步推广应用于不同条件下沥青混合料微观力学响应仿真提供理论依据.     

Visualization and Simulation of Asphalt Concrete with Randomly Generated Three-Dimensional Models

The objective of this study is to visualize and simulate microscale properties of asphalt concrete with three-dimensional discrete element models under mechanical loading. The microstructure of the asphalt concrete sample was composed of three ingredients: coarse aggregates, sand mastic (a combination of fines, fine aggregates, and asphalt binder), and air voids. Coarse aggregates were represented with the irregular polyhedron particles which were randomly created with an algorithm developed for this study. The gaps among the irregular particles were filled with air voids and discrete elements of sand mastic. The mechanical behaviors of the three ingredients were simulated with specific constitutive models at different contacts of discrete elements. Based on the geometric and mechanical models, visualization and simulation of asphalt mixtures were conducted in this study.     

Determining Hardness and Elastic Modulus of Asphalt by Nanoindentation

Nanoindentation is a relatively new technique which has been used to measure nanomechanical properties of surface layers of bulk materials and of thin films. In this study, micromechanical properties such as hardness and Young’s modulus of asphalt binders and asphalt concrete are determined by nanoindentation experiments. Indentation tests are conducted on a base binder and two polymer-modified performance grade (PG) binders such as PG-70-22 and PG76-28. In addition, two Superpave asphalt mixes such as SP-B and SP-III are designed using these PG binders, and the corresponding mixes are compacted to prepare asphalt concrete. Aggregate, matrix (Materials Passing No. 4 sieve) and mastic (Materials Passing No. 200 sieve) phases of each asphalt concrete sample are indented using both Berkovich and Spherical indenters. In nanoindentation, an indenter penetrates into asphalt material and the load (milli-Newton) and the depth (nanometers) of indentation are recorded continuously. Indentation load versus displacement data are analyzed using Oliver and Pharr method to measure hardness and Young’s modulus. The unloading data of base binder is a straight line and therefore could not be analyzed using Oliver and Pharr’s method. However, the indentation data of the PG grade binders are successfully analyzed. Young’s modulus value is less than 3 GPa for mastic, 3 to 12 GPa for matrix, and greater than 12 GPa for aggregate studied herein. Based on the hardness data, mastic is 2 to 15 times softer than matrix materials, and matrix is 10 times softer than aggregate materials. The fact that the properties of the mastic can be measured while in the mixture, this study has great potential for realistic characterization of asphalt mixture components. In this study, spherical indenter is found to be suitable for asphalt binders based on the fact that the spherical indenter produces higher indentation depths than the Berkovich indenter. The study contributes significantly to the use of nanoindentation for transportation material characterization.     

Three-Dimensional Micromechanical Finite-Element Network Model for Elastic Damage Behavior of Idealized Stone-Based Composite Materials

This paper presents a three-dimensional (3D) micromechanical finite-element (FE) network model for predicting elastic damage behavior of the idealized stone-based materials. Stone-based composite materials have multiphase structures: an aggregate (or stone) skeleton, a binding medium, fillers, and air voids. Numerical simulation of the micromechanical behavior of the idealized stone-based materials was accomplished by using a microframe element network model that incorporated the mechanical load transfer between adjacent particles. The elastic stiffness matrix of this special element was obtained from an approximate elastic stress-strain analysis of straight cement between particle pairs. A damage-coupled microframe element was then formulated with bilinear damage laws, including elastic and softening behavior based on the equivalent fracture release energy. Indirect tension and compression simulations were conducted with developed FE models on the idealized digital samples of the stone-based materials. These simulations predicted the internal microdamage distribution and global fracture behavior of these samples, which qualitatively agree with the laboratory observations. The results indicate that the developed FE models have the capability to predict the typical loading-related damage behavior observed from the stone-based materials.     

Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling

The linear viscoelastic properties of bituminous mixtures are used to design pavement structure. Usually, only complex moduli E* (complex Young modulus) or G* (complex shear modulus) characterizing the stiffness of the materials in one direction (1D) are measured by classical tests. In this paper, the three-dimensional (3D) behavior is investigated. The complex Poisson's ratio (ν*) is introduced. Its evolution with temperature and frequency is studied for a bitumen, a mastic, and a mix. Experimental results show that the time–temperature superposition principle is applicable in the 3D case. The same shift factor applies for E* and ν*. The Di Benedetto–Neifar model developed at Ecole Nationale des Travaux Publics de l’Etat to simulate so far the 1D thermo-elastoviscoplastic behavior of bituminous materials has been extended to simulate their 3D isotropic behavior. Calibration of the model and comparison between simulations in the linear viscoelastic domain and experimental data are proposed.     

