Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method

A user-defined three-dimensional （3D） discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete （AC）. The 3D discrete element method （DEM） model of AC was constructed employing a user-defined computer program developed using the ＂Fish＂ language in PFC3D. Important microstructural features of AC were modeled, including aggregate gradation, air voids and mastic. The irregular shape of aggregate particle was modeled using a clump of spheres. The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test, based on which the dynamic modulus and phase angle were calculated from the output stress- strain relationship. The effects of air void content, aggregate stiffness and volumetric fraction on AC modulus were further investigated. The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies. The user- defined 3D model also demonstrated significant improvement over the general existing two-dimensional models.

Microstructure modeling and virtual test of asphalt mixture based on three-dimensional discrete element method

The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions(PFC^(3D))based on three-dimensional discrete element method.A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate.And then,modeling algorithm and method for graded aggregates were built.Based on the combination of modeling of coarse aggregates,asphalt mastic and air voids,three-dimensional virtual sample of asphalt mixture was modeled by using PFC^(3D).Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC^(3D).By comparison of the testing results between virtual tests and actual laboratory tests,the validity of the microstructure modeling and virtual test built in this study was verified.Additionally,compared with laboratory test,the virtual test is easier to conduct and has less variability.It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.

Micromechanical modeling of asphalt concrete fracture using a user-defined three-dimensional discrete element method

A user-defined micromechanical model was developed to investigate the fracture mechanism of asphalt concrete （AC） using the discrete element method （DEM）. A three-dimensional （3D） AC beam was built using the ＂Fish＂ language provided by PFC3D and was employed to simulate the three-point bending beam test at two temperature levels： -10 ℃ and 15℃. The AC beam was modeled with the consideration of the microstructural features of asphalt mixtures. Uniaxial complex modulus test and indirect tensile strength test were conducted to obtain material input parameters for numerical modeling. The 3D predictions were validated using laboratory experimental measurements of AC beams prepared by the same mixture design. Effects of mastic stiffness, cohesive and adhesive strength on AC fracture behavior were investigated using the DEM model. The results show that the 3D DEM fracture model can accurately predict the fracture patterns of asphalt concrete. The ratio of stress at interfaces to the stress in mastics increases as the mastic stiffness decreases; however, the increase in the cohesive strength or adhesive strength shows no significant influence on the tensile strength.

Discrete Element Modeling of Asphalt Concrete Cracking Using a User-def ined Three-dimensional Micromechanical Approach

We established a user-defined micromechanical model using discrete element method （DEM） to investigate the cracking behavior of asphalt concrete （AC）. Using the ＂Fish＂ language provided in the particle flow code in 3-Demensions （PFC3D）, the air voids and mastics in asphalt concrete were realistically built as two distinct phases. With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes, the three-dimensional （3D） discrete element model was able to account for aggregate gradation and fraction. Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation. A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature, i e, -10 ℃ and 15 ℃. The predicted results of the numerical simulation were compared with laboratory experimental measurements. Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures. Based on the DEM model, the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to non-continuum.The wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this code.By comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is proved.Furthermore,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to non-continuum.The results of calculation can be displayed by animation.The damage modes are similar to the experimental results.The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum.It also shows that the discrete element method(DEM)will have broad prospects for development and application.

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.

Constructing exact solutions to discrete systems with the trial function method

Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the.help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear （2 ＋ 1） dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional （3D） hybridfinite-discrete element method （FDEM） to investigate the development of an excavation damaged zone（EDZ） around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibratedagainst standard laboratory experiments, including Brazilian disc test and uniaxial compression test. Theeffect of increasing confining pressure on the mechanical response and fracture propagation of the rockwas quantified under triaxial compression tests. Polyaxial （or true triaxial） simulations highlighted theeffect of the intermediate principal stress （s2） on fracture directions in the model： as the intermediateprincipal stress increased, fractures tended to align in the direction parallel to the plane defined by themajor and intermediate principal stresses. The peak strength was also shown to vary with changing s2. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Extracting Information on Implied Volatilities and Discrete Dividends From American Option Prices

This paper deals with options on assets, such as stocks or indexes, which pay cash dividends. Pricing methods which consider discrete dividends are usually computationally expensive and become infeasible when one considers multiple dividends paid during the option lifetime. This is the case of long-term options and options on indexes. The first purpose of this paper is to assess efficient and accurate numerical procedures which yield consistent prices for both European and American options when the underlying asset pays discrete dividends. The authors then analyze some methodologies to extract information on implied volatilities and dividends from quoted option prices. Implied dividends can also be computed using a modified version of the well-known put-call parity relationship. This technique is straightforward, nevertheless, its use is limited to European options, and when dealing with equities, most traded options are of American type. As an alternative, the numerical inversion of pricing methods, such as efficient interpolated binomial method, can be used. This paper applies different procedures to obtain implied volatilities and dividends of listed stocks of the Italian derivatives market （IDEM）.