Micromechanical Modeling of the Viscoelastic Behavior of Asphalt Mixtures Using the Discrete-Element Method

This paper presents a methodology for analyzing the viscoelastic response of asphalt mixtures using the discrete-element method (DEM). Two unmodified (neat) and seven modified binders were mixed with the same aggregate blend in order to prepare the nine hot mix asphalt (HMA) mixtures used in this study. The HMA microstructure was captured using images of vertically cut sections of specimens. The captured grayscale images were processed into black and white images representing the mastic and the aggregate phases, respectively. These microstructure images were used to represent the DEM model geometry. Rheological data for the nine binders were obtained using the dynamic shear rheometer. These data were used to estimate the parameters of the viscoelastic contact models that define the interaction among the mix constituents. The DEM models were subjected to sinusoidal loads similar to those applied in the simple performance test (SPT). The DEM model predictions compared favorably with the SPT measurements. However, the simulation results tended to overpredict the dynamic modulus, E*, for mixtures made with neat binders and underpredict E* for those that consisted of modified binders. The DEM models gave mix phase angles, ?mix, higher than the experimental measurements.     

Prediction of Damage Behaviors in Asphalt Materials Using a Micromechanical Finite-Element Model and Image Analysis

A study of the micromechanical damage behavior of asphalt concrete is presented. Asphalt concrete is composed of aggregates, mastic cement, and air voids, and its load carrying behavior is strongly related to the local microstructural load transfer between aggregate particles. Numerical simulation of this micromechanical behavior was accomplished by using a finite-element model that incorporated the mechanical load-carrying response between aggregates. The finite-element scheme used a network of special frame elements each with a stiffness matrix developed from an approximate elasticity solution of the stress and displacement field in a cementation layer between particle pairs. Continuum damage mechanics was then incorporated within this solution, leading to the construction of a microdamage model capable of predicting typical global inelastic behavior found in asphalt materials. Using image processing and aggregate fitting techniques, simulation models of indirect tension, and compression samples were generated from surface photographic data of actual laboratory specimens. Model simulation results of the overall sample behavior and evolving microfailure/fracture patterns compared favorably with experimental data collected on these samples.     

Discrete-Element Modeling: Impacts of Aggregate Sphericity, Orientation, and Angularity on Creep Stiffness of Idealized Asphalt Mixtures

Hot-mix asphalt (HMA) contains a significant amount of mineral aggregate, approximately 95% by weight and 85% by volume. The aggregate sphericity, orientation, and angularity are very important in determining HMA mechanical behaviors. The objective of this study is to investigate the isolated effects of the aggregate sphericity index, fractured faces, and orientation angles on the creep stiffness of HMA mixtures. The discrete-element method was employed to simulate creep compliance tests on idealized HMA mixtures. Two user-defined models were used to build 102 idealized asphalt-mix digital specimens. They were the R-model and the A-model, short for a user-defined rounded aggregate model and a user-defined angular aggregate model, respectively. Of the 102 digital specimens, 84 were prepared with the R-model to investigate the effects of aggregate sphericity and orientation, whereas the remaining 18 were built with the A-model to address the effect of aggregate angularity. A viscoelastic model was used to capture the interactions within the mix specimens. It was observed that (1) as the sphericity increased, the creep stiffness of the HMA mixture increased or decreased, depending on the angles of aggregate orientation; (2) as the angle of aggregate orientation increased, the creep stiffness of the HMA mixture increased, with the rate depending on the sphericity index values; and (3) compared with the sphericity index and orientation angles, the influence of aggregate fractured faces was insignificant.     

Microstructural Finite-Element Analysis of Influence of Localized Strain Distribution on Asphalt Mix Properties

Hot mix asphalt (HMA) is a composite material that consists of mineral aggregates, asphalt binders, and air voids. A finite element model of the HMA microstructure is developed to study the influence of localized strain distribution on the HMA mechanical response. Image analysis techniques are used to capture the HMA microstructure. Due to limitations on the image resolution, the microstructure is divided into two phases: aggregates larger than 0.3 mm and mastic (binder and aggregates smaller than 0.3 mm). A viscoelastic constitutive relationship is used to represent the mastic phase of the HMA microstructure. The mastic viscoelastic properties are obtained from the results of testing asphalt binders in a dynamic shear rheometer and microstructure analysis of idealized mastic. A step-wise finite element procedure is employed in order to account for the influence of the localized high strains on the mastic viscoelastic properties, and HMA mechanical response. The mastic and binder elements of the microstructure are shown to exhibit high strain values within the nonlinear viscoelastic range. The HMA viscoelastic properties are calculated at different strain levels, and the results are compared with experimental data obtained from the frequency sweep shear test.     

Accelerated Discrete-Element Modeling of Asphalt-Based Materials with the Frequency-Temperature Superposition Principle

This paper presents a methodology to reduce the computation time for discrete-element (DE) modeling of asphalt-based materials, based on the frequency-temperature superposition principle. Laboratory tests on the dynamic modulus of asphalt sand mastics and asphalt mixtures were conducted at temperatures of -5, 4, 13, and 21°C and frequencies of 1, 5, 10, and 25?Hz, respectively. The test results of the asphalt sand mastics were fitted with the Burger’s model to obtain the microparameters for DE models. To reduce the computation time of the DE modeling, the regular loading frequencies were amplified to virtual frequencies. Simultaneously, the Burger’s model parameters (microparameters in DE models) of asphalt sand mastic at regular frequencies were modified to those at virtual frequencies on the basis of the frequency-temperature superposition principle. Because the virtual frequencies were much larger than the regular frequencies, the computation time was significantly reduced by conducting the DE modeling with the virtual frequencies and the corresponding modified Burger’s model parameters. The modeling work, which typically takes several months or years with the traditional methods, only took a few hours or less in this study.     

Modeling Nonlinear Anisotropic Elastic Properties of Unbound Granular Bases Using Microstructure Distribution Tensors

The resilient properties of unbound aggregate bases are important parameters in the design of asphalt pavements. Previous studies have shown that these resilient properties exhibit nonlinear and transverse anisotropic characteristics. The paper in hand presents a micromechanics-based approach to model the nonlinear and anisotropic properties of unbound aggregate bases. The anisotropic behavior is captured using two microstructure parameters representing the preferred orientation of aggregate particles, and the ratio of the normal contact stiffness to shear contact stiffness among particles. The nonlinear response is modeled using a relationship that relates the shear modulus to particle packing, material properties, particle size, and confining pressure. The micromechanics model is used to represent the resilient properties for a total of 18 different combinations of material conditions with different aggregate types, moisture contents, and gradation characteristics. Anisotropic and nonlinear resilient properties were measured at ten different stress states for each of the material conditions. The results presented in this paper show that the micromechanics model is capable of successfully representing the experimental measurements.     

Artificial neural network and finite element modeling of nanoindentation tests

This study first presents two-dimensional (2-D) axisymmetric and three-dimensional (3-D) finite element (FE) models of nanoindentation tests. Calculated load-displacement curves from the FE models are compared with the load-displacement curves from nanoindentation measurements on annealed copper. Numerical parametric studies are also performed to examine the effect of indenter geometry and the material’s stress-strain behavior on the load-displacement response. The 2-D and 3-D FE load-displacement curves compare well with the measured results on annealed copper. The second aspect of this study introduces a new modeling approach for indentation tests using artificial neural networks (ANN). In this approach, ANN models are generated to approximate the FE load-displacement curves for a wide range of material and geometric parameters. The ability of the ANN models to predict the indentation response is examined against other FE results not used as part of the training data. These models are shown to accurately predict the load-displacement behavior of a nonlinear homogeneous material as well as one with a hard film, such as an oxide film, on a relatively soft substrate. It is shown that the monotonic indentation load-displacement response during loading contains ample information for the ANN model to extract material flow properties of the indented material.     

Micromechanics-Based Predictions on the Overall Stress-Strain Relations of Cement-Matrix Composites

A micromechanics-based model is proposed to determine the nonlinear stress-strain relations of cement-matrix composites at different concentrations of inclusions (aggregates). We first conducted some experiments to uncover the stress-strain behavior of the cement paste with a water-to-cement ratio of 0.45, and those of the mortar with the same cement paste but at three different volume concentrations of aggregates. The behavior of the cement paste is then simulated by Burgers’ rheological model. In the development of the composite model, we extend the linear elastic response to the nonlinear one through the replacement of elastic moduli by the corresponding secant moduli. The nonlinear stress-strain curves of the cement-matrix composite are then determined from those of the cement paste and inclusions. It is shown that the predicted stress-strain curves of the mortar are in close agreement with the experimental curves up to an aggregate volume fraction of 49% or 60?wt?%.     