Three-dimensional heat transfer in a particulate bed in a rotary drum studied via the discrete element method

We simulated three-dimensional heat transfer inside a horizontal rotating drum using the discrete element method and a thermal conduction model.The aim was to determine the effect of end-wall heating on thermal behavior of a granular bed.The simulation showed that the end-wall heating significantly affects the axial temperature profile of the bed,particularly when the length-to-diameter ratio is low.Particles near the wall heated faster and became more thermally uniform than those in the center of the drum.The region affected by the end heating gradually increased over time.Increasing the rotation speed enhanced the heat conduction rate,and increasing the fill level reduced the mean temperature and thermal uniformity of the granular bed.Heat transfer was also simulated for drums with different length-to-diameter ratios.

A Novel Dynamic Quadrature Scheme for Solving Boltzmann Equation with Discrete Ordinate and Lattice Boltzmann Methods

The Boltzmann equation(BE)for gas flows is a time-dependent nonlinear differential-integral equation in 6 dimensions.The current simplified practice is to linearize the collision integral in BE by the BGK model using Maxwellian equilibrium distribution and to approximate the moment integrals by the discrete ordinatemethod(DOM)using a finite set of velocity quadrature points.Such simplification reduces the dimensions from 6 to 3,and leads to a set of linearized discrete BEs.The main difficulty of the currently used(conventional)numerical procedures occurs when the mean velocity and the variation of temperature are large that requires an extremely large number of quadrature points.In this paper,a novel dynamic scheme that requires only a small number of quadrature points is proposed.This is achieved by a velocity-coordinate transformation consisting of Galilean translation and thermal normalization so that the transformed velocity space is independent of mean velocity and temperature.This enables the efficient implementation of Gaussian-Hermite quadrature.The velocity quadrature points in the new velocity space are fixed while the correspondent quadrature points in the physical space change from time to time and from position to position.By this dynamic nature in the physical space,this new quadrature scheme is termed as the dynamic quadrature scheme(DQS).The DQS was implemented to the DOM and the lattice Boltzmann method(LBM).These new methods with DQS are therefore termed as the dynamic discrete ordinate method(DDOM)and the dynamic lattice Boltzmann method(DLBM),respectively.The new DDOM and DLBMhave been tested and validated with several testing problems.Of the same accuracy in numerical results,the proposed schemes are much faster than the conventional schemes.Furthermore,the new DLBM have effectively removed the incompressible and isothermal restrictions encountered by the conventional LBM.

Numerical analysis of multicomponent responses of surface-hole transient electromagnetic method

We calculate the multicomponent responses of surface-hole transient electromagnetic method. The methods and models are unsuitable as geoelectric models of conductive surrounding rocks because they are based on regular local targets. We also propose a calculation and analysis scheme based on numerical simulations of the subsurface transient electromagnetic fields. In the modeling of the electromagnetic fields, the forward modeling simulations are performed by using the finite-difference time-domain method and the discrete image method, which combines the Gaver–Stehfest inverse Laplace transform with the Prony method to solve the initial electromagnetic fields. The precision in the iterative computations is ensured by using the transmission boundary conditions. For the response analysis, we customize geoelectric models consisting of near-borehole targets and conductive wall rocks and implement forward modeling simulations. The observed electric fields are converted into induced electromotive force responses using multicomponent observation devices. By comparing the transient electric fields and multicomponent responses under different conditions, we suggest that the multicomponent-induced electromotive force responses are related to the horizontal and vertical gradient variations of the transient electric field at different times. The characteristics of the response are determined by the varying the subsurface transient electromagnetic fields, i.e., diffusion, attenuation and distortion, under different conditions as well as the electromagnetic fields at the observation positions. The calculation and analysis scheme of the response consider the surrounding rocks and the anomalous field of the local targets. It therefore can account for the geological data better than conventional transient field response analysis of local targets.

An MPI parallel DEM-IMB-LBM framework for simulating fluid-solid interaction problems

The high-resolution DEM-IMB-LBM model can accurately describe pore-scale fluid-solid interactions,but its potential for use in geotechnical engineering analysis has not been fully unleashed due to its prohibitive computational costs.To overcome this limitation,a message passing interface(MPI)parallel DEM-IMB-LBM framework is proposed aimed at enhancing computation efficiency.This framework utilises a static domain decomposition scheme,with the entire computation domain being decomposed into multiple subdomains according to predefined processors.A detailed parallel strategy is employed for both contact detection and hydrodynamic force calculation.In particular,a particle ID re-numbering scheme is proposed to handle particle transitions across sub-domain interfaces.Two benchmarks are conducted to validate the accuracy and overall performance of the proposed framework.Subsequently,the framework is applied to simulate scenarios involving multi-particle sedimentation and submarine landslides.The numerical examples effectively demonstrate the robustness and applicability of the MPI parallel DEM-IMB-LBM framework.

Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I:Mathematical Derivation of Adjoint Lattice Boltzmann Equations

The significance of flow optimization utilizing the lattice Boltzmann(LB)method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques.These unique characteristics of the LB method form the main idea of its application to optimization problems.In this research,for the first time,both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost.The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector.Moreover,this approach was not limited to flow fields and could be employed for steady as well as unsteady flows.Initially,the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time,respectively.Meanwhile,new adjoint concepts in lattice space were introduced.Finally,the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

基于不规则骨料堆积结构的混凝土水渗透性的研究

为了揭示骨料形状对混凝土水渗透性的影响,基于超椭球颗粒构建了不规则骨料的几何模型,对伸长率、平整度、圆度、球形度等形状参数进行了量化表征。通过离散元方法实现了骨料动态堆积模拟,考虑了颗粒之间的相互作用力,建立了混凝土材料的三相介观模型。采用基于格子玻尔兹曼模型的部分反弹算法研究了混凝土的水分传输行为,在验证模型正确性的基础上,探究了骨料含量和形状对混凝土水渗透性的影响。研究表明:混凝土的水分渗透系数随骨料体积分数增大呈现先降低后增加的变化趋势。当骨料体积分数大于50%时,界面过渡区相互交叠形成连通路径是导致混凝土水分渗透系数增加的主要原因。骨料形状的变化会改变传输路径和界面过渡区的体积分数,从而影响水渗透性。与平整度相比,伸长率对水分渗透系数的影响更为明显。随着圆度的不断增加,球形度先增大后减小,水分渗透系数则呈现相反的变化趋势。当圆度为1时,水分渗透系数达到最小值。

利用LBM-DEM方法模拟研究粗颗粒管道水力输送

管道水力输送是运输固体物料的一种重要方式。采用Fortran语言在Visual Studio平台建立了一套描述粗颗粒管道水力输送过程的LBM-DEM(lattice Boltzmann method-discrete element method)数值模拟方法,并用该方法对相同体积的双层颗粒群和三层颗粒群在水平管道中的运动进行了模拟,研究了不同颗粒堆积方式下的水力输送特性。结果表明:推移运动是粗颗粒在水平管道中的主要运动形式,部分颗粒在水流的作用下会产生跃移运动;颗粒群前方存在水流低速度区,且管道初始流速越低、颗粒直径越大时,低速度区的存在越明显;颗粒群上层颗粒在运动的过程中会产生坍塌,随着管道初始流速的增大和颗粒直径的减小,上层颗粒由向下层坍塌逐渐转变为向颗粒群前方坍塌;堆积方式对颗粒群在管道中的运动具有重要影响,双层颗粒群和三层颗粒群在低速度区特性、颗粒坍塌方式等方面存在部分差异。该研究可为粗颗粒管道水力输送技术的发展起到一定的指导作用。

裂缝性页岩气储层三维多簇水力裂缝竞争扩展数值模拟

页岩气水平井多簇水力裂缝延伸效率是影响压裂效果的关键,现场监测发现大量射孔簇无法进液、多簇非均匀起裂扩展问题突出,深入认识三维空间中天然裂缝对多簇水力裂缝竞争扩展的影响规律具有重要意义。为此,基于离散格子方法建立三维全耦合随机裂缝性页岩储层三簇压裂数值模型,精细刻画多簇水力裂缝竞争起裂、扩展以及天然裂缝相互作用的全过程演化规律,研究地应力差、簇间距、压裂液黏度及排量等参数影响下多簇水力裂缝扩展行为,提出多簇延伸效率的施工对策。结果表明:水力裂缝与天然裂缝相遇时表现为穿透、转向、分叉等单一或多种复合模式;天然裂缝网络会加剧多簇裂缝竞争扩展时的应力阴影效应,中间受到抑制的射孔簇容易沿天然裂缝转向或者分叉并与其他射孔簇发生融合,降低整体改造面积;地应力差越小、簇间距越小,缝间应力干扰越明显,裂缝延伸规模越小;增大压裂液黏度或排量,中间簇水力裂缝受应力干扰程度减弱,延伸距离更远,建议现场在前置液阶段适当提高压裂液黏度、在主压裂阶段增大排量,以提高多簇水力裂缝的延伸效率。研究成果可为页岩气储层射孔分段以及压裂参数优化设计提供指导。

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential-difference equations. The proposed method is based on the Laplace trans- form with the homotopy analysis method （HAM）. This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained.

Application of three-dimensional discrete element face-to-face contact model with fissure water pressure to stability analysis of landslide in Panluo iron mine

Three-dimensional discrete element face-to-face contact model with fissure water pressure is established in this paper and the model is used to simulate three-stage process of landslide under fissure water pressure in the opencast mine, according to the actual state of landslide in Panluo iron mine where landslide happened in 1990 and was fathered in 1999. The calculation results show that fissure water pressure on the sliding surface is the main reason causing landslide and the local soft interlayer weakens the stability of slope. If the discrete element method adopts the same assumption as the limit equilibrium method, the results of two methods are in good agreement; while if the assumption is not adopted in the discrete element method, the critical φ numerically calculated is less than the one calculated by use of the limit equilibrium method for the sameC. Thus, from an engineering point of view, the result from the discrete element model simulation is safer and has more widely application since the discrete element model takes into account the effect of rock mass structures.