Three-Dimensional Micromechanics-Based Constitutive Framework for Analysis of Pultruded Composite Structures

A new 3D micromechanics-based framework is proposed for the nonlinear analysis of pultruded fiber-reinforced polymeric composites. The proposed 3D modeling framework is a nested multiscale approach that explicitly recognizes the response of the composite systems (layers) within the cross section of the pultruded member. These layers can have reinforcements in the form of roving, continuous filament mat (CFM), and∕or woven fabrics. Different 3D micromechanical models for the layers can be used to recognize the basic response of the fiber and matrix materials. The framework is implemented with both shell and 3D finite elements. The 3D lamination theory is used to generate a homogenized nonlinear effective response for a through-thickness representative stacking sequence. The proposed modeling framework for pultruded composites is used to predict the stiffness and nonlinear stress-strain response of E-glass∕vinylester pultruded materials reinforced with roving and CFM. The roving layer is idealized using a 3D nonlinear micromechanics model for a unidirectional fiber-reinforced material. A simple nonlinear micromechanics model for the CFM layer is also applied. The proposed model shows very good predictive capabilities of the overall effective properties and the nonlinear response of pultruded composites, based on the in situ material properties, and the volume fractions of the constituents. Experimental data from off-axis tests of pultruded plates under uniaxial compression are used to verify the proposed model. The proposed framework can be easily incorporated within displacement-based finite-element models of composite structures.     

沥青混合料动态压缩弹性模量试验方法与影响因素

为了研究应变测试方法、加载频率、试验温度和应力幅值对沥青混合料动态压缩弹性模量的影响,用MTS路面材料动态试验系统对常用的两种沥青混合料AC-16和AC-20的动态压缩弹性模量进行了系统的测试,通过分析建立了各因素与动态压缩弹性模量之间的关系,以及动态与静态弹性模量的关系.结果表明,采用侧面法测定的结果与现行规范中的推荐值更接近,也能够消除由顶面法引起的试件端面的接触误差,建议在静态和动态模量试验中首选侧面法,在动态测试中要选择合适的加载频率,使得试验结果的偏差系数控制在20%以下.     

一种光敏树脂结构的力学性能

新设计三维打印光敏树脂结构,其主要用在减震隔震组合结构中作为阻尼元件.首先利用微机控制电子试验机对其进行静力加载试验,得到静载下载荷—位移特性曲线,并计算得到特定点处等效弹性模量,利用疲劳机进行动力加载试验,得到结构件在从5 Hz到20 Hz不同频率下滞回曲线,并计算出相应等效阻尼系数.基于有限元法,建立光敏树脂结构有限元模型,并以和实验相同的工况进行静力学和动力学计算分析,并对试验数据和数值计算结果进行对比,得到计算结果与实测结果吻合良好,从而验证有限元模型的可行性.在此基础上通过有限元计算方法,研究不同几何参数缝隙宽度、内弧半径、外弧半径、厚度对光敏树脂结构特定点等效弹性模量以及等效阻尼系数的影响.此结构受力时,纵向保持刚度输出,维持小变形,横向位移放大,具有良好的减振和抵抗变形的能力.      

Finite Element Studies of Asphalt Concrete Pavement Reinforced with Geogrid

Many geotechnical applications are becoming more sophisticated and solutions derived from simplistic procedure are no longer reasonable or solutions do not exist. This paper describes two-dimensional finite element studies that analyzed the behavior of reinforced asphalt pavement under plane strain conditions and subject to monotonic loading. The asphalt material and soils were expressed using triangular elements of elastoplastic behavior that obeys Mohr–Coulomb criteria with associated and nonassociated flow rules. The geogrid was modeled using a one-dimensional linear elastic bar element. The finite element procedure was validated by comparing the results of analysis with the results obtained from a series of model tests. The load–settlement relationships, settlement profile, and strains in the geogrid were compared. The failure load obtained by assuming subgrade foundation with nonassociated flow rule was smaller than that of associated flow rule. There was only minor difference between the results obtained from the associated and nonassociated plastic models. The finite element procedure was capable of determining most measured quantities satisfactorily except the tensile strain in the geogrid, which was assumed linear elastic. The effects of the stiffness of geogrid reinforcement, thickness of asphalt layer, and strength of subgrade foundation were also investigated. The finite element procedure is a versatile tool for enhanced design of reinforced pavement systems.     

Small-Strain Shear Moduli of Chemically Stabilized Sulfate-Bearing Cohesive Soils

An experimental study was conducted to measure small-strain shear moduli of chemically treated sulfate-bearing expansive soils using the bender element test. The bender element test was chosen because it provides reliable and repeatable small strain shear modulus measurements and allows for the periodical monitoring of stiffness property responses of soil specimens under varying curing conditions. Bender element tests were conducted on cement and lime treated soils and the results were then analyzed to study the variations in stiffness properties of soil specimens at different sulfate levels and curing conditions. Both cement and lime treated natural and artificial clays with low sulfate level of 1,000?ppm showed considerable enhancements in small strain shear moduli, whereas the same treated soils at high sulfate level of 10,000?ppm showed less enhancements in shear moduli due to sulfate heaving. Also, enhancements in shear moduli were lower for soil specimens continuously soaked under water compared to those cured in the humidity room. Rates of stiffness enhancements due to stabilizer type, compaction moisture content, type of curing, and sulfate levels are quantified and summarized